Test Bank For Mathematics All Around, 7th Edition by Thomas Pirnot Margaret Moore

INSTRUCTOR’S TESTING MANUAL MATHEMATICS ALL AROUND SEVENTH EDITION

Thomas L. Pirnot Kutztown University of Pennsylvania

Margaret H. Moore University of Southern Maine

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ISBN-13: 978-0-13-696574-9 ISBN-10: 0-13-696574-1

Chapter 1 Exam A Name___________________________________

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Determine whether the statement is true or false. If it is true, give two examples to illustrate it. If it is false, give a single counterexample.

1) If the price of an air conditioner is raised by 17% and then lowered by 17%, the price will 1) be the same as the original price.

2) If A is the father of B, and B is the father of C, then C is the grandson of A.

2)

Draw a picture to illustrate the situation.

3) At Moiraʹs birthday party, each guest has a choice of chocolate, strawberry, or banana topping on vanilla ice cream.

Explain the difference between the symbols.

4) |-2| and [-2]

3)

4)

5) ⊇ and ⊃

5)

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Decide which set of names would be most meaningful for the indicated items.

6) On a bookshelf there are 4 math books, 5 science books, and 5 history books.

B) 4, 5, and 5 A) b1 , b2 , and b3 C) x, y, and z

6) D) m, s, and h

7) Raoul and Carlotta are sharing servings of root beer and cake.

A) R, C, b, and k B) p1 , p2 , f1 , and f2 C) x, w, z, and w

D) r, c, r, and c

Decide whether the two sequences of operations give the same result.

8) Subtracting y from x and adding the difference to z; adding x to z and then subtracting y A) No B) Yes 9) Dividing r by 5, then dividing s by 5, then multiplying the quotients; multiplying r and s, then dividing by 5.

A) No B) Yes Continue the pattern for five more items in the list.

10) 180, 169, 158, 147, ...

A) 136, 125, 114, 103, 92 C) 305, 452, 757, 1209, 2076 11) 6, 12, 18, 24, ...

A) 30, 37, 44, 51, 58 C) 30, 36, 42, 48, 54

7)

8)

9)

10) B) 139, 131, 123, 115, 107 D) 136, 132, 128, 124, 120 11) B) 11, 17, 24, 32, 41 D) 31, 38, 45, 52, 59

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List the items mentioned. Try to organize your list in a systematic way.

12) A frozen yogurt stand has chocolate and vanilla yogurt. For toppings it has nuts, coconut syrup, or candy pieces. List all combinations that use one flavor and one topping.

A) (chocolate, nuts), (nuts, chocolate), (vanilla, coconut syrup), (coconut syrup, chocolate), (nuts, vanilla), (candy, vanilla), (chocolate, candy) B) (chocolate, nuts), (chocolate, coconut syrup), (chocolate, candy), (vanilla, nuts), (vanilla, coconut syrup), (vanilla, candy) C) (chocolate, nuts), (chocolate, coconut syrup), (chocolate, candy), (vanilla, nuts), (vanilla, coconut syrup), (vanilla, candy), (candy, chocolate), (candy, vanilla), (coconut syrup, chocolate), (coconut syrup, vanilla) D) (chocolate, nuts), (vanilla, coconut syrup), (coconut syrup, chocolate), (nuts, vanilla), (candy, vanilla), (chocolate, candy), (chocolate, vanilla) 13) A coin is flipped and a 6-sided number cube is rolled. Use H for heads and T for tails, and list all possible outcomes.

A) (1, H), (H, 1), (1, T), (T, 1), (2, H), (H, 2), (2, T), (3, H), (H, 3), (3, T), (T, 3), (4, H), (H, 4). (4, T), (T, 4). (5, H), (H, 5), (5, T), (T, 5), (6, H), (H, T), (6, T), (T, 6) B) (H, 1), (H, 2), (H, 3), (H,4), (H, 5), (H, 6) C) (H, 1), (T, 2), (H, 3), (T, 4), (H, 5), (T, 6) D) (1, H), (1, T), (2, H), (2, T), (3, H), (3, T), (4, H), (4, T), (5, H), (5, T), (6, H), (6, T) Solve the problem by guessing and adjusting.

14) Mitra created a mosaic design using square 4-by-4 cm white tiles and rectangular 4-by-5 centimeter black tiles. She used twice as many white tiles as black tiles. The finished pattern was 2704 square centimeters in area. How many rectangular tiles did she use?

A) 104 B) 212 C) 52 D) 20 15) Corinne is making a beaded necklace. She has 3 times as many green beads as red beads, and twice as many blue beads as green beads. If she has 150 beads all together, how many of the beads are blue?

A) 45 B) 90 C) 75 D) 30 Decide whether the argument is an example of inductive or deductive reasoning.

16) The last four answers were false, therefore the next will be false.

A) Inductive B) Deductive 17) |-p| = p, therefore |-97| = 97 A) Inductive

12)

13)

14)

15)

16)

17) B) Deductive

18) Practice makes perfect. Therefore, if I practice, Iʹll be perfect.

A) Inductive B) Deductive

18)

19) If (-p)2 = p2 , then (-6)2 = 36 A) Inductive

19) B) Deductive

Illustrate Goldbackʹs conjecture for the following number.

20) 60 A) 30 + 30 B) 2 2 · 3 · 5

20) C) 3 + 57

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D) 19 + 41

21) 40

21) A) 2 3 · 5

B) 17 + 23

C) 20 + 20

D) 13 + 27

22) 50

22) A) 2 · 5 2

B) 25 + 25

C) 13 + 37

D) 17 + 33

A) 15 + 15

B) 5 + 25

C) 7 + 23

D) 2 · 3 · 5

A) 12 + 12

B) 2 3 · 3

23) 30

23)

24) 24

24) C) 3 + 21

D) 11 + 13

Use inductive reasoning.

25) How many different squares are there in a 4 by 4 square? Use inductive reasoning to answer.

A) 21 B) 16 C) 14 D) 30

25)

26) How many different squares are there in an 8 by 8 square? Use inductive reasoning to answer.

A) 64 B) 204 C) 285 D) 65

26)

27) Use inductive reasoning to predict the next term in the sequence of numbers.

37, 31, 25, 19, 13, ?

A) 2 B) 7 C) 6

27)

28) Use inductive reasoning to predict the next term in the sequence of numbers.

2, 5, 4, 10, 8, 20, ?

A) 16 B) 40 C) 30

D) 0 28) D) 12

29) How many different squares are there in a 6 by 6 square? Use inductive reasoning to answer.

A) 50 B) 91 C) 36 D) 37 Estimate the answer using compatible numbers.

30) 8.9% × 196 A) 8 B) 80

30) C) 18

D) 180

Estimate the answer by rounding as indicated.

31) Estimate by rounding to the nearest ten.

83 - 46 A) 130

B) 30

31)

C) 40

D) 37

32) Estimate by rounding to the nearest hundred.

461 - 242 A) 200

B) 219

29)

32)

C) 700

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D) 300

33) Estimate by rounding to the nearest hundred.

766 × 668 A) 560,000

B) 1500

Round the number to the place value indicated.

34) 4295 A) 3900 B) 4100

33)

C) 511,700

D) 511,688

C) 4000

D) 5000

34)

35) 98,213 A) 99,000

B) 98,100

C) 98,000

D) 108,000

36) 63,037 A) 63,010

B) 63,100

C) 62,900

D) 63,000

37) 6619 A) 7100

B) 8000

C) 7000

D) 6890

38) 829 A) 810

35)

36)

37)

38) B) 800

C) 900

D) 700

Estimate the answer. State whether the estimate is larger or smaller than the exact answer.

39) Each gallon of porch and deck paint covers 200 square feet. How many gallons are needed to cover 1980 square feet?

A) 11; larger B) 9; smaller C) 8; smaller D) 10; larger

39)

Refer to the double-bar graph below which shows the number of male (M) and female (F) athletes at a university over a four-year period. Solve the problem.

YEAR 40) How many more male athletes than female athletes were there in 1987?

A) 50 B) 100 C) 0

D) 150

41) How many female athletes were there in 1987?

A) 150 B) 500

C) 200

D) 300

42) In which year was the number of male athletes equal to 375?

A) 1989 B) 1987 C) 1986

D) 1988

40)

41)

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42)

43) Find the increase in the number of female athletes from 1986 to 1987.

A) 100 B) 75 C) 50

43) D) 200

In a school survey, students showed these preferences for instructional materials. Answer the question.

44) About how many students would you expect to prefer lectures in a school of 950 students?

A) About 342 students B) About 190 students C) About 18 students D) About 171 students

44)

45) About how many students would you expect to prefer films in a school of 900 students?

A) About 20 students B) About 162 students C) About 108 students D) About 180 students

45)

46) About how many students would you expect to prefer TV in a school of 700 students?

A) About 140 students B) About 126 students C) About 12 students D) About 84 students

46)

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Answer Key Testname: CHAPTER 1 EXAM A

1) False. Possible counterexample: Let the original price be $1000. After the price is raised, it will be 1000 + 170 = $1170.

After this is reduced by 17% it will be 1170 - 0.17 · 1170 = $971.10.

2) False. Possible counterexample is that C is the granddaughter of A. 3) Answers will vary. Possible answer is a circle labeled ʺice creamʺ connected by lines to three other circles labeled ʺchocolate,ʺ strawberry,ʺ and ʺbanana.ʺ 4) Answers will vary. One possibility is: the first -2 is enclosed in absolute value bars and the second is in brackets.

5) Answers will vary. One possibility: the first symbol has a line beneath it, and the second does not.

6) D 7) A 8) B 9) A 10) A 11) C 12) B 13) D 14) C 15) B 16) A 17) B 18) B 19) B 20) D 21) B 22) C 23) C 24) D 25) D 26) B 27) B 28) A 29) B 30) C 31) B 32) D 33) A 34) C 35) C 36) D 37) C 38) B 39) D 40) B 41) C 42) D 43) C 44) D 45) D 46) D

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Chapter 1 Exam B Name___________________________________

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Determine whether the statement is true or false. If it is true, give two examples to illustrate it. If it is false, give a single counterexample.

1) 1) If A is the father of B, and B is the father of C, then C is the grandson of A. 2) If the price of an air conditioner is raised by 15% and then lowered by 15%, the price will be the same as the original price.

Draw a picture to illustrate the situation.

3) At Moiraʹs birthday party, each guest has a choice of chocolate, strawberry, or banana topping on vanilla ice cream.

4) A school has a Spanish Club, a French Club, and a Drama Club, which have 20 members each. The Spanish and Drama Club have 4 members in common. The Drama and French Club have 4 members in common. The Spanish and French club have no members in common.

Explain the difference between the symbols.

5) ↑ and ⇑

2)

3)

4)

5)

6) |-11| and [-11]

6)

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Decide which set of names would be most meaningful for the indicated items.

7) Karina is buying fabric to make a cloth for a table that is 3 times as long as it is wide.

A) f, c B) L, W C) a, b D) K, c 8) On a bookshelf there are 5 math books, 3 science books, and 5 history books.

C) m, s, and h A) x, y, and z B) b1 , b2 , and b3

8) D) 5, 3, and 5

Decide whether the two sequences of operations give the same result.

9) Adding m and n and then multiplying the sum by 7; multiplying m by 7, multiplying n by 7, and then adding the two products A) No B) Yes 10) Subtracting y from x and adding the difference to z; adding x to z and then subtracting y A) Yes B) No Continue the pattern for five more items in the list.

11) 7, 10, 13, 16, ...

A) 19, 21, 23, 25, 27 C) 19, 22, 25, 28, 31

7)

9)

10)

11) B) 20, 24, 28, 31, 35 D) 20, 25, 31, 38, 46

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12) aaa, aab, aba, ...

A) abc, acb, cab, caa, cba C) bab, baa, aba, bbb, bba

12) B) baa, aba, abb, bbb, baa D) baa, abb, bab, bba, bbb

List the items mentioned. Try to organize your list in a systematic way.

13) A coin is flipped and a 6-sided number cube is rolled. Use H for heads and T for tails, and list all possible outcomes.

A) (1, H), (H, 1), (1, T), (T, 1), (2, H), (H, 2), (2, T), (3, H), (H, 3), (3, T), (T, 3), (4, H), (H, 4). (4, T), (T, 4). (5, H), (H, 5), (5, T), (T, 5), (6, H), (H, T), (6, T), (T, 6) B) (1, H), (1, T), (2, H), (2, T), (3, H), (3, T), (4, H), (4, T), (5, H), (5, T), (6, H), (6, T) C) (H, 1), (T, 2), (H, 3), (T, 4), (H, 5), (T, 6) D) (H, 1), (H, 2), (H, 3), (H,4), (H, 5), (H, 6) 14) A frozen yogurt stand has chocolate and vanilla yogurt. For toppings it has nuts, coconut syrup, or candy pieces. List all combinations that use one flavor and one topping.

A) (chocolate, nuts), (chocolate, coconut syrup), (chocolate, candy), (vanilla, nuts), (vanilla, coconut syrup), (vanilla, candy) B) (chocolate, nuts), (nuts, chocolate), (vanilla, coconut syrup), (coconut syrup, chocolate), (nuts, vanilla), (candy, vanilla), (chocolate, candy) C) (chocolate, nuts), (vanilla, coconut syrup), (coconut syrup, chocolate), (nuts, vanilla), (candy, vanilla), (chocolate, candy), (chocolate, vanilla) D) (chocolate, nuts), (chocolate, coconut syrup), (chocolate, candy), (vanilla, nuts), (vanilla, coconut syrup), (vanilla, candy), (candy, chocolate), (candy, vanilla), (coconut syrup, chocolate), (coconut syrup, vanilla) SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Solve the problem by guessing and adjusting.

15) After he had worked at the video store for 6 months, Hilton got a 10% raise and a $ 60 bonus. If he earned $368 with the raise and bonus, how much was he earning before?

16) Corinne is making a beaded necklace. She has 3 times as many green beads as red beads, and twice as many blue beads as green beads. If she has 150 beads all together, how many of the beads are blue?

Decide whether the argument is an example of inductive or deductive reasoning.

17) All U.S. Presidents have come from the original 48 states. No person from Alaska can be President.

15)

16)

17)

18) Practice makes perfect. Therefore, if I practice, Iʹll be perfect.

18)

19) If (-p)2 = p2 , then (-6)2 = 36

19)

Illustrate Goldbackʹs conjecture for the following number.

20) 32

20)

21) 30

21)

22) 48

22)

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13)

14)

23) 40

23)

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Use inductive reasoning.

24) Use inductive reasoning to predict the next term in the sequence of numbers.

0, 3, 3, 0, -3, ?

A) 3 B) 0 C) -3 25) Use inductive reasoning to predict the next term in the sequence of numbers.

37, 31, 25, 19, 13, ?

A) 7 B) 2 C) 6

24) D) 6 25) D) 0

26) Use inductive reasoning to predict the next term in the sequence of numbers.

1 1 1 1 1, - , , - , ,?

2 4 8 16 A)

1 64

B) -

1 32

C)

1 32

27) Use inductive reasoning to predict the next term in the sequence of numbers.

2, 5, 4, 10, 8, 20, ?

A) 16 B) 12 C) 30 Estimate the answer using compatible numbers.

28) 518 ÷ 52 A) 11 B) 12

26)

D) -

1 64 27)

D) 40

28) C) 10

D) 9

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Estimate the answer by rounding as indicated.

29) Estimate by rounding to the nearest hundred.

461 - 242

29)

30) Estimate by rounding to the nearest ten.

83 - 46

30)

31) Estimate by rounding to the nearest hundred.

766 × 668

31)

Round the number to the place value indicated.

32) 98,213 33) 63,037

32) 33)

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34) 21,629,336

34)

35) 61,005

35)

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Estimate the answer. State whether the estimate is larger or smaller than the exact answer.

36) Each gallon of porch and deck paint covers 200 square feet. How many gallons are needed to cover 1980 square feet?

C) 8; smaller D) 9; smaller A) 10; larger B) 11; larger

36)

Refer to the double-bar graph below which shows the number of male (M) and female (F) athletes at a university over a four-year period. Solve the problem.

YEAR 37) In which year was the number of male athletes equal to 375?

A) 1987 B) 1989 C) 1986

D) 1988

38) How many more male athletes than female athletes were there in 1987?

A) 50 B) 150 C) 100

D) 0

37)

38)

39) What was the amount of the decrease in the number of female athletes from 1988 to 1989?

A) 50 B) 100 C) 75 D) 200

39)

In a school survey, students showed these preferences for instructional materials. Answer the question.

40) About how many students would you expect to prefer written materials in a school of 300 students?

A) About 9 students B) About 54 students C) About 108 students D) About 27 students

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40)

41) About how many students would you expect to prefer lectures in a school of 950 students?

A) About 342 students B) About 190 students C) About 18 students D) About 171 students

41)

42) About how many students would you expect to prefer films in a school of 900 students?

A) About 162 students B) About 108 students C) About 20 students D) About 180 students

42)

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Answer Key Testname: CHAPTER 1 EXAM B

1) False. Possible counterexample is that C is the granddaughter of A. 2) False. Possible counterexample: Let the original price be $1000. After the price is raised, it will be 1000 + 150 = $1150.

After this is reduced by 15% it will be 1150 - 0.15 · 1150 = $977.50.

3) Answers will vary. Possible answer is a circle labeled ʺice creamʺ connected by lines to three other circles labeled ʺchocolate,ʺ strawberry,ʺ and ʺbanana.ʺ 4) Answers will vary. Possible answer is 3 circles linked like a chain.

5) Answers will vary. One possibility: the first arrow is single-lined, and the second is double-lined.

6) Answers will vary. One possibility is: the first -11 is enclosed in absolute value bars and the second is in brackets.

7) B 8) C 9) B 10) A 11) C 12) D 13) B 14) A 15) $280 16) 90 17) Inductive 18) Deductive 19) Deductive 20) 13 + 19 21) 7 + 23 22) 17 + 31 23) 17 + 23 24) C 25) A 26) B 27) A 28) C 29) 300 30) 30 31) 560,000 32) 98,000 33) 63,000 34) 22,000,000 35) 61,000 36) A 37) D 38) C 39) A 40) D 41) D 42) D

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Chapter 2 Exam A Name___________________________________

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Use the following definitions to determine if the statement is true or false.

N = {x : x is a natural number} I = {x : x is an integer} R = {x : x is a real number} W = {x : x is a whole number} Q = {x : x is a rational number} 1) W is a proper subset of I, Q, and R. A) True B) False 2) Q is a proper subset of R. A) True

B) False

3) I is a proper subset of Q and R. A) True

B) False

1)

2)

3)

4) W is a proper subset of I, Q, N, and R. A) True

4) B) False

Let U = {all soda pops}; A = {all diet soda pops}; B = {all cola soda pops}; C = {all soda pops in cans}; and D = {all caffeine-free soda pops}. Describe the given set in words.

5) Aʹ ∩ C A) All non-diet soda pops in cans B) All diet soda pops and all soda pops in cans C) All non-diet soda pops and all soda pops in cans D) All diet soda pops in cans 6) A ∩ B A) All soda pops C) All diet or all cola soda pops

5)

6) B) All diet and all cola soda pops D) All diet-cola soda pops

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Determine whether the set is well defined or not.

7) {x : x is an expensive boat on the Great Lakes}

7)

8) {x : x is stock on the AmEx today}

8)

9) {x : x is a low-fat ice cream}

9)

Identify the set as finite or infinite.

10) {2, 4, 6, 8, ...}

10)

11) The set of multiples of 3 between 0 and 100

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11)

12) The set of stars in the Milky Way Galaxy at 12:00 A.M. on January 1, 2000

12)

13) {1, 1/3, 1/9, 1/27, . . .}

13)

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Decide whether the sets are equivalent.

14) {d: d is a month of the year} and {g : g is a state in the United States} A) No B) Yes 15) {64, 26, 87, 9, 68} and {z, m, c, u, y} A) Yes

14)

15) B) No

Determine which labeled sections make up the indicated set.

16) B ∩ C A) v, p

B) s, v, p

C) n, o, p, r, v, s

D) p

17) C ∩ A ∩ B A) n, v, s, p

B) v

C) o

D) t, s, v, n, o, p, r

16)

17)

Shade the Venn diagram to represent the set.

18) (A ∩ B) ∪ (A ∪ B)ʹ

A)

18)

B)

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19) Aʹ ∪ Bʹ

19)

A)

B)

20) (A ∪ B ∪ Cʹ)ʹ

20)

A)

B)

Decide whether the sets are equal.

21) {b: b is a positive integer} and {k : k is a counting number} A) Yes B) No 22) {parsley, thyme, saffron, oregano} and {y : y is an herb} A) No B) Yes Use an alternative method to express the set.

23) {t, a, b, l, e} A) {z : z is a letter in the word table} C) {z : z is a table}

21)

22)

23) B) {table} D) (z is a letter in table)

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24) {d : d is a letter in the word cat and also in the word in} C) {c, a, t, i, n} A) {∅} B) (c, a, t, i, n)

24) D) { }

Use the Venn diagram below to find the number of elements in the region.

25) n(A ∩ B ∩ C) A) 8

25) B) 18

C) 44

D) 16

26) n((C ∪ B) - (A ∪ B)) A) 5

B) 2

C) 15

D) 11

27) n(A) A) 9

B) 17

C) 4

D) 12

26)

27)

Use set notation to list all the elements of the set.

28) The letters needed to spell these words: tear, rate, rat, tea A) {t,t,t,t,r,r,r,a,a,a,a,e,e,e} C) {a,e,r,t} 29) {x : x is an integer between 15 and 18 not inclusive} A) {16, 17} C) {14, 15, 16, 17, 18, 19}

28) B) {t,t,a,a,r,r,e} D) {r,a,t} 29) B) {16} or {17} D) {15, 16, 17, 18}

30) {x : x is an even natural number less than 10} A) {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} C) {1, 2, 3, 4, 5, 6, 7, 8, 9}

B) {0, 2, 4, 6, 8} D) {2, 4, 6, 8}

31) The whole numbers between -3 and 0, not inclusive A) {0} B) ∅

C) {-3, -2, -1, 0}

30)

31) D) {-2, -1}

Let A and B be sets with cardinal numbers, n(A) = a and n(B) = b, respectively. Decide whether the statement is true or false.

32) (B ∪ A) ⊂ B 32) A) True B) False 33) If B ⊆ A, n(B) = n(A - B).

A) True

B) False

34) n(A - B) = n(B - A) A) True

B) False

33)

34)

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35) n(A ∪ B) = n(A) - n(B) A) True

35) B) False

Find the cardinal number of the indicated set by referring to the given table.

36) A - (F ∪ S), given the following table: U.S. Production (in Thousands of Tons) of Certain Nuts Year Pecans (P) Almonds (A) Walnuts (W) Hazelnuts (H) 1993 (T) 184 584 232 41 1994 (F) 99 587 232 21 1995 (V) 134 304 230 39 1996 (S) 111 412 205 22 A) 888 B) 175 C) 999 37) V ∩ (P ∪ W), given the following table: U.S. Production (in Thousands of Tons) of Certain Nuts Year Pecans (P) Almonds (A) Walnuts (W) Hazelnuts (H) 1993 (T) 183 584 232 41 1994 (F) 99 586 232 21 1995 (V) 134 304 235 39 1996 (S) 111 412 205 22 A) 158 B) 0 C) 369 Replace the # with either ∈ or ∉ to express a true statement.

38) -4.5 # {n : n is a whole number} A) ∉

B) ∈

39) Iowa # {r : r is a state in the United States} A) ∉

B) ∈

Find n(A) for the set.

40) A = {∅, 0} A) n(A) = 0

36)

D) 759 37)

D) 343

38)

39)

40) B) n(A) = 2

C) n(A) = ∅

D) n(A) = 1

41) A = {-9, -8, -7, . . ., 0} A) n(A) = 1

B) n(A) = 10

C) n(A) = 9

D) n(A) = 4

42) A = {0, 2, 4, 6, 8} A) n(A) = 4

B) n(A) = 8

C) n(A) = 5

D) n(A) = 2

41)

42)

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Find, if possible, the number of elements in sets A, B, and C using the given information.

43) n(A - C) = 10 n(C - A) = 3 n(A ∩ B) = 8 n(C ∩ A) = 8 n(C ∩ B) = 6 n(B - A) = 8 n(A ∩ B ∩ C) = 4 A) n(A) = 22, n(B) = 20, n(C) = 15 B) n(A) = 18, n(B) = 16, n(C) = 11 C) n(A) = 11, n(B) = 27, n(C) = 18 D) The information is inconsistent or incomplete.

43)

44) n(A - C) = 10 n(C - A) = 2 n(A ∪ C) = 22 n(A ∩ B) = 10 n((C ∩ A) - B) = 4 n((A ∩ B) - C) = 4 n(B - (A ∪ C)) = 3 n(B ∩ C) = 7 A) n(A) = 12, n(B) = 25, n(C) = 20 B) n(A) = 20, n(B) = 14, n(C) = 12 C) n(A) = 16, n(B) = 18, n(C) = 12 D) The information is inconsistent or incomplete.

44)

Show that the set has cardinal number ℵ0 by establishing a one-to-one correspondence between the natural numbers and the given set. Be sure to indicate the general correspondence.

45) {5, 25, 125, 625, ...} A) 1, 2, 3, 4, ..., n, ...

B) 1, ↕ ↕ ↕ ↕ ↕ ↕ 5, 25, 125, 625, ..., 5 2n, ...

5, C) 1, 2, 3, 4, ..., n, ...

D) 1, ↕ ↕ ↕ ↕ ↕ ↕ n 5, 5, 25, 125, 625, ..., 5 , ...

46)

45) 2, ↕ 25, 2, ↕ 25,

3, ↕

4, ↕

..., n, ↕ 125, 625, ..., n 5 , 3, 4, ..., n, ↕ ↕ ↕ 125, 625, ..., 5n,

... ... ... ...

1 3 5 7 9 , , , , ...

3 5 7 9 11

46)

A) 1, 2, 3, 4, 5, ..., n, ... ↕ ↕ ↕ ↕ ↕ ↕ 1 3 5 7 9 3n - 1 , , , , , ... , , ...

3 5 7 9 11 n+1

B) 1, 2, 3, 4, 5, ..., n, ... ↕ ↕ ↕ ↕ ↕ ↕ 1 3 5 7 9 2n + 1 , , , , , ... , , ...

3 5 7 9 11 2n - 1

C)

D) 1, 2, 3, 4, 5, ..., n, ... ↕ ↕ ↕ ↕ ↕ ↕ 1 3 5 7 9 n+1 , , , , , ... , , ...

3 5 7 9 11 3n - 1

1, 2, 3, 4, 5, ..., n, ... ↕ ↕ ↕ ↕ ↕ ↕ 1 3 5 7 9 2n - 1 , , , , , ... , , ...

3 5 7 9 11 2n + 1

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47) {0, 3, 6, 9, 12, ...} A) 1, 2, 3, ↕ ↕ ↕ 0, 3, 6, C) 1, 2, 3, ↕ ↕ ↕ 0, 3, 6,

47) 4, ..., n, ... ↕ ↕ 9, ..., 3n, ...

4, ..., n, ... ↕ ↕ 9, ..., 3n - 3, ...

B) 1, ↕ 0, D) 1, ↕ 0,

2, ↕ 3, 2, ↕ 3,

3, ↕ 6, 3, ↕ 6,

4, ..., ↕ 9, ..., 4, ..., ↕ 9, ...,

n, ... ↕ 3n + 3, ... n, ... ↕ 3n - 1, ...

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

List the subsets.

48) List all of the three element subsets of the set {a, b, c, d}.

48)

49) List all of the two element subsets of the set {a, b, c, d, e}.

49)

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Find the number of subsets of the set.

50) {math, English, history, science, art} A) 24 B) 16

50) C) 32

D) 28

51) {14, 15, 16} A) 3

B) 7

C) 6

D) 8

51)

52) {0} A) 4

B) 0

C) 2

D) 1

52)

Decide whether the statement is true or false.

53) {12, 84, 145, 264} ⊆ {12, 24, 36, ..., 1080} A) True

B) False

54) {12, 20, 32, 52} ⊆ {2, 4, 6, 8, ..., 98} A) True

B) False

53)

54)

Describe a one-to-one correspondence between the given set and one of its proper subsets. For example, if we gave you the set {3, 5, 7, 9, 11, ...}, the nth term is 2n +1. You could then write the correspondence by matching the elements of {3, 5, 7, 9, 11, ...} with the elements of the subset {5, 7, 9, 11, 13, ...}. The general correspondence would match 2n + 1 with 2n + 3.

55) 55) {5, 6, 7, 8, ...} B) 5, 6, 7, 8, ..., n + 4, ...

A) 5, 6, 7, 8, ..., n + 4, ... ↕ ↕ ↕ ↕ ↕ ↕ ↕ ↕ ↕ ↕ 4, 5, 6, 7, ..., n + 3, ...

6, 7, 8, 9, ..., n + 5, ...

C) 5, 6, 7, 8, ..., n + 5, ...

D) 5, 6, 7, 8, ..., n + 4, ... ↕ ↕ ↕ ↕ ↕ ↕ ↕ ↕ ↕ ↕ 4, 5, 6, 7, ..., n + 3, ...

6, 7, 8, 9, ..., n + 6, ...

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Let U = {q, r, s, t, u, v, w, x, y, z} A = {q, s, u, w, y} B = {q, s, y, z} C = {v, w, x, y, z}. List the elements in the set.

56) A ∩ (B ∪ C) A) {q, y, z} B) {q, s, u, w, y, z}

56) C) {q, s, w, y}

57) Cʹ ∪ Aʹ A) {w, y} C) {s, t}

B) {q, s, u, v, w, x, y, z} D) {q, r, s, t, u, v, x, z}

58) (A ∩ B)ʹ A) {q, s, t, u, v, w, x, y} C) {s, u, w}

B) {r, t, u, v, w, x, z} D) {t, v, x}

D) {q, r, w, y, z} 57)

58)

Describe the indicated set in words and find the set.

59) P - (E ∪ C)′ , given the following information: The table gives features of different dishwashers price clean clean energy model (dollars) china glassware efficiency water usage a 712 excellent good good low b 455 excellent good fair moderate c 554 excellent good good high d 606 excellent good good high e 556 good fair good low f 385 excellent fair good moderate g 480 good fair fair moderate h 361 good fair fair moderate i 263 fair poor good moderate In the universal set U = {a, b, c, ..., i}, let the following characteristics be defined: P = price is at or below $455 C = does an excellent job of cleaning china G = does an excellent job of cleaning glassware E = has a good energy efficiency rating F = has low water usage A) Dishwashers that cost $455 or less and either have a good energy efficiency rating or do an excellent job of cleaning china; {h} B) Dishwashers that cost $455 or less and have both a low energy efficiency rating and do an excellent job of cleaning china; {f} C) Dishwashers that cost $455 or less and have either a low energy efficiency rating or do an excellent job of cleaning china; {a, b, c, d, e, f, h, i} D) Dishwashers that cost $455 or less and either have a good energy efficiency rating or do an excellent job of cleaning china; {b, f, i}

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59)

60) (P ∪ L) - (S ∩ C) , given the following information: The table gives the approximate nutritional value per serving of foods at a certain restaurant. protein fat calcium sodium vitamin A food calories (grams) (grams) (mg) (mg) (A.U.) Chow Mein 240 23 16 75 1250 1100 Pizza (cheese) 120 15 9 220 705 2720 Bean Burrito 340 20 4 185 1230 80 Linguini & Meatballs 330 19 13 124 1009 1590 Pea Soup 250 7 7 158 900 850 Chicken Salad 210 33 8 28 360 100 Ice Cream 270 3 13 145 98 420

60)

Let: C = {m : m provides 251 or more calories} P = {m : m provides 20 or more grams of protein} F = {m : m provides 10 or more grams of fat} L = {m : m provides 150 or more mg of calcium} S = {m : m provides 1000 or more mg of sodium} A = {m : m provides 1000 or more A.U. of Vitamin A} A) Foods that have either 20 or more grams of protein or 150 or more mg of calcium, but do not have both 1000 or more mg of sodium and 251 or more calories; {Chow Mein, Pizza, Pea Soup, Chicken Salad} B) Foods that have either 20 or more grams of protein or 150 or more mg of calcium, but do not have either 1000 or more mg of sodium or 251 or more calories; {Chow Mein, Pizza, Pea Soup, Chicken Salad} C) Foods that have both 20 or more grams of protein and 150 or more mg of calcium, but do not have both 1000 or more mg of sodium and 251 or more calories; ∅ D) Foods that have either 20 or more grams of protein or 150 or more mg of calcium, and also have either 1000 or more mg of sodium or 251 or more calories; {Chow Mein, Pizza, Bean Burrito, Pea Soup, Chicken Salad} Solve the problem.

61) A local television station sends out questionnaires to determine if viewers would rather see a documentary, an interview show, or reruns of a game show. There were 450 responses with the following results: 135 were interested in an interview show and a documentary, but not reruns.

18 were interested in an interview show and reruns but not a documentary.

63 were interested in reruns but not an interview show.

108 were interested in an interview show but not a documentary.

45 were interested in a documentary and reruns.

27 were interested in an interview show and reruns.

36 were interested in none of the three.

How many are interested in exactly one kind of show?

B) 226 C) 196 A) 216

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D) 206

61)

62) A survey of 240 families showed that 91 had a dog; 70 had a cat; 31 had a dog and a cat; 91 had neither a cat nor a dog nor a parakeet; 7 had a cat, a dog, and a parakeet.

How many had a parakeet only?

A) 24 B) 29

62)

C) 19

D) 34

Write a description of the shaded region using the symbols A, B, C, ∪, ∩, -, and ′ as needed.

63)

A) B′ ∩ A ∪ C

B) C ∩ B′ ∪ A

C) A ∪ C - B

63)

D) A ∪ C 64)

64)

A) B ∩ (A ∩ C)′

B) B′ - (A ∪ B)

C) B - (A ∩ C)

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D) A′ ∩ C′ ∩ B

Answer Key Testname: CHAPTER 2 EXAM A

1) A 2) A 3) A 4) B 5) A 6) D 7) Not well defined 8) Well defined 9) Not well defined 10) Infinite 11) Finite 12) Finite 13) Infinite 14) A 15) A 16) A 17) B 18) B 19) B 20) A 21) A 22) A 23) A 24) D 25) A 26) C 27) B 28) C 29) A 30) D 31) B 32) B 33) B 34) B 35) B 36) A 37) C 38) A 39) B 40) B 41) B 42) C 43) B 44) B 45) C 46) C 47) C 48) {a, b, c}, {a, b, d}, {a, c, d}, {b, c, d} 49) {a, b}, {a, c}, {a, d}, {a, e}, {b, c}, {b, d}, {b, e}, {c, d}, {c, e}, {d, e} 50) C Copyright © 2022 Pearson Education, Inc.

Answer Key Testname: CHAPTER 2 EXAM A

51) D 52) C 53) B 54) A 55) B 56) C 57) D 58) B 59) D 60) A 61) A 62) C 63) B 64) D

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Chapter 2 Exam B Name___________________________________

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Find n(A) for the set.

1) A = {{a, b}, {c, d}, {e, b}}

1)

2) A = {0, 2, 4, 6, 8}

2)

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Replace the # with either ∈ or ∉ to express a true statement.

3) 88 # {8, 16, 24, 32, ... } A) ∈

3) B) ∉

4) Ohio # {California, Vermont, Colorado, New Jersey, Washington, Kentucky} A) ∈ B) ∉

4)

Use an alternative method to express the set.

5) {21, 28, 35, ..., 105} A) {b : b is a multiple of 7 greater than or equal to 21} B) {t : t is a multiple of 7 greater than 20 and less than 106} C) {w : w is a multiple of 7} D) {x : x is a multiple of 7 greater than 21 and less than 105} 6) {t, a, b, l, e} A) {table} C) (z is a letter in table)

5)

6) B) {z : z is a table} D) {z : z is a letter in the word table}

Use set notation to list all the elements of the set.

7) The whole numbers greater than 3 and less than 7 A) {3, 4, 5, 6} B) {4, 5, 6, 7}

7) C) {3, 4, 5, 6, 7}

8) The natural numbers between -3 and 1, not inclusive A) ∅ B) {0} C) {0, 1} Decide whether the sets are equal.

9) {y : y was an American President in the year 1573} and ∅ A) Yes B) No 10) {b: b is a positive integer} and {k : k is a counting number} A) Yes B) No Decide whether the sets are equivalent.

11) {d: d is a month of the year} and {g : g is a state in the United States} A) Yes B) No

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D) {4, 5, 6} 8) D) {-2, -1, 0}

9)

10)

11)

12) {∅} and {x : x is a state in the U.S. with a minimum voting age of 64} A) No B) Yes Find the number of subsets of the set.

13) {14, 15, 16} A) 3 B) 6

12)

13) C) 8

D) 7

14) {x | x is a day of the week} A) 124 B) 256

14) C) 128

D) 127

15) {1, 2, 3, . . . , 8} A) 16

B) 252

C) 512

D) 256

Decide whether the statement is true or false.

16) ∅ ⊆ {4, 8, 12, 16, 20} A) False

B) True

15)

17) {12, 84, 145, 264} ⊆ {12, 24, 36, ..., 1080} A) False

16)

17) B) True

Use the following definitions to determine if the statement is true or false.

N = {x : x is a natural number} I = {x : x is an integer} R = {x : x is a real number} W = {x : x is a whole number} Q = {x : x is a rational number} 18) I is a proper subset of N, W, Q, and R. A) True B) False 19) W is a proper subset of I, Q, N, and R. A) True

B) False

20) W is a subset of W, I, Q, and R. A) True

B) False

18)

19)

20)

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

List the subsets.

21) List all of the three element subsets of the set {a, b, c, d, e}.

22) List all of the three element subsets of the set {a, b, c, d}.

21) 22)

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Let A and B be sets with cardinal numbers, n(A) = a and n(B) = b, respectively. Decide whether the statement is true or false.

23) n(A - B) = n(B - A) 23) A) True B) False

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24) (B ∪ A) ⊂ B A) True

B) False

25) If B ⊆ A, n(B) = n(A - B).

A) True

B) False

24)

25)

Let U = {all soda pops}; A = {all diet soda pops}; B = {all cola soda pops}; C = {all soda pops in cans}; and D = {all caffeine-free soda pops}. Describe the given set in words.

26) Aʹ ∩ C A) All non-diet soda pops in cans B) All diet soda pops and all soda pops in cans C) All diet soda pops in cans D) All non-diet soda pops and all soda pops in cans 27) (A ∪ D) ∩ Cʹ A) All diet, caffeine-free soda pops not in cans B) All non-diet, non-caffeine-free soda pops not in cans C) All non-cola soda pops not in cans D) All soda pops not in cans that are diet or caffeine -free

27)

Write a description of the shaded region using the symbols A, B, C, ∪, ∩, -, and ′ as needed.

28)

A) B ∩ (A ∩ C)′

B) A′ ∩ C′ ∩ B

C) B′ - (A ∪ B)

26)

28)

D) B - (A ∩ C)

29)

29)

A) (A ∩ B)′

B) A - B

C) A ∪ B

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D) A′ ∩ B′

Describe the indicated set in words and find the set.

30) (P ∪ L) - (S ∩ C) , given the following information: The table gives the approximate nutritional value per serving of foods at a certain restaurant. protein fat calcium sodium vitamin A food calories (grams) (grams) (mg) (mg) (A.U.) Chop Suey 240 23 16 75 1250 1100 Pizza (cheese) 120 15 9 220 704 2720 Bean Burrito 340 20 4 185 1230 80 1590 Linguini & Meatballs 330 19 13 124 1009 Tomato Soup 250 7 7 158 900 850 Chicken Salad 210 33 8 28 360 100 Milkshake 270 3 13 145 98 420

30)

Let: C = {m : m provides 251 or more calories} P = {m : m provides 20 or more grams of protein} F = {m : m provides 10 or more grams of fat} L = {m : m provides 150 or more mg of calcium} S = {m : m provides 1000 or more mg of sodium} A = {m : m provides 1000 or more A.U. of Vitamin A} A) Foods that have either 20 or more grams of protein or 150 or more mg of calcium, and also have either 1000 or more mg of sodium or 251 or more calories; {Chop Suey, Pizza, Bean Burrito, Tomato Soup, Chicken Salad} B) Foods that have both 20 or more grams of protein and 150 or more mg of calcium, but do not have both 1000 or more mg of sodium and 251 or more calories; ∅ C) Foods that have either 20 or more grams of protein or 150 or more mg of calcium, but do not have both 1000 or more mg of sodium and 251 or more calories; {Chop Suey, Pizza, Tomato Soup, Chicken Salad} D) Foods that have either 20 or more grams of protein or 150 or more mg of calcium, but do not have either 1000 or more mg of sodium or 251 or more calories; {Chop Suey, Pizza, Tomato Soup, Chicken Salad} Let U = {q, r, s, t, u, v, w, x, y, z} A = {q, s, u, w, y} B = {q, s, y, z} C = {v, w, x, y, z}. List the elements in the set.

31) A ∪ (B ∩ C) A) {q, s, u, w, y, z} B) {q, w, y} 32) (A ∩ B)ʹ A) {r, t, u, v, w, x, z} C) {s, u, w} 33) A ∩ (B ∪ C) A) {q, s, u, w, y, z}

31) C) {q, r, w, y, z}

D) {q, y, z} 32)

B) {q, s, t, u, v, w, x, y} D) {t, v, x} 33) B) {q, s, w, y}

C) {q, y, z}

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D) {q, r, w, y, z}

Shade the Venn diagram to represent the set.

34) (A ∪ B) ∩ (A ∩ B)ʹ

A)

34)

B)

35) Cʹ ∩ (A ∪ B)

A)

35)

B)

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36) B ∪ (A ∩ Cʹ)

36)

A)

B)

Use the Venn diagram below to find the number of elements in the region.

37) n(A ∩ B ∩ C) A) 18

B) 8

C) 44

D) 16

38) n((C ∪ B) - (A ∪ B)) A) 15

B) 5

C) 11

D) 2

39) n(C - A) A) 13

B) 20

C) 11

D) 15

37)

38)

39)

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SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Determine which labeled sections make up the indicated set.

40) A - B

40)

41) C - (A ∩ B)

41)

Find the cardinal number of the indicated set by referring to the given table.

42) H ∪ A, given the following table: U.S. Production (in Thousands of Tons) of Certain Nuts Year Pecans (P) Almonds (A) Walnuts (W) Hazelnuts (H) 1993 (T) 181 584 232 41 1994 (F) 99 584 232 21 1995 (V) 134 304 233 39 1996 (S) 111 412 205 20 43) A - (F ∪ S), given the following table: U.S. Production (in Thousands of Tons) of Certain Nuts Year Pecans (P) Almonds (A) Walnuts (W) Hazelnuts (H) 1993 (T) 184 584 232 41 1994 (F) 99 587 232 21 1995 (V) 134 304 235 39 1996 (S) 111 412 205 20

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42)

43)

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Find, if possible, the number of elements in sets A, B, and C using the given information.

44) n(A - C) = 10 n(C - A) = 2 n(A ∪ C) = 22 n(A ∩ B) = 10 n((C ∩ A) - B) = 4 n((A ∩ B) - C) = 4 n(B - (A ∪ C)) = 3 n(B ∩ C) = 7 A) n(A) = 12, n(B) = 25, n(C) = 20 B) n(A) = 16, n(B) = 18, n(C) = 12 C) n(A) = 20, n(B) = 14, n(C) = 12 D) The information is inconsistent or incomplete.

45) n(A ∪ B ∪ C) = 21 n(A ∩ B) = 4 n(A ∩ C) = 5 n(A - B) = 6 n(C ∩ B) = 8 n(A ∩ B ∩ C) = 2 n(C - (A ∪ B)) = 2 A) n(A) = 8, n(B) = 11, n(C) = 15 B) n(A) = 8, n(B) = 15, n(C) = 13 C) n(A) = 10, n(B) = 13, n(C) = 13 D) The information is inconsistent or incomplete.

45)

Solve the problem.

46) A survey of 240 families showed that 91 had a dog; 70 had a cat; 31 had a dog and a cat; 91 had neither a cat nor a dog nor a parakeet; 7 had a cat, a dog, and a parakeet.

How many had a parakeet only?

A) 34 B) 19

44)

46)

C) 29

D) 24

Describe a one-to-one correspondence between the given set and one of its proper subsets. For example, if we gave you the set {3, 5, 7, 9, 11, ...}, the nth term is 2n +1. You could then write the correspondence by matching the elements of {3, 5, 7, 9, 11, ...} with the elements of the subset {5, 7, 9, 11, 13, ...}. The general correspondence would match 2n + 1 with 2n + 3.

47) 47) {5, 6, 7, 8, ...} B) 5, 6, 7, 8, ..., n + 4, ...

A) 5, 6, 7, 8, ..., n + 4, ... ↕ ↕ ↕ ↕ ↕ ↕ ↕ ↕ ↕ ↕ 6, 7, 8, 9, ..., n + 6, ...

4, 5, 6, 7, ..., n + 3, ...

C) 5, 6, 7, 8, ..., n + 5, ...

D) 5, 6, 7, 8, ..., n + 4, ... ↕ ↕ ↕ ↕ ↕ ↕ ↕ ↕ ↕ ↕ 4, 5, 6, 7, ..., n + 3, ...

6, 7, 8, 9, ..., n + 5, ...

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Show that the set has cardinal number ℵ0 by establishing a one-to-one correspondence between the natural numbers and the given set. Be sure to indicate the general correspondence.

48) {0, 3, 6, 9, 12, ...} A) 1, 2, 3, 4, ..., n, ...

B) ↕ ↕ ↕ ↕ ↕ 0, 3, 6, 9, ..., 3n, ...

C) 1, 2, 3, 4, ..., n, ...

D) ↕ ↕ ↕ ↕ ↕ 0, 3, 6, 9, ..., 3n + 3, ...

49) {5, 25, 125, 625, ...} A) 1, 2, 3, 4, ..., n, ↕ ↕ ↕ ↕ ↕ 5, 25, 125, 625, ..., 5n, C) 1, ↕

2, ↕

5,

25,

3, ↕

4, ↕

..., n, ↕ 125, 625, ..., 5 n ,

50) {8, 13, 18, 23, 28, ...} A) 1, 2, 3, 4, 5, ..., ↕ ↕ ↕ ↕ ↕ 8, 13, 18, 23, 28, ..., C) 1, 2, 3, 4, 5, ..., ↕ ↕ ↕ ↕ ↕ 8, 13, 18, 23, 28, ...,

48) 1, ↕ 0, 1, ↕ 0,

2, ↕ 3, 2, ↕ 3,

3, ↕ 6, 3, ↕ 6,

4, ..., ↕ 9, ..., 4, ..., ↕ 9, ...,

n, ... ↕ 3n - 3, ... n, ... ↕ 3n - 1, ...

3, ↕

4, ↕

49) ...

B) 1, ↕

2, ↕

... ...

5, D) 1, ↕

25, 2, ↕

...

5,

25,

..., n, ... ↕ 2n 125, 625, ..., 5 , ...

3, 4, ..., n, ... ↕ ↕ ↕ 125, 625, ..., n 5 , ...

50)

n, ... ↕ 5n + 3, ... n, ... ↕ 4n - 2, ...

B) 1, 2, 3, 4, 5, ..., ↕ ↕ ↕ ↕ ↕ 8, 13, 18, 23, 28, ..., D) 1, 2, 3, 4, 5, ..., ↕ ↕ ↕ ↕ ↕ 8, 13, 18, 23, 28, ...,

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n, ... ↕ 5n + 2, ... n, ... ↕ 4n + 3, ...

Answer Key Testname: CHAPTER 2 EXAM B

1) n(A) = 3 2) n(A) = 5 3) A 4) B 5) B 6) D 7) D 8) A 9) A 10) A 11) B 12) A 13) C 14) C 15) D 16) B 17) A 18) B 19) B 20) A 21) {a, b, c}, {a, b, d}, {a, b, e}, {a, c, d}, {a, c, e}, {a, d, e}, {b, c, d}, {b, c, e}, {b, d, e}, {c, d, e} 22) {a, b, c}, {a, b, d}, {a, c, d}, {b, c, d} 23) B 24) B 25) B 26) A 27) D 28) B 29) D 30) C 31) A 32) A 33) B 34) A 35) B 36) B 37) B 38) A 39) B 40) t, s 41) p, r, s 42) 2005 43) 888 44) C 45) C 46) B 47) D 48) B 49) C 50) A Copyright © 2022 Pearson Education, Inc.

Chapter 3 Exam A Name___________________________________

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Represent the logical form by a circuit.

1) (p ∧ ~r) ∨ q

1)

2) p ∧ (~q ∨ r)

2)

Decide whether the following is a statement or not a statement.

3) My favorite baseball team will win the pennant.

4) Mary has a cat.

3) 4)

Identify the statement as simple or compound.

5) The car is in the garage and the bicycle is in the driveway.

5)

6) If you forget to bring the book back to the library, you will have to pay a fine.

6)

7) The apartment is rented or it is available.

7)

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Negate each quantified statement and rewrite it in English in an alternative way.

8) Some photographs are not displayed at this exhibition.

A) All photographs are displayed at this exhibition.

B) No photographs are displayed at this exhibition.

C) All photographs are not displayed at this exhibition.

D) Some photographs are displayed at this exhibition.

9) All dinosaurs were carnivores.

A) All dinosaurs were not carnivores.

B) There existed dinosaurs that were carnivores.

C) There existed dinosaurs that were not carnivores.

D) Some dinosaurs were carnivores.

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8)

9)

Represent the circuit with a logical form.

10)

A) (p ∧ q) ∧ (r ∧ s) C) (p ∧ q) ∨ (r ∧ s)

10)

B) p ∧ (q ∨ r) ∧ s D) (p ∨ q) ∨ (r ∨ s)

11)

11)

A) p ∧ (q ∨ r)

B) p ∨ (q ∨ r)

C) p ∧ q ∧ r

D) (p ∨ q) ∧ r

Use the following definitions to translate the statement into words. p: The monitor is included. q: The color printer is optional. r: The zip drive is extra.

12) ~(p ∨ r) A) It is true that the monitor is included and the zip drive is not extra.

B) It is not true that the monitor is not included and the zip drive is extra.

C) The monitor is included and the zip drive is extra.

D) It is not true that the monitor is included or the zip drive is extra.

12)

13) q ↔ (~p ∧ r) A) The color printer is optional if and only if the monitor is not included and the zip drive is extra.

B) If the color printer is not optional, then the monitor is not included and the zip drive is extra.

C) The color printer is not optional if and only if the monitor is not included and the zip drive is extra.

D) If the color printer is optional, then the monitor is not included and the zip drive is extra.

Write the statement in symbolic form.

14) The Democrats will control the Senate and environmental programs will not be cut.

A) ~p ∨ ~q B) p ∨ ~q C) p ∧ ~q D) p ∧ q 15) If you exercise, then you will feel great or you will sleep better.

A) r → ~(s ∨ t) B) r → (s ∨ t) C) r ↔ (s ∨ t)

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13)

14)

15) D) (r → s) ∨ t

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Construct a truth table for the given compound statement.

16) ~r ∧ ~q

16)

17) ~(~(p ∨ q))

17)

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

18) (p ∧ ~q) ∧ t A) p q t (p ∧ ~q) ∧ t T T T F T T F T T F T F T F F F F T T F F T F T F F T T F F F T C) p q t (p ∧ ~q) ∧ t T T T F T T F F T F T F T F F T F T T F F T F T F F T T F F F T

18) B) p q t (p ∧ ~q) ∧ t T T T F T T F F T F T T T F F F F T T F F T F F F F T F F F F F D) p q t (p ∧ ~q) ∧ t T T T F T T F F T F T F T F F F F T T F F T F T F F T T F F F T

Assuming that p represents a false statement and q represents a true statement, determine the truth value of the following.

19) p ∨ q 19) A) False B) True 20) ~(p ∨ ~q) A) False

20) B) True

Determine whether the statements are logically equivalent.

21) ~(p ∨ ~q) ∧ ~(p ∧ q), p ∧ (p ∧ q) A) Not equivalent 22) (p ∨ ~q) ∧ ~(p ∧ q), p ∧ (p ∧ q) A) Not equivalent

21) B) Equivalent 22) B) Equivalent

Determine how many lines will be in the truth table for the following statement.

23) p ∧ (~q ∨ r) A) 3 B) 6 C) 8

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23) D) 9

24) ~(p ∧ q) ∧ (q ∧ ~r) A) 4

24) B) 9

C) 8

D) 3

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Determine whether the sentence uses the inclusive or or the exclusive or.

25) Study now or study later.

25)

26) The insurance policy will not cover misuse or acts of God.

26)

Use DeMorganʹs Laws to rewrite the negation of the statement.

27) Joaquim has red hair and freckles.

27)

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Construct a truth table for the statement.

28) ~(p → q) → (p ∧ ~q)

28)

A) p

q

~(p → q) → (p ∧ ~q)

B) p

q

~(p → q) → (p ∧ ~q)

T T F F C) p

T F T F q

T F T T ~(p → q) → (p ∧ ~q)

T T F F D) p

T F T F q

T F F F ~(p → q) → (p ∧ ~q)

T T F F

T F T F

T T F F

T F T F

B) p

q

(~p ∨ ~q) → ~(q ∧ p)

T T F F D) p

T F T F q

T T T F (~p ∨ ~q) → ~(q ∧ p)

T T F F

T F T F

T F F T

29) (~p ∨ ~q) → ~(q ∧ p) A) p q (~p ∨ ~q) → ~(q ∧ p) T T F F C) p

T F T F q

T T F F

T F T F

T F F T (~p ∨ ~q) → ~(q ∧ p) F F F F

T T T T 29)

T T T T

Assume that p represents a true statement, q represents a true statement, and r represents a false statement. Determine the truth value of the following.

30) (q ∧ ~r) → (~p ∨ r) 30) A) False B) True 31) (p ∨ q) → (p ∧ r) A) True

31) B) False

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Determine whether the statements are equivalent.

32) If the wind speed is over 70 miles per hour, then the tree will be uprooted.

If the tree is not uprooted, then the wind speed is not over 70 miles per hour.

A) Not equivalent B) Equivalent 33) If it is cold outside, then you light the fireplace.

If you light the fireplace, then it is cold outside.

A) Not equivalent

32)

33) B) Equivalent

Rewrite the statement in the form ʺif p, then qʺ.

34) Practice is necessary for making the team.

A) If you donʹt practice, then you wonʹt make the team.

B) If you practice, then you will make the team.

C) If you make the team, then you must practice.

D) If you make the team, then you wonʹt have to practice.

35) I will lose weight if I diet.

A) If I diet, then Iʹll lose weight.

C) If I diet, then I gain weight.

34)

35) B) If I lose weight, then Iʹll diet.

D) If I donʹt diet, then I wonʹt lose weight.

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Rephrase the statement in the requested symbolic form.

36) contrapositive of a → ~(b ∨ c)

36)

37) inverse of ~a → ~b

37)

38) contrapositive of a → b

38)

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Write, as indicated, the converse, inverse, or contrapositive for the statement.

39) If the sum of the interior angles of a geometric figure is 180 degrees, then the figure is a triangle. (contrapositive) A) If a geometric figure is a triangle, then the sum of the interior angles is 180 degrees.

B) If a geometric figure is not a triangle, then the sum of the interior angles is not 180 degrees.

C) If the sum of the interior angles of a geometric figure is not 180 degrees, then the figure is not a triangle.

D) If a geometric figure is not a triangle, then the sum of the interior angles is 180 degrees.

40) If the sun shines, they will bask. (inverse) A) If they do not bask, then the sun does not shine.

B) If the sun does not shine, then they will not bask.

C) If they bask, then the sun shines.

D) If they do not bask, then the sun shines.

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39)

40)

Determine whether the form represents a valid argument.

41) ~p q → ~p ~p ∨ q A) Invalid

41)

B) Valid

Determine whether the argument is valid or invalid.

42) If your father fixes the car, then you will go to the museum.

Your father will buy a wrench or you will not go to the museum.

Your father fixes the car.

Therefore, your father will buy a wrench and you will go to the museum.

A) Valid B) Invalid

42)

Identify the form of the argument and state whether the argument is valid or invalid.

43) If the bell rings, then we answer the door.

The bell rings.

Therefore, we answer the door.

A) Disjunctive syllogism; valid B) Fallacy of the converse; invalid C) Fallacy of the inverse; invalid D) Law of detachment; valid 44) If the bough breaks, then the cradle will fall.

The bough breaks.

Therefore, the cradle will fall.

A) Fallacy of the converse; invalid C) Law of detachment; valid 45) If it rains, then the squirrels hide.

The squirrels are hiding.

Therefore, it is raining.

A) Fallacy of the inverse; invalid C) Disjunctive syllogism; valid

43)

44)

B) Fallacy of the inverse; invalid D) Law of syllogism; valid 45)

B) Law of contraposition; valid D) Fallacy of the converse; invalid

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Complete the syllogism so that it is valid and the conclusion is true. Answers may vary.

46) No animal raised as a pet has been successfully reintroduced into the wild.

Some animals born in captivity have been successfully reintroduced into the wild. ∴ 47) No artist who was an impressionist became famous while still alive.

Some artists who were realists became famous while still alive. ∴ Determine whether the syllogism is valid or invalid.

48) Some teachers believe in corporal punishment.

All who believe in corporal punishment are cruel.

Mr. Harrington is not cruel. ∴ Mr. Harrington is not a teacher.

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46)

47)

48)

49) All astronauts are healthy.

Lawrence is not healthy. ∴ Lawrence is not an astronaut.

49)

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Calculate the truth value of the negation of the fuzzy statement. The truth value of the fuzzy statement is given in parentheses.

50) There is no remainder in the mathematics of infinity. (0.69) 50) A) 0.69 B) 0.31 C) 1 D) 0 Determine the truth value of the following statement.

51) Assume that p has a truth value of 0.32, and q has a truth value of 0.58. ~(p ∧ q) A) 0.68

B) 0.42

C) 0.58

51)

D) 0.32

52) Consider the following fuzzy statements: p: Employees work in cubicles because they are fun. (0.32) q: Employees work in cubicles because they provide independent work space. (0.71) Employees work in cubicles because they provide independent work space and not because they are fun.

A) 0.39 B) 0.68 C) 0.32 D) 0.71

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52)

Answer Key Testname: CHAPTER 3 EXAM A

1)

2)

3) Not a statement 4) Statement 5) Compound 6) Compound 7) Compound 8) A 9) C 10) C 11) B 12) D 13) A 14) C 15) B 16) r q (~r ∧ ~q) T T F T F F F T F F F T 17) p q ~(~(p ∨ q)) T T T T F T F T T F F F 18) B 19) B 20) B 21) A 22) A 23) C 24) C 25) Exclusive or 26) Inclusive or 27) Joaquim does not have red hair or Joaquim does not have freckles.

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Answer Key Testname: CHAPTER 3 EXAM A

28) D 29) D 30) A 31) B 32) B 33) A 34) C 35) A 36) (b ∨ c) → ~a 37) a → b 38) ~b → ~a 39) B 40) B 41) B 42) A 43) D 44) C 45) D 46) Possible answer: Some animals born in captivity have not been successfully reintroduced into the wild.

47) Possible answer: Some artists who were realists did not become famous while still alive.

48) Invalid 49) Valid 50) B 51) A 52) B

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Chapter 3 Exam B Name___________________________________

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Determine whether the syllogism is valid or invalid.

1) Some teachers believe in corporal punishment.

All who believe in corporal punishment are cruel.

Mr. Harrington is not cruel. ∴ Mr. Harrington is not a teacher.

A) Valid 2) All astronauts are healthy.

Lawrence is not healthy. ∴ Lawrence is not an astronaut.

A) Invalid Determine whether the statements are logically equivalent.

3) ~(~p ∧ q), p ∨ ~q A) Equivalent

1)

B) Invalid 2)

B) Valid

3) B) Not equivalent

Determine how many lines will be in the truth table for the following statement.

4) ~p ∨ ~q A) 4 B) 16 C) 8 5) p ∧ (~q ∨ r) A) 9

5) B) 6

Decide whether or not the following is a statement.

6) My favorite baseball team will win the pennant.

A) Statement 7) July 4 was a Monday.

A) Statement

4) D) 2

C) 8

D) 3

6) B) Not a statement 7) B) Not a statement

Identify the statement as simple or compound.

8) If you forget to bring the book back to the library, you will have to pay a fine.

A) Simple B) Compound 9) The animal is a mammal if and only if it nurses its young.

A) Simple B) Compound Determine whether the argument is valid or invalid.

10) The boat has a new battery.

If the boat has a new battery, then you can go fishing by the bridge.

The boat does not have gasoline or you will not go fishing by the bridge.

Therefore, the boat has gasoline.

A) Invalid B) Valid

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8)

9)

10)

11)

11) If your father fixes the car, then you will go to the museum.

Your father will buy a wrench or you will not go to the museum.

Your father fixes the car.

Therefore, your father will buy a wrench and you will go to the museum.

A) Valid B) Invalid Determine whether the form represents a valid argument.

12) p ~q → ~p ~p ∧ q A) Invalid

12)

B) Valid

Determine whether the sentence uses the inclusive or or the exclusive or.

13) The prize is a new car or $10,000 cash.

A) Inclusive or B) Exclusive or

13)

14) Shaun will win the race if he eats carbohydrates beforehand or if he has slept well.

A) Inclusive or B) Exclusive or Rewrite the statement in the form ʺif p, then qʺ.

15) I will lose weight if I diet.

A) If I donʹt diet, then I wonʹt lose weight.

C) If I lose weight, then Iʹll diet.

16) I will go to class only if you go.

A) If you go to class, then Iʹll go to class.

C) If I go to class, then you go to class.

15) B) If I diet, then Iʹll lose weight.

D) If I diet, then I gain weight.

16) B) If I donʹt go to class, you donʹt go to class.

D) If I go to class, then you donʹt go to class.

Write the statement in symbolic form.

17) The Democrats will control the Senate and environmental programs will not be cut.

A) p ∧ ~q B) p ∧ q C) p ∨ ~q D) ~p ∨ ~q 18) You, as president, may declare war, but Congress may override your declaration if and only if their constituents are against war and there is a majority vote.

A) p ∧ (q ↔ (r ∧ s)) B) p ↔ (r ∧ s) C) p ∧ (q → r ∨ s) D) p ∨ (q ↔ r ∧ s) Construct a truth table for the statement.

19) ~(p → q) → (p ∧ ~q)

17)

18)

19)

A) p

q

~(p → q) → (p ∧ ~q)

B) p

q

~(p → q) → (p ∧ ~q)

T T F F C) p

T F T F q

T F T T ~(p → q) → (p ∧ ~q)

T T F F D) p

T F T F q

T T T T ~(p → q) → (p ∧ ~q)

T T F F

T F T F

T T F F

T F T F

T F F F

14)

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T F F T

20) (p → q) → (~p ∨ q)

20)

A) p

q

(p → q) → (~p ∨ q)

B) p

q

(p → q) → (~p ∨ q)

T T F F C) p

T F T F q

T F T T

T F T F q

T T T T

(p → q) → (~p ∨ q)

T T F F D) p

(p → q) → (~p ∨ q)

T T F F

T F T F

F T F F

T T F F

T F T F

T F T F

21) (~p ∨ ~q) → ~(q ∧ p) A) p q (~p ∨ ~q) → ~(q ∧ p) T T F F C) p

T F T F q

T T F F

T F T F

T T T F (~p ∨ ~q) → ~(q ∧ p) F F F F

21) B) p

q

(~p ∨ ~q) → ~(q ∧ p)

T T F F D) p

T F T F q

T F F T (~p ∨ ~q) → ~(q ∧ p)

T T F F

T F T F

T T T T

Determine the truth value of the following statement.

22) Assume that p has a truth value of 0.32, and q has a truth value of 0.58. ~(p ∧ q) A) 0.58

B) 0.68

C) 0.42

22)

D) 0.32

23) Consider the following fuzzy statements: p: Employees work in cubicles because they are fun. (0.32) q: Employees work in cubicles because they provide independent work space. (0.71) Employees work in cubicles because they provide independent work space and not because they are fun.

A) 0.68 B) 0.71 C) 0.39 D) 0.32

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23)

Construct a truth table for the given compound statement.

24) (p ∧ w) ∧ (~w ∨ t) A) p w t (p ∧ w) ∧ (~w ∨ t) T T T F T T F F T F T T T F F T F T T T F T F F F F T T F F F T C) p w t (p ∧ w) ∧ (~w ∨ t) T T T T T T F F T F T F T F F F F T T F F T F F F F T F F F F F 25) (p ∧ ~q) ∧ t A) p q t (p ∧ ~q) ∧ t T T T F T T F F T F T F T F F F F T T F F T F T F F T T F F F T C) p q t (p ∧ ~q) ∧ t T T T F T T F F T F T F T F F T F T T F F T F T F F T T F F F T

24) B) p w T T T T T F T F F T F T F F F F

t (p ∧ w) ∧ (~w ∨ t) T F F T T T F T T T F F T T F F

p w T T T T T F T F F T F T F F F F

t (p ∧ w) ∧ (~w ∨ t) T F F T T T F T T T F F T T F T

D)

25) B) p q t (p ∧ ~q) ∧ t T T T F T T F F T F T T T F F F F T T F F T F F F F T F F F F F D) p q t (p ∧ ~q) ∧ t T T T F T T F T T F T F T F F F F T T F F T F T F F T T F F F T

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26) p ∨ ~(s ∧ c) A)

26) B)

p s c p ∨ ~(s ∧ c) T T T T T T F T T F T T T F F T F T T F F T F T F F T T F F F F C)

p s c p ∨ ~(s ∧ c) T T T T T T F F T F T T T F F T F T T F F T F T F F T T F F F F D)

p s c p ∨ ~(s ∧ c) T T T T T T F T T F T T T F F T F T T F F T F T F F T T F F F T

p s c p ∨ ~(s ∧ c) T T T T T T F T T F T T T F F F F T T F F T F T F F T T F F F F

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Represent the logical form by a circuit.

27) (~p ∧ q) ∧ (r ∧ ~q)

27)

28) (p ∧ ~r) ∨ q

28)

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Assuming that p represents a false statement and q represents a true statement, determine the truth value of the following.

29) ~(p ∧ q) 29) A) False B) True Use DeMorganʹs Laws to rewrite the negation of the statement.

30) The number x is not less than 7 and y is not greater than 0.

A) The number x is not less than 7 or y is not greater than 0.

B) The number x is less than 7 and y is greater than 0.

C) The number x is less than 7 and y is not greater than 0.

D) The number x is less than 7 or y is greater than 0.

31) You cannot make a deposit or a withdrawal with that ATM card.

A) You can make a deposit or you can make a withdrawal with that ATM card.

B) You cannot make a deposit and you cannot make a withdrawal with that ATM card.

C) You can make a deposit and you can make a withdrawal with that ATM card.

D) You cannot make a deposit and you can make a withdrawal with that ATM card.

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30)

31)

Identify the form of the argument and state whether the argument is valid or invalid.

32) You get soup or you get salad.

You did not get soup.

Therefore, you got salad.

A) Fallacy of the inverse; invalid B) Disjunctive syllogism; valid C) Fallacy of the converse; invalid D) Law of syllogism; valid 33) If it is cold, then you need a coat.

You do not need a coat.

Therefore, it is not cold.

A) Law of contraposition; valid C) Law of syllogism; valid 34) If you eat well, you will be well.

If you are well, you will be happy.

Therefore, if you eat well, you will be happy.

A) Law of syllogism; valid C) Fallacy of the inverse; invalid 35) If the bough breaks, then the cradle will fall.

The bough breaks.

Therefore, the cradle will fall.

A) Law of detachment; valid C) Fallacy of the inverse; invalid Rephrase the statement in the requested symbolic form.

36) converse of ~a → ~b A) b → a B) ~b → ~a

33)

B) Fallacy of the inverse; invalid D) Fallacy of the converse; invalid 34)

B) Law of contraposition; valid D) Fallacy of the converse; invalid 35)

B) Law of syllogism; valid D) Fallacy of the converse; invalid

36) C) ~a → b

D) a → b

37) converse of a → b A) ~a → b

B) b → a

C) ~a → ~b

D) ~b → ~a

38) inverse of a → ~(b ∨ c) A) ~(b ∨ c) → a

B) ~a → ~(b ∨ c)

C) (b ∨ c) → ~a

D) ~a → (b ∨ c)

39) inverse of a → b A) ~a → ~b

32)

37)

38)

39) B) ~a → b

C) ~b → ~a

D) b → a

Negate each quantified statement and rewrite it in English in an alternative way.

40) All dinosaurs were carnivores.

A) There existed dinosaurs that were not carnivores.

B) All dinosaurs were not carnivores.

C) There existed dinosaurs that were carnivores.

D) Some dinosaurs were carnivores.

41) Some citizens obey traffic laws.

A) Some citizens do not obey traffic laws.

C) All citizens do not obey traffic laws.

40)

41) B) All citizens obey traffic laws.

D) No citizens obey traffic laws.

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Assume that p represents a true statement, q represents a true statement, and r represents a false statement. Determine the truth value of the following.

42) ~(p ∧ q) → ~q 42) A) False B) True 43) r → (~p ∨ q) A) False

43) B) True

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Complete the syllogism so that it is valid and the conclusion is true. Answers may vary.

44) No artist who was an impressionist became famous while still alive.

Some artists who were realists became famous while still alive. ∴

44)

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Determine whether the statements are equivalent.

45) If it is cold outside, then you light the fireplace.

If you light the fireplace, then it is cold outside.

A) Equivalent

45) B) Not equivalent

46) If the wind speed is over 70 miles per hour, then the tree will be uprooted.

If the tree is not uprooted, then the wind speed is not over 70 miles per hour.

A) Not equivalent B) Equivalent

46)

Calculate the truth value of the negation of the fuzzy statement. The truth value of the fuzzy statement is given in parentheses.

47) Michael Jordan is the best basketball player to ever play in the NBA. ( 0.71) 47) A) 0.71 B) 1 C) 0.29 D) 0 Write, as indicated, the converse, inverse, or contrapositive for the statement.

48) If the sun shines, they will bask. (inverse) A) If they bask, then the sun shines.

B) If they do not bask, then the sun does not shine.

C) If the sun does not shine, then they will not bask.

D) If they do not bask, then the sun shines.

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48)

Represent the circuit with a logical form.

49)

A) (p ∨ r) ∧ (q ∧ ~r) C) (p ∨ r) ∨ (q ∨ ~r)

49)

B) (p ∧ r) ∨ (q ∧ ~r) D) (p ∨ r) ∨ (q ∧ ~r)

50)

50)

A) p ∧ (q ∨ r)

B) (p ∨ q) ∧ r

C) p ∧ q ∧ r

D) p ∨ (q ∨ r)

Use the following definitions to translate the statement into words. p: The monitor is included. q: The color printer is optional. r: The zip drive is extra.

51) ~(p ∧ q) → (r ∨ ~q) A) If the monitor is included and the color printer is optional, then it is not true that the zip drive is extra or the color printer is not optional.

B) It is not true that if the monitor is included and the color printer is optional, then the zip drive is extra or the color printer is not optional.

C) It is not true that if the monitor is included or the color printer is optional, then the zip drive is extra and the color printer is not optional.

D) If the monitor is included and the color printer is optional, then the zip drive is extra or the color printer is not optional.

52) ~(p ∨ r) A) It is true that the monitor is included and the zip drive is not extra.

B) It is not true that the monitor is included or the zip drive is extra.

C) It is not true that the monitor is not included and the zip drive is extra.

D) The monitor is included and the zip drive is extra.

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51)

52)

Answer Key Testname: CHAPTER 3 EXAM B

1) B 2) B 3) A 4) A 5) C 6) B 7) B 8) B 9) B 10) A 11) A 12) A 13) B 14) A 15) B 16) A 17) A 18) A 19) B 20) B 21) D 22) B 23) A 24) C 25) B 26) C 27)

28)

29) B 30) D 31) C 32) B 33) A 34) A 35) A 36) B 37) B 38) D 39) A 40) A Copyright © 2022 Pearson Education, Inc.

Answer Key Testname: CHAPTER 3 EXAM B

41) C 42) B 43) B 44) Possible answer: Some artists who were realists did not become famous while still alive.

45) B 46) B 47) C 48) C 49) D 50) D 51) B 52) B

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Chapter 4 Exam A Name___________________________________

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Determine whether the graph can be traced.

1)

A) No

1)

B) Yes

2)

2)

A) Yes

B) No

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Determine whether the graph is connected or nonconnected.

3)

A) Nonconnected

3)

B) Connected

4)

4)

A) Connected

B) Nonconnected 5)

5)

A) Connected

B) Nonconnected

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6)

6)

A) Nonconnected

B) Connected

Determine whether the indicated vertex is even or odd.

7)

7)

Vertex ʺEʺ A) ʺOddʺ

B) ʺEvenʺ 8)

8)

Vertex ʺDʺ A) ʺOddʺ

B) ʺEvenʺ

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If the given graph is Eulerian, find an Euler circuit in it. If it is not Eulerian, first Eulerize it and then find an Euler circuit.

9) 9)

A) A, B, C, D, E, A B) Add edge BD; A, B, E, D, A, C, B, D, C, E, A C) Add edges AB and AD; A, B, E, D, A, C, B, E, D, A D) Add edges BC and CD; A, B, E, D, A 10)

10)

A) Add edge BC; A, C, A, C, B, C, B, A C) Add edge AB; A, B, C, B, C, A, C, A

B) Add edge AC; A, C, A, C, B, C, B, C, A D) A, B, C, A

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Represent the following with a graph.

11)

11)

A)

B)

C)

D)

12)

12)

A)

B)

C)

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D)

Solve the problem.

13) The U.S. House of Representatives decides to have committee meetings on Thursdays from 2:00 to 5:00 PM. To avoid conflicts, it is important not to schedule two committee meetings at the same time if the two committees have House members in common. Use the table below, which lists possible conflicts, to determine an acceptable schedule for the meetings.

Committee has members Committee in common with Science Armed Services, Veteransʹ Affairs Armed Services Budget, Ways and Means Budget Judiciary, Veteransʹ Affairs Judiciary International Affairs International Affairs Rules, Appropriations Veteransʹ Affairs Small Business Small Business Ways and Means Ways and Means Budget, Rules Rules Appropriations Appropriations International Affairs, Rules A) First Thursday: Science, Budget, International Affairs, and Small Business ; Second Thursday: Armed Services and Veteransʹ Affairs; Third Thursday: Judiciary and Rules ; Fourth Thursday: Ways and Means and Appropriations.

B) First Thursday: Science, Budget, Judiciary, Appropriations, Rules, and Small Business ; Second Thursday: Armed Forces, International Affairs, Veteransʹ Affairs, and Ways and Means.

C) First Thursday: Science, Budget, International Affairs, and Small Business, Ways and Means, and Appropriations ; Second Thursday: Armed Services, Judiciary, Veteransʹ Affairs, Rules.

D) First Thursday: Science, Budget, International Affairs, and Small Business ; Second Thursday: Armed Services, Judiciary, Veteransʹ Affairs, and Rules ; Third Thursday: Ways and Means and Appropriations.

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13)

14) A chemistry lab uses the liquid solvents listed below. Once the chemicals have been used, they are poured into appropriate waste containers. However, certain of these chemicals cannot be mixed without causing violent reactions. The table indicates which chemical pairs are incompatible.

Determine the minimum number of waste disposal containers needed to store the waste solvents safely, and give a list of the chemicals that are to be stored in each container.

Chemical Acetic Anhydride Acetone Acetonitrile Benzene Cyclopentane Ethanol Methanol Toluene

14)

Cannot be mixed with Hydrogen peroxide, ethanol, methanol Hydrogen peroxide Hydrogen peroxide Hydrogen peroxide Hydrogen peroxide Hydrogen peroxide Hydrogen peroxide Hydrogen peroxide

A) Container 1: acetone, acetonitrile, benzene, cyclopentane, and toluene ; Container 2: ethanol and methanol; Container 3: acetic anhydride ; Container 4: hydrogen peroxide B) Container 1: acetone, acetonitrile, benzene, cyclopentane, and toluene ; Container 2: ethanol and methanol; Container 3: acetic anhydride and hydrogen peroxide C) Container 1: acetone, acetonitrile, benzene, cyclopentane, ethanol, methanol, and toluene ; Container 2: acetic anhydride ; Container 3: hydrogen peroxide D) Container 1: acetone, acetonitrile, benzene, cyclopentane, ethanol, methanol, and toluene ; Container 2: acetic anhydride and hydrogen peroxide Determine how many Hamilton circuits the graph has.

15) A complete graph with 7 vertices.

A) 6!

B) 7

16) A complete graph with 13 vertices.

A) 132 B) 13!

15) C) 7!

D) 7 2 16)

C) 13

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D) 12!

Find a Hamilton circuit in the graph that begins with the specified edge.

17)

17)

Edge ʺEDʺ A) ʺEDFACDEʺ

B) ʺEDBCAFEʺ

C) ʺEDABCFEʺ

D) ʺEDCAFEʺ 18)

18)

Edge ʺEFʺ A) ʺEFABFECDEʺ

B) ʺEFDCABEʺ

C) ʺEFBACDEʺ

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D) ʺEFBACFʺ

Use the figure to find the weight of the indicated path.

19)

19)

Path: ʺDEACBʺ A) 25

B) 20

C) 30

D) 23 20)

20)

Path: ʺECDBAʺ A) 65

B) 72

C) 60

D) 67

Solve the problem.

21) If a computer can examine 10,000 Hamilton circuits per second, how long would it take to examine all the Hamilton circuits in K12? Round to the nearest second.

A) 39,916,800 seconds C) 622,702 seconds

B) 47,900 seconds D) 3992 seconds

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21)

22) There is a package delivery company located at the position marked X on the map. Assume that packages must be delivered to the following locations: M, P, A, E, L, and N. The route starts and ends at X. Use the nearest-neighbor algorithm to devise a delivery route that will minimize the number of blocks traveled. Assume the streets are two-way.

A) XELMNPAX

B) XAEPLMNX

C) XELMNPX

22)

D) XEALMNPX

Use the brute force algorithm to find a minimum Hamilton circuit for the graph. Also, determine the total weight of the minimum Hamilton circuit.

23) 23)

A) Minimum Hamilton circuit is A → B → E → C → D → A; weight = 70 B) Minimum Hamilton circuit is A → B → C → D → E → A; weight = 78 C) Minimum Hamilton circuit is A → B → C → E → D → A; weight = 72 D) Minimum Hamilton circuit is A → B → D → C → E → A; weight = 71

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24)

24)

A) Minimum Hamilton circuit is A → B → C → E → D → A; weight = 83 B) Minimum Hamilton circuit is A → B → E → D → C → A; weight = 83 C) Minimum Hamilton circuit is A → B → C → D → E → A; weight = 83 D) Minimum Hamilton circuit is A → B → E → C → D → A; weight = 83 25)

25)

A) Minimum Hamilton circuit is W → X → Y → Z → W; weight = 19 B) Minimum Hamilton circuit is W → Y → X → Z → W; weight = 22 C) Minimum Hamilton circuit is W → Y → X → Z → W; weight = 17 D) Minimum Hamilton circuit is W → X → Z → Y → W; weight = 16 26)

26)

A) Minimum Hamilton circuit is W → X → Y → Z → W; weight = 15 B) Minimum Hamilton circuit is W → Z → X → Y → W; weight = 18 C) Minimum Hamilton circuit is W → Z → Y → X → W; weight = 14 D) Minimum Hamilton circuit is W → X → Z → Y → W; weight = 15

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For the graph below, use the nearest neighbor algorithm to find an approximate minimum Hamilton circuit and its weight, starting at the indicated vertex.

27) 27)

Starting at E A) E → B → A → D → C → F →E; weight = 99 B) E → B → F → D → A → C →E; weight = 99 C) E → B → F → D → C → A →E; weight = 99 D) E → B → F → D → C → A →E; weight = 102 28)

28)

Starting at D A) D → A → E → B → C → D; weight = 28 C) D → C → A → B → E → D; weight = 31

B) D → E → A → B → C → D; weight = 30 D) D → B → E → C → A → D; weight = 30

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29)

29)

Starting at B A) B → F → D → A → C → E → B; weight = 102 B) B → F → E → C → A → D → B; weight = 99 C) B → F → D → C → A → E → B; weight = 99 D) B → A → D → C → F → E → B; weight = 103 30)

30)

Starting at C A) C → D → B → F → A → E → C; weight = 99 B) C → D → B → F → E → A → C; weight = 102 C) C → D → B → F → E → A → C; weight = 99 D) C → D → A → F → E → B → C; weight = 102

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Construct a table that displays the number of directed paths of length 1 or 2 between each pair of vertices in the following graph.

31) 31)

A)

B) A B C D E F

A 0 1 2 1 2 1

B 0 0 1 0 1 1

C 0 0 0 1 1 0

D 0 0 1 0 1 1

E 1 1 1 1 0 1

F 1 2 1 0 2 0

A B C D E F

A 0 1 2 1 1 1

B 0 0 1 0 1 1

C 0 0 0 0 1 0

D 0 0 1 0 1 1

E 1 1 1 1 0 1

F 0 2 1 0 1 0

C)

A B C D E F

A 0 1 2 1 1 1

B 0 0 2 0 2 1

C 0 0 0 1 1 0

D 0 0 1 0 1 1

E 1 1 1 1 0 1

F 1 2 1 0 1 0

A B C D E F

A 0 1 2 1 1 1

B 0 0 1 0 1 1

C 0 0 0 1 2 0

D 0 0 1 0 1 1

E 1 1 1 1 0 0

F 1 2 1 0 1 0

D)

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32)

32)

A)

B) A B C D E F

A 0 1 1 3 1 1

B 0 0 1 1 1 0

C 1 1 0 1 1 1

D 0 0 0 0 0 0

E 1 2 1 2 0 2

F 0 1 1 1 0 0

A B C D E F

A 0 1 1 2 1 1

B 0 0 1 1 1 0

C 1 1 0 1 1 1

D 0 0 0 0 0 0

E 1 2 1 1 0 1

F 0 1 1 1 0 0

C)

A B C D E F

A 0 1 1 3 1 1

B 0 0 2 1 1 2

C 1 1 0 1 1 1

D 0 0 0 0 0 0

E 1 2 1 1 0 2

F 0 1 1 2 0 0

A B C D E F

A 0 1 1 3 1 1

B 0 0 1 1 0 0

C 1 1 0 1 1 1

D 0 0 0 0 0 0

E 1 2 1 1 0 2

F 0 1 0 1 0 0

D)

Find the indicated directed path.

33) Find a directed path of length 4 from ʺF to Dʺ.

A) ʺFBECDʺ C) ʺFECDʺ

33)

B) ʺFECADʺ D) ʺNo such route exists.ʺ Copyright © 2022 Pearson Education, Inc.

34) Find a directed path from ʺA to Cʺ.

A) ʺACʺ

B) ʺADECʺ

34)

C) ʺADCʺ

D) ʺADBECʺ

Solve the problem.

35) Deer, rabbits, and bears eat grass. Wolves, pumas, and humans eat deer and rabbits. Bears also eat deer and rabbits. Draw a directed graph to model this food chain.

A)

B)

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35)

C)

D)

36) A round-robin intramural basketball tournament is played with the following results: Team Defeated Heyday Wuzzup, Pitiful Boys, AKA Smooth, Chemistry Club No Brainers Chemistry Club, Pitiful Boys, Heyday Pitiful Boys Chemistry Club Chemistry Club No team AKA Smooth Chemistry Club, No Brainers, Pitiful Boys Wuzzup AKA Smooth, No Brainers, Pitiful Boys, Chemistry Club Determine a ranking order for the teams using one- and two-stage dominance.

A) Heyday (12) ; Wuzzup (11) ; No Brainers (8) ; AKA Smooth (7) ; Pitiful Boys (1) ; Chemistry Club (0) B) Wuzzup (12) ; Heyday (11) ; No Brainers (8) ; AKA Smooth (7) ; Pitiful Boys (1) ; Chemistry Club (0) C) Heyday and Wuzzup (4) ; No Brainers and AKA Smooth (3) ; Pitiful Boys (1) ; Chemistry Club (0) D) Wuzzup (12) ; Heyday (11) ; AKA Smooth and No Brainers (7) ; Pitiful Boys (1) ; Chemistry Club (0)

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36)

Use the PERT diagram to answer the question.

37) Find a critical path for task I.

A) Begin, ADGI C) Begin, BCHI, End

37)

B) Begin, ADGFI D) Begin, AGFI

38) Find a critical path for task G.

A) Begin, ADG C) Begin, ADEG

38)

B) Begin, ADFH, End D) Begin, CEG

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Answer Key Testname: CHAPTER 4 EXAM A

1) A 2) B 3) A 4) B 5) B 6) B 7) A 8) A 9) B 10) A 11) D 12) C 13) D 14) C 15) A 16) D 17) B 18) C 19) D 20) D 21) D 22) A 23) C 24) A 25) A 26) A 27) C 28) A 29) C 30) B 31) A 32) A 33) A 34) B 35) B 36) A 37) B 38) C

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Chapter 4 Exam B Name___________________________________

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Determine whether the graph is connected or nonconnected.

1)

A) Connected

1)

B) Nonconnected

2)

2)

A) Nonconnected

B) Connected 3)

3)

A) Connected

B) Nonconnected

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4)

4)

A) Connected

B) Nonconnected

Solve the problem.

5) A band is planning to tour the United States. The subtasks for this project and the dependencies among them are listed in the following table. Draw a PERT diagram for this project.

Preceding Time Required Task Tasks (weeks) 1. Contact Venues none 1 2. Practice Setlist none 4 3. Confirm Shows 1 2 4. Find Opening Act 1, 2, 3 3 1, 2, 4 2 5. Arrange Transportation 6. Arrange Sound System 1, 3, 4 3 7. Advertise 1, 2, 3, 4, 5, 6 5 A)

B)

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5)

C)

D)

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

6) Below is a floor plan of a suite of offices. Place a door in one of the rooms so that a security guard can enter by the door marked ʺenterʺ, pass through each door and lock it behind him, and then exit by the door you have placed in the plan.

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6)

7) There is a pizza delivery store located at the position marked A on the map. Assume that deliveries must be made at the following locations: C, G, L, O, B, E, and M, and then the delivery driver must return to the store. Use the nearest-neighbor algorithm to devise a delivery route that will minimize the number of blocks traveled. Assume the streets are two-way.

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7)

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

8) The U.S. House of Representatives decides to have committee meetings on Thursdays from 2:00 to 5:00 PM. To avoid conflicts, it is important not to schedule two committee meetings at the same time if the two committees have House members in common. Use the table below, which lists possible conflicts, to determine an acceptable schedule for the meetings.

8)

Committee has members Committee in common with Science Armed Services, Veteransʹ Affairs Armed Services Budget, Ways and Means Budget Judiciary, Veteransʹ Affairs Judiciary International Affairs International Affairs Rules, Appropriations Veteransʹ Affairs Small Business Small Business Ways and Means Ways and Means Budget, Rules Rules Appropriations Appropriations International Affairs, Rules A) First Thursday: Science, Budget, International Affairs, and Small Business ; Second Thursday: Armed Services, Judiciary, Veteransʹ Affairs, and Rules ; Third Thursday: Ways and Means and Appropriations.

B) First Thursday: Science, Budget, Judiciary, Appropriations, Rules, and Small Business ; Second Thursday: Armed Forces, International Affairs, Veteransʹ Affairs, and Ways and Means.

C) First Thursday: Science, Budget, International Affairs, and Small Business ; Second Thursday: Armed Services and Veteransʹ Affairs; Third Thursday: Judiciary and Rules ; Fourth Thursday: Ways and Means and Appropriations.

D) First Thursday: Science, Budget, International Affairs, and Small Business, Ways and Means, and Appropriations ; Second Thursday: Armed Services, Judiciary, Veteransʹ Affairs, Rules.

9) The following influence has been observed on a local school board: Board Member Metz Healy Carroll Rashaad OʹConnor Influences Kline, no one Metz, OʹConnor, Metz Jeffers Rashaad Kline, Jeffers Determine a ranking order for the board members using one- and two-stage influence.

A) Carroll (5) ; Rashaad (4) ; OʹConnor and Metz (2) ; Healy, Kline, and Jeffers (0) B) Rashaad (3) ; Carrol and Metz (2) ; OʹConnor (1) ; Healy (0) C) Carroll (7) ; Rashaad (4) ; OʹConnor (3) ; Metz (2) ; Healy, Kline, and Jeffers (0) D) Carroll and Rashaad (4) ; OʹConnor (3) ; Metz (2) ; Healy, Kline, and Jeffers (0)

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9)

10) Deer, rabbits, and bears eat grass. Wolves, pumas, and humans eat deer and rabbits. Bears also eat deer and rabbits. Draw a directed graph to model this food chain.

A)

B)

C)

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10)

D)

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

11) There is a package delivery company located at the position marked X on the map.

Assume that packages must be delivered to the following locations: M, P, A, E, L, and N. The route starts and ends at X. Use the nearest-neighbor algorithm to devise a delivery route that will minimize the number of blocks traveled. Assume the streets are two-way.

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11)

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Use the brute force algorithm to find a minimum Hamilton circuit for the graph. Also, determine the total weight of the minimum Hamilton circuit.

12) 12)

A) Minimum Hamilton circuit is W → X → Z → Y → W; weight = 213 B) Minimum Hamilton circuit is W → X → Y → Z → W; weight = 220 C) Minimum Hamilton circuit is W → Y → X → Z → W; weight = 217 D) Minimum Hamilton circuit is W → Z → X → Y → W; weight = 220 13)

13)

A) Minimum Hamilton circuit is W → Y → X → Z → W; weight = 450 B) Minimum Hamilton circuit is W → X → Y → Z → W; weight = 435 C) Minimum Hamilton circuit is W → X → Z → Y → W; weight = 435 D) Minimum Hamilton circuit is W → Y → Z → X → W; weight = 445 14)

14)

A) Minimum Hamilton circuit is A → B → E → C → D → A; weight = 70 B) Minimum Hamilton circuit is A → B → C → D → E → A; weight = 78 C) Minimum Hamilton circuit is A → B → C → E → D → A; weight = 72 D) Minimum Hamilton circuit is A → B → D → C → E → A; weight = 71

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Construct a table that displays the number of directed paths of length 1 or 2 between each pair of vertices in the following graph.

15) 15)

A)

B) A B C D E F

A 0 1 2 1 2 1

B 0 0 1 0 1 1

C 0 0 0 1 1 0

D 0 0 1 0 1 1

E 1 1 1 1 0 1

F 1 2 1 0 2 0

A B C D E F

A 0 1 2 1 1 1

B 0 0 1 0 1 1

C 0 0 0 1 2 0

D 0 0 1 0 1 1

E 1 1 1 1 0 0

F 1 2 1 0 1 0

C)

A B C D E F

A 0 1 2 1 1 1

B 0 0 2 0 2 1

C 0 0 0 1 1 0

D 0 0 1 0 1 1

E 1 1 1 1 0 1

F 1 2 1 0 1 0

A B C D E F

A 0 1 2 1 1 1

B 0 0 1 0 1 1

C 0 0 0 0 1 0

D 0 0 1 0 1 1

E 1 1 1 1 0 1

F 0 2 1 0 1 0

D)

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Determine whether the graph can be traced.

16)

A) Yes

16)

B) No

17)

17)

A) No

B) Yes

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SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Determine whether the indicated vertex is even or odd.

18)

18)

Vertex ʺCʺ

19)

19)

Vertex ʺAʺ

Find the indicated directed path.

20) Find a directed path from ʺE to Aʺ.

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20)

21) Find a directed path from ʺD to Aʺ.

Find a Hamilton circuit in the graph that begins with the specified edge.

22)

Edge ʺCDʺ

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21)

22)

23)

23)

Edge ʺBCʺ

If the given graph is Eulerian, find an Euler circuit in it. If it is not Eulerian, first Eulerize it and then find an Euler circuit.

24) 24)

25)

25)

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Use the figure to find the weight of the indicated path.

26)

26)

Path: ʺDEACBʺ

27)

27)

Path: ʺECDBAʺ

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MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

For the graph below, use the nearest neighbor algorithm to find an approximate minimum Hamilton circuit and its weight, starting at the indicated vertex.

28) 28)

Starting at B A) B → F → D → C → A → E → B; weight = 99 B) B → F → E → C → A → D → B; weight = 99 C) B → F → D → A → C → E → B; weight = 102 D) B → A → D → C → F → E → B; weight = 103 29)

29)

Starting at C A) C → D → B → F → E → A → C; weight = 102 B) C → D → A → F → E → B → C; weight = 102 C) C → D → B → F → A → E → C; weight = 99 D) C → D → B → F → E → A → C; weight = 99

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30)

30)

Starting at C A) C → B → E → D → A → C; weight = 30 C) C → E → A → B → D → C; weight = 27

B) C → D → A → B → E → C; weight = 28 D) C → B → E → A → D → C; weight = 28

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Determine how many Hamilton circuits the graph has.

31) A complete graph with 11 vertices.

32) A complete graph with 28 vertices.

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31) 32)

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Represent the following with a graph.

33)

33)

A)

B)

C)

D)

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34)

34)

A)

B)

C)

D)

Use the PERT diagram to answer the question.

35) Find a critical path for task G.

A) Begin, ADG C) Begin, ADEG

35)

B) Begin, CEG D) Begin, ADFH, End

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36) Find a critical path for task I.

A) Begin, AGFI C) Begin, ADGI

36)

B) Begin, BCHI, End D) Begin, ADGFI

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Answer Key Testname: CHAPTER 4 EXAM B

1) A 2) A 3) B 4) A 5) C 6) Place door in room B. 7) AEMBOLCGA 8) A 9) C 10) D 11) XELMNPAX 12) A 13) B 14) C 15) A 16) A 17) A 18) ʺEvenʺ 19) ʺEvenʺ 20) ʺNo route exists.ʺ 21) ʺDECAʺ 22) ʺCDFBAECʺ 23) ʺBCAFEDBʺ 24) Add edge BC; A, C, A, C, B, C, B, A 25) Add edge BE; A, C, B, E, D, A, F, E, B, A 26) 23 27) 67 28) A 29) A 30) D 31) 10!

32) 27!

33) B 34) A 35) C 36) D

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Chapter 5 Exam A Name___________________________________

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Write the number as a binary number.

1) 257 8 A) 101,010,0002

1)

B) 11,110,101 2

C) 10,101,111 2

D) 100,010,1002

2) 76038

2)

A) 111,110,000,0102

B) 100,001,111,1012

C) 100,001,111,1002

D) 111,110,000,0112

Divide in the indicated base.

3) 25006 ÷ 4 6 A) 313 6

3) B) 410 6

C) 413 6

D) 423 6

4) 13067 ÷ 4 7 A) 224 7 Perform the operation.

5) 8 + 7 (mod 11) A) 1

4) B) 135 7

C) 134 7

D) 235 7

B) 15

C) 4

D) 26

C) 20

D) 16

5)

Convert the numeral to a numeral in base 10.

6) 31 5 A) 155

B) 80

6)

7) 42 7 A) 210

7) B) 42

C) 30

D) 294

8) 11111001 2 A) 22,222,002

8) B) 498

C) 249

D) 12

9) 61547 8 A) 184

9) B) 492,376

C) 25,447

D) 135

Subtract in the indicated base.

10) FE116 - 2516 A) EFD16

10) B) FDC16

C) FDF16

D) FBC16

11) 412 5 - 335 A) 324 5

11) B) 342 5

C) 442 5

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D) 343 5

12) 301 4 - 102 4 A) 199 4

12) B) 143 4

C) 133 4

D) 232 4

List the numbers that precede and follow the given number in the given base.

13) 32467 A) 32457 ; 32507

B) 165 7 ; 166 7

C) 32547 ; 32507

13) D) 52307 ; 54237

Convert the numeral to Egyptian form.

14) 312,602

14)

A)

B)

C)

D)

15) 1100 A)

15) B)

C)

D)

Simplify the expansion.

16) (7 × 101 ) + (0 × 100 ) A) 71

16) B) 70

C) 7

D) 17

Add in the indicated base.

17) 427 + 357 A) 140 7

17) B) 210 7

C) 117 7

D) 110 7

18) 10112 + 111 2 A) 11,0002

18) B) 10,0102

C) 11112

D) 11,0012

19) 111 2 + 102 A) 10012

19) B) 11012

C) 11112

D) 10002

20) 568 + 728 A) 142 8

20) B) 131 8

C) 156 8

D) 150 8

21) 435 7 + 317 A) 406 7

21) B) 536 7

C) 566 7

D) 466 7

22) 303 4 + 224 A) 10314

22) B) 331 4

C) 10014

D) 325 4

Write the binary number as the indicated number.

23) 10,011,011 2 to an octal number A) 233 8

B) 244 8

23) C) 122 8

D) 155 8

24) 1,101,101,101 2 to a hexadecimal number A) 223 16

B) 36D16

24) C) 877 16

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D) 446 16

25) 11,000,110,111 2 to an octal number A) 3067 8

B) 4046 8

25) C) 15918

Answer the question.

26) What does the digit 4 mean in the number 247,189?

A) 4 ten thousands C) 4 hundreds

B) 4 thousands D) 4 hundred thousands

27) What does the digit 4 mean in the number 301,475?

A) 4 hundreds C) 4 tens

B) 4 thousands D) 4 hundred thousands

D) 2023 8

26)

27)

Determine the letters or numbers.

28) Break 1001101100111110011111001110 into groups of seven digits and write as capital letters.

A) MEND B) MASH C) MOON D) SOON

28)

29) Translate the word ʺCOUCHʺ into an ASCII string of binary digits.

A) 11000111101101111010111100111101010 B) 10000111001111101010110000111001000 C) 10111001100110011011101111000110011 D) 11000111101111111010110001111101000

29)

30) Translate ʺMEXICOʺ into an ASCII string of binary digits.

A) 100110101001011111000110100111000111101111 B) 100110111011011101000110100111000111110011 C) 110110111001011011011100111000111111001101 D) 100110110001011011000100100110000111001111

30)

31) Write the binary code for the letter P. A) 1101000 B) 1010000

31) C) 1101100

D) 1011100

32) Write the binary code for the letter C. A) 1000111 B) 1110011

C) 1000011

D) 1100001

32)

Perform the operation and give the answer in Hindu -Arabic form.

33) A) 32 B) 38 C) 22

33) D) 28

-

34)

34)

A) 217

B) 93

C) 113

D) 357

B) 1300

C) 1400

D) 130

+

35) A) 140

35)

Perform the operation in expanded notation. Write answer in simplified form.

36) 57 + 31 A) 88 B) 108 C) 544 37) 53 - 33 A) 40

36) D) 98 37)

B) 550

C) 20

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D) 30

Multiply using Napier rods.

38) 49 × 325 A) 16,250

B) 15,974

C) 15,876

D) 15,925

39) 7 × 212 A) 1491

B) 1477

C) 1696

D) 1484

38)

39)

Convert the decimal form numeral to a numeral in the base indicated.

40) 13,562 to base 7 A) 54,3537 B) 54,1217 C) 53,4567

40) D) 53,7437

41) 68 to base 8 A) 140 8

B) 104 8

C) 120 8

D) 102 8

42) 503 to base 8 A) 676 8

B) 656 8

C) 565 8

D) 767 8

C) 48

D) 68

41)

42)

Write the Babylonian numeral as a Hindu -Arabic numeral.

43)

43) A) 52

B) 73

Convert the numeral to Hindu-Arabic form.

44)

A) 34,460 45) DMMMCCCXXXIII A) 502,222

B) 34,233

44)

C) 34,213

D) 31,333 45)

B) 504,444

C) 503,333

D) 500,333

B) 11,001

C) 1011

D) 1110

46)

46) A) 1101

47)

47)

A) 13,156

B) 14,596

C) 14,900

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D) 14,956

48) XLDCLV A) 6655

48) B) 43,655

C) 42,655

D) 41,655

Write the number in expanded form.

49) 38,451 A) (3 × 105 ) + (4 × 103 ) + (5 × 102 ) + (1 × 101 )

49)

B) (3 × 100 ) + (8 × 101 ) + (4 × 102 ) + (5 × 103 ) + (1 × 104 ) C) (3 × 104 ) + (8 × 103 ) + (4 × 102 ) + (5 × 101 ) + (1 × 100 ) D) (3 × 105 ) + (8 × 104 ) + (4 × 103 ) + (5 × 102 ) + (1 × 101 ) Use the Egyptian method of doubling to calculate the product.

50) How much would King Solomon have to pay the King of Tyre for the use of 200 tree cutters at 3 shekels per week for a total of 9 weeks?

A) 5400 shekels B) 1800 shekels C) 212 shekels D) 600 shekels

Copyright © 2022 Pearson Education, Inc.

50)

Answer Key Testname: CHAPTER 5 EXAM A

1) C 2) D 3) C 4) D 5) C 6) D 7) C 8) C 9) C 10) D 11) A 12) C 13) A 14) B 15) C 16) B 17) D 18) B 19) A 20) D 21) D 22) B 23) A 24) B 25) A 26) A 27) A 28) C 29) B 30) D 31) B 32) C 33) D 34) B 35) A 36) A 37) C 38) D 39) D 40) A 41) B 42) D 43) D 44) C 45) C 46) C 47) B 48) C 49) C 50) A Copyright © 2022 Pearson Education, Inc.

Chapter 5 Exam B Name___________________________________

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Add in the indicated base.

1) 445 + 125 A) 131 5

1) B) 111 5

C) 122 5

D) 231 5

2) 111 2 + 112 A) 11012

2) B) 10102

C) 10002

D) 11112

3) 435 7 + 517 A) 516 7

3) B) 536 7

C) 406 7

D) 566 7

4) 303 4 + 224 A) 10314

4) B) 331 4

C) 325 4

D) 10014

5) 527 + 357 A) 140 7

5) B) 210 7

C) 117 7

Answer the question.

6) What does the digit 2 mean in the number 189,247?

A) 2 hundred thousands C) 2 hundreds

B) 2 thousands D) 2 tens

7) What does the digit 4 mean in the number 301,475?

A) 4 hundreds C) 4 hundred thousands

B) 4 tens D) 4 thousands

D) 120 7

6)

7)

Convert the decimal form numeral to a numeral in the base indicated.

8) 503 to base 8 A) 676 8 B) 656 8 C) 565 8

8) D) 767 8

Convert the numeral to Egyptian form.

9) 312,602

9)

A)

B)

C)

D)

10) 367

10)

A)

B)

C)

D)

11) 2000 A)

11) B)

C) Copyright © 2022 Pearson Education, Inc.

D)

12) 3067

12)

A)

B)

C)

D)

13) 4233

13)

A)

B)

C)

D)

Convert the numeral to Hindu-Arabic form.

14) A) 2,031,210 B) 2,310,021

14) C) 231,210

D) 2,310,210 15)

15)

A) 2100

B) 2105

C) 2185

D) 2385

A) 3670

B) 3607

C) 367

D) 3067

16)

16)

17)

17)

A) 2742

B) 1066

C) 2502

D) 2662

A) 3607

B) 367

C) 3670

D) 3067

B) 44

C) 52

D) 54

18)

18)

19) LIV A) 64

19)

Convert the numeral to a numeral in base 10.

20) 1EE12 (T = 1010, E = 1110) A) 287

B) 3444

20) C) 276

D) 2652

21) 1T12 (T = 1010, E = 1110) A) 22

21) B) 132

C) 264

D) 240

Determine the letters or numbers.

22) Break 1001100100000110011011010000 into groups of seven digits and write as capital letters.

A) LAMP B) DAMP C) SWAMP D) MAP Copyright © 2022 Pearson Education, Inc.

22)

23) Translate ʺBOBʺ into an ASCII string of binary digits.

A) 100001010011111000010 B) 100010110100010011101 C) 100001011011111000010 D) 100001011011001100001

23)

24) Break 100001010001011000100 into groups of seven digits and write as lower case letters.

A) BAD B) CUE C) ARM D) BED

24)

25) Write the binary code for the letter P. A) 1101000 B) 1010000

25) C) 1011100

D) 1101100

26) Translate the word ʺCOUCHʺ into an ASCII string of binary digits.

A) 11000111101101111010111100111101010 B) 10111001100110011011101111000110011 C) 11000111101111111010110001111101000 D) 10000111001111101010110000111001000 List the numbers that precede and follow the given number in the given base.

27) 10445 A) 10435 ; 11005

B) 10435 ; 10455

C) 10425 ; 11015

27) D) 10435 ; 11115

Multiply in the indicated base.

28) 648 × 2 8 A) 156 8

28) B) 147 8

C) 150 8

D) 172 8

29) 325 × 2 5 A) 645

29) B) 124 5

C) 114 5

D) 104 5

30) 235 7 × 2 7 A) 403 7 Multiply using Napier rods.

31) 49 × 323 A) 15,827 Multiply using the galley method.

32) 79 × 19 A) 1501

26)

30) B) 524 7

C) 503 7

D) 603 7

B) 16,150

C) 15,778

D) 15,876

31)

32) B) 1511

C) 1601

D) 1491

33) 33 × 83 A) 2729

B) 2749

C) 2839

D) 2739

34) 27 × 40 A) 1070

B) 1090

C) 1080

D) 1180

33)

34)

Perform the operation and give the answer in Hindu -Arabic form.

35)

+ A) 1311

35) B) 1131

C) 1113

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D) 3111

Simplify the expansion.

36) (7 × 101 ) + (1 × 100 ) A) 170 Solve the congruence.

37) 2 - x ≡ 8 (mod 9) A) 4

36) B) 71

C) 17

D) 710

B) 8

C) 3

D) 5

37)

Subtract in the indicated base.

38) 231 5 - 325 A) 144 5

38) B) 143 5

C) 244 5

D) 104 5

Write the Babylonian numeral as a Hindu -Arabic numeral.

39)

39) A) 731

B) 791

C) 801

D) 34

A) 60

B) 85

C) 140

D) 120

A) 47

B) 46

C) 36

D) 37

A) 4965

B) 4905

C) 1245

D) 4785

A) 1705

B) 1930

C) 1805

D) 1803

40)

40)

41)

41)

42)

42)

43)

43)

Write the binary number as the indicated number.

44) 11,000,110,111 2 to an octal number A) 4046 8

B) 3067 8

44) C) 15918

D) 2023 8

45) 1,011,000,010,110,000 2 to a hexadecimal number A) 1,31316

B) B,00A16

45) C) B,0B016

D) 130,260 16

Write the number as a binary number.

46) 6BD16 A) 10,011,011,101 2

46)

B) 11,010,111,101 2

Write the number in expanded form.

47) 5253 A) (5 × 104 ) + (2 × 103 ) + (5 × 102 ) + (3 × 101 ) C) (5 × 100 ) + (2 × 101 ) + (5 × 102 ) + (3 × 103 )

C) 10,110,101,110 2

D) 11,010,111,011 2

47) B) (5 × 101 ) + (2 × 102 ) + (5 × 103 ) + (3 × 104 ) D) (5 × 103 ) + (2 × 102 ) + (5 × 101 ) + (3 × 100 )

Copyright © 2022 Pearson Education, Inc.

Write the numeral as a Babylonian numeral.

48) 122 A)

B)

48) C)

D)

49) 745

49)

A)

B)

C)

D)

Write the numeral as a Roman numeral.

50) 842 A) DCCCLXII B) CCMXLII

50) C) CMMXLII

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D) DCCCXLII

Answer Key Testname: CHAPTER 5 EXAM B

1) B 2) B 3) A 4) B 5) D 6) C 7) A 8) D 9) D 10) B 11) D 12) A 13) B 14) D 15) C 16) C 17) C 18) D 19) D 20) A 21) A 22) A 23) A 24) D 25) B 26) D 27) A 28) C 29) C 30) C 31) A 32) A 33) D 34) C 35) A 36) B 37) C 38) A 39) C 40) C 41) A 42) D 43) D 44) B 45) C 46) B 47) D 48) D 49) C 50) D Copyright © 2022 Pearson Education, Inc.

Chapter 6 Exam A Name___________________________________

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Determine whether the following statement is true or false.

1) 7 divides 56.

A) True 2) 7 is a divisor of 56.

A) True

1) B) False 2) B) False

Estimate the square root of the following number, n, by finding a natural number a such that a < 3) 182 A) 196 B) 169 C) 14 D) 13 4) 334 A) 19

B) 361

C) 324

D) 18

5) 450 A) 441

B) 22

C) 484

D) 21

3)

4)

5)

Identify the number as either prime or composite.

6) 197 A) Composite

6) B) Prime

Determine whether the number is divisible by 2, 3, 4, 5, 6, 8, 9, and/or 10.

7) 1067 A) 3 B) None C) 3, 9

7) D) 3, 5

8) 89,267 A) 5

B) None

C) 3

D) 3, 5

9) 11,766 A) 3, 4, 6

B) 2, 3, 6

C) 2, 3, 4

D) 4, 5, 6

8)

9)

Find the GCD for the pair of natural numbers.

10) 864, 1296 A) 2592 B) 144 11) 88, 45 A) 6

n < a + 1.

10) C) 6

D) 432

C) 1

D) 44

C) 4536

D) 1512

11) B) 55

Find the LCM for the pair of natural numbers.

12) 168, 378 A) 3024 B) 42

12)

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Determine whether or not one or more pairs of twin primes exist between the pair of numbers given. If so, identify the twin primes.

13) 99 and 105 13) A) No B) 103, 105 C) 101, 103, 105 D) 101, 103 Calculate the sum.

14) (+24) + (+3) A) 21

14) B) 27

C) -27

D) -21

Rewrite the subtraction problem as an addition problem.

15) (-38) - (+22) A) (-38) - (-22) C) (-38) + (-22)

B) (-38) + (+22) D) None of the above

Subtract.

16) (-8) - (+2) A) 10

B) -6

C) 6

D) -10

17) (+25) - (-4) A) 21

B) -21

C) -29

D) 29

18) (-8) - (-20) A) -12

B) -28

C) 28

D) 12

15)

16)

17)

18)

Divide.

19)

-36 -2 A) 18

20)

19) B) 24

C) -18

D) -24

30 -3 A) 15

20) B) -15

C) -10

D) 10

Perform the following calculations.

21) (+8)(+22) + (+2)(+22) A) 132

B) 54

C) 50

D) 220

22) (-7)(+24) + (+8)(3) A) -192

B) 12

C) -144

D) 28

21)

22)

Solve the problem.

23) During one year 13 new employees began work at Danielʹs Manufacturing Company and 14 employees left. At the beginning of the year there were 398 employees. What was the number of employees at the end of the year?

A) 411 employees B) 397 employees C) 425 employees D) 371 employees 24) Nikki is fishing from a bank 23 feet above water level. In this location, the fish tend to feed at 45 feet below the surface. How long must Nikkiʹs fish line be to reach the fish?

A) -23 feet B) 22 feet C) 68 feet D) -22 feet

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23)

24)

State whether the fractions are equal or not equal.

2 6 25) , 5 14 A) Equal

26)

25) B) Not equal

7 20 , 3 9

26)

A) Equal

B) Not equal

Reduce the fraction.

39 27) 45 A)

28) -

15 13

27) B)

22 19

C)

13 15

D)

39 45

6 9 A)

28) 2 3

B) -

2 3

C) -

3 2

D)

8 5

Simplify.

29)

1 1 + 6 12 A)

30)

1 9

B)

1 6

C)

19 72

D)

1 4

6 1 4 - + 7 2 7 A) -

31)

29)

3 7

30) B)

5 7

C)

13 14

D) -

13 14

4 11 · 17 12 A) -

32) -

15 29

31) B)

11 3

C)

11 17

D) -

11 51

5 17 ÷ 6 2 A)

5 17

32) B) -

7 23

C) -

5 51

D)

5 3

Convert the improper fraction to a mixed number.

29 33) 4 A) 7

1 4

B) 7

1 7

33) C) 8

1 4

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D) 6

1 4

Express the terminating decimal number as a quotient of two integers.

34) 1.83 183 1 183 A) B) C) 50 183 200

34) 183 D) 100

35) 1.76

35)

88 A) 5

22 B) 125

44 C) 25

1611 D) 100

Find the rational fraction in lowest terms represented by the periodic decimal.

36) 0.7

36)

7 A) 99

7 B) 9

70 C) 99

70 D) 999

Solve.

37) The floor of a rectangular room is to be tiled with many tiles will be needed along the wall?

1 tiles B) 29 tiles A) 3 12 Decide if the number is rational or irrational.

38) 36 A) Irrational 39)

Simplify.

40)

C) 27

1 tiles 4

D) 27

3 tiles 4

38) B) Rational

B) Irrational

40) 2

B) 2

15

C) 7

D) 30

Perform the indicated operations.

41) 28 3 - 7 3 A) 21

41) B) 63

Perform the indicated operation and simplify if possible.

42) 6 10 A) 4 15 B) 60

C) 35 3

D) 21 3

C)

D) 2 15

42) 30

Rationalize the denominator.

3 43) 7 A)

9 7 7

37)

39)

197 A) Rational

60 A) 15

1 1 foot square tiles along a 9 foot wall. How 3 4

43) B)

3 7 7

C) 3 7

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D) 52

44)

20 75 A)

44) 2 5 3

B)

2 15 3

C)

2 3 15

D)

2 15 15

Decide whether the statement is true or false.

45) The difference of two irrational numbers is always irrational.

A) True B) False Answer the question.

46) Find a rational number between 1.67 and 1.68.

A) 1.681 C) 1.673

45)

46) B) 1.673133133313333...

D) 1.683133133313333...

47) Find an irrational number between 0.676776777... and 0. 67 .

A) 0.676767686868...

B) 0.676776776

C) 0.674674674...

D) 0.676 5 6 and .

11 11

48) Find a rational number between A) 0.45

47)

B) 0.5455

48) C) 0.554554554...

D) 0.464664666...

Identify the property illustrated by the statement.

49) (5 + 2) + 6 = (2 + 5) + 6 A) Associative B) Commutative C) Distributive D) Identity E) Inverse

49)

50) 9 + 0 = 9 A) Associative B) Commutative C) Distributive D) Identity E) Inverse

50)

51) 5(x + 4) = 5x + 20 A) Associative B) Commutative C) Distributive D) Identity E) Inverse

51)

Evaluate the expression.

52) 3 3 A) 27

52) B) 4

C) 9

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D) 6

53) (-4)2 A) 8

53) B) -16

C) 16

D) -8

B) -1

C) 1

D) 0

54) 4 0

54) A) 4

Use the rules for exponents to rewrite the expression and then evaluate the new expression.

55) (-2)4 (-2)2 A) -256

1 256

55) 1 64

C) 64

D) -

C) 2.1 x 10-7

D) 2.1 x 107

B) 4.556 x 10-5

C) 4.556 x 105

D) 4.556 x 10-4

B) 6.0316 x 10-6

C) 6.0316 x 106

D) 6.0316 x 10-7

B)

Express the number in scientific notation.

56) 21,000,000 A) 2.1 x 106 B) 2.1 x 10-6

56)

57)

57) 0.00004556 A) 4.556 x 104

58)

58) 0.0000060316 A) 6.0316 x 10-5

59)

59) 0.000000083402 A) 8.3402 x 10-7

B) 8.3402 x 10-9

C) 8.3402 x 10-8

D) 8.3402 x 108

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Rewrite the following number in scientific notation.

60) 534.28 × 103

60)

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Rewrite each number using scientific notation before performing the operation. Leave your answer in scientific notation form.

61) (2,000,000)(0.003) 61) A) 6.0 × 101 B) 6.0 × 102 C) 0.0 D) 6.0 × 103 Use scientific notation to solve the problem.

62) Assume that the volume of the earth is 5 x 10 14 cubic meters and the volume of a bacterium is 2.5 x 10-16 cubic meters. If the earth could be filled with bacteria, how many would it contain?

62)

B) 5.0 x 10 -31 bacteria D) 2.0 x 10 30 bacteria

A) 5.0 x 10 31 bacteria C) 2.0 x 10 -30 bacteria

For the given arithmetic sequence, find the specified term a n and the sum of the terms from a 1 to a n, inclusive.

63) 5, 7, 9, 11, ... ; find a 27 A) 57; 1620

63) B) 57; 837

C) 27; 1674

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D) 57; 729

For the given geometric sequence, find a n and the sum of the terms from a 1 to a n.

64) 2, 10, 50, 250 ... ; find a 9 A) 250; 976,562 C) 781,250; 18

64) B) 781,250; 976,562 D) 390,627; 45

Solve the problem.

65) Assume that your starting salary is $3138 and that you are getting an increase of $53 per month.

Find the amount that you will earn in a year.

A) $3721 B) $82,308 C) $3774 D) $41,154

Copyright © 2022 Pearson Education, Inc.

65)

Answer Key Testname: CHAPTER 6 EXAM A

1) A 2) A 3) D 4) D 5) D 6) B 7) B 8) B 9) B 10) D 11) C 12) D 13) D 14) B 15) C 16) D 17) D 18) D 19) A 20) C 21) D 22) C 23) B 24) C 25) B 26) B 27) C 28) B 29) D 30) C 31) D 32) C 33) A 34) D 35) C 36) B 37) D 38) B 39) B 40) B 41) D 42) D 43) B 44) D 45) B 46) C 47) A 48) A 49) B 50) D Copyright © 2022 Pearson Education, Inc.

Answer Key Testname: CHAPTER 6 EXAM A

51) C 52) A 53) C 54) C 55) C 56) D 57) B 58) B 59) C 60) 5.3428 × 105 61) D 62) D 63) B 64) B 65) D

Copyright © 2022 Pearson Education, Inc.

Chapter 6 Exam B Name___________________________________

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Answer the question.

1) Find an irrational number between A) 0.535353...

B) 0.5455

2) Find a rational number between A) 0.50

6 5 and .

11 11

1) C) 0.464664666...

D) 0.45

1 5 and .

2 9

B) 0.50

2) C) 0.565656...

D) 0.554554554...

A sign is hung on the wall of a building as in the figure below. Given the downward force and the horizontal force, determine the minimum required strength of a cable from point A to point B.

3) Downward force: 8 pounds; horizontal force: 8 pounds A) 64 pounds B) 11.31 pounds C) 128 pounds

D) 16 pounds

3)

4) Downward force: 10 pounds; horizontal force: 24 pounds A) 21.82 pounds B) 26 pounds C) 34 pounds

D) 14 pounds

4)

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Decide whether the statement is true or false.

12 is irrational.

5) 3

5)

Simplify.

6)

1 2 · 4 5

6)

7)

14 18 ÷ 15 5

7)

8)

1 2 + 4 5

8)

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9)

4 5 7 ÷ - ÷ 3 2 10

9)

Find the product.

10) (-11)(-25)

10)

Solve.

11) There were 24

3 7 yards of wire on a spool. After a customer bought 9 yards of wire from 8 8

11)

the spool, how many yards were left?

12) The floor of a rectangular room is to be tiled with

1 1 foot square tiles along a 6 foot wall.

3 4

12)

How many tiles will be needed along the wall?

13) Tim needs to apply 1

1 gallons of herbicide per acre of soybeans. How many gallons of 4

13)

herbicide are needed for 288 acres?

14) A snail is moving at 2

1 3 feet per minute. How far will it move in 3 minutes?

5 8

15) A car traveled 408 miles on 15

1 gallons of gas. How many miles per gallon did it get?

9

14)

15)

Find the rational fraction in lowest terms represented by the periodic decimal.

16) 0.83

16)

17) 0.98

17)

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Write the numbers in order from smallest to largest.

18) 1.754, 1.547, 1.574, 1.457 A) 1.754, 1.574, 1.547, 1.457 C) 1.457, 1.574, 1.547, 1.754 19) 5.09, 5.9, 5.099, 5.999 A) 5.999, 5.9, 5.099, 5.09 C) 5.09, 5.099, 5.9, 5.999

18) B) 1.754, 1.547, 1.574, 1.457 D) 1.457, 1.547, 1.574, 1.754 19) B) 5.09, 5.9, 5.099, 5.999 D) 5.099, 5.09, 5.999, 5.9

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Solve the problem.

20) The temperature at the North Pole was 9°F at 8 am. At 3 pm, it was -40°F. By how many degrees did the temperature drop?

Copyright © 2022 Pearson Education, Inc.

20)

21) Two runners run around a circular track. The first runner completes a lap in 4 minutes.

The second runner completes a lap in 15 minutes. If they both start at the same place and the same time and go in the same direction, after how many minutes will they meet again at the starting place?

21)

22) Tom and Larry are food inspectors at a cookie making company. Tom tests every 8th batch of dough for fat percentage. Larry tests every 28th batch of dough for carbohydrate percentage. If they both start working at the same time, which batch will be the first that they both test?

22)

23) Mark has 575 hot dogs and 475 hot dog buns. He wants to put the same number of hot dogs and hot dog buns on each tray. What is the greatest number of trays Mark can use to accomplish this?

23)

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Express the number in scientific notation.

24) 0.000000977016 A) 9.77016 x 10-7 B) 9.77016 x 106

24) C) 9.77016 x 10-6

D) 9.77016 x 107

B) 6.587 x 10-2

C) 6.587 x 101

D) 6.587 x 10-1

B) 1.9 x 107

C) 1.9 x 106

D) 1.9 x 10-6

25)

25) 658.7 A) 6.587 x 102

26)

26) 19,000,000 A) 1.9 x 10-7

Rewrite each number using scientific notation before performing the operation. Leave your answer in scientific notation form.

27) (300)(40,000) 27) A) 1.2 × 109 B) 1.2 × 108 C) 1.2 × 106 D) 1.2 × 107 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Perform the indicated operations.

28) 3 2 + 9 18

28)

Decide if the number is rational or irrational.

29) 195

29)

30)

289

30)

Find the LCM for the pair of natural numbers.

31) 56, 48

31)

Rewrite the subtraction problem as an addition problem.

32) (-38) - (-38)

32)

33) (+39) - (-35)

33)

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Convert the mixed number to an improper fraction.

3 34) 337 7

34)

Perform the following calculations.

35) (+6)(+19) + (-7)(29)

35)

Rationalize the denominator.

10 36) 10

36)

Identify the number as either prime or composite.

37) 126

37)

Calculate the sum.

38) (-8) + (+6)

38)

Restate the following statement in two other ways.

39) 45 is a multiple of 9

39)

40) 48 is a multiple of 8

40)

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Use the rules for exponents to rewrite the expression and then evaluate the new expression.

41) 3 -2 0 1 D) 1 A) 0 B) -9 C) 9

41)

Evaluate the expression.

42) -5 -2 1 A) 25

42) B) 25

C) -25

1 D) 10

Estimate the square root of the following number, n, by finding a natural number a such that a < 43) 230 A) 256 B) 16 C) 15 D) 225

n < a + 1.

43)

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Write the fraction in decimal notation.

3 44) 8

44)

Reduce the fraction.

152 45) 164

45)

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MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Two terms in the Fibonacci sequence are given. Find the specified term.

46) F18 = 2584 and F19 = 4181. Find F20.

A) 1597

B) 8362

C) 5168

46) D) 6765

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Rewrite the following number in scientific notation.

47) 28.45 × 105

47)

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Write the number in standard notation.

48) 7.96 x 10-4 A) 0.00796

48)

B) 0.0000796

C) 0.000796

D) -796,000

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Determine whether the number is divisible by 2, 3, 4, 5, 6, 8, 9, and/or 10.

49) 2278

49)

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

For the given geometric sequence, find a n and the sum of the terms from a 1 to a n.

50) 4, 16, 64, 256 ... ; find a 8 A) 256; 87,380

50) B) 65,536; 87,380

C) 16,388; 32

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D) 65,536; 32

Answer Key Testname: CHAPTER 6 EXAM B

1) C 2) A 3) B 4) B 5) False 1 6) 10 7)

7 27

8)

13 20

9) -

21 16

10) + 275 1 11) 14 yards 2 12) 18

3 tiles 4

13) 360 gallons 17 feet 14) 7 40 15) 27 mpg 83 16) 99 17)

89 90

18) D 19) C 20) by 49°F 21) 60 22) 56 23) 25 24) A 25) A 26) B 27) D 28) 30 2 29) Irrational 30) Rational 31) 336 32) (-38) + (+38) 33) (+39) + (+35) 2362 34) 7 35) -89 36) 10 37) Composite Copyright © 2022 Pearson Education, Inc.

Answer Key Testname: CHAPTER 6 EXAM B

38) -2 39) 9 is a factor of 45 9 divides 45 40) 8 is a factor of 48 8 divides 48 41) D 42) A 43) C 44) 0.375 38 45) 41 46) D 47) 2.845 × 106 48) C 49) 2 50) B

Copyright © 2022 Pearson Education, Inc.

Chapter 7 Exam A Name___________________________________

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Solve the equation by applying the rules for rewriting equations.

1) 2x + 2 = 5x - 7 1 A) 9 B) C) 3 3 2) 0.2x + 3 = 3x - 0.6 90 A) 7

1) D)

1 9 2)

9 C) 70

B) 9

9 D) 7

Solve the equation for the specified variable. nE 3) I = for n nr + R A) n =

-IR Ir - E

B) n =

3)

IR Ir + E

C) n =

-R Ir - E

D) n = IR(Ir - E)

Find the x- and y-intercepts for the equation. Then graph the equation.

4) 3x - 9y = 9

4)

y 10

5

-10

-5

5

10

x

-5

-10

A) (0, -1), (-3, 0)

B) (0, -1), (3, 0) y

-10

y

10

10

5

5

-5

5

10

x

-10

-5

5

-5

-5

-10

-10

Copyright © 2022 Pearson Education, Inc.

10

x

Find the slope of the line passing through the two given points.

5) (-6, -7) and (-2, 8) 1 1 A) - 5 B) C) 4 5

5) 15 D) 4

Solve the problem.

6) An office desk costs $7000. After 5 years, it depreciates to a value of $5500. Assuming linear depreciation, answer the following.

6)

a) Write a linear equation that gives the value of the desk, y, in terms of the number of years after it was purchased, x. b) Using the equation found in part a, find the value of the desk after 9 years. c) After how many years would the desk have no value?

B) y = 7000 + 300x; $9700; 20 years A) y = 7000 - 200x; $4300; 23 years C) y = 7000 - 300x; $4300; 23 years D) y = 7000 - 300x; $2700; 23 years Interpret the meaning of the slope and the y -intercept of the equation in terms of the conditions stated in the problem.

7) The cost, in dollars, of retaining the services of a computer repairman in Anchorville is given by 7) y = 42x + 32, where x is the number of hours worked.

A) 32 signifies the hourly rate, and 42 signifies the overhead charge.

B) -42 signifies the hourly rate, and 32 signifies the travel cost.

C) 74 signifies the cost for an on-site inspection.

D) 42 signifies the hourly rate, and 32 signifies the overhead charge.

Find a linear equation whose graph has the indicated slope and passes through the given point.

8) slope -6, point (-2, -6) A) y = -6x + 18 B) y = 6x - 6 C) y = -6x - 18 D) y = 6x + 6

8)

Find a linear equation whose graph passes through the given points. Write the equation in slope -intercept form.

9) (6, 8) and (0, -3) 9) 11 2 11 2 A) y = x-3 B) y = x - 3 C) y = x-3 D) y = - x - 3 6 3 6 3 Solve the problem.

10) Suppose that a sales person observes that if an item is priced at $7 per item then 5 items are sold. If 3 items are sold for $9 per item then find an equation to model the number y of items sold for x dollars per item.

C) y = -x + 12 D) y = -x - 2 A) y = x - 2 B) y = x + 12

10)

11) In 1984, the life expectancy for a female born in the United States was 75.7 years and was increasing at a rate of 0.25 years per year. Assume that this rate of increase remains constant. Using an appropriate linear equation as a model, estimate the life expectancy of a female born in the U.S. in 1998.

B) 79.20 years C) 80.20 years D) 89.20 years A) 3.50 years

11)

12) In 1994, there were 642,000 males enrolled in college who were between the ages of 18 and 22, and over the next several years this number increased at a rate of 56.5 thousand per year. Using an appropriate linear equation as a model, estimate the number of males enrolled in college in the year 2002.

B) 1,090,000 C) 1,102,000 D) 1,094,000 A) 650,000

12)

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Solve the quadratic equation.

13) x2 - 12x + 36 = 0

13)

A) -6 C) -6, 6

B) 2, 3 D) 6

Find the vertex of the quadratic equationʹs graph and determine whether the graph opens up or down.

14) y = -x2 + 4x - 12 A) - 2, 16 , up

B) - 2, -64 , down

C) 2, 8 , up

14)

D) 2, - 8 , down

Find the x-intercepts and y-intercept of the graph of the given quadratic equation.

15) y = x2 + 7x + 10

15)

A) x-intercepts (-2, 0) and (-5, 0); y-intercept (0, 10) B) x-intercepts (2, 0) and (5, 0); y-intercept (0, -10) C) x-intercepts (-2, 0) and (-5, 0); y-intercept (0, -10) D) x-intercepts (2, 0) and (5, 0); y-intercept (0, 10) Solve the problem.

16) A projectile is thrown upward so that its distance, in feet, above the ground after t seconds is h = -16t2 + 608t. What is its maximum height?

A) 9472 ft

B) 5776 ft

C) 304,304 ft

16)

D) 18,411 ft

You are given the principal in a bank account, a yearly interest rate, and the time the money is in the account. Assuming that no withdrawals are made and that the interest is compounded annually, compute the amount in the account after the specified time period.

17) 17) $6000, 7.5 percent, 1 year A) $6869.40 B) $10,200.00 C) $64,200.00 D) $6450.00 18) $3500, 4 percent, 4 years A) $3120.00 19) $3000, 4 percent, 3 years A) $3120.00

18) B) $3649.96

C) $2924.65

D) $4094.50 19)

B) $3244.80

C) $3374.59

D) $3509.58

B) -0.86

C) 1.86

D) 1.30

Solve the equation for x.

20) 5 x = 20 A) 0.14

20)

Solve the problem.

21) Assume that a population is growing initially at a rate of 5.5%. If P2 = 0.72, use the logistic growth

21)

model to compute the value of P3 .

A) 0.73

B) 0.78

C) 0.85

D) 0.70

22) Assume that a population is growing initially at a rate of 7%. If P0 = 0.1, use the logistic growth model to compute the value of P2 .

A) 0.14

B) 0.04

C) 0.26

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D) 0.11

22)

23) John Leeʹs savings account has a balance of $1509. After 9 years, what will the amount of interest be at 6% compounded annually? Round to the nearest dollar.

A) $1031 B) $1040 C) $1045 D) $90 Solve for x. x 4 24) = 12 84 A) 4 25) x : 8 = 1 : 2 A) 4

23)

24) B) 28

C) 48

D) 336 25)

B) 5

C) 6

D) 2

Solve the problem.

26) Suppose that z varies jointly with x and y and that z = 196 when x = 7 and y = 14. Find the constant of proportionality k. Then, find z when x = 6 and y = 3.

A) k = 2; z = 36

B) k = 4; z = 72

C) k = 0.2; z = 3.6

D) k = 19,208; z =

27) If f varies jointly as q2 and h, and f = 54 when q = 3 and h = 3, find k.

A) k = 48 B) k = 6 C) k = 3

26)

9604 9 27) D) k = 2

28) If f varies jointly as q2 and h, and f = 36 when q = 3 and h = 2, find q when f = 192 and h = 6.

A) q = 6 B) q = 2 C) q = 3 D) q = 4

28)

29) If f varies jointly as q2 and h, and f = -64 when q = 4 and h = -2, find k.

A) k = -2 B) k = 2 C) k = 4

29) D) k = 6

30) If f varies jointly as q2 and h, and f = 144 when q = 4 and h = 3, find f when q = 3 and h = 5.

A) f = 135 B) f = 15 C) f = 45 D) f = 27

30)

31) If s varies directly as t 2 , and s = 72 when t = 3, find s when t is 4.

A) s = 12 B) s = 24 C) s = 96

31)

32) If x varies inversely as y 2 , and x = 5 when y = 12, find x when y = 4.

A) x = 75 B) x = 3 C) x = 45

D) s = 128 32) D) x = 80

33) If y varies directly as x and inversely as the square root of w, and y = 63 when x = 9 and w = 12, find y when x = 5 and w = 27.

140 70 A) y = 70 3 B) y = C) y = 14 3 D) y = 3 3

33)

34) Maria and Charlie can deliver 90 papers in 3 hours. How long would it take them to deliver 111 papers?

A) 4.9 hours B) 3.7 hours C) 333 hours D) 2.4 hours

34)

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35) A machine can fill 7676 cartons of milk in 0.8 hour. How many cartons of milk can it fill per hour?

A) 6141 cartons B) 7677 cartons C) 8529 cartons D) 9595 cartons

35)

36) The shadow cast by an object on a sunny day varies directly as the height of the object. If a person 61 inches tall casts a shadow 65 inches long, how tall is a tree which casts a shadow 49 feet in length?

A) 45.98 feet B) 80.92 feet C) 63 feet D) 52.21 feet

36)

Solve the system by graphing.

37) 2x + y = 2 x + 6y = -21

37)

y 10

5

-10

-5

5

10

x

-5

-10

B) (3, -4)

A) (3, 2)

C) (-1, 4)

D) (-3, -4)

38) 3x + 2y = 28 -2x + 3y = 16

38) y 10

5

-10

-5

5

10

x

-5

-10

A) (3, 22)

B) (4, 8)

C) (8, 4)

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D) No solution

39) 4x + y = 20 16x + 4y = 80

39) y 10

5

-10

-5

5

10

x

-5

-10

A) (0, 20) C) (5, 0)

B) Infinite number of solutions D) No solution

40) 3x - 2y = 4 -6x + 4y = 7

40) y 10

5

-10

-5

5

10

x

-5

-10

A) (1, 2) C) (2, 1)

B) Infinite number of solutions D) No solution

Use the elimination method to solve the system of linear equations.

41) x + 8y = 67 2x + 7y = 62 B) No solution C) (2, 9) A) (3, 8) 42) 9x + 9y = 63 2x - 7y = -49 A) (0, 8)

41) D) (-3, 9) 42)

B) No solution

C) (-1, 8)

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D) (0, 7)

Graph the linear inequality.

43) x - y > -5

43) y

10

5

-10

-5

5

10

x

-5

-10

A)

B) y

-10

y

10

10

5

5

-5

5

10

x

-10

-5

-5

-5

-10

-10

C)

5

10

x

5

10

x

D) y

-10

y

10

10

5

5

-5

5

10

x

-10

-5

-5

-5

-10

-10

Copyright © 2022 Pearson Education, Inc.

44) x ≥ -6

44) y 10

5

-10

-5

5

10

x

-5

-10

A)

B) y

-10

y

10

10

5

5

-5

5

10

x

-10

-5

-5

-5

-10

-10

C)

5

10

x

5

10

x

D) y

-10

y

10

10

5

5

-5

5

10

x

-10

-5

-5

-5

-10

-10

Copyright © 2022 Pearson Education, Inc.

45) x ≤ -6

45) y 10

5

-10

-5

5

10

x

-5

-10

A)

B) y

-10

y

10

10

5

5

-5

5

10

x

-10

-5

-5

-5

-10

-10

C)

5

10

x

5

10

x

D) y

-10

y

10

10

5

5

-5

5

10

x

-10

-5

-5

-5

-10

-10

Copyright © 2022 Pearson Education, Inc.

46) y ≥ 5

46) y 10

5

-10

-5

5

10

x

-5

-10

A)

B) y

-10

y

10

10

5

5

-5

5

10

x

-10

-5

-5

-5

-10

-10

C)

5

10

x

5

10

x

D) y

-10

y

10

10

5

5

-5

5

10

x

-10

-5

-5

-5

-10

-10

Copyright © 2022 Pearson Education, Inc.

Solve the system. Indicate all corner points and shade the solution set.

47) 3x - 2y ≥ -6 x-1≤0 5

47)

y

5x

-5

-5

A)

B) 5

y

5

5x

-5

y

5x

-5

(1, -3/2)

-5

(1, -9/2)

-5

C)

D) 5

y

5

y (1, 9/2)

(1, 3/2) 5x

-5

-5

5x

-5

-5

Copyright © 2022 Pearson Education, Inc.

48) 3x + 2y ≤ -6 x-1≥0

48) 5

y

5x

-5

-5

A)

B) 5

y

5

5x

-5

y

5x

-5 (1, -3/2)

(1, -9/2)

-5

-5

C)

D) 5

y

5

y (1, 9/2)

(1, 3/2) 5x

-5

-5

5x

-5

-5

Solve.

49) Sue wants to plan a meal with 55 grams of fat and 1095 calories. If hot dogs have 13 grams of fat and 145 calories each and if baked beans have 8 grams of fat and 330 calories per half -cup serving, how many hot dogs and servings of beans should she use?

A) 8 hot dogs and 13 half-cup servings of baked beans B) 2 hot dogs and 3 half-cup servings of baked beans C) 3 hot dogs and 2 half-cup servings of baked beans D) 13 hot dogs and 8 half-cup servings of baked beans

Copyright © 2022 Pearson Education, Inc.

49)

50) A mother is choosing which baby foods to serve her infant. A jar of meat has 2 g of protein and 36 calories. A jar of vegetables has 1 g of protein and 18 calories. How much of each will she need to serve to get 5 g of protein and 111 calories?

A) 1.5 jars of meat and 2 jars of vegetables B) 2 jars of meat and 1.5 jars of vegetables C) There are infinitely many such combinations.

D) There is no such combination.

Copyright © 2022 Pearson Education, Inc.

50)

Answer Key Testname: CHAPTER 7 EXAM A

1) C 2) D 3) A 4) B 5) D 6) C 7) D 8) C 9) A 10) C 11) B 12) D 13) D 14) D 15) A 16) B 17) D 18) D 19) C 20) C 21) A 22) D 23) B 24) B 25) A 26) A 27) D 28) D 29) B 30) A 31) D 32) C 33) D 34) B 35) D 36) A 37) B 38) B 39) B 40) D 41) A 42) D 43) D 44) A 45) B 46) A 47) D 48) A 49) C 50) D Copyright © 2022 Pearson Education, Inc.

Chapter 7 Exam B Name___________________________________

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Solve the problem.

1) Jane invested $7500 at 8% compounded annually. How much will be in the account in 8 years?

Round to the nearest cent.

A) $7503.99 B) $13,881.98 C) $6381.98 D) $7909.46 Use the substitution method to solve the system.

2) x + 9y = 18 3x + 10y = 20 B) (-2, 0) A) (0, 2)

1)

2) C) (1, 1)

D) No solution

You are given the principal in a bank account, a yearly interest rate, and the time the money is in the account. Assuming that no withdrawals are made and that the interest is compounded annually, compute the amount in the account after the specified time period.

3) 3) $2000, 4 percent, 1 year A) $20,800.00 B) $2163.20 C) $2080.00 D) $2800.00 Solve the problem.

4) Bob owns a watch repair shop. He has found that the cost of operating his shop is given by c = 4x2 - 344x + 86, where c is the cost in dollars, and x is the number of watches repaired. How many watches must he repair to have the lowest cost?

A) 43 watches B) 43 watches C) 40 watches

4)

D) 86 watches

You are given the principal in a bank account, a yearly interest rate, and the time the money is in the account. Assuming that no withdrawals are made and that the interest is compounded annually, compute the amount in the account after the specified time period.

5) 5) $7000, 7.5 percent, 1 year A) $74,900.00 B) $8014.30 C) $7525.00 D) $11,900.00 Find a linear equation whose graph has the indicated slope and passes through the given point.

6) slope 4, point (-3, -6) A) y = 3x - 18 B) y = 4x + 6 C) y = 3x + 18 D) y = 4x + 18 Solve the problem.

7) Dr. Taylor can see 11 patients in 3 hours. At this rate, how long would it take him to see 33 patients?

A) 33 hours B) 9 hours C) 8 hours D) 121 hours 8) Andrea Gilfordʹs savings account has a balance of $ 1262. After 5 years, what will the amount of interest be at 6% compounded annually? Round to the nearest dollar.

A) $37 B) $432 C) $418 D) $427

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6)

7)

8)

Use the elimination method to solve the system of linear equations.

9) x + 3y = 11 -6x + 3y = -3 C) (2, 3) A) No solution B) (-3, 2)

9) D) (3, 2)

Solve for x. x 1 10) = 7 42 A) 42

10) B) 35

Use the substitution method to solve the system.

11) x + 7y = 12 -5x + 6y = -19 A) No solution B) (-5, 2)

C) 6

D) 7

11) C) (5, 1)

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D) (4, 2)

Solve the system. Indicate all corner points and shade the solution set.

12) 3x - 2y ≤ 6 x-1≥0 5

12)

y

5x

-5

-5

A)

B) 5

y

5

y

(1, 3/2) 5x

-5

5x

-5

(1, -3/2)

-5

-5

C)

D) 5

y

5

5x

-5

-5

(1, -9/2)

y (1, 9/2)

5x

-5

-5

Copyright © 2022 Pearson Education, Inc.

Solve the problem.

13) The number of births in County A has been increasing in recent years. Use the information given on the bar graph for the years 1960 and 1990, letting x = 0 represent the year 1960 and letting y represent the number of births.

A) y =

497 x + 1693 30

B) y =

497 x + 1693 1990

C) y =

1990 x - 2190 497

D) y =

30 930140 x+ 497 497

13)

You are given the population and the growth rate as of 2000 for a hypothetical country. Assume that the growth rate remains the same from year to year. Using an exponential function to model population growth, determine the size of the population in the specified year.

14) 14) Population = 28 million, growth rate = 1.8 percent, year: 2019 B) 28.0 million C) 38.6 million D) 40.0 million A) 39.3 million

Copyright © 2022 Pearson Education, Inc.

Solve the system. Indicate all corner points and shade the solution set.

15) 2x + y ≤ 4 y-1≤0 4

15)

y

4x

-4

-4

A)

B) 4

y

4

y

(3/2, 1)

(3/2, 1)

4x

-4

4x

-4

-4

-4

C)

D) 4

y

4

(1, 2)

(1, 2)

4x

-4

-4

y

4x

-4

-4

Solve the problem.

16) Suppose that y is inversely proportional to x and that y = 12 when x = 5. Find the constant of proportionality k. Then, find y when x = 25.

A) k = 60; y = 2.4 B) k = 2.4; y = 60 C) k = 52; y = 2.4 D) k = 72.5; y = 2.9 17) There are currently 55 million cars in a certain country, decreasing by 7.9 % annually. How many years will it take for this country to have 31 million cars? (Round to the nearest year.)

A) 40 years B) 8 year(s) C) 3 year(s) D) 2 years

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16)

17)

Model the situation with a dynamical system. Use your model to answer the question.

18) You take a 251-mg dose of an antibiotic every 3 hours. Your body eliminates 40% of the drug in a 3-hour period. How much antibiotic will be in your bloodstream after two doses?

A) Dn+1 = 0.6Dn + 251, n = 0, 1, 2, ..., where D0 = 0; 401.60 mg

18)

B) Dn+1 = 0.4Dn + 251, n = 0, 1, 2, ..., where D0 = 0; 351.40 mg C) Dn+1 = 60Dn + 251, n = 0, 1, 2, ..., where D0 = 0; 15,311.00 mg D) Dn+1 = 0.6Dn + 251, n = 0, 1, 2, ..., where D0 = 251; 652.60 mg Find the x-intercepts and y-intercept of the graph of the given quadratic equation.

19) y = x2 + 10x + 21

19)

A) x-intercepts (3, 0) and (7, 0); y-intercept (0, 21) B) x-intercepts (-3, 0) and (-7, 0); y-intercept (0, 21) C) x-intercepts (3, 0) and (7, 0); y-intercept (0, -21) D) x-intercepts (-3, 0) and (-7, 0); y-intercept (0, -21) You are given the principal in a bank account, a yearly interest rate, and the time the money is in the account. Assuming that no withdrawals are made and that the interest is compounded annually, compute the amount in the account after the specified time period.

20) 20) $5500, 4 percent, 3 years A) $5849.29 B) $6186.75 C) $5200.00 D) $5061.89 Find the slope of the line passing through the two given points.

21) (9, 6) and (3, 6) A) 1 B) 11 C) 5

21) D) 0

Solve the problem.

22) A plumber charges a fixed rate plus an hourly rate to do house calls. The ordered pair ( 2, 61) indicates total charges of $61 for a job taking 2 hours, and the ordered pair (10, 165) indicates total charges of $165 for a job taking 10 hours.

22)

a) Write a linear equation giving the total charges, y, in terms of the number of hours x. b) Use the equation found in part a to find how much it costs for 6 hours. c) How many hours would result in a total charge of $100?

B) y = 13x; $78; 5 hours A) y = 13x + 35; $113; 5 hours C) y = 13x + 35; $78; 5 hours D) y = 13x + 35; $113; 7 hours Solve for x.

1 x 23) = 28 7 A) 7

23) B) 5

C) 6

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D) 4

Solve the system by graphing.

24) 4x + y = 15 4x + y = 23

24)

y 10

5

-10

-5

5

10

x

-5

-10

A) (13, -37) C) (8, 7)

B) Infinite number of solutions D) No solution

Find the slope of the line passing through the two given points.

25) (-3, -5) and (3, 7) 1 6 A) B) - 2 C) 2 5

25) D) 2

Find the vertex of the quadratic equationʹs graph and determine whether the graph opens up or down.

26) y = 3x2 + 6x - 9 A) 1, 24 , down

B) 1, 72 , down

C) - 1, - 12 , up

Solve the equation by applying the rules for rewriting equations.

27) 4x + 3 = 6x - 7 1 1 B) C) 5 A) 10 5

26)

D) - 1, 12 , up

27) D) 10

Solve the problem.

28) If f varies jointly as q2 and h, and f = 96 when q = 4 and h = 2, find q when f = 135 and h = 5.

A) q = 5 B) q = 2 C) q = 4 D) q = 3 Solve the quadratic equation.

29) x2 - 8x + 16 = 0 A) 2, 2 C) 4

28)

29) B) -4 D) -4, 4

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Solve the problem.

30) The graph below shows the decrease in the percentage of Canadians below the poverty level from 1992 to 1997.

30)

Assume that the rate of decrease continues for the next several years and can be modeled by a linear equation of the form p = mx + b. Based on such a model, predict the percentage of Canadians below the poverty level in 2012.

A) 22.4% B) 58.0% C) 27.4% D) 25.2% 31) College students can purchase points for use in the food service areas instead of cash. If you initially pay the basic food service fee of $10, then points can be purchased for 30 cents each; otherwise, points cost 50 cents each. How many points must you use in order for it to be cheaper to pay the basic food service fee?

B) 51 points C) 50 points D) 60 points A) 45 points

31)

32) If x varies inversely as y 2 , and x = 2 when y = 20, find x when y = 5.

A) x = 50 B) x = 4 C) x = 32

32)

Use the substitution method to solve the system.

33) x + y = 3 8x + 8y = 24 A) (6, -3) C) Infinite number of solutions

D) x = 16

33) B) (0, 0) D) (3, 8)

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Graph.

34) y = x2 + 2x + 1

34) y 10

5

-10

-5

5

10

x

-5

-10

A)

B) y

-10

y

10

10

5

5

-5

5

10

x

-10

-5

-5

-5

-10

-10

C)

5

10

x

5

10

x

D) y

-10

y

10

10

5

5

-5

5

10

x

-10

-5

-5

-5

-10

-10

Model the situation with a dynamical system. Use your model to answer the question.

35) You deposit $940 in a bank account paying 6% yearly interest that is compounded annually. How much will be in your account at the end of 3 years?

A) An+1 = 1.06An , n = 0, 1, 2, ..., where A0 = 940; $1119.56 B) An+1 = 0.06An , n = 0, 1, 2, ..., where A0 = 940; $0.20 C) An+1 = 1.06An , n = 0, 1, 2, ..., where A0 = 940; $996.40 D) An+1 = 6An , n = 0, 1, 2, ..., where A0 = 940; $203,040.00

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35)

Solve the problem.

36) In 1996, there were 651,000 males enrolled in college who were between the ages of 18 and 22, and over the next several years this number increased at a rate of 54.5 thousand per year. Using an appropriate linear equation as a model, estimate the number of males enrolled in college in the year 2003.

B) 1,032,500 C) 1,029,000 D) 658,000 A) 1,039,500 Use the elimination method to solve the system of linear equations.

37) x - 7y = -3 5x - 6y = -15 B) (-3, 0) C) No solution A) (-2, -3)

37) D) (3, -1)

Solve the quadratic equation.

38) 3x2 - 14x - 5 = 0 A) -3, 5

36)

38) 1 1 B) ,14 3

1 C) - , 3 3

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1 D) - , 5 3

Graph the linear inequality.

39) -2x - 5y ≤ -10

39) y

10

5

-10

-5

5

10

x

-5

-10

A)

B) y

-10

y

10

10

5

5

-5

5

10

x

-10

-5

-5

-5

-10

-10

C)

5

10

x

5

10

x

D) y

-10

y

10

10

5

5

-5

5

10

x

-10

-5

-5

-5

-10

-10

Copyright © 2022 Pearson Education, Inc.

40) y ≥ -5

40) y 10

5

-10

-5

5

10

x

-5

-10

A)

B) y

-10

y

10

10

5

5

-5

5

10

x

-10

-5

-5

-5

-10

-10

C)

5

10

x

5

10

x

D) y

-10

y

10

10

5

5

-5

5

10

x

-10

-5

-5

-5

-10

-10

Find a linear equation whose graph has the indicated slope and passes through the given point.

41) slope 5, point (3, 6) A) y = 5x - 9 B) y = -5x - 9 C) y = 5x + 9 D) y = 3x - 9

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41)

Solve the problem.

42) The intensity I of light varies inversely as the square of the distance D from the source. If the intensity of illumination on a screen 5 ft from a light is 2 foot-candles, find the intensity on a screen 10 ft from the light.

1 A) 2 foot-candles B) 1 foot-candles 2 C)

50 foot-candle 101

D)

Solve the equation for the specified variable.

43) A = P(1 + nr) for r A P-A B) r = A) r = n Pn

42)

1 foot-candle 2

43) Pn C) r = A-P

A- P D) r = Pn

Solve.

44) Sophie can work at A-1 Computers for a base pay of $700 per week plus a $65 commission for each computer system that she sells. At One Stop Computers her base pay would be $475 with a $ 80 commission for each computer system that she sells. How should Sophie decide which position to take?

A) At 14 systems, she makes $1610 at either store. After that, she earns more at A-1 Computers.

B) At 15 systems, she makes $1675 at either store. After that, she earns more at One Stop Computers.

C) At 14 systems, she makes $1610 at either store. After that, she earns more at One Stop Computers.

D) At 15 systems, she makes $1675 at either store. After that, she earns more at A-1 Computers.

44)

Find a linear equation whose graph passes through the given points. Write the equation in slope -intercept form.

45) (7, 4) and (4, 2) 45) 2 3 2 2 2 3 A) y = x B) y = - x C) y = x - 4 D) y = - x - 4 3 2 3 3 3 2 Solve the problem.

46) Maria and Charlie can deliver 90 papers in 2 hours. How long would it take them to deliver 81 papers?

A) 2.7 hours B) 1.8 hours C) 2.2 hours D) 162 hours 47) A projectile is thrown upward so that its distance, in feet, above the ground after t seconds is h = -16t2 + 544t. What is its maximum height?

A) 235,280 ft

B) 14,161 ft

C) 8448 ft

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D) 4624 ft

46)

47)

Solve the system by graphing.

48) 3x - 2y = 4 -6x + 4y = 7

48)

y 10

5

-10

-5

5

10

x

-5

-10

A) (2, 1) C) No solution

B) (1, 2) D) Infinite number of solutions

Solve the problem.

49) Suppose that y is inversely proportional to x and that y = 40 when x = 9. Find the constant of proportionality k. Then, find y when x = 2.

40 80 A) k = ;y= B) k = 360; y = 180 C) k = 72; y = 36 D) k = 180; y = 90 9 9

49)

Find a linear equation whose graph passes through the given points. Write the equation in slope -intercept form.

50) (3, -6) and (0, 5) 50) 11 11 9 9 A) y = x+5 B) y = x + 5 C) y = x+5 D) y = - x + 5 3 3 5 5

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Answer Key Testname: CHAPTER 7 EXAM B

1) B 2) A 3) C 4) B 5) C 6) B 7) B 8) D 9) C 10) C 11) C 12) A 13) A 14) A 15) B 16) A 17) B 18) A 19) B 20) B 21) D 22) A 23) D 24) D 25) D 26) C 27) C 28) D 29) C 30) D 31) B 32) C 33) C 34) D 35) A 36) B 37) B 38) D 39) D 40) B 41) A 42) D 43) D 44) B 45) A 46) B 47) D 48) C 49) B 50) A Copyright © 2022 Pearson Education, Inc.

Chapter 8 Exam A Name___________________________________

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Convert to a percent.

92 1) 100 A) 0.92%

1) B) 92%

C) 102%

D) 184%

C) $141.03

D) $101.61

Use the table to find the monthly payment on the given loan.

2) amount: $4500; rate: 4%; time: 4 years A) $132.89 B) $134.87

2)

Solve the problem.

3) Mark takes a bank loan of $2400 to start up a business at an annual interest rate of 7%. How much will he have to repay in 4 months?

A) $3200 B) $3400 C) $2456 D) $2624 Find decimal notation.

4) 700% A) 0.7

3)

4) B) 7.01

C) 7

D) 70

Find the present value of the annuity. Assume that all interest rates are annual rates.

5) If Peter can afford car payments of $185 per month for 5 years, what is the price of a car that he can afford now? Assume an interest rate of 8.5%.

A) $9017.12 B) $8995.62 C) $8777.12 D) $9167.22 Solve the problem.

6) Alex and Juana went on a 32-mile canoe trip with their class. On the first day they traveled 24 miles. What percent of the total distance did they canoe?

A) 1% B) 100% C) 75% D) 0.75%

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5)

6)

7) Tracy wants to save $40,000 for a down payment towards a house. She puts $26 every month in an annuity that has a 5% annual interest rate. How long will it take her to save for the down payment? Round your answer to the nearest month.

A) 479 months B) 484 months C) 482 months D) 490 months Solve the problem. Round to the nearest hundredth.

8) 18 is 5% of what number?

A) 90.00 B) 36.00

8) C) 3600.00

D) 360.00

Convert to a percent.

17 9) 40 A) 17.00%

7)

9) B) 4.25%

C) 34.00%

D) 42.5%

Given the current cost of an item and the inflation rate, find the cost of the item in the specified number of years.

10) Home: $1,400,000, inflation rate: 2%, after 6 years 10) A) $1,586,627.39 B) $1,576,627.39 C) $1,581,627.39 D) $1,582,627.39 Use the average daily balance method to compute the finance charge on the credit card for the previous month.

11) Month: April (30 days) 11) Previous monthʹs balance: $960 Interest rate: 21% Date Transaction April 3 charged $102 for phone bill April 12 made payment of $350 April 21 charged $93 for electricity bill April 29 returned $68 for lawn service A) $11.57 B) $14.84 C) $17.39 D) $14.00 Find percent notation.

12) 0.011 A) 1.1%

12) B) 0.11%

C) 11%

D) 0.0011%

Use the table to find the monthly payment on the given loan.

13) amount: $63,000; rate: 6%; time: 30 years A) $338.31 B) $378.00

13) C) $462.42

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D) $451.08

For an amortized loan, you are given the loan, annual interest rate, and length of the loan. Find the monthly payment necessary to pay off the loan.

14) amount: $3600; rate 11%; time: 3 years.

14) A) $217.86 B) $112.36 C) $117.86 D) $143.36 Find percent notation.

15) 0.91 A) 910%

15) B) 91%

C) 0.091%

D) 9.1%

You are given the principal, the annual interest rate, and the compounding period. Determine the value of the account at the end of the specified time period.

16) $2100, 8%, monthly, 2 years 16) A) $13,316.48 B) $2128.09 C) $2449.44 D) $2463.06 Find percent notation.

17) 9.0 A) 900%

17) B) 90%

C) 0.009%

D) 0.9%

Solve the problem.

18) Use the table to find the APR to the nearest whole percent. Assume that all interest rates are annual rates.

Number of Payments 6 12 24 36 48

10%

11%

12%

$2.94 $5.50 $10.75 $16.16 $21.74

$3.23 $6.06 $11.86 $17.86 $24.06

APR 13%

14%

Finance Charge per $100 $3.53 $3.83 $4.12 $6.62 $7.18 $7.74 $12.98 $14.10 $15.23 $19.57 $21.30 $23.04 $26.40 $28.77 $31.17

15%

16%

$4.42 $8.31 $16.37 $24.80 $33.59

$4.72 $8.88 $17.51 $26.57 $36.03

18)

Amanda has agreed to pay off a $4100 loan by making 12 monthly payments. The total finance charge on her loan is $328.

A) 12% B) 15% C) 14% D) 13% Solve the problem. Round to the nearest hundredth.

19) What is 89% of 298?

A) 26.52 B) 2652.20

C) 265.22

D) 26,522.00

Find percent notation.

20) 0.128 A) 128%

C) 0.0128%

D) 12.8%

x10 - 1

x11 - 1

19)

20) B) 0.128%

Simplify the given algebraic expression.

21) x9 + x8 + ... + x3 + x2 + x + 1 A)

x9 - 1 x+1

B)

21) x9 - 1 x-1

C)

x-1

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D)

x-1

Solve the problem.

22) Kevin buys a motorcycle for $8000. The dealer is charging him an annual interest rate of 9.75%. If he pays off the loan in 108 months, what are his monthly payments? If he makes a down payment of $2700, how much will his monthly payments be?

A) $139.07; $186.01 B) $139.07; $92.14 C) $278.15; $92.14 D) $139.07; $184.27 23) Use the table to find the APR to the nearest whole percent. Assume that all interest rates are annual rates.

Number of Payments 6 12 24 36 48

10%

11%

12%

$2.94 $5.50 $10.75 $16.16 $21.74

$3.23 $6.06 $11.86 $17.86 $24.06

APR 13%

14%

Finance Charge per $100 $3.53 $3.83 $4.12 $6.62 $7.18 $7.74 $12.98 $14.10 $15.23 $19.57 $21.30 $23.04 $26.40 $28.77 $31.17

15%

16%

$4.42 $8.31 $16.37 $24.80 $33.59

$4.72 $8.88 $17.51 $26.57 $36.03

22)

23)

Sue took out a 24-month, $19,000 add-on loan at an interest rate of 8.1% to pay off her SUV. A) 14% B) 13% C) 16% D) 15% Find decimal notation.

24) 497% A) 4.98

24) B) 4.97

C) 49.7

D) 0.497

C) $614.60

D) $720.30

Use the table to find the monthly payment on the given loan.

25) amount: $70,000; rate: 10%; time: 30 years A) $675.50 B) $513.80

25)

Solve the problem.

26) Maya bought a car for $11,000. To pay for it, she took a bank add-on interest loan at an annual interest rate of 10.5%. The loan term is 7 years. How much interest will she pay and what are her monthly payments?

A) $8085.00; $340.80 B) $8085.00; $454.40 C) $8185; $227.20 D) $8085.00; $227.20

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26)

Find decimal notation.

27) 0.1% A) 0.002

27) B) 0.1

C) 0.001

D) 0.01

You are given the principal, the annual interest rate, and the compounding period. Determine the value of the account at the end of the specified time period.

28) 28) $15,000, 9%, yearly, 6 years A) $25,656.50 B) $26,156.50 C) $25,856.50 D) $25,156.50 Solve the problem.

29) Anne purchased a bond for a museum valued at $8000 for $2400. If the bond pays 5.5% annual interest compounded monthly, how long must she hold it until it reaches its full face value?

A) 23.94 years B) 19.94 years C) 20.94 years D) 21.94 years

29)

Use the unpaid balance method to find the finance charge on the credit card account. The last monthʹs balance and any other transactions are given.

30) Last monthʹs balance, $505; payment, $206; interest rate, 20%; bought camera, $84; bought jacket, 30) $126 A) $517.42 B) $12.70 C) $15.49 D) $8.62 Find decimal notation.

31) 97.12% A) 9.712

31) B) 0.9612

C) 0.09712

D) 0.9712

Solve the problem.

32) Find the monthly payment, m, needed to have a sinking fund accumulate the future value, $ 15,000.

The yearly interest rate is 9.7% and the number of payments is 20. Interest is compounded monthly. Round your answer to the nearest cent.

A) $694.03 B) $994.03 C) $444.03 D) $944.03 Solve the given equation.

33) x4 = 37 A) 2.4663

33) B) 9.25

C) 6.0828

D) 18.5

Solve using the formula for the future value of an ordinary annuity.

34) Find the value of the annuity at the end of the indicated time period. The amount, frequency of deposits, annual interest rate, and time period are given. amount: $200; monthly; 10%; 7 years A) $24,790.21 B) $24,590.10 C) $24,190.08 D) $24,890.20 Solve the problem. Round to the nearest hundredth.

35) 56 is 30% of what number?

A) 16.80 B) 186.67

A)

x-1

B)

34)

35) C) 18.67

D) 1866.70

x4 +1

x4 - 1

Simplify the given algebraic expression.

36) x3 + x2 + x + 1 x4 - 1

32)

36) x3 - 1 x-1

C)

x-1

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D)

x+1

Solve the problem.

37) Students at Maple School earned $540 selling candles. They want to accumulate $2000 for a club trip. What percent of their goal has been reached?

A) 40% B) 4% C) 0.27% D) 27%

37)

Increasing the down payment on a mortgage reduces both the size of the monthly payments and the total interest paid.

Calculate the reduction in the monthly payment by increasing the down payment by the amount specified, and the amount saved on interest over the life of the loan. Assume the mortgage is for 20 years and use the table to find the monthly payments.

38)

Amount Interest of Loan Rate $187,000 8% A) $96.50, $23,160.00 C) $73.40, $17,616.00

Find decimal notation.

39) 0.067% A) 0.00067

Down Payment $38,000

Increase in Down Payment $10,000 B) $83.60, $20,064.00 D) $71.60, $17,184.00

38)

39) B) 0.0067

C) 6.7

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D) 0.000067

The annual interest rate and a line of an amortization schedule for a loan are given. Complete the next line of the schedule. Assume that payments are made monthly.

Annual Interest Paid on Interest Rate Payment Paid Principal Balance 40) 40) 8% $160.89 $14.57 $146.32 $2857.22 ? ? ? ? ?

Annual A) Interest Rate 8%

Payment $141.84

Interest Paid $19.05

Paid on Principal $160.89

Balance $2696.33

Annual B) Interest Rate 8%

Payment $160.89

Interest Paid $19.05

Paid on Principal $141.84

Balance $2715.38

Annual C) Interest Rate 8%

Payment $160.89

Interest Paid $14.57

Paid on Principal $146.32

Balance $2710.90

Annual D) Interest Rate 8%

Payment $19.05

Interest Paid $141.84

Paid on Principal $160.89

Balance $2715.38

Solve the problem.

41) Carol has a bail bondsman post a bail of $5000 for her trial that will take place in 4 months. The bondsman charges a $110 fee plus 7% of the bail. What interest rate is being charged by the bail bondsman?

A) 55.2% B) 27.6% C) 7% D) 36.8% Use the formula for simple interest, I = P × r × t, to find the missing quantity.

42) P = $5500; r = 6%; t = 3 years A) I = $990 B) I = $1190 C) I = $9900

Copyright © 2022 Pearson Education, Inc.

41)

42) D) I = $99,000

Solve the problem. Use the given table to find monthly payments.

43) Jesseʹs new snowmobile cost $10,000. After his down payment of $3000, he financed the remainder at 6% for 4 years. Find the monthly payment for the amortized loan, and find the total interest paid on the loan. Assume that all interest rates are annual rates.

A) $161.21; $738.08 B) $164.43; $892.64 C) $164.43; $7000.00 D) $212.94; $3221.12

43)

For an amortized loan, you are given the loan, annual interest rate, and length of the loan. Find the monthly payment necessary to pay off the loan.

44) amount: $2200; rate 6%; time: 15 years.

44) A) $18.56 B) $16.21 C) $16.61 D) None of the above Use the average daily balance method to compute the finance charge on the credit card for the previous month.

45) Month: July (31 days) 45) Previous monthʹs balance: $780 Interest rate: 20% Date Transaction July 5 made payment of $208 July 15 charged $45 for groceries July 20 charged $87 for golf equipment July 27 charged $69 for school supplies A) $9.64 B) $9.79 C) $10.00 D) $11.35 Use the formula for simple interest, I = P × r × t, to find the missing quantity.

46) I = $832; r = 8%; t = 4 years A) P = $2900 B) P = $2800 C) P = $2600

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46) D) P = $2700

Use the table to find the monthly payment on the given loan.

47) amount: $29,000; rate: 8%; time: 20 years A) $207.64 B) $212.86

47) C) $242.44

D) $351.77

C) 2

D) 1.3333

Solve the given equation.

48) x3 = 4 A) 1.5874

48) B) 64

Solve using the formula for the future value of an ordinary annuity.

49) Given the monthly payment, R, the annual interest rate, r, and the number of monthly payments, nt, find the future value of the annuity.

R = $1300; r = 8.5%; nt = 17 A) $23,397.81 B) $24,198.38 C) $17,548.36 D) $24,398.04 Solve the problem.

50) 9 x = 100 A) 0.4771

49)

50) B) 2.0959

C) 3.0959

Copyright © 2022 Pearson Education, Inc.

D) 2.8459

Answer Key Testname: CHAPTER 8 EXAM A

1) B 2) D 3) C 4) C 5) A 6) C 7) C 8) D 9) D 10) B 11) B 12) A 13) B 14) C 15) B 16) D 17) A 18) C 19) C 20) D 21) C 22) B 23) D 24) B 25) C 26) D 27) C 28) D 29) D 30) D 31) D 32) A 33) A 34) C 35) B 36) A 37) D 38) B 39) A 40) B 41) B 42) A 43) B 44) A 45) D 46) C 47) C 48) A 49) A 50) B Copyright © 2022 Pearson Education, Inc.

Chapter 8 Exam B Name___________________________________

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

For an amortized loan, you are given the loan, annual interest rate, and length of the loan. Find the monthly payment necessary to pay off the loan.

1) amount: $3600; rate 12%; time: 4 years.

1) Solve the given equation.

2) 7 x = 20

2)

Solve using the formula for the future value of an ordinary annuity.

3) Starting in January, you make monthly payments at the end of each month into an account paying the specified yearly interest. Interest is compounded monthly. How much will you have available by the specified date? monthly payment, $225; yearly interest rate, 3%; date, August 1

3)

Solve the problem. Use the given table to find monthly payments.

4) Jesseʹs new snowmobile cost $11,000. After his down payment of $2000, he financed the remainder at 6% for 4 years. Find the monthly payment for the amortized loan, and find the total interest paid on the loan. Assume that all interest rates are annual rates.

4)

Find the effective interest rate for the specified account.

5) nominal yield, 9%; compounded daily

5)

Simplify the given algebraic expression.

6) x9 + x8 + ... + x3 + x2 + x + 1

6)

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Use the average daily balance method to compute the finance charge on the credit card for the previous month.

7) Month: April (30 days) 7) Previous monthʹs balance: $960 Interest rate: 20% Date Transaction April 3 charged $100 for phone bill April 12 made payment of $340 April 21 charged $91 for electricity bill April 29 returned $65 for lawn service Simplify the given algebraic expression.

8) x3 + x2 + x + 1

8)

Given the current cost of an item and the inflation rate, find the cost of the item in the specified number of years.

9) Car insurance: $550, inflation rate: 2%, after 10 years 9) Use the table to find the monthly payment on the given loan.

10) amount: $90,000; rate: 8%; time: 10 years Find decimal notation.

11) 60%

10)

11)

Use the unpaid balance method to find the finance charge on the credit card account. The last monthʹs balance and any other transactions are given.

12) Month: April (30 days) 12) Previous monthʹs balance: $450 Interest rate: 19% Date Transaction April 3 charged $110 for phone bill April 12 made payment of $200 April 21 charged $63 for electricity bill April 29 charged $87 for lawn service

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Find the present value of the annuity. Assume that all interest rates are annual rates.

13) Genie has agreed to contribute $36 per month for the next 2 years toward a new park in town. Assuming an interest rate of 6.5%, how much must she contribute now if she decides to make one lump sum contribution?

13)

Find percent notation.

14) 0.009

14)

Find the effective interest rate for the specified account.

15) nominal yield, 6%; compounded monthly

15)

Find the present value of the annuity. Assume that all interest rates are annual rates.

16) If Peter can afford car payments of $205 per month for 6 years, what is the price of a car that he can afford now? Assume an interest rate of 5.5%.

16)

Use the table to find the monthly payment on the given loan.

17) amount: $6000; rate: 5%; time: 4 years

17)

Solve the problem. Round to the nearest hundredth.

18) 13.54 is what percent of 121?

18)

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Use the table to find the monthly payment on the given loan.

19) amount: $160,000; rate: 4%; time: 10 years Solve the problem. Round to the nearest hundredth.

20) What is 31% of 1529?

19)

20)

Use the table to find the monthly payment on the given loan.

21) amount: $120,000; rate: 12%; time: 20 years Solve the problem.

22) Emily is buying a new table for $1400. The dealer is charging her an annual interest rate of 10.7%. If she pays off the loan in 36 months, what are her monthly payments? If she makes a down payment of $220, how much will her monthly payments be?

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21)

22)

Solve the problem. Use the given table to find monthly payments.

23) Harold took out a 4-year amortized loan for $21,000 at 10% to pay his tuition at a technical institute. After 1 year, he refinanced the unpaid balance of $16,505 at a 6% interest rate. Find the monthly payment on the original loan; the monthly payment on the new loan; and total amount saved on interest by refinancing. All interest rates are annual interest rates.

23)

Find percent notation.

24) 0.14

24)

Solve the problem.

25) The price of a printer was reduced from $400 to $ 240. What was the percent of decrease?

25)

Use the compound interest formula A = P(1 + r) t and the given information to find the missing quantity.

26) 26) A = $8992.38 P = $5600 r= % (Round to the nearest percent.) t = 7 yr

Solve the problem.

27) Find the monthly payment, m, needed to have a sinking fund accumulate the future value, $16,000. The yearly interest rate is 10.5% and the number of payments is 18. Interest is compounded monthly. Round your answer to the nearest cent.

Use the formula for simple interest, I = P × r × t, to find the missing quantity.

28) I = $972; P = $5400; r = 6% Solve the problem.

29) Maya bought a car for $14,000. To pay for it, she took a bank add-on interest loan at an annual interest rate of 11%. The loan term is 7 years. How much interest will she pay and what are her monthly payments?

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27)

28)

29)

Estimate the annual percentage rate for the add -on loan using the given number of payments and annual interest rate.

2nr .

Use the formula APR ≈ n+1 30) n=30; r =5.1%

30)

Solve the problem.

31) Tracy wants to save $35,000 for a down payment towards a house. She puts $27 every month in an annuity that has a 7% annual interest rate. How long will it take her to save for the down payment? Round your answer to the nearest month.

31)

You are given the principal, the annual interest rate, and the compounding period. Determine the value of the account at the end of the specified time period.

32) $11,000, 10%, yearly, 9 years 32) Given the current cost of an item and the inflation rate, find the cost of the item in the specified number of years.

33) Milk: $2.93, inflation rate: 3.5%, after 5 years 33) Find the effective interest rate for the specified account.

34) nominal yield, 10%; compounded twice a year

34)

Solve the problem.

35) 2 x = 1000

35)

Increasing the down payment on a mortgage reduces both the size of the monthly payments and the total interest paid.

Calculate the reduction in the monthly payment by increasing the down payment by the amount specified, and the amount saved on interest over the life of the loan. Assume the mortgage is for 20 years and use the table to find the monthly payments.

36)

Amount of Loan $177,000

Interest Rate 8%

Down Payment $39,000

Increase in Down Payment $11,000

36)

37)

Amount of Loan $253,000

Interest Rate 5%

Down Payment $58,000

Increase in Down Payment $22,000

37)

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Solve the given equation.

38) x2 = 24

38)

Find decimal notation.

39) 100%

39)

Find percent notation.

40) 0.568

40)

Use the formula for simple interest, I = P × r × t, to find the missing quantity.

41) P = $2500; r = 6%; t = 4 years

41)

Solve the problem.

42) Find the finance charge per $100 for a loan of $ 3500 with a finance charge of $910.

42)

You are given the principal, the annual interest rate, and the compounding period. Determine the value of the account at the end of the specified time period.

43) 43) $2700, 8%, monthly, 2 years Solve the problem.

44) All 36 of the students in a mathematics class attended class on Monday. On Tuesday only 31 students attended. What was the percent of decrease?

Use the formula for simple interest, I = P × r × t, to find the missing quantity.

45) I = $1260; r = 7%; t = 6 years

44)

45)

Given the current cost of an item and the inflation rate, find the cost of the item in the specified number of years.

46) 46) College tuition: $20,000.00, inflation rate: 2.2%, after 7 years The annual interest rate and a line of an amortization schedule for a loan are given. Complete the next line of the schedule. Assume that payments are made monthly.

Annual Interest Paid on Paid Principal Balance 47) 47) Interest Rate Payment 9% $184.24 $33.21 $151.03 $2635.70 ? ? ? ? ?

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Solve the problem.

48) Use the following table to calculate the federal income tax due for the taxable income $ 239,750.

If your taxable income is over Line 1 $0 Line 2 9,275 Line 3 37,650 Line 4 91,150 Line 5 190,150 Line 6 413,350 Line 7 415,050

But not over $9,275 37,650 91,150 190,150 413,350 415,050 ...

The tax is $0 + 10% 927.50 + 15% 5,183.75 + 25% 18,558.75 + 28% 46,278.75 + 33% 119,934.75 + 35% 120,529.75 + 39.6%

48)

Of the amount over $0 9,275 37,650 91,150 190,150 413,350 415,050

Find decimal notation.

49) 0.2%

49)

Solve the problem. Round to the nearest hundredth.

50) 24 is 5% of what number?

50)

Copyright © 2022 Pearson Education, Inc.

Answer Key Testname:

1) $94.80 2) 1.5395 3) $1586.86 4) $211.41; $1147.68 5) 9.42% x10 - 1 6) x-1 7) $14.20 x4 - 1 8) x-1 9) $670.45 10) $1091.70 11) 0.6 12) $8.19 13) $808.15 14) 0.9% 15) 6.17% 16) $12,547.52 17) $138.18 18) 11.19% 19) $1619.20 20) 473.99 21) $1321.20 22) $51.37; $43.30 23) $532.56; $502.08; $1097.28 24) 14% 25) 40% 26) 7% 27) $824.60 28) t = 3 years 29) $10,780.00; $295.00 30) 9.87% 31) 369 months 32) $25,937.42 33) $3.48 34) 10.25% 35) 9.9658 36) $91.96, $22,070.40 37) $145.20, $34,848.00 38) 4.899 39) 1 40) 56.8% 41) I = $600 42) $26 43) $3166.80 44) 13.9% 45) P = $3000 46) $23,290.90 Copyright © 2022 Pearson Education, Inc.

Answer Key Testname:

Annual 47) Interest Rate 9%

Payment $184.24

Interest Paid $19.77

Paid on Principal $164.47

Balance $2471.23

48) $62,646.75 49) 0.002 50) 480.00

Copyright © 2022 Pearson Education, Inc.

Chapter 9 Exam A Name___________________________________

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Provide an appropriate response. Round your answer to the nearest hundredth if necessary.

1) How many line segments will the Koch curve have in step 9?

A) 262,144 B) 262,145 C) 36 D) 13 Give the measure of the requested angle.

2) The complement of angle x is two times the angle. Find the measure of the angle and its complement.

A) 45° and 90° B) 60° and 120° C) 30° and 60° D) 22.5° and 67.5° Find the area. Use 3.14 for π as necessary.

3) 26 ft 20 ft 43 ft A) 200 ft2 Convert the units.

4) 2.55 m = A) 255 cm

1)

2)

3)

B) 430 ft2

C) 260 ft2

D) 860 ft2

B) 25.5 cm

C) 0.255 cm

D) 0.0255 cm

cm

4)

Give the measure of the requested angle.

5) The supplement of angle x is 60° more than twice the complement of angle x. Find the measure of angle x.

A) 40° B) 120° C) 30° D) 60°

Copyright © 2022 Pearson Education, Inc.

5)

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Reflect the figure about the indicated axis of reflection on the graph.

6) Reflect the figure about line segment A. 10

6)

y

9 8 7 6 5 4 3 2 1 -10 -9

-8

-7

-6

-5

-4

-3

-2

-1

1

2

3

4

5

6

7

8

9

10

x

-1 -2 -3 -4

A

-5 -6 -7 -8 -9 -10

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Find the area of the triangle using Heronʹs formula. Round your answer to two decimal places as needed.

7) 12 in.

20 in.

A) 67.88 in.2

7)

16 in.

B) 96 in. 2

C) 24 in.2

Convert the temperature. Give your answer to the nearest tenth of a degree.

8) -34°C = °F A) -29.2°F B) 36.7°F C) -61.2°F

Copyright © 2022 Pearson Education, Inc.

D) 33.94 in. 2

8) D) -18.9°F

Find the area. Use 3.14 for π as necessary.

9) 22 m

9)

26 m

A) 96 m 2 Find the requested angle.

10) Complement of 11° A) 22°

B) 572 m 2

C) 48 m 2

D) 1144 m 2

B) 79°

C) 169°

D) 349°

10)

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Perform the indicated operation.

11) Translate the figure by vector A.

11)

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MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Refer to the figure and provide an appropriate name for the indicated angles.

12) ∠2 and ∠7 A) Corresponding angles C) Alternate interior angles Convert the units.

13) 3 kg =

12) B) Alternate exterior angles D) Complementary Angles

mg

A) 300 mg

13) B) 3,000,000 mg

C) 0.03 mg

Solve the problem.

14) What is the angle sum of a regular polygon with 7 sides?

A) 900° B) 450° C) 1260°

D) 0.003 mg

14) D) 1350°

Provide an appropriate response.

15) Solve 4 D = 11.

A) 2.40

15) B) 1.39

C) 1.73

D) 0.58

Describe the rigid motion(s) that would be used to transform the above figure into the figure shown below.

16) 16)

A) Reflect about diagonal axis B) Rotate 90°, then reflect about vertical axis C) Rotate 90°, then reflect about horizontal axis D) Impossible to solve

Copyright © 2022 Pearson Education, Inc.

Find the area of the triangle. Round your answer to two decimal places as needed.

17) 26 in.

22 in.

17)

24 in.

A) 92 in.2 Convert the units.

18) 49 kg =

B) 460 in.2

C) 230 in. 2

D) 120 in.2

B) 0.49 g

C) 0.049 g

D) 4900 g

g

18)

A) 49,000 g

Refer to the figure and provide an appropriate name for the indicated angles.

19) ∠4 A) Obtuse angle

19) B) Right angle

C) Vertical angle

D) Acute angle

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Rotate the figure about the point as indicated.

20) Rotate the figure 180° about point A.

20)

15 14 13 12 11 10 9 8 A

7 6 5 4 3 2 1 1

2

3

4

5

6

7

8

9

10 11 12 13 14 15

Copyright © 2022 Pearson Education, Inc.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Refer to the figure and provide an appropriate name for the indicated angles.

21) ∠1 and ∠4 A) Corresponding angles C) Alternate interior angles

21) B) Vertical angles D) Alternate exterior angles

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Rotate the figure about the point as indicated.

22) Rotate the figure -90° about point A.

22)

15 14 13 12 11 10 9 8 A

7 6 5 4 3 2 1 1

2

3

4

5

6

7

8

9

10 11 12 13 14 15

Copyright © 2022 Pearson Education, Inc.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Find the surface area of the figure.

23)

a = 3 ft, b = 4 ft, c = 3 ft A) 72 ft2

23)

B) 33 ft2

C) 54 ft2

D) 66 ft2

Choose the most reasonable unit of measure.

24) Hammer length 30 (mm, cm, m, km) A) m

24)

B) mm

C) km

D) cm

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Reflect the figure about the indicated axis of reflection on the graph.

25) Reflect the figure about line segment B, then about line segment A.

25)

y 10 9 8 7 6

B

5 4 3 2 1

A -10 -9

-8

-7

-6

-5

-4

-3

-2

-1

1

2

3

4

5

6

7

8

9

-1 -2 -3 -4 -5 -6 -7 -8 -9 -10

Copyright © 2022 Pearson Education, Inc.

10

x

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Find the area of the figure on the geoboard. Assume that the dots are 1 inch apart.

26)

A) 12 in.2

B) 13 in. 2

C) 10 in.2

26)

D) 14 in. 2

Solve the problem.

27) A spherical storage tank has a diameter of 24 ft and is full of water. How many delivery trucks with cylindrical tanks measuring 4 ft in diameter and 10 ft long can be completely filled from the storage tank?

A) 576 trucks B) 57 trucks C) 115 trucks D) 43 trucks Use similar figures to determine the value of X .

28)

27)

28)

156 cm 13 cm 52 cm A) 117 cm

B) 26 cm

C) 78 cm

Convert the temperature. Give your answer to the nearest tenth of a degree.

29) 8°C = °F A) 30.0°F B) 46.4°F C) 72.0°F

D) 39 cm

29) D) 36.4°F

Find the area of the triangle using Heronʹs formula. Round your answer to two decimal places as needed.

30)

8m 4m 6m A) 16.43 m 2

B) 5.81 m 2

C) 8.22 m 2

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D) 11.62 m 2

30)

Choose the most reasonable unit of measure.

31) Paperback book height 19 (mm, cm, m, km) A) km

B) m

31) C) mm

D) cm

Refer to the figure and provide an appropriate name for the indicated angles.

32) ∠3 and ∠7 A) Complementary angles C) Supplementary angles

32) B) Alternate exterior angles D) Alternate interior angles

Find the area of the triangle. Round your answer to two decimal places as needed.

33)

33)

12 ft 10 ft

10 ft

A) 8 ft2

B) 33.17 ft2

Find the measures of angles A, B, and C in △ABC. 34) m∠B = 3m∠A m∠C = m∠A + 105 B) 10°, 30°, 140° A) 14°, 42°, 124°

C) 66.33 ft2

D) 132.66 ft2

34) C) 10°, 30°, 115°

D) 15°, 45°, 120°

Determine whether perimeter or area is the most appropriate measure needed for a solution.

35) You want to install motion detectors around your property line to detect intruders.

A) Area B) Perimeter Find the area of the triangle. Round your answer to two decimal places as needed.

36)

36)

15 m 12 m A) 99 m 2

21 m B) 247.5 m 2

C) 297 m 2

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35)

D) 148.5 m 2

Find the surface area of the figure.

37)

37)

a = 6 ft A) 36 ft2

B) 108 ft2

C) 144 ft2

Convert the temperature. Give your answer to the nearest tenth of a degree. °C 38) -15°F = A) -27.0°C B) 5.0°C C) -26.1°C

D) 216 ft2

38) D) -8.3°C

Find the area of the shaded region of the figure. Use 3.14 for π as necessary.

39)

39)

4 in.

12 in.

A) 24 in.2 Convert the units.

40) 417 mL = A) 0.417 L

B) 16 in. 2

C) 40 in.2

D) 48 in. 2

L

40) B) 4.17 L

C) 41,700 L

D) 417,000 L

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Determine whether the figure is a polygon. If the figure is not a polygon, state what part of the definition fails.

41) 41)

Copyright © 2022 Pearson Education, Inc.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Find the volume of the figure.

42)

42)

Area = 62 sq. in.

7 in.

A) 62 in.3

B) 434 in.3

C) 3038 in. 3

D) 26,908 in.3

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Determine whether the figure is a polygon. If the figure is not a polygon, state what part of the definition fails.

43) 43)

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Find the missing length in the right triangle. If necessary, round to the nearest tenth.

44)

44)

8 cm

17 cm A) 176.5 cm

B) 12.5 cm

C) 353.0 cm

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D) 18.8 cm

Refer to the figure and provide an appropriate name for the indicated angles.

45) ∠2 and ∠8 A) Complementary Angles C) Alternate interior angles

45) B) Alternate exterior angles D) Corresponding angles

Solve the problem.

46) One kitchen ladle has a diameter of 3 in. Another has a diameter of 4 in. Do you get a larger portion in one serving from the larger ladle or two servings from the smaller ladle? (Both are hemispherically shaped.)

A) Two from the smaller B) One from the larger C) They are the same D) Not enough information to solve

46)

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Perform the indicated operation.

47) Reflect the figure about line segment B, then glide it by vector A.

Copyright © 2022 Pearson Education, Inc.

47)

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Find the area of the figure on the geoboard. Assume that the dots are 1 inch apart.

48)

A) 7 in.2

B) 10 in. 2

C) 8 in.2

48)

D) 9 in. 2

Describe the rigid motion(s) that would be used to transform the above figure into the figure shown below.

49) 49)

A) Rotate 90°, then reflect about vertical axis C) Reflect about diagonal axis

B) Rotate 180° D) Impossible to solve

Solve the problem.

50) A water delivery truck with a cylindrical tank measuring 8 ft in diameter and 8 ft long dispenses water to drought victims in cartons measuring 6 in. × 6 in. × 12 in. How many victims will get a full container of water?

A) 1608 people B) 804 people C) 402 people D) 201 people

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50)

51) A gazebo is designed with 5 sides, and a roof truss runs from each corner to the center. You make two cuts on the end of each truss so that a point is formed as illustrated. What angle (to the nearest degree) must each cut be so that the trusses fit together in the center of the roof?

A) 72°

B) 54°

C) 108°

51)

D) 90°

Decide whether the statement is true or false.

52) The sum of the interior angles of a regular heptagon is 900 °.

A) False B) True

52)

Give the measure of the requested angle.

53) The supplement plus the complement of the angle x is equal to 170°. Find the measure of angle x.

A) 130° B) 50° C) 40° D) 85°

53)

Solve the problem.

54) A tree casts a shadow that is 60 ft long when a 5 ft tall woman casts a shadow of 9 ft. How tall is the tree?

1 B) 45 ft C) 60 ft D) 108 ft A) 33 ft 3 Find the height of the triangle using Heronʹs formula. Round your answer to two decimal places as needed.

55)

15 in.

15 in.

X in.

10 in.

A) 4 in.

B) 2.83 in.

C) 10 in.

Copyright © 2022 Pearson Education, Inc.

D) 14.14 in.

54)

55)

Answer Key Testname: CHAPTER 9 EXAM A

1) A 2) C 3) B 4) A 5) D 6) 10

y

9 8 7 6 5 4 3 2 1 -10 -9

-8

-7

-6

-5

-4

-3

-2

-1

1

2

3

4

5

6

7

8

9

10

-1 -2 -3 -4

A

-5 -6 -7 -8 -9 -10

7) B 8) A 9) B 10) B

Copyright © 2022 Pearson Education, Inc.

x

Answer Key Testname: CHAPTER 9 EXAM A

11)

12) A 13) B 14) A 15) C 16) B 17) C 18) A 19) A

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Answer Key Testname: CHAPTER 9 EXAM A

20) 15 14 13 12 11 10 9 8 7

A

6 5 4 3 2 1 1

2

3

4

5

6

7

8

9

10 11 12 13 14 15

9

10 11 12 13 14 15

21) B 22) 15 14 13 12 11 10 9 8 7

A

6 5 4 3 2 1 1

2

3

4

5

6

7

8

23) D 24) D

Copyright © 2022 Pearson Education, Inc.

Answer Key Testname: CHAPTER 9 EXAM A

25) y 10 9 8 7 6

B

5 4 3 2 1

A -10 -9

-8

-7

-6

-5

-4

-3

-2

-1

1

2

3

4

5

6

7

8

9

10

-1 -2 -3 -4 -5 -6 -7 -8 -9 -10

26) A 27) B 28) D 29) B 30) D 31) D 32) D 33) C 34) D 35) B 36) D 37) D 38) C 39) A 40) A 41) Yes 42) B 43) No; no line segments 44) D 45) B 46) B

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x

Answer Key Testname: CHAPTER 9 EXAM A

47)

48) C 49) B 50) A 51) B 52) B 53) B 54) A 55) D

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Chapter 9 Exam B Name___________________________________

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Find the volume of the figure.

1) Use 3.14 for π.

1)

8.5 yd

19 yd

Choose the most reasonable unit of measure. (mm, cm, m, km) 2) Paperback book height 21

2)

Find the surface area of the figure.

3)

3)

a = 2 ft, b = 3 ft, c = 2 ft

Describe the rigid motion(s) that would be used to transform the above figure into the figure shown below.

4) 4)

Copyright © 2022 Pearson Education, Inc.

Refer to the figure and provide an appropriate name for the indicated angles.

5) ∠2 and ∠1

5)

6) ∠6 and ∠7

6)

Find the area of the triangle. Round your answer to two decimal places as needed.

7) 39 in.

33 in.

7)

36 in.

Convert the units.

8) 179 mm =

cm

8)

Solve the problem.

9) A tree casts a shadow that is 60 ft long when a 5 ft tall woman casts a shadow of 6 ft. How tall is the tree?

9)

Make an approximate conversion as indicated. Round to the nearest tenth. The precise value of your approximation will depend on the conversion path that you choose.

10) 0.75 kg = oz 10) Find the area. Use 3.14 for π as necessary.

11) 5 ft

11)

4 ft

10 ft

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Reflect the figure about the indicated axis of reflection on the graph.

12) Reflect the figure about the x-axis.

10

12)

y

9 8 7 6 5 4 3 2 1 -10 -9

-8

-7

-6

-5

-4

-3

-2

-1

1

2

3

4

5

6

7

8

9

10

x

-1 -2 -3 -4 -5 -6 -7 -8 -9 -10

Choose the most reasonable unit of measure. (mm, cm, m, km) 13) Basketball court length 26

13)

Solve the problem.

14) What is the angle sum of a regular polygon with 12 sides?

14)

Find the height of the triangle using Heronʹs formula. Round your answer to two decimal places as needed.

15) 15)

12 mm

8 mm X mm 16 mm

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Find the volume of the figure.

16) Use 3.14 for π. Round your answer to the nearest thousandth if necessary.

16)

radius = 3.0 yd Decide whether the statement is true or false.

17) A circle is an irregular polygon.

17)

Refer to the figure and provide an appropriate name for the indicated angles.

18) ∠4 and ∠7

18)

Find the missing length in the right triangle. If necessary, round to the nearest tenth.

19) 4 cm

19)

11 cm

Find the missing measurement in the figure.

20) Arc AC = 4 m, Circumference = 72 m, ∠B = ?

Determine whether perimeter or area is the most appropriate measure needed for a solution.

21) You want to order enough seed to plant a corn field.

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20)

21)

Find the surface area of the figure.

22)

22)

a = 11 ft Choose the most reasonable unit of measure. (mg, g, kg) 23) Weight of a quarter 12 Find the area of the shaded region of the figure. Use 3.14 for π as necessary.

24) 9 ft

23)

24)

9 ft

18 ft Make an approximate conversion as indicated. Round to the nearest tenth. The precise value of your approximation will depend on the conversion path that you choose.

25) 184 mi = km 25)

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Reflect the figure about the indicated axis of reflection on the graph.

26) Reflect the figure about line segment A, then about line segment B.

26)

y 10 9 8 7 6

B

5

A

4 3 2 1 -10 -9

-8

-7

-6

-5

-4

-3

-2

-1

1

2

3

4

5

6

7

8

9

10

x

-1 -2 -3 -4 -5 -6 -7 -8 -9 -10

Convert the units.

27) 3.43 m =

cm

27)

Make an approximate conversion as indicated. Round to the nearest tenth. The precise value of your approximation will depend on the conversion path that you choose. in.

28) 28) 5.8 m = Find the volume of the figure.

29)

29)

3m 5m

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Provide an appropriate response. Round your answer to the nearest hundredth if necessary.

30) Steps 0 and 1 for constructing a fractal are given below. Assume that the length of the line segment in step 0 is 1. Find the length of the curve in step 8.

Solve the problem. Round to the nearest hundredth if necessary.

31) The windshield wiper on a car sweeps in the pattern depicted in the figure. The wiper blade is 21 in. long, but the blade does not cover the first 7 in. of the pattern. How long is the arc at each end of the blade?

30)

31)

21 in.

7 in.

32) In the figure, if the pattern continues, what is the expression for the hypotenuse of the fourth segment? What is the expression for the hypotenuse of the n th segment?

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32)

Rotate the figure about the point as indicated.

33) Rotate the figure 180° about point A.

33)

15 14 13 12 11 10 9 8 A

7 6 5 4 3 2 1 1

2

3

4

5

6

7

8

9

10 11 12 13 14 15

Provide an appropriate response. Round your answer to the nearest hundredth if necessary.

34) What is the length of the Koch curve have at step 8?

34)

Make an approximate conversion as indicated. Round to the nearest tenth. The precise value of your approximation will depend on the conversion path that you choose. g 35) 35) 6 lb = Determine whether the figure is a polygon. If the figure is not a polygon, state what part of the definition fails.

36) 36)

Find the missing measurement in the figure.

37) ∠B = 45°, Arc AC = 14 cm, Circumference = ?

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37)

Determine whether it is true or false that the described rigid movement(s) will produce a figure with symmetry to the figure shown.

38) 38) Rotate 90°, then reflect about axis L

Find the area of the figure on the geoboard. Assume that the dots are 1 inch apart.

39)

39)

Determine whether it is true or false that the described rigid movement(s) will produce a figure with symmetry to the figure shown.

40) Rotate 180° 40)

Convert the units.

41) 315 mL =

L

41)

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Describe the rigid motion(s) that would be used to transform the above figure into the figure shown below.

42) 42)

Reflect the figure about the indicated axis of reflection on the graph.

43) Reflect the figure about line segment B, then about line segment A.

43)

y 10 9 8 7 6

B

5 4 3 2 1

A -10 -9

-8

-7

-6

-5

-4

-3

-2

-1

1

2

3

4

5

6

7

8

9

-1 -2 -3 -4 -5 -6 -7 -8 -9 -10

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10

x

Find the height of the triangle using Heronʹs formula. Round your answer to two decimal places as needed.

44) 44) 9 cm

12 cm X cm 15cm

Refer to the figure and provide an appropriate name for the indicated angles.

45) ∠5

45)

Solve the problem.

46) You place a mirror on the ground 100 ft away from a flag pole. You then back up from the mirror until you see the top of the flag pole in the mirror. If the distance from your eyes to the ground is 5 ft and you are standing 13 ft from the mirror, how tall is the flag pole to the nearest foot?

Provide an appropriate response. Round your answer to the nearest hundredth if necessary.

47) How many line segments will the Koch curve have in step 7?

Give the measure of the requested angle.

48) The supplement of angle x is 50° less than five times its complement. Find the measure of angle x.

46)

47)

48)

Refer to the figure and provide an appropriate name for the indicated angles.

49) ∠2 and ∠8

49)

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Find the missing measurement in the figure.

50) ∠B = 60°, Circumference = 30ʹ, Arc AC = ?

50)

Choose the most reasonable unit of measure. (mm, cm, m, km) 51) Hammer length 38

51)

Use similar figures to determine the value of X .

52)

52)

72 cm 6 cm 24 cm Find the surface area of the figure.

53) A right circular cylinder with r = 9 cm, h = 8 cm

53)

Provide an appropriate response.

54) Solve 4 D = 5.

54)

Find the missing length in the right triangle. If necessary, round to the nearest tenth.

55)

55)

11 cm

19 cm

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Answer Key Testname: CHAPTER 9 EXAM B

1) 4310.435 yd3 2) cm 3) 32 ft2 4) Rotate 90°, then reflect about horizontal axis 5) Supplementary angles 6) Complementary angles 7) 517.5 in.2 8) 17.9 cm 9) 50 ft 10) 26.8 11) 30 ft2 12) 10

y

9 8 7 6 5 4 3 2 1 -10 -9

-8

-7

-6

-5

-4

-3

-2

-1

1

2

3

4

5

6

7

8

9

10 x

-1 -2 -3 -4 -5 -6 -7 -8 -9 -10

13) m 14) 1800° 15) 5.81 mm 16) 113.04 yd3 17) False 18) Interior angles same side of the transversal 19) 10.2 cm 20) 20° 21) Area 22) 726 ft2 23) g Copyright © 2022 Pearson Education, Inc.

Answer Key Testname: CHAPTER 9 EXAM B

24) 40.5 ft2 25) 296.1 26) y 10 9 8 7 6

B

5

A

4 3 2 1 -10 -9

-8

-7

-6

-5

-4

-3

-2

-1

1

2

3

4

5

6

7

8

9

10

-1 -2 -3 -4 -5 -6 -7 -8 -9 -10

27) 343 cm 28) 228.3 29) 29.44 m 3 30) 59.54 31) Outside arc = 29.31 in. , inside arc = 7.33 in.

32) 5a2 , (n + 1)a 2

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x

Answer Key Testname: CHAPTER 9 EXAM B

33) 15 14 13 12 11 10 9 8 7

A

6 5 4 3 2 1 1

2

3

4

5

6

7

8

9

10 11 12 13 14 15

34) 9.99 35) 2688.0 36) Yes 37) 112 cm 38) True 39) 8 in.2 40) True 41) 0.315 L 42) Reflect about horizontal axis

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Answer Key Testname: CHAPTER 9 EXAM B

43) y 10 9 8 7 6

B

5 4 3 2 1

A -10 -9

-8

-7

-6

-5

-4

-3

-2

-1

1

2

3

4

5

6

7

8

9

10

-1 -2 -3 -4 -5 -6 -7 -8 -9 -10

44) 7.2 cm 45) Right angle 46) 38 ft 47) 16,384 48) 55° 49) Alternate exterior angles 50) 5ʹ 51) cm 52) 18 cm 53) 960.8 cm 2 54) 1.16 55) 22.0 cm

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x

Chapter 10 Exam A Name___________________________________

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Determine whether the specified paradox occurs.

1) In a small country consisting of 5 provinces, 300 federal judges are apportioned according to the population of each province. The population of each province is shown for the years 1995 and 2000.

Province A B C D E 1995 Population 25,312 8,911 11,451 33,611 15,932 2000 Population 26,011 9,732 12,678 35,977 17,311 Does the population paradox occur using Hamiltonʹs method of apportionment?

A) Yes B) No Find the standard divisor for the given situation. Round your answer to two decimals.

2) A small country consists of 7 provinces with the following populations: Province A B C D E F G Population 25,312 19,734 33,407 29,591 13,288 22,751 31,992 There are 320 federal judges to be apportioned according to the population of each province.

A) 472.25 B) 600.37 C) 702.49 D) 550.23 Assign as indicated using the Huntington-Hill method.

3) A police chief wishes to assign ten police officers to three regions. The numbers of incidents reported during an average month in the three regions are as follows: Region 1: 145 Region 2: 131 Region 3: 89 Help the police chief assign the officers to each region. Begin by giving each region one police officer.

B) Region 1: 4; Region 2: 3; Region 3: 3 A) Region 1: 5; Region 2: 4; Region 3: 1 C) Region 1: 4; Region 2: 4; Region 3: 2 D) Region 1: 5; Region 2: 3; Region 3: 2 Find the apportionment asked for.

4) A small country consists of 7 provinces with the following populations: Province A B C D E F G Population 25,312 19,734 33,407 29,591 13,288 22,751 31,992 There are 300 federal judges to be apportioned according to the population of each province. Find the apportionment for province G using Jeffersonʹs method.

A) 55 B) 54 C) 53 D) 56

1)

2)

3)

4)

Use the apportionment criterion to decide who should get an additional representative if another member is added to the total number of representatives.

5) For the U.S. House of Representatives: 5) State A: population 5.7 million, 10 representatives State B: population 11.4 million, 16 representatives A) State A B) State B

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Find the standard divisor for the given situation. Round your answer to two decimals.

6) A small country consists of seven states; there are 194 seats in the legislature that need to be apportioned among the seven states; and the population of each state is shown in the table.

State A B C D E F G Population 1283 2374 2725 2155 1592 2511 2017 A) 75.55 B) 61.51 C) 62.61 D) 68.94 Find the apportionment asked for.

7) A small city has 50 police officers to be apportioned among 8 precincts based on the population of each precinct. The populations are given in the following table.

Precinct 1 2 3 4 5 6 7 8 Population 2115 3659 3117 1883 4912 4027 2776 3174 Find the apportionment for the Seventh Precinct using Websterʹs method.

A) 4 B) 6 C) 5 D) 7 Determine whether the specified paradox occurs.

8) A town has 13 police officers to be apportioned among 3 precincts based on the population of each precinct. The populations for the years 1998 and 1999 are given in the following table.

Precinct 1 2 3 1998 Population 930 738 415 1999 Population 975 750 421 Does the population paradox occur using Hamiltonʹs method of apportionment?

A) Yes B) No 9) A country with two states has 75 seats in the legislature. The population of each state (in thousands) is given by: State A B Total Population 3184 8475 11659 A third state is added with 2 additional seats as shown below.

State A B C Total Population 3184 8475 330 11989 Does the new-states paradox occur using Hamiltonʹs method of apportionment?

A) Yes B) No Assign as indicated using the Huntington-Hill method.

10) A hospital administrator wishes to assign six emergency room medical teams to three outreach centers. The numbers of patients treated in an average week at the three centers are as follows: Center 1: 120 patients Center 2: 85 patients Center 3: 68 patients Help the administrator assign the medical teams to the three centers. Begin by giving each center one team.

B) Center 1: 1; Center 2: 2; Center 3: 3 A) Center 1: 2; Center 2: 3; Center 3: 1 C) Center 1: 3; Center 2: 2; Center 3: 1 D) Center 1: 2; Center 2: 2; Center 3: 2

6)

7)

8)

9)

10)

Use the apportionment criterion to decide who should get an additional representative if another member is added to the total number of representatives.

11) The Artistʹs Association has 7 representatives from the Painterʹs Group, which has 200 members, 11) and 8 representatives from the Sculptorʹs Association, which has 480 members.

B) Sculptorʹs Association A) Painterʹs Group

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12) For the U.S. House of Representatives: State A: population 17.3 million, 26 representatives State B: population 10.7 million, 15 representatives A) State B

12)

B) State A

Find the standard divisor for the given situation. Round your answer to two decimals.

13) A university has 21 scholarships to be apportioned among the engineering students based on the enrollment in each department. There are three departments - Mechanical Engineering (M), Electrical Engineering (E), and Civil Engineering (C). The number of students in each department is given in the following table.

Department M E C Enrollment 233 297 153 A) 35.38 B) 32.52 C) 33.86 D) 37.95

13)

Determine when the Hamilton method gives an Alabama paradox on increasing committee size and who loses a seat.

14) City A, City B, and City C are cooperating to build a community center catering to the three cities.

14) Seats on the 7-member committee are assigned according to the populations of the cities. The population of City A is 7755, City B is 6105, and City C is 2640. Increase the committeeʹs size by one seat at a time and reassign the seats.

B) Assignment of 10th seat; City A A) Assignment of 12th seat; City C C) Assignment of 11th seat; City C D) Assignment of 10th seat; City C Determine whether the specified paradox occurs.

15) A small country consists of 7 provinces with the following populations: Province A B C D E F G Population 25,312 19,734 33,407 29,591 13,288 22,751 31,992 There are 300 federal judges to be apportioned according to the population of each province. Does the Alabama paradox occur using Hamiltonʹs method if the number of judges is increased from 300 to 301?

A) Yes B) No

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15)

Use the method of sealed bids to complete the table.

16) Tom and Axel have inherited their fatherʹs sailboat and want to decide who should receive it.

1 1 Tom Axel 2 2

16)

Bid on sailboat $49,000 $59,000 Fair share of estate Item obtained with highest bid A) 1 1 Tom Axel 2 2 Bid on sailboat $49,000 $59,000 Fair share of estate $29,500 $24,500 Item obtained with highest bid sailboat B) Tom

1 1 Axel 2 2

Bid on sailboat $49,000 $59,000 Fair share of estate $29,500 $24,500 Item obtained with highest bid sailboat C) Tom

1 1 Axel 2 2

Bid on sailboat $49,000 $59,000 Fair share of estate $24,500 $29,500 Item obtained with highest bid sailboat D) Tom

1 1 Axel 2 2

Bid on sailboat $49,000 $59,000 Fair share of estate $24,500 $29,500 Item obtained with highest bid sailboat Find the standard quota asked for. Round your answer to two decimals.

17) The faculty senate of a university has 55 senators to be apportioned among its four colleges based on the number of faculty in each college. The colleges are Liberal Arts (L), Sciences (S), Business (B), and Engineering (E). The number of faculty in each college is shown in the following table.

L S B E College Number of Faculty 279 355 312 423 Find the standard quota for the College of Sciences.

A) 15.96 B) 14.26 C) 17.53 D) 19.94 Calculate the Huntington-Hill number.

18) Association of 1410 members having 11 representatives on the board.

A) 15,461.36 B) 15,171.36 C) 15,311.36

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17)

18) D) 15,061.36

Find the standard quota asked for. Round your answer to two decimals.

19) A small country consists of seven states; there are 186 seats in the legislature that need to be apportioned among the seven states; and the population of each state is shown in the table.

State A B C D E F G Population 1283 2374 2725 2155 1592 2511 2017 Find the standard quota for state C. A) 37.9 B) 42.48 C) 41.73 D) 34.58 Solve the problem.

20) The sum of the percentages 31.542%, 17.467%, 22.42%, 12.861%, and 15.71% is 100.000%. Adjust the list so that there are no fractional parts. The following table shows the numbers truncated and the discarded portions.

Original Number (%) Number Truncated (%) Discarded Portion (%) 31.542 31 0.542 17.467 17 0.467 22.42 22 0.42 12.861 12 0.861 15.71 15 0.71 100.000 97 A) 32%, 18%, 22%, 13%, 16% B) 32%, 17%, 22%, 13%, 16% C) 31%, 17%, 22%, 12%, 16% D) 31%, 17%, 22%, 13%, 15% Determine whether the specified paradox occurs.

21) A country with two states has 16 seats in the legislature. The population of each state (in thousands) is given by: State A B Total Population 134 52 186 A third state is added with 3 additional seats as shown below.

State A B C Total Population 134 52 38 224 Does the new-states paradox occur using Hamiltonʹs method of apportionment?

A) Yes B) No Solve the problem.

22) If the Jefferson Method is used to apportion 132 legislative seats to four states with the populations given in the table, then a violation of the Quota Rule occurs. a b c d State Population 17,180 7,500 49,400 5,820 The apportionment for which state violates the Quota Rule?

A) d B) c C) a D) b

19)

20)

21)

22)

Use the Huntington-Hill apportionment principle to decide who is most deserving of an additional representative.

23) The Artistʹs Association has 5 representatives from the Painterʹs Group, which has 220 members, 23) 11 representatives from the Actorʹs Association, which has 670 members, and 7 representatives from the Sculptorʹs Association, which has 460 members.

B) Sculptorʹs Association C) Actorʹs Association A) Painterʹs Group

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Find the standard quota asked for. Round your answer to two decimals.

24) A small country consists of 7 provinces with the following populations: Province A B C D E F G Population 25,312 19,734 33,407 29,591 13,288 22,751 31,992 There are 300 federal judges to be apportioned according to the population of each province.

Find the standard quota for province G. A) 42.69 B) 54.51 C) 49.96 D) 63.51 Use the Hamilton method to make the assignment.

25) The students of 5th, 6th, and 7th grades of Great Middle School are putting up a charity show. The 11-person committee making decisions is in proportion to the number of students in each grade.

There are 126 5th-graders, 105 6th-graders and 97 7th-graders. Assign members to the committee.

B) 5th: 3; 6th: 4; 7th: 4 A) 5th: 4; 6th: 4; 7th: 3 C) 5th: 4; 6th: 3; 7th: 4 D) 5th: 3; 6th: 3; 7th: 4 Determine which state is more poorly represented.

26) State A with a population of 383,537 and 11 representatives or state B with a population of 488,138 and 14 representatives.

A) State A B) State B C) The two have equal representation.

Find the apportionment asked for.

27) A small country consists of seven states; there are 160 seats in the legislature that need to be apportioned among the seven states; and the population of each state is shown in the table.

State A B C D E F G Population 1283 2374 2725 2155 1592 2511 2017 Find the apportionment for state D using Adamsʹ method.

A) 25 B) 24 C) 23 D) 26 Assign as indicated using the Huntington-Hill method.

28) A health club instructor has a course load that allows her to teach seven two-credit hour classes. A pre-registration survey indicates the following interests: 54 want to take high-impact aerobics 28 want to take low-impact aerobics 14 want to take jazzercise 7 want to take step exercise Assume that the instructor will teach at least one class for each activity. Apportion the remaining three classes.

A) One each of high-impact aerobics, low-impact aerobics, and jazzercise B) Two of high-impact aerobics and one of low-impact aerobics C) One each of high-impact aerobics, low-impact aerobics, and step exercise D) One of high-impact aerobics and two of low-impact aerobics Solve the problem.

29) If the Jefferson Method is used to apportion 200 legislative seats to four states with the populations given in the table, then a violation of the Quota Rule occurs. a b c d e State Population 4590 1515 2015 1120 1110 The apportionment for which state violates the Quota Rule?

A) d B) a C) e D) b

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24)

25)

26)

27)

28)

29)

Determine which state is more poorly represented.

30) State A with a population of 489,798 and 9 representatives or state B with a population of 323,994 and 11 representatives.

A) State B B) State A C) The two have equal representation.

30)

Use the Huntington-Hill apportionment principle to decide who is most deserving of an additional representative.

31) The Artistʹs Association has 5 representatives from the Painterʹs Group, which has 240 members, 31) 11 representatives from the Actorʹs Association, which has 670 members, and 7 representatives from the Sculptorʹs Association, which has 490 members. Assign two additional seats, one at a time.

A) Painterʹs Group and Actorʹs Association B) Sculptorʹs Association and Painterʹs Group C) Sculptorʹs Association and Actorʹs Association D) Actorʹs Association and Painterʹs Group Calculate the Huntington-Hill number.

32) State A: population 10,200, 12 representatives A) 666,923.077 B) 667,023.077

32) C) 666,983.077

D) 666,933.077

Find the standard quota asked for. Round your answer to two decimals.

33) A school district receives a grant to purchase 44 new computers to be apportioned among the 6 schools in the district based on the student population of each school. The student populations are given in the following table.

School A B C D E F Population 314 211 197 243 279 325 Find the standard quota for school A. A) 10.17 B) 8.81 C) 11.58 D) 11.11 Determine the absolute and relative unfairness of the given apportionment.

34) State A with a population of 254,000 and 10 representatives or state B with a population of 540,000 and 15 representatives.

A) 10,600; 0.417 B) 36,000; 0.586 C) 25,400; 0.414 D) 10,600; 0.294 Find the standard quota asked for. Round your answer to two decimals.

35) A university has 30 scholarships to be apportioned among the engineering students based on the enrollment in each department. There are three departments - Mechanical Engineering (M), Electrical Engineering (E), and Civil Engineering (C). The number of students in each department is given in the following table.

Department M E C Enrollment 233 297 153 Find the standard quota for the Mechanical Engineering Department.

A) 8.77 B) 10.23 C) 9.83 D) 9.41

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33)

34)

35)

Use the Huntington-Hill numbers listed in the table to assign seats as indicated.

36) Eleven seats on a condominium association board for buildings Amity, Buddy, and Chum are to be apportioned. Use the given table of Huntington-Hill numbers to list the order in which the seats on the board will be apportioned. Begin by apportioning one seat to each building.

Current Representation (A)mity (B)uddy (C)hum 1 800 2113 4050 2 267 704 1350 3 133 352 675 4 80 211 405 5 53 141 270 A) A, B, C, C, B, A, A, B, C, C, B B) A, B, C, C, C, B, A, B, A, C, C C) A, B, C, B, C, C, A, B, C, C, A D) A, B, C, C, B, C, A, B, C, C, B Use the Hamilton method to make the assignment.

37) In a recent census, Georgiaʹs population in thousands was 3,503, Floridaʹs was 4,220, and South Carolinaʹs was 4,300. Allocate 25 members of the U.S. House of Representatives to these three states.

A) Georgia: 7; Florida: 10; South Carolina: 8 B) Georgia: 9; Florida: 8; South Carolina: 8 D) Georgia: 6; Florida: 8; South Carolina: 11 C) Georgia: 7; Florida: 9; South Carolina: 9 Assign as indicated using the Huntington-Hill method.

38) A hospital administrator wishes to assign ten emergency room medical teams to three outreach centers. The numbers of patients treated in an average week at the three centers are as follows: Center 1: 280 patients Center 2: 175 patients Center 3: 95 patients Help the administrator assign the medical teams to the three centers. Begin by giving each center one team.

B) Center 1: 4; Center 2: 4; Center 3: 2 A) Center 1: 4; Center 2: 3; Center 3: 3 C) Center 1: 5; Center 2: 3; Center 3: 2 D) Center 1: 5; Center 2: 4; Center 3: 1 Determine whether the specified paradox occurs.

39) A country with two states has 16 seats in the legislature. The population of each state is given by: State A B Total Population 86,342 77,312 163,654 A third state is added with 5 additional seats as shown below.

State A B C Total Population 86,342 77,312 53,792 217,446 Does the new-states paradox occur using Hamiltonʹs method of apportionment?

A) Yes B) No

36)

37)

38)

39)

Use the Huntington-Hill apportionment principle to decide who is most deserving of an additional representative.

40) For the U.S. House of Representatives: 40) State A: population 5.6 million, 10 representatives State B: population 14.2 million, 20 representatives State C: population 11.7 million, 15 representatives A) State C B) State A C) State B

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Answer Key Testname: CHAPTER 10 EXAM A

1) B 2) D 3) C 4) A 5) B 6) A 7) C 8) A 9) A 10) C 11) B 12) A 13) B 14) D 15) B 16) D 17) B 18) D 19) D 20) B 21) A 22) B 23) B 24) B 25) A 26) C 27) B 28) B 29) B 30) B 31) C 32) A 33) B 34) A 35) B 36) D 37) C 38) C 39) B 40) A

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Chapter 10 Exam B Name___________________________________

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Find the standard quota asked for. Round your answer to two decimals.

1) The faculty senate of a university has 50 senators to be apportioned among its four colleges based on the number of faculty in each college. The colleges are Liberal Arts (L), Sciences (S), Business (B), and Engineering (E). The number of faculty in each college is shown in the following table.

L S B E College Number of Faculty 279 355 312 423 Find the standard quota for the College of Sciences.

1)

2) A university has 26 scholarships to be apportioned among the engineering students based on the enrollment in each department. There are three departments - Mechanical Engineering (M), Electrical Engineering (E), and Civil Engineering (C). The number of students in each department is given in the following table.

Department M E C Enrollment 233 297 153 Find the standard quota for the Mechanical Engineering Department.

2)

3) A school district receives a grant to purchase 63 new computers to be apportioned among the 6 schools in the district based on the student population of each school. The student populations are given in the following table.

School A B C D E F Population 314 211 197 243 279 325 Find the standard quota for school A.

3)

Assign as indicated using the Huntington-Hill method.

4) A hospital administrator wishes to assign ten emergency room medical teams to three outreach centers. The numbers of patients treated in an average week at the three centers are as follows: Center 1: 280 patients Center 2: 175 patients Center 3: 95 patients Help the administrator assign the medical teams to the three centers. Begin by giving each center one team.

Use the Huntington-Hill numbers listed in the table to assign seats as indicated.

5) Eleven seats on a condominium association board for buildings Amity, Buddy, and Chum are to be apportioned. Use the given table of Huntington-Hill numbers to list the order in which the seats on the board will be apportioned. Begin by apportioning one seat to each building.

Current Representation (A)mity (B)uddy (C)hum 1 800 2113 4050 2 267 704 1350 3 133 352 675 4 80 211 405 5 53 141 270

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4)

5)

Determine when the Hamilton method gives an Alabama paradox on increasing committee size and who loses a seat.

6) An apartment complex has three buildings. Building A has 200 units, building B has 235 6) units, and building C has 65 units. A 9-person committee will set rules to govern the complex. This committee is proportioned to the numbers of units in the buildings. Increase the members in the committee one at a time and reassign the seats.

7) City A, City B, and City C are cooperating to build a community center catering to the three cities. Seats on the 12-member committee are assigned according to the populations of the cities. The population of City A is 6000, City B is 13,500, and City C is 18,600.

Increase the committeeʹs size by one seat at a time and reassign the seats.

7)

8) City A, City B, and City C are cooperating to build a community center catering to the three cities. Seats on the 8-member committee are assigned according to the populations of the cities. The population of City A is 7755, City B is 6105, and City C is 2640. Increase the committeeʹs size by one seat at a time and reassign the seats.

8)

Solve the problem.

9) If the Jefferson Method is used to apportion 200 legislative seats to four states with the populations given in the table, then a violation of the Quota Rule occurs. a b c d e State Population 4590 1515 2015 1120 1110 The apportionment for which state violates the Quota Rule?

9)

10) If the Jefferson Method is used to apportion 131 legislative seats to six states with the populations given in the table, then a violation of the Quota Rule occurs. a b c d e f State Population 5672 8008 2400 6789 4972 20000 The apportionment for which state violates the Quota Rule?

10)

11) The sum of the percentages 32.542%, 17.467%, 21.42%, 12.861%, and 15.71% is 100.000%.

Adjust the list so that there are no fractional parts. The following table shows the numbers truncated and the discarded portions.

Original Number (%) Number Truncated (%) Discarded Portion (%) 32.542 32 0.542 17.467 17 0.467 21.42 21 0.42 12.861 12 0.861 15.71 15 0.71 100.000 97

11)

12) If the Jefferson Method is used to apportion 132 legislative seats to four states with the populations given in the table, then a violation of the Quota Rule occurs. a b c d State Population 17,180 7,500 49,400 5,820 The apportionment for which state violates the Quota Rule?

12)

13) Use the Huntington-Hill method to apportion eleven seats among State X, State Y, and State Z. The populations of the states are state X, 4.0 million; State Y, 6.5 million; and State Z, 5.2 million. The current assignment of ten seats is State X has two seats, State Y has four seats, and State Z has four seats. Assign the eleventh and twelfth seat.

13)

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14) The sum of the numbers 22.432, 16.634, 26.562, 22.315, and 12.057 is 100.000. Adjust the list so that the numbers are shown to the tenths place and their sum is 100.0.

14)

15) If the Jefferson Method is used to apportion 250 legislative seats to five states with the populations given in the table, then a violation of the Quota Rule occurs. a b c d e State Population 912,000 1,117,000 4,537,000 739,000 695,000 The apportionment for which state violates the Quota Rule?

15)

16) Use the Huntington-Hill method to apportion eleven seats among State P, State Q, and State R. The populations of the states are State P, 0.75 million; State Q, 1.2 million; and State R, 1.5 million. Begin by giving one representative to each state. List the order in which the representatives are apportioned.

16)

Use the apportionment criterion to decide who should get an additional representative if another member is added to the total number of representatives.

17) For the U.S. House of Representatives: 17) State A: population 5.6 million, 9 representatives State B: population 11.6 million, 15 representatives 18) The Artistʹs Association has 7 representatives from the Painterʹs Group, which has 230 members, and 8 representatives from the Sculptorʹs Association, which has 500 members.

18)

Use the Huntington-Hill apportionment principle to decide who is most deserving of an additional representative.

19) Subdivision A, with 1450 residents, has 11 representatives in the City Hall, while 19) Subdivision B, with 2650 residents, has 17 representatives, and Subdivision C, with 900 residents, has 7 representatives.

20) For the U.S. House of Representatives: State A: population 5.6 million, 9 representatives State B: population 14.2 million, 19 representatives State C: population 11.6 million, 14 representatives

20)

Use the method of sealed bids to complete the table.

21) Use the first table to complete the fair division accounting of the estate cash in the empty table.

1 1 Meghan Oliver 2 2 Bid on painting Fair share of estate Item obtained with highest bid

$10,000 $5000

$16,000 $8000 painting Oliver

1 2

Meghan

Pays to estate (+) or receives from estate (-) Division of estate balance ($ ) Summary of cash

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1 2

21)

22) Tom and Axel have inherited their fatherʹs sailboat and want to decide who should receive it.

1 1 Axel Tom 2 2

22)

Bid on sailboat $52,000 $64,000 Fair share of estate Item obtained with highest bid Find the standard divisor for the given situation. Round your answer to two decimals.

23) A school district receives a grant to purchase 60 new computers to be apportioned among the 6 schools in the district based on the student population of each school. The student populations are given in the following table.

School A B C D E F Population 314 211 197 243 279 325

23)

24) A university has 26 scholarships to be apportioned among the engineering students based on the enrollment in each department. There are three departments - Mechanical Engineering (M), Electrical Engineering (E), and Civil Engineering (C). The number of students in each department is given in the following table.

Department M E C Enrollment 233 297 153

24)

25) A small country consists of 7 provinces with the following populations: Province A B C D E F G Population 25,312 19,734 33,407 29,591 13,288 22,751 31,992 There are 370 federal judges to be apportioned according to the population of each province.

25)

26) A small city has 35 police officers to be apportioned among 8 precincts based on the population of each precinct. The populations are given in the following table.

Precinct 1 2 3 4 5 6 7 8 Population 2115 3659 3117 1883 4912 4027 2776 3174

26)

27) A small country consists of seven states; there are 194 seats in the legislature that need to be apportioned among the seven states; and the population of each state is shown in the table.

State A B C D E F G Population 1283 2374 2725 2155 1592 2511 2017

27)

Use the Hamilton method to make the assignment.

28) In a recent census, Iowaʹs population in thousands was 4,503, Illinoisʹ was 8,220, and Indianaʹs was 5,300. Allocate 30 members of the U.S. House of representatives to these three states.

29) In a recent census, Georgiaʹs population in thousands was 3,503, Floridaʹs was 4,220, and South Carolinaʹs was 4,300. Allocate 26 members of the U.S. House of Representatives to these three states.

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28)

29)

30) The students of 5th, 6th, and 7th grades of Great Middle School are putting up a charity show. The 11-person committee making decisions is in proportion to the number of students in each grade. There are 124 5th-graders, 105 6th-graders and 95 7th-graders.

Assign members to the committee.

30)

Determine which state is more poorly represented.

31) State A with a population of 651,864 and 12 representatives or state B with a population of 538,500 and 15 representatives.

31)

Determine the absolute and relative unfairness of the given apportionment.

32) State A with a population of 276,100 and 11 representatives or state B with a population of 534,000 and 15 representatives.

32)

Find the apportionment asked for.

33) A small country consists of seven states; there are 160 seats in the legislature that need to be apportioned among the seven states; and the population of each state is shown in the table.

State A B C D E F G Population 1283 2374 2725 2155 1592 2511 2017 Find the apportionment for state D using Jeffersonʹs method.

34) A small city has 50 police officers to be apportioned among 8 precincts based on the population of each precinct. The populations are given in the following table.

Precinct 1 2 3 4 5 6 7 8 Population 2115 3659 3117 1883 4912 4027 2776 3174 Find the apportionment for the Seventh Precinct using Websterʹs method.

Determine whether the specified paradox occurs.

35) A small country consists of seven states; there are 160 seats in the legislature that need to be apportioned among the seven states; and the population of each state is shown in the table.

State A B C D E F G Population 1283 2374 2725 2155 1592 2511 2017 Does the Alabama paradox occur using Hamiltonʹs method if the number of seats is increased from 160 to 161?

33)

34)

35)

36) A country with two states has 16 seats in the legislature. The population of each state (in thousands) is given by: State A B Total Population 134 52 186 A third state is added with 3 additional seats as shown below.

State A B C Total Population 134 52 38 224 Does the new-states paradox occur using Hamiltonʹs method of apportionment?

36)

37) A city has 204 police officers to be apportioned among 4 precincts based on the population of each precinct. The populations are given in the following table.

Precinct 1 2 3 4 Population 3462 7470 4265 5300 Does the Alabama paradox occur using Hamiltonʹs method if the number of police officers is increased from 204 to 205?

37)

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38) A small country consists of 7 provinces with the following populations: Province A B C D E F G Population 25,312 19,734 33,407 29,591 13,288 22,751 31,992 There are 300 federal judges to be apportioned according to the population of each province. Does the Alabama paradox occur using Hamiltonʹs method if the number of judges is increased from 300 to 301?

38)

39) A country with two states has 16 seats in the legislature. The population of each state is given by: State A B Total Population 86,342 77,312 163,654 A third state is added with 5 additional seats as shown below.

State A B C Total Population 86,342 77,312 53,792 217,446 Does the new-states paradox occur using Hamiltonʹs method of apportionment?

39)

Calculate the Huntington-Hill number.

40) City A: population 4700, 11 representatives

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40)

Answer Key Testname: CHAPTER 10 EXAM B

1) 12.97 2) 8.87 3) 12.61 4) Center 1: 5; Center 2: 3; Center 3: 2 5) A, B, C, C, B, C, A, B, C, C, B 6) Assignment of the 12th seat; building C 7) Assignment of 16th seat; City A 8) Assignment of 10th seat; City C 9) a 10) f 11) 33%, 17%, 21%, 13%, 16% 12) c 13) Eleventh seat: State X; Twelfth seat: State Y 14) 22.4, 16.6, 26.6, 22.3, 12.1 15) c 16) R, Q, P, R, Q, R, P, Q, R, Q, R 17) State B 18) Sculptorʹs Association 19) Subdivision B 20) State C 21) Oliver

1 1 Meghan 2 2

Pays to estate (+) or receives from estate (-) $5000 (-) Division of estate balance ($3000) $1500 (-) Receives Summary of cash $6500

$8000 (+) $1500 (-) Pays $6500

22) Tom

1 1 Axel 2 2

Bid on sailboat $52,000 $64,000 Fair share of estate $26,000 $32,000 Item obtained with highest bid sailboat 23) 26.15 24) 26.27 25) 475.88 26) 733.23 27) 75.55 28) Iowa: 7; Illinois: 14; Indiana: 9 29) Georgia: 8; Florida: 9; South Carolina: 9 30) 5th: 4; 6th: 4; 7th: 3 31) State A 32) 10,500; 0.418 33) 24 34) 5 35) No 36) Yes 37) Yes 38) No Copyright © 2022 Pearson Education, Inc.

Answer Key Testname: CHAPTER 10 EXAM B

39) No 40) 167,348.485

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Chapter 11 Exam A Name___________________________________

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Determine the Shapley-Shubik index of each voter in the weighted voting system 1) [9 : 6, 4, 3] 1 2 1 A) All have index .

B) A has index ; B and C have index .

3 3 6 C) A and C have index

2 1 ; B has index .

3 6

D) A and B have index

2 1 ; C has index .

3 6

2) [10 : 4, 4, 4]

2)

1 A) All have index .

6 C) All have index

1)

2 1 B) C has index ; A and B have index .

3 6

1 .

3

D) B has index

2 1 ; A and C have index .

3 6

Determine the answer as requested.

3) The city council gave a questionnaire to its citizens, asking them to rank their priorities for next yearʹs budget. People were asked to rank the following four choices: (P)olice, (R)oads, (S)chools, and (T)rash removal. The results are summarized in the table below.

Number of Ballots Preference 15 30 18 17 P T P R 1st 2nd R R S T 3rd S S T S 4th T P R P

3)

10 2 R S S P P R T T

Which option is selected using the plurality method?

A) R B) S C) P

D) T

Determine whether any of the listed candidates has a majority.

4) Four candidates running for senate receive votes as follows: Edwards: 90,162, Fong: 35,063, Goodman: 15,027, Haddad: 25,045 A) No B) Yes For the indicated voting system, determine the quota, the number of voters, and the weights of the voters.

5) [16 : 1, 5, 7, 9] A) Quota: 9, number of voters: 16, weights: 1, 5, 7, and 9 B) Quota: 16, number of voters: 22, weights: 1, 5, 7, and 9 C) Quota: 16, number of voters: 4, weights: 1, 5, 7, and 9 D) Quota: 4, number of voters: 16, weights: 1, 5, 7, and 9

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4)

5)

6) [5 : 1, 1, 1, 1, 1] A) Quota: 1, number of voters: 5, weights: 1, 1, 1, 1, and 1 B) Quota: 5, number of voters: 1, weights: 1, 1, 1, 1, and 1 C) Quota: 5, number of voters: 5, weights: 1, 1, 1, 1, and 1 D) Quota: 1, number of voters: 5, weights: 1, 2, 3, 4, and 5

6)

7) [51 : 20, 20, 20, 10, 10] A) Quota: 80, number of voters: 51, weights: 20, 20, 20, 10, and 10 B) Quota: 20, number of voters: 51, weights: 20, 20, 20, 10, and 10 C) Quota: 5, number of voters: 51, weights: 20, 20, 20, 10, and 10 D) Quota: 51, number of voters: 5, weights: 20, 20, 20, 10, and 10

7)

8) [15 : 1, 2, 3, 3, 4, 5] A) Quota: 15, number of voters: 6, weights: 1, 2, 3, 3, 4, and 5 B) Quota: 5, number of voters: 5, weights: 1, 2, 3, 3, 4, and 5 C) Quota: 6, number of voters: 15, weights: 1, 2, 3, 3, 4, and 5 D) Quota: 5, number of voters: 15, weights: 1, 2, 3, 3, 4, and 5

8)

In the given voting system, the weights represent, in order, voters A, B, C, and so on. Determine which voters are critical in the indicated coalition.

9) [16 : 1, 5, 7, 9] ; coalition {A, C, D} 9) A) Only D is critical.

B) Only C and D are critical.

C) Only A is critical.

D) None are critical.

10) [12 : 1, 3, 5, 7] ; coalition {B, C, D} A) Only C and D are critical.

C) Only B is critical.

10) B) Only D is critical.

D) All are critical.

In the given voting system, the weights represent, in order, voters A, B, C, and so on. Determine the Banzhaf power index for each voter.

11) 11) [16 : 1, 5, 7, 9] 1 A) A has an index of . All others have an index of 0.

2 B) A has an index of 0. All others have an index of C) All have an index of

1 .

2

1 .

2

D) A and B have an index of 0. C and D have an index of

1 .

2

In the indicated voting system, the weights represent, in order, voters A, B, C, and so on. Identify the dictator if there is one, and identify those voters with veto power if there are any.

12) 12) [16 : 1, 5, 7, 17] A) D is a dictator; each voter has veto power.

B) D is a dictator; D has veto power.

C) No dictator; D has veto power.

D) No dictator; A has veto power.

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13) [15 : 1, 2, 3, 3, 4, 5] A) No dictator; voters E and F have veto power.

B) Voter F is a dictator; no voters have veto power.

C) No dictator; voter F has veto power.

D) Voter F is a dictator; voter F has veto power.

13)

14) [51 : 20, 20, 20, 10, 10] A) No dictator; each voter has veto power.

B) No dictator; voters D and E have veto power.

C) No dictator; no voter has veto power.

D) No dictator; voters A, B, and C have veto power.

14)

15) [5 : 1, 1, 1, 1, 1] A) No dictator; each voter has veto power.

B) No dictator; no voter has veto power.

C) Each voter is a dictator; each voter has veto power.

D) No dictator; voter A has veto power.

15)

Rank the choices as requested.

16) An airline is deciding which type of movie to show during a flight. The passengers are asked to rank the following four choices: (A)ction, (C)omedy, (M)usical, and (Drama). The results are summarized below.

16)

Number of Ballots Preference 20 26 38 16 8 22 1st A M C M C D 2nd M A M D A M 3rd C D D C D A 4th D C A A M C Rank the four choices using the plurality-with-elimination method.

A) C, M, D, A B) M, D, A, C C) A, M, D, C

D) M, C, D, A

Solve the problem.

17) A committee is set up to vote yes or no on a logo design. The committee is composed of one person whose favorite color is (A)zure, three people whose favorite color is (B)lack, five people whose favorite color is (C)herry, and seven people whose favorite color is (G)reen. At least twelve votes are required for a decision, and the committee members will vote in blocs according to their favorite colors. List all winning coalitions, and identify those blocs that are critical to each of the winning coalitions.

A) {A, B, C, G}, {A, C, G}, {B, C, G}, {C, G} ; B, C, and G are critical to the coalition {A, B, C, G} ; C and G are critical to all other winning coalitions.

B) {A, C, G}, {B, C, G}, {C, G} ; C and G are critical to all winning coalitions.

C) {A, C, G}, {B, C, G}, {C, G} ; G is critical to all winning coalitions.

D) {A, B, C, G}, {A, C, G}, {B, C, G}, {C, G} ; C and G are critical to all winning coalitions.

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17)

18) A committee is set up to vote yes or no on a logo design. The committee is composed of one person whose favorite color is (A)zure, five people whose favorite color is (B)lack, seven people whose favorite color is (C)herry, and nine people whose favorite color is (G)reen. At least sixteen votes are required for a decision, and the committee members will vote in blocs according to their favorite colors. List all winning coalitions, and identify those blocs that are critical to each of the winning coalitions.

A) {A, B, C, G}, {A, C, G}, {B, C, G}, {C, G} ; B, C, and G are critical to the coalition {A, B, C, G} ; C and G are critical to all other winning coalitions.

B) {A, C, G}, {B, C, G}, {C, G} ; G is critical to all winning coalitions.

C) {A, C, G}, {B, C, G}, {C, G} ; C and G are critical to all winning coalitions.

D) {A, B, C, G}, {A, C, G}, {B, C, G}, {C, G} ; C and G are critical to all winning coalitions.

18)

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Construct the requested preference table.

19) Construct a preference table for a vote in which voters make an ordered selection of three, where the winner by the plurality method represents a violation of the independence-of-irrelevant-alternatives criterion.

Find all the permutations of the set.

20) {E F, G}

19)

20)

21) How many permutations are there of a ten-element set?

21)

In the indicated voting system, the weights represent, in order, voters A, B, C, and so on. Write out all of the winning coalitions.

22) [12 : 1, 3, 5, 7] 22) 23) [16 : 1, 5, 7, 9]

23)

Provide a response as requested.

24) The city council gave a questionnaire to its citizens, asking them to rank their priorities for next yearʹs budget. People were asked to rank the following four choices: (P)olice, (R)oads, (S)chools, and (T)rash removal. The results are summarized in the table below.

Number of Ballots Preference 30 90 20 14 P T P R 1st 2nd R R R T 3rd S S T S 4th T P S P

20 4 R S S P P R T T

State who the Borda count winner is. Explain whether this satisfies the majority, Condorcet, and independence-of-irrelevant-alternatives criteria.

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24)

Rank the choices as requested.

25) An airline is deciding which type of movie to show during a flight. The passengers are asked to rank the following four choices: (A)ction, (C)omedy, (M)usical, and (Drama). The results are summarized below.

Number of Ballots Preference 30 39 57 24 1st A M C M 2nd M A M D 3rd C D D C 4th D C A A

12 C A D M

33 D M A C

Rank the four choices using the Borda count method.

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25)

Answer Key Testname: CHAPTER 11 EXAM A

1) B 2) C 3) C 4) B 5) C 6) C 7) D 8) A 9) B 10) A 11) D 12) B 13) A 14) C 15) A 16) D 17) D 18) D 19) Answers will vary.

20) {E, F, G}, {E, G, F}, {F, G, E}, {F,E, G}, {G, E, F}, {G, F, E} 21) 3,628,800 22) {A, B, C, D}, {A, C, D}, {B, C, D}, {C, D} 23) {A, B, C, D}, {A, C, D}, {B, C, D}, {C, D} 24) R wins the Borda count, but fails the majority criterion. This does not satisfy the independence-of-irrelevant-alternatives criterion.

25) M, C, D, A

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Chapter 11 Exam B Name___________________________________

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Determine the answer as requested.

1) The city council gave a questionnaire to its citizens, asking them to rank their priorities for next yearʹs budget. People were asked to rank the following four choices: (P)olice, (R)oads, (S)chools, and (T)rash removal. The results are summarized in the table below.

Number of Ballots Preference 30 60 36 34 P T P R 1st 2nd R R S T 3rd S S T S 4th T P R P

1)

20 4 R S S P P R T T

Which option is selected using the plurality-with-elimination method?

2) The city council gave a questionnaire to its citizens, asking them to rank their priorities for next yearʹs budget. People were asked to rank the following four choices: (P)olice, (R)oads, (S)chools, and (T)rash removal. The results are summarized in the table below.

Number of Ballots Preference 15 30 18 17 1st P T P R R R S T 2nd 3rd S S T S 4th T P R P

2)

10 2 R S S P P R T T

Which option is selected using the plurality method?

In the given voting system, the weights represent, in order, voters A, B, C, and so on. Determine the Banzhaf power index for each voter.

3) [16 : 1, 5, 7, 9] 3) 4) [12 : 1, 3, 5, 7]

4)

In the given voting system, the weights represent, in order, voters A, B, C, and so on. Determine which voters are critical in the indicated coalition.

5) [23 : 3, 5, 6, 8, 9] ; coalition {A, B, D, E} 5) Determine the Shapley-Shubik index of each voter in the weighted voting system 6) [9 : 6, 4, 3] 7) [10 : 4, 4, 4]

6) 7)

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Provide a response as requested.

8) The city council gave a questionnaire to its citizens, asking them to rank their priorities for next yearʹs budget. People were asked to rank the following four choices: (P)olice, (R)oads, (S)chools, and (T)rash removal. The results are summarized in the table below.

Number of Ballots Preference 45 135 30 21 P T P R 1st 2nd R R R T 3rd S S T S 4th T P S P

8)

30 6 R S S P P R T T

State who the Borda count winner is. Explain whether this satisfies the majority, Condorcet, and independence-of-irrelevant-alternatives criteria.

For the indicated voting system, determine the quota, the number of voters, and the weights of the voters.

9) [51 : 20, 20, 20, 10, 10] 9) 10) [15 : 1, 2, 3, 3, 4, 5]

10)

In the indicated voting system, the weights represent, in order, voters A, B, C, and so on. Identify the dictator if there is one, and identify those voters with veto power if there are any.

11) [5 : 1, 1, 1, 1, 1] 11) In the indicated voting system, the weights represent, in order, voters A, B, C, and so on. Write out all of the winning coalitions.

12) [12 : 1, 3, 5, 7] 12) In the indicated voting system, the weights represent, in order, voters A, B, C, and so on. Identify the dictator if there is one, and identify those voters with veto power if there are any.

13) [15 : 1, 2, 3, 3, 4, 5] 13) Determine whether any of the listed candidates has a majority.

14) Four candidates running for mayor receive votes as follows: Ito: 38,772, Johnson: 17,232, Kennedy: 8616, Lieberman: 12,924

14)

15) Four candidates running for senate receive votes as follows: Edwards: 99,594, Fong: 38,731, Goodman: 16,599, Haddad: 27,665

15)

16) Four candidates running for congress receive votes as follows: Alberts: 49,082, Brown: 13,386, Cassimatis: 35,696, DʹAmico: 31,234

16)

Construct the requested preference table.

17) Construct a preference table for a vote in which voters make an ordered selection of three, where the winner by the plurality method represents a violation of the independence-of-irrelevant-alternatives criterion.

18) Construct a preference table showing an election using the plurality method that violates Condorcetʹs criterion.

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17)

18)

Rank the choices as requested.

19) The city council gave a questionnaire to its citizens, asking them to rank their priorities for next yearʹs budget. People were asked to rank the following four choices: (P)olice, (R)oads, (S)chools, and (T)rash removal. The results are summarized in the table below.

Number of Ballots Preference 30 60 36 34 P T P R 1st 2nd R R S T 3rd S S T S 4th T P R P

19)

20 4 R S S P P R T T

Rank the four choices using the pairwise comparison method.

20) An airline is deciding which type of movie to show during a flight. The passengers are asked to rank the following four choices: (A)ction, (C)omedy, (M)usical, and (Drama). The results are summarized below.

Number of Ballots Preference 30 39 57 24 1st A M C M 2nd M A M D 3rd C D D C 4th D C A A

12 C A D M

20)

33 D M A C

Rank the four choices using the plurality-with-elimination method.

Determine the voting method being used and complete the table.

21) The table below summarizes the voting of members of a professional society for their president.

Candidate 1st 2nd Walker 586 A Topp B 285 Singh 25 72 Klauss 4 89 Silverman 21 45

3rd 42 136 C 121 D

21)

Total 2036 994 321 311 247

22) The table summarizes the results of voting in a student council election.

Student 1st 2nd 3rd Total Points Boris 17 3 A 59 Rudy B 10 4 54 Lucinda 3 8 C 38 Leonardo 1 D 12 37 Trudie 4 2 4 24

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22)

Solve the problem.

23) A law firm has two senior partners (A and B) and three associate partners (C, D, and E). In order for any decision to be made concerning the practice, both senior partners and at least two associate partners must agree. Compute the Banzhaf power index for each voter. If another senior partner, F, is added, compute the new Banzhaf power index for each voter assuming that two senior partners and two associates must agree.

24) A committee is set up to vote yes or no on a logo design. The committee is composed of one person whose favorite color is (A)zure, five people whose favorite color is (B)lack, seven people whose favorite color is (C)herry, and nine people whose favorite color is (G)reen. At least sixteen votes are required for a decision, and the committee members will vote in blocs according to their favorite colors. List all winning coalitions, and identify those blocs that are critical to each of the winning coalitions.

Find all the permutations of the set.

25) How many permutations are there of a four-element set?

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23)

24)

25)

Answer Key Testname: CHAPTER 11 TEST B

1) T 2) P 3) A and B have an index of 0. C and D have an index of

1 .

2

4) A and B have an index of 0. C and D have an index of

1 .

2

5) All are critical.

1 2 6) A has index ; B and C have index .

6 3 7) All have index

1 .

3

8) R wins the Borda count, but fails the majority criterion. This does not satisfy the independence-of-irrelevant-alternatives criterion.

9) Quota: 51, number of voters: 5, weights: 20, 20, 20, 10, and 10 10) Quota: 15, number of voters: 6, weights: 1, 2, 3, 3, 4, and 5 11) No dictator; each voter has veto power.

12) {A, B, C, D}, {A, C, D}, {B, C, D}, {C, D} 13) No dictator; voters E and F have veto power.

14) No 15) Yes 16) No 17) Answers will vary.

18) Answers will vary.

19) T, R, S, P 20) M, C, D, A 21) Borda count method with 3 points for 1st, 2 points for 2nd, and 1 point for 3rd; A: 118 B: 96 C: 102 D: 94 22) Borda count method with 3 points for 1st, 2 points for 2nd, and 1 point for 3rd; A: 2 B: 10 C: 13 D: 11 1 2 23) Prior: A and B have index of ; C, D, and E have index of .

7 7 New: A, B, C, D, E, and F have index of

1 .

6

24) {A, B, C, G}, {A, C, G}, {B, C, G}, {C, G} ; C and G are critical to all winning coalitions.

25) 24

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Chapter 12 Exam A Name___________________________________

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Use the depiction of a slot machine to answer the question.

1) In how many ways can we obtain cherries on only the first and third wheels?

1)

2) In how many ways can we obtain bar on only the second and third wheels?

2)

Solve the problem.

3) How many different three-digit numbers can you form using the digits 1, 2, 3, 5, 6, 7, and 9 without repetition?

3)

4) Using the digits 3, 4, 5, 6, 7, 8, and 9, how many 5-digit numbers can be constructed if the number must begin with an odd digit and digits may not be repeated?

4)

5) How many license plates are possible consisting of 3 letters followed by 3 digits, if the first letter must be a C?

5)

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6) Stephanie is at the Mall and wants to stop at the bank on the way home. How many different direct routes can she take to make the trip from the Mall to her house, stopping at the bank on the way?

6)

7) The frequency setting for a garage door opener is determined by the positions of ten switches, each of which can be set to a ʺ+ʺ or ʺ-ʺ position. In how many ways can the switches be set?

7)

8) A law firm has nine male and nine female lawyers. A committee of five, two male lawyers and three female lawyers, is to be chosen to represent the firm at a conference. How many committees are possible?

8)

9) A twelve-sided die is rolled twice. In how many ways can this happen?

9)

10) A club has 21 members. In how many ways can they select a person to be President and a different person to be Treasurer?

10)

Evaluate the expression.

7!

11) 4! 3!

11)

12) C(4, 0)

12)

13)

5!

3! 2!

13)

14)

10!

(10 - 2)!

14)

15) P(13, 6)

15)

16) 5!

16)

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Use Pascalʹs triangle to answer the question.

17) Use the eighth row of Pascalʹs triangle to determine how many six-element subsets can be chosen from an eight-element set?

17)

Use a tree diagram to answer the question.

18) Using a tree diagram that shows how many ways a nickel, a dime, and a quarter can be flipped, determine how many ways you can get exactly one tail.

18)

19) Using a tree diagram that shows how many ways a nickel, a dime, and a quarter can be flipped, determine how many ways you can get exactly two heads.

Describe where the following number can be found in Pascalʹs triangle.

20) C(7,7)

19)

20)

21) C(14, 7)

21)

22) C(15, 0)

22)

Find the requested number.

23) Find the number of combinations when 9 objects are taken 6 at a time.

23)

Determine the required number of branches in the tree diagram described.

24) A tree diagram showing how many ways three dice could be rolled

24)

25) A tree diagram showing how many ways 3 coins could be flipped

25)

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Answer Key Testname: CHAPTER 12 EXAM A

1) 240 2) 54 3) 210 4) 1440 5) 676,000 6) 40 7) 1024 ways 8) 3024 9) 144 ways 10) 420 ways 11) 35 12) 1 13) 10 14) 90 15) 1,235,520 16) 120 17) 28 18) 3 19) 3 20) The last entry in the seventh row 21) The seventh entry in the 14th row 22) The 0 entry in the 15th row 23) 84 24) 216 25) 8

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Chapter 12 Exam B Name___________________________________

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Solve the problem.

1) Suppose that we wish to seat eight people, 4 men and 4 women, in a row of eight chairs. In how many ways can we seat the people with no restrictions?

A) 40,320 ways B) 576 ways C) 20,160 ways D) 16 ways 2) Stephanie is at the Mall and wants to stop at the bank on the way home. How many different direct routes can she take to make the trip from the Mall to her house, stopping at the bank on the way?

A) 24

B) 40

C) 30

1)

2)

D) 48

3) A club has 28 members. In how many ways can they select a person to be President and a different person to be Treasurer?

A) 378 ways B) 764 ways C) 756 ways D) 744 ways

3)

4) How many license plates are possible consisting of 3 letters followed by 2 digits, if the first letter must be a C? A) 67,600 B) 1,757,600 C) 68,440 D) 67,500

4)

Evaluate the expression.

5) P(9, 1) A) 80,640

5) B) 4.5

C) 362,880

D) 9

Use a tree diagram to answer the question.

6) Using a tree diagram that shows how many ways a nickel, a dime, and a quarter can be flipped, determine how many ways you can get exactly two heads.

A) 3 B) 4 C) 2 D) 5

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6)

Construct a list as requested.

7) Let M = S, P, O, M . List all of the ways that you can select two members of M with repetition allowed. The order in which you select the members is not important.

A) SP, SO, SM, PO, PM, OM B) SS, SP, SO, SM, PP, PS, PO, PM, OO, OS, OP, OM, MM, MS, MP, MO C) SS, SP, SO, SM, PP, PO, PM, OO, OM, MM D) SP, SO, SM, PS, PO, PM, OS, OP, OM, MS, MP, MO Find the requested number.

8) Find the number of combinations when 10 objects are taken 5 at a time.

A) 252 B) 15,120 C) 30,240 Determine the required number of branches in the tree diagram described.

9) A tree diagram showing how many ways three dice could be rolled A) 18 B) 186 C) 216

8) D) 240

9) D) 228

Use a tree diagram to answer the question.

10) Using a tree diagram that shows how many ways a nickel, a dime, and a quarter can be flipped, determine how many ways you can get exactly one tail.

A) 4 B) 6 C) 3 D) 2 Describe where the following number can be found in Pascalʹs triangle.

11) C(57, 3) A) The 57th entry in the third row B) The third entry in the 57th row C) The fifteenth entry in the 61st row D) The last entry in the third row Use a tree diagram to answer the question.

12) A family has 4 children. Using a tree diagram that shows how many ways the children could have been born, from first born to last born, determine how many ways the family could have had 2 boys and 2 girls.

A) 1 B) 8 C) 5 D) 6 Describe where the following number can be found in Pascalʹs triangle.

13) C(12, 3) A) The third entry in the 12th row B) The 11th entry in the third row C) The eighth entry in the 13th row D) The 12th entry in the third row Solve the problem.

14) The frequency setting for a garage door opener is determined by the positions of seven switches, each of which can be set to a ʺ+ʺ or ʺ-ʺ position. In how many ways can the switches be set?

A) 248 ways B) 49 ways C) 128 ways D) 2187 ways Evaluate the expression.

15) 3!

A) 2

7)

10)

11)

12)

13)

14)

15) B) 6

C) 12

D) 3

Describe where the following number can be found in Pascalʹs triangle.

16) C(13, 0) A) The 0 entry in the 14th row B) The 0 entry in the 13th row C) The 1st entry in the 12th row D) The 13th entry in the 0 row

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16)

Solve the problem.

17) How many different three-digit numbers can you form using the digits 1, 2, 3, 5, 6, 7, and 9 without repetition?

A) 160 B) 340 C) 35 D) 210 Describe where the following number can be found in Pascalʹs triangle.

18) C(7,7) A) The last entry in the eighth row B) The last entry in the seventh row C) The next to the last entry in the eighth row D) The next to the last entry in the seventh row

17)

18)

Use the depiction of a slot machine to answer the question.

19) In how many ways can we obtain cherries on only the second and third wheels?

A) 724 B) 722 C) 718 D) 720 Evaluate the expression.

9!

20) 8!

A) 9!

19)

20) B)

9 8

C) 9

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D) 1

Solve the problem.

21) A fourteen-sided die is rolled twice. In how many ways can this happen?

A) 196 ways B) 28 ways C) 392 ways

D) 206 ways

Determine the required number of branches in the tree diagram described.

22) A tree diagram showing how many ways 6 coins could be flipped A) 36 B) 13 C) 64

D) 128

21)

22)

Solve the problem.

23) Assume that you are rolling two dice  the first one is red; the second one is green.

In how many ways can you roll a sum less than 4?

A) 3 ways B) 4 ways C) 2 ways D) 5 ways Evaluate the expression.

6!

24) 8!

A)

1 2!

25) P(4, 0) A) 0.5

23)

24) 1 56

B) 2!

C) 56

D)

B) 48

C) 24

D) 1

25)

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Answer Key Testname: CHAPTER 12 EXAM B

1) A 2) B 3) C 4) A 5) D 6) A 7) C 8) A 9) C 10) C 11) B 12) D 13) A 14) C 15) B 16) B 17) D 18) B 19) D 20) C 21) A 22) C 23) A 24) D 25) D

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Chapter 13 Exam A Name___________________________________

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Answer the question.

6 1) If P(A) = then find the odds in favor of A happening.

7 A) 6 : 1 C) 1 : 6

1)

B) 6 : 7 D) None of the above is correct.

2) If the probability that an identified hurricane will make a direct hit on a certain stretch of beach is 1 , what are the odds against a direct hit?

50 A) 50 to 1

B) 48 to 1

C) 1 to 50

D) 49 to 1

3) If it has been determined that the probability of an earthquake occurring on a certain day in a 1 certain area is , what are the odds against an earthquake?

50 A) 1 to 50

B) 48 to 1

2)

C) 50 to 1

3)

D) 49 to 1

Find the indicated probability.

4) The following table relates the grades in an advanced mathematics course to the studentʹs year in college: Totals A B C D E (%) Freshmen 1 5 6 4 1 17 Sophomores 6 4 8 2 3 23 Juniors 5 7 14 6 2 34 Seniors 5 4 1 3 5 18 Grad Students 4 2 2 0 0 8 Totals (%) 21 22 31 15 11 100

4)

Let E be the event that the student is a sophomore. Let F be the event that the student received a grade of B. Find P(F∣E).

2 4 3 5 B) C) D) A) 11 23 23 22 5) You roll two fair dice. Let E be the event that an even total shows on the dice. Let F be the event that a four shows on at least one of the dice. Find P(F) and P(F∣E).

5 11 7 11 , P(F∣E) = B) P(F) = , P(F∣E) = A) P(F) = 18 36 18 36 C) P(F) =

1 5 , P(F∣E) = 3 18

D) P(F) =

1 1 , P(F∣E) = 3 13

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5)

List all equally likely outcomes in the sample space for the indicated experiment.

6) A box contains 2 blue cards numbered 1 through 2, and 3 green cards numbered 1 through 3. List the sample space of picking a blue card followed by a green card.

B) {(2, 3)} A) {(1, 1), (1, 2), (1, 3), (2, 1), (2, 2), (2, 3)} C) {(1,1), (1,2), (2, 1), (2, 2), (3, 1), (3, 2)} D) {(1, 2, 3)} 7) A box contains 3 blue cards numbered 1 through 3, and 4 green cards numbered 1 through 4. List the sample space of picking a blue card followed by a green card.

A) {(3, 4)} B) {(1, 2, 3, 4)}

C) {(1, 1), (1, 2), (1, 3), (1, 4), (2, 1), (2, 2), (2, 3), (2, 4), (3, 1), (3, 2), (3, 3), (3, 4)}

6)

7)

D) {(1, 1), (1, 2), (1, 3), (2, 1), (2, 2), (2, 3), (3, 1), (3, 2), (3, 3), (4, 1), (4, 2), (4, 3)}

Provide an appropriate response.

8) What is the probability that 18 flips of a coin will show exactly 12 tails?

A) 0.0142 B) 0.1416 C) 0.0708

8) D) 0.0354

9) Two dice are rolled until the sum of the two numbers is ten. Determine whether this experiment is a binomial experiment. If not, explain what property of a binomial experiment fails.

A) No; the probability of success is not the same from trial to trial.

B) Yes C) No; the number of trials is not fixed.

D) No; there are more than two outcomes.

9)

10) Select 5 cards with replacement from a standard 52-card deck and observe whether a queen is drawn.

Determine whether this experiment is a binomial experiment. If not, explain what property of a binomial experiment fails.

A) Yes B) No; the number of trials is not fixed.

C) No; the probability of success is not the same from trial to trial.

D) No; there are more than two outcomes.

10)

Solve the problem.

11) Seven slips of paper marked with the numbers 1, 2, 3, 4, 5, 6, and 7 are placed in a box and mixed well. Two are drawn. What are the odds that the sum of the numbers on the two selected slips is not 6?

A) 19 to 1 B) 21 to 2 C) 19 to 2 D) 9 to 1

11)

12) If you are given a 10-question true-false quiz, what is the probability that you will answer exactly 4 of the questions correctly by guessing?

A) 4.9219 B) 0.2051 C) 147.6563 D) 210.0000

12)

13) A survey of senior citizens at a doctorʹs office shows that 51% of the seniors take blood pressure lowering medication and 50% take cholesterol lowering medication. 17% take both medications.

What is the probability that a senior citizen takes either blood pressure or cholesterol lowering medication?

A) 0.670 B) 1.010 C) 1.180 D) 0.840

13)

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14) If two cards are drawn without replacement from a deck, find the probability that the second card is a spade, given that the first card was a spade.

3 4 11 11 B) C) D) A) 13 17 51 12

14)

15) Find the odds against correctly guessing the answer to a multiple choice question with 4 possible answers.

A) 4 : 1 B) 3 : 4 C) 3 : 1 D) 4 : 3

15)

16) A student is taking a standardized test consisting of multiple choice questions for which there are five options for each question. Five points are awarded for each correct answer, but the student loses 2 points for an incorrect answer. Questions left blank neither receive nor lose points. What is the minimum number of options that the student should be able to rule out before making a guess on any particular question?

B) None C) One D) Two A) Three

16)

17) If three cards are drawn without replacement from a deck, find the probability that the third card is a face card, given that the first card was a queen and the second card was a 5.

1 6 3 11 B) C) D) A) 5 25 13 50

17)

18) The odds against Chip beating his friend in a round of golf are 1 : 2. Find the probability that Chip will beat his friend.

2 1 1 1 B) C) D) A) 3 2 3 4

18)

19) We roll a pair of dice. If the sum of the dice is 7, you pay me $32. If the sum is not 7, I pay you the number of dollars indicated by the sum of the dice. What is the price that you should pay to play the game that would make the game fair?

B) $2.07 C) $0.50 D) $3.94 A) -$1.80

19)

20) If two fair dice are rolled, what is the probability that a total showing is either even or less than three?

17 1 5 5 B) C) D) A) 36 2 9 12

20)

21) We roll a pair of dice. If the sum of the dice is 7, you pay me $26. If the sum is not 7, I pay you the number of dollars indicated by the sum of the dice. What is your expected value for the game?

A) -$1.50 B) -$8.50 C) $1.50 D) $8.5

21)

22) If we toss four fair coins, what is the probability that we get exactly three heads?

1 1 1 1 A) B) C) D) 5 8 2 4

22)

23)

23) What are the odds of drawing a number greater than 2 from these cards?

A) 4 : 1 B) 4 : 5 C) 3 : 2

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D) 3 : 5

24) If a card is selected randomly from a standard 52 -card deck, what is the probability that we draw a five?

11 7 1 1 B) C) D) A) 52 52 26 13

24)

25) A survey of senior citizens at a doctorʹs office shows that 47% of the seniors take blood pressure lowering medication and 43% take cholesterol lowering medication. 7% take both medications.

What is the probability that a senior citizen takes only one of these medications given that he or she takes at least one of the medications?

B) 0.47 C) 0.920 D) -0.060 A) 0.43

25)

26) You are playing a game in which a single die is rolled. If an even number comes up, you win $18.

If an odd number comes up, you lose $18. Is this a fair game?

A) No B) Yes

26)

27) In a raffle, one thousand tickets are sold at $10 apiece. There is a grand prize of $4000, two second prizes of $600, and three third prizes of $100. Is this a fair game?

A) No B) Yes

27)

28) If two cards are drawn without replacement from a deck, find the probability that the second card is an ace, given that the first card was an ace.

1 3 4 3 B) C) D) A) 3 52 51 51

28)

29) If a single card is drawn from a standard 52-card deck, what is the probability that it is neither a King nor a club?

19 35 9 10 B) C) D) A) 26 52 13 13

29)

30)

30) What are the odds of drawing a 2 from these cards?

A) 1 : 4 B) 5 : 1

C) 1 : 5

D) 4 : 1

31) If a single fair die is rolled, find the probability of a 5 given that the number rolled is odd.

1 1 1 2 A) B) C) D) 2 6 3 3

31)

32) A survey revealed that 47% of people are entertained by reading books, 35% by watching TV, and 17% are entertained by both books and TV. What is the probability that a person will be entertained by books given that the person is entertained by TV? Give results to the nearest tenth of a percent.

B) 0.35 C) 0.47 D) 0.486 A) 0.362

32)

33) Of the coffee makers sold in an appliance store, 4% have either a faulty switch or a defective cord, 1.1% have a faulty switch, and 0.7% have both defects. What is the probability that a coffee maker will have a defective cord given that it has either a faulty switch or defective cord? Give results to the nearest tenth of a percent.

B) 0.900 C) 0.007 D) 0.011 A) 0.275

33)

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34) Bob earns both a salary and a commission as a salesman at an auto dealership. The following table lists his estimates of the probabilities of earning various commissions for the next month: Probability that Commission this will happen Less than $500 0.19 $500 - $999 0.23 $1000 - $1499 0.22 $1500 - $1999 0.17 $2000 - $2499 0.12 0.05 $2500 - $2999 $3000 - $3499 0.02 What is the probability that he will earn at least $500 in commissions?

A) 0.58 B) 0.81 C) 0.62

34)

D) 0.85

35) You play a game for which you pay the banker $3 to play. The banker then tosses 3 fair coins. If all coins show the same (all heads or all tails), you get $12, otherwise you get nothing. Is this a fair game?

A) Yes B) No

35)

36) If a single card is drawn from a standard 52-card deck, what is the probability that it is either a Ace or a heart?

7 4 17 3 B) C) D) A) 26 13 52 13

36)

37)

37) What are the odds of drawing an even number from these cards?

A) 3 : 2 B) 5 : 2 C) 2 : 5

D) 2 : 3

Use a Punnett square constructed for the stated situation to answer the associated question.

38) In crossbreeding certain types of flowers, color does not dominate. For example, a flower with one blue gene and one red gene will have purple flowers. Consider the result of crossing two of these purple flowers. What is the probability of getting blue flowers ?

1 1 3 B) C) D) A) 0 4 2 4 Write the event as a set of outcomes.

39) When we roll two dice, the total showing is eight.

A) {(2, 6), (3, 5), (5, 3), (6, 2)} B) {(1, 7), (2, 6), (3, 5), (4, 4), (5, 3), (6, 2), (7, 1)} C) {(2, 6), (3, 5), (4, 4)} D) {(2, 6), (3, 5), (4, 4), (5, 3), (6, 2)}

39)

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Answer the question.

40) A pair of fair dice are rolled. Let E be the event that the total showing is greater than five.

Let F be the event that the total showing is odd. Are E and F dependent events?

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38)

40)

Construct a Punnett square for the stated situation.

41) In crossbreeding certain types of flowers color does not dominate. For example, a flower with one blue gene and one red gene will have purple flowers. Show the result of crossing a pure-bred blue flower with a purple flower.

41)

Imagine that you are taking part in a study to test a new cold medicine. Although you donʹt know exactly what drug you are taking, the probability that it is drug A is 30%, that it is drug B is 10%, and that it is drug C, 60%. From past clinical trials, the probabilities that these drugs will improve your condition are: A (20%), B (50%), and C (70%).

42) 42) What is the probability that you donʹt improve?

43) What is the probability that you will improve given that you are taking drug C?

43)

44) If you improve, what is the probability that you are taking drug A?

44)

45) What is the probability that you will improve given that you are taking drug B?

45)

Solve the problem.

46) The odds against Carl beating his friend in a round of golf are 9 : 4. Find the probability that Carl will beat his friend.

46)

47) A student is taking a standardized test consisting of multiple choice questions for which there are five options for each question. Four points are awarded for each correct answer, but the student loses 2 points for an incorrect answer. Questions left blank neither receive nor lose points. Is it in the studentʹs best interest to guess?

47)

48) If two fair dice are rolled, find the probability of a sum of 6 given that the roll is a ʺdoubleʺ.

48)

49) The table gives information, broken down by year in college, about the number of credit hours for which students are enrolled.

49)

14+ 11-13 10 or less hours hours hours TOTALS Freshmen 237 105 386 728 Sophomores 336 360 423 1119 Juniors 57 325 154 636 Seniors 111 276 95 482 TOTALS 841 1066 1058 2965 What is the probability that a student selected at random is a sophomore or is taking between 11 and 13 hours? Round your answer to 2 decimal places.

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Use the complement formula to answer the question.

50) The table gives information about the high temperature in Bristol, Wisconsin for the 365 days in a given year.

High Temp Number of Days in °F During the Year 2 -30 to -11 20 -10 to 9 10 to 29 58 30 to 49 79 50 to 69 91 70 to 89 93 90 to 109 22 If we select one day at random from the 365 days in that year, what is the probability that the high temperature that day was greater than 9 ° F? Round your answer to 2 decimal places.

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50)

Answer Key Testname: CHAPTER 13 EXAM A

1) A 2) D 3) D 4) C 5) A 6) A 7) C 8) C 9) C 10) A 11) C 12) B 13) D 14) C 15) C 16) D 17) A 18) B 19) C 20) C 21) C 22) D 23) C 24) A 25) C 26) B 27) A 28) A 29) D 30) A 31) C 32) D 33) B 34) B 35) A 36) C 37) D 38) B 39) D 40) Yes 41)

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Answer Key Testname: CHAPTER 13 EXAM A

42) 0.47 43) 0.70 44) 0.113 45) 0.50 4 46) 13 47) No 1 48) 6 49) 0.62 50) 0.94

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Chapter 13 Exam B Name___________________________________

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Answer the question.

1) A pair of fair dice are rolled. Let E be the event that a one shows on the second die. Let F be the event that the total showing is even. Are E and F dependent events?

A) Yes B) No 2) If it has been determined that the probability of an earthquake occurring on a certain day in a 1 certain area is , what are the odds against an earthquake?

25 A) 23 to 1 3) If P(A) =

B) 25 to 1

C) 1 to 25

2)

D) 24 to 1

1 then find the odds in favor of A happening.

7

A) 6 : 1 C) 1 : 6

1)

3)

B) 1 : 7 D) None of the above is correct.

Find the indicated probability.

4) The following table relates the grades in an advanced mathematics course to the studentʹs year in college: Totals A B C D E (%) Freshmen 1 5 6 4 1 17 Sophomores 6 6 8 2 3 25 Juniors 5 7 10 6 2 30 Seniors 5 4 1 5 5 20 Grad Students 4 2 2 0 0 8 Totals (%) 21 24 27 17 11 100 Let E be the event that the student is a graduate student. Let F be the event that the student received an A. Find P(F∣E) .

1 5 4 4 A) B) C) D) 2 8 21 9

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4)

5) The following table relates the grades in an advanced mathematics course to the studentʹs year in college: Totals A B C D E (%) Freshmen 3 5 6 4 1 19 Sophomores 6 2 8 2 3 21 Juniors 5 7 13 6 2 33 Seniors 5 4 1 4 5 19 Grad Students 4 2 2 0 0 8 Totals (%) 23 20 30 16 11 100

5)

Let E be the event that the student received a grade of A. Let F be the event that the student is a graduate student. Find P(F∣E) .

4 8 1 3 B) C) D) A) 23 23 2 23 6) The following table relates the grades in an advanced mathematics course to the studentʹs year in college: Totals A B C D E (%) Freshmen 3 5 6 4 1 19 Sophomores 6 4 8 2 3 23 Juniors 5 7 11 6 2 31 Seniors 5 4 1 5 5 20 Grad Students 3 2 2 0 0 7 Totals (%) 22 22 28 17 11 100

6)

Let E be the event that the student is a sophomore. Let F be the event that the student received a grade of B. Find P(F∣E).

5 4 3 2 B) C) D) A) 22 23 23 11 7) The following table relates the grades in an advanced mathematics course to the studentʹs year in college: Totals A B C D E (%) Freshmen 1 5 6 4 1 17 Sophomores 6 5 8 2 3 24 Juniors 5 7 12 6 2 32 Seniors 5 4 1 3 5 18 Grad Students 5 2 2 0 0 9 Totals (%) 22 23 29 15 11 100

7)

Let E be the event that the student received a grade of B. Let F be the event that the student is a sophomore. Find P(F∣E).

1 6 5 5 B) C) D) A) 6 23 23 24 8) A single card is drawn from a standard 52-card deck. Find P(jack ∣ face card).

1 A) 1 B) C) 0 3 Copyright © 2022 Pearson Education, Inc.

8) 2 D) 3

9) A box contains 24 blue marbles, 13 green marbles, and 13 red marbles. Two marbles are selected at random without replacement. Let E be the event that the first marble selected is green. Let F be the event that the second marble selected is green. Find P(F ∣E) .

13 13 6 12 B) C) D) A) 50 49 25 49 Find the requested probability.

10) If P(A ∪ B) = 0.63, P(B) = 0.45, and P(A ∩ B) = 0.13, find P(A).

A) 0.43 B) 0.31 C) 0.21

D) 0.26

11) If P(A ∩ B) = 0.16, P(A) = 0.34, and P(B) = 0.47, find P(A ∪ B).

A) 0.76 B) 0.65 C) 0.7

D) 0.61

10)

11)

List all equally likely outcomes in the sample space for the indicated experiment.

12) The aces are separated from a deck of standard playing cards and shuffled. Two are randomly selected.

A) {(C, D, H, S)} B) {(4, 4)} C) {(C, D), (C, H), (C, S), (D, H), (D, S), (H, S)} D) {(C, D), (C, H), (C, S), (D, C), (D, H), (D, S), (H, C), (H, D), (H, S), (S, C), (S, D), (S, H)} 13) A box contains 3 blue cards numbered 1 through 3, and 4 green cards numbered 1 through 4. List the sample space of picking a blue card followed by a green card.

A) {(3, 4)} B) {(1, 1), (1, 2), (1, 3), (2, 1), (2, 2), (2, 3), (3, 1), (3, 2), (3, 3), (4, 1), (4, 2), (4, 3)} D) {(1, 1), (1, 2), (1, 3), (1, 4), C) {(1, 2, 3, 4)} (2, 1), (2, 2), (2, 3), (2, 4), (3, 1), (3, 2), (3, 3), (3, 4)} Provide an appropriate response.

14) Select 7 cards with replacement from a standard 52-card deck and observe whether a queen is drawn.

Determine whether this experiment is a binomial experiment. If not, explain what property of a binomial experiment fails.

A) No; the number of trials is not fixed.

B) No; the probability of success is not the same from trial to trial.

C) Yes D) No; there are more than two outcomes.

Solve the problem.

15) A company estimates that it has a 40% chance of being successful in bidding on a $45,000 contract.

If it costs $8000 in consultant fees to prepare the bid, what is the expected gain or loss for the company if it decides to bid on this contract?

A) $30,237.72 B) $29,875.06 C) $30,057.57 D) $10,000.00 16) In a certain lottery game, you must pick five digits in order from 0 to 9 and duplicates are allowed.

If you win, the prize is $12,000. What lottery ticket price would make this game fair?

A) $0.12 B) $0.10 C) $0.26 D) $0.19

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9)

12)

13)

14)

15)

16)

17) We roll a pair of dice. If the sum of the dice is 7, you pay me $28. If the sum is not 7, I pay you the number of dollars indicated by the sum of the dice. What is the price that you should pay to play the game that would make the game fair?

B) $2.74 C) -$1.13 D) $1.17 A) $4.61

17)

18) You play a game for which you pay the banker $7 to play. The banker then tosses 3 fair coins. If all coins show the same (all heads or all tails), you get $28, otherwise you get nothing. Is this a fair game?

A) No B) Yes

18)

19) You are playing a game in which a single die is rolled. If an even number comes up, you win $4. If an odd number comes up, you lose $4. Is this a fair game?

A) No B) Yes

19)

20) You are playing a game in which a single die is rolled. If a 2 or a 5 comes up, you win $48, otherwise you lose $36. What is your expected value for the game?

A) -$8 B) -$10 C) -$9 D) $8

20)

21) A survey of senior citizens at a doctorʹs office shows that 52% of the seniors take blood pressure lowering medication and 40% take cholesterol lowering medication. 17% take both medications.

What is the probability that a senior citizen takes only one of these medications given that he or she takes at least one of the medications?

B) 0.770 C) 0.40 D) -0.060 A) 0.52

21)

22) Of the coffee makers sold in an appliance store, 3% have either a faulty switch or a defective cord, 1.7% have a faulty switch, and 0.1% have both defects. What is the probability that a coffee maker will have a defective cord given that it has either a faulty switch or defective cord? Give results to the nearest tenth of a percent.

B) 0.567 C) 0.467 D) 0.017 A) 0.001

22)

23) A survey revealed that 46% of people are entertained by reading books, 35% by watching TV, and 17% are entertained by both books and TV. What is the probability that a person will be entertained by books given that the person is entertained by TV? Give results to the nearest tenth of a percent.

B) 0.486 C) 0.370 D) 0.35 A) 0.46

23)

24) If three cards are drawn without replacement from a deck, find the probability that the third card is a face card, given that the first card was a queen and the second card was a 5.

1 11 6 3 B) C) D) A) 5 50 25 13

24)

25) If two cards are drawn without replacement from a deck, find the probability that the second card is a spade, given that the first card was a spade.

11 4 11 3 B) C) D) A) 51 17 12 13

25)

26) If a single fair die is rolled, find the probability of a 5 given that the number rolled is odd.

1 2 1 1 A) B) C) D) 3 3 2 6

26)

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27) For a school project, Sue interviewed a total of 100 persons who were either lawyers or salesmen.

She asked them if they were happy or unhappy with their occupation. Of the 59 lawyers interviewed, 14 were unhappy, however, only 9 of the salesmen were unhappy. Suppose that one of the persons interviewed is selected at random. Find the probability that the person selected is happy.

B) 0.77 C) 0.84 D) 0.74 A) 0.8

27)

28) Bob earns both a salary and a commission as a salesman at an auto dealership. The following table lists his estimates of the probabilities of earning various commissions for next month: Probability that Commission this will happen Less than $500 0.11 $500 - $999 0.23 $1000- $1499 0.28 $1500- $1999 0.17 $2000- $2499 0.12 $2500- $2999 0.07 $3000- $3499 0.02

28)

What is the probability that he will earn no more than $1999 in commissions?

A) 0.83 B) 0.79 C) 0.21

D) 0.24

29) Bob earns both a salary and a commission as a salesman at an auto dealership. The following table lists his estimates of the probabilities of earning various commissions for the next month: Probability that Commission this will happen Less than $500 0.12 $500 - $999 0.25 $1000 - $1499 0.29 $1500 - $1999 0.17 $2000 - $2499 0.12 0.03 $2500 - $2999 $3000 - $3499 0.02 What is the probability that he will earn at least $500 in commissions?

A) 0.88 B) 0.67 C) 0.92

D) 0.63

30) The table gives information, broken down by year in college, about the number of credit hours for which students are enrolled.

14+ 11-13 10 or less hours hours hours TOTALS Freshmen 237 464 386 1087 Sophomores 326 360 423 1109 Juniors 57 325 151 633 Seniors 110 276 109 495 TOTALS 830 1425 1069 3324 What is the probability that a student selected at random is a sophomore or is taking between 11 and 13 hours? Round your answer to 2 decimal places.

A) 0.65 B) 0.82 C) 0.88 D) 0.52

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29)

30)

31) The odds against Chip beating his friend in a round of golf are 1 : 5. Find the probability that Chip will beat his friend.

5 5 1 1 B) C) D) A) 7 6 7 6

31)

32) The odds in favor of Jerome beating his friend in a round of golf are 1 : 3. Find the probability that Jerome will beat his friend.

1 1 B) C) 1 D) A) 4 5

32)

33) In horse racing, a trifecta is a bet for which you must pick the first, second, and third place winners in their proper order in order to win a payoff. If there are thirteen horses racing, and you randomly select three as your bet in the trifecta, what is the probability that you will win?

1 1 1 1 B) C) D) A) 286 1706 1716 572

33)

34) If we toss four fair coins, what is the probability that we get exactly four tails?

1 1 1 B) C) A) 32 20 16

34) 1 D) 8

35) If a card is selected randomly from a standard 52 -card deck, what is the probability that we draw a heart?

5 11 1 4 B) C) D) A) 13 52 4 13

35)

36) A number cube labeled with numbers 1, 2, 3, 4, 5, and 6 is tossed. What are the odds for the cube showing a number less than 3?

A) 1 : 3 B) 1 : 2 C) 2 : 1 D) 1 : 1

36)

37)

37) What are the odds of drawing a 5 from these cards?

A) 4 : 1 B) 1 : 4

C) 5 : 1

D) 1 : 5

Use a Punnett square constructed for the stated situation to answer the associated question.

38) Consider the genetic possibilities for a child of parents who both have sickle cell anemia. What is the probability that the child will have sickle cell anemia?

1 1 D) A) 1 B) 0 C) 2 4

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38)

Use the complement formula to answer the question.

39) The table gives information about the high temperature in Bristol, Wisconsin for the 365 days in a given year.

High Temp Number of Days in °F During the Year 4 -30 to -11 30 -10 to 9 10 to 29 46 30 to 49 78 50 to 69 89 70 to 89 96 90 to 109 22 If we select one day at random from the 365 days in that year, what is the probability that the high temperature that day was greater than 9 ° F? Round your answer to 2 decimal places.

A) 1.02 B) 0.88 C) 0.92 D) 0.91 40) If two fair dice are rolled, what is the probability that a total showing is more than three?

5 17 8 11 B) C) D) A) 6 18 9 12

40)

Write the event as a set of outcomes.

41) We select a black Jack from a standard 52 -card deck.

A) {Jack of spades, Jack of clubs} B) {Jack of spades} C) {Jack of spades, Jack of clubs, Jack of diamonds, Jack of hearts} D) {Jack of clubs} 42) We flip three coins and obtain more tails than heads.

A) {ttt, tth, tht, htt} B) {ttt} C) {ttt, tth}

41)

42) D) {tth, tht, htt}

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Construct a Punnett square for the stated situation.

43) Show the genetic possibilities for a child whose mother has cystic fibrosis and whose father is a carrier of cystic fibrosis. Denote the normal gene by N and the cystic fibrosis gene by c to indicate its recessive nature.

43)

44) In crossbreeding certain types of flowers color does not dominate. For example, a flower with one blue gene and one red gene will have purple flowers. Show the result of crossing a pure-bred blue flower with a purple flower.

44)

45) In crossbreeding certain types of flowers color does not dominate. For example, a flower with one blue gene and one red gene will have purple flowers. Show the result of crossing a pure-bred blue flower with a pure-bred red flower.

45)

46) Both parents are carriers of sickle cell anemia.

46)

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39)

Imagine that you are taking part in a study to test a new cold medicine. Although you donʹt know exactly what drug you are taking, the probability that it is drug A is 30%, that it is drug B is 10%, and that it is drug C, 60%. From past clinical trials, the probabilities that these drugs will improve your condition are: A (20%), B (50%), and C (70%).

47) 47) If you improve, what is the probability that you are taking drug A? 48) What is the probability that you will improve given that you are taking drug B?

48)

49) What is the probability that you will improve given that you are taking drug A?

49)

50) Fill in the probabilities on the following tree to illustrate this drug trial situation.

50)

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Answer Key Testname: CHAPTER 13 EXAM B

1) B 2) D 3) C 4) A 5) B 6) C 7) D 8) B 9) A 10) B 11) B 12) D 13) D 14) C 15) D 16) A 17) D 18) B 19) B 20) A 21) B 22) C 23) B 24) C 25) C 26) A 27) B 28) B 29) A 30) A 31) C 32) B 33) D 34) A 35) D 36) B 37) B 38) A 39) D 40) A 41) A 42) A

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Answer Key Testname: CHAPTER 13 EXAM B

43)

44)

45)

46)

47) 0.113 48) 0.50 49) 0.20

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Answer Key Testname: CHAPTER 13 EXAM B

50)

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Chapter 14 Exam A Name___________________________________

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Calculate the linear correlation coefficient.

1) (3, 4), (5, 8), (6, 7), (6, 8) A) 0.78 B) -0.87

C) -0.78

D) 0.87

2) (2, 11), (2, 6), (10, 6), (18, 2) A) -0.81 B) 0.83

C) 0.81

D) -0.83

1)

2)

Complete the frequency/relative frequency table for the data given.

3) Lori asked 24 students how many hours they spent doing homework during the previous week.

11

11

11

9

11

11

15

11

11

8

12

11

11

12

11 11

12

11

11

11

11 12

12

9

Hours Frequency Relative Frequency 8-9 10-11 12-13 14-15 A)

B) Hours Frequency Relative Frequency 8-9 3 1/8 10-11 13 13/24 12-13 7 7/24 14-15 1 1/24

Hours Frequency Relative Frequency 8-9 3 1/8 10-11 15 5/8 12-13 5 5/24 14-15 1 1/24

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3)

Construct a bar graph as requested.

4) Students in Mr. Masonʹs classes collected items from different countries. The data show how many of each item one class collected. Construct a bar graph for the frequency data.

Stamps, 9 Postcards, 11 Coins, 7 Books, 13 A)

B)

Collected Items from Foreign Countries

Collected Items from Foreign Countries

5) The table lists blood types in a sample of hospital patients. Construct a bar graph for the relative frequency data.

Blood type O A B AB

4)

Frequency

Relative frequency

22 19 6 3

0.44 0.38 0.12 0.06

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5)

A)

B)

C)

6) The table lists winners of the Wimbledon womenʹs singles title for the years 1976 -1995. Construct a bar graph for the relative frequency data.

Winner C. Evert V. Wade M. Navratilova C. Martinez S. Graf E. Goolagong

Frequency 2 1 9 1 6 1

Relative frequency 0.10 0.05 0.45 0.05 0.30 0.05

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6)

A)

B)

C)

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Construct a box-and-whisker plot for the given data.

7) The test scores of 40 students are listed below.

25 59 72 81

35 62 73 82 A)

43 63 74 83

44 65 76 85

47 66 77 89

48 68 77 92

54 69 78 93

55 69 79 94

56 71 80 97

7)

57 72 81 98 B)

C)

D)

Determine the linear correlation coefficient for the data and also determine whether we can be 95% or 99% confident that there is significant linear correlation between the variables.

8) 8) The table below lists the number of years of education past high school and the annual income of five people.

Years of Education Annual Income Past High School (in $thousands) 0 21 2 23 3 24 4 26 5 26 A) 0.98; 99% confident C) -0.98; 99% confident Find the line of best fit for the data.

9) (24, 15), (26, 13), (28, 20), (30, 16), (32, 24) A) y = -1.05x - 11.8 C) y = 1.05x + 11.8

B) -0.98; 95% confident D) 0.98; 95% confident

9) B) y = 1.05x - 11.8 D) y = -1.05x + 11.8

10) As a car begins to accelerate, the gas mileage is poor. As the speed increases, the gas mileage continues to increase. The gas mileage increases for a while, then as the speed increases further, the mileage begins to decrease. The table of data below illustrates this.

Speed in Miles Mileage in Miles per Hour per Gallon 25 30 40 30 50 31 60 30 70 28 A) y = 0.06x + 25.8 C) y = -0.06x - 25.8

B) y = 0.06x - 25.8 D) y = -0.06x + 25.8

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10)

Find the mean and standard deviation of the given data. Round to the nearest tenth, if necessary.

11) The following are the ages of 17 people at their 50-year college reunion: Score 69 71 72 73 76 79 Frequency 2 7 4 2 1 1 A) Mean = 72, standard deviation = 2.4 B) Mean = 71, standard deviation = 2.9 C) Mean = 71, standard deviation = 2.4 D) Mean = 72, standard deviation = 2.9 12) The office manager at an accounting firm counted the number of employees that were in the coffee room each hour during the work week. The results are summarized in the following bar graph.

A) Mean = 3.4, standard deviation = 2.6 C) Mean = 3.8, standard deviation = 2.6 Find the missing value.

13) 95 = mean 9 = standard deviation 99 = raw score ______ = z-score A) 0.947

12)

B) Mean = 3.4, standard deviation = 1.9 D) Mean = 3.8, standard deviation = 1.9

13)

B) 0.444

Find the range for the set of data given.

14) 120 504 202 602 449 248 A) 504 B) 482 15) 6 17 1 14 10 A) 16

11)

C) 2.25

D) -0.947

C) 46

D) 120

14)

15) B) 17

C) 4

D) 1

Solve the problem.

16) Assume that in your psychology class you have earned the following test scores: 93, 87, 66, 77; and only one test remains. If you need a mean score of 80 to earn a ʺBʺ, then what minimum score must you obtain on the last test?

A) 80 B) 84 C) 83 D) 77

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16)

17) The ages of people randomly surveyed on a college campus are summarized in the bar graph.

How many people were 22 years old or older?

A) 17 people B) 8 people

C) 13 people

17)

D) 15 people

18) A manufacturer plans to provide a warranty on a CD player. Assume that the set of failure times for the player is normally distributed with a mean time of 12,000 hours and a standard deviation of 2,000 hours. Assume that the typical purchaser will use the CD player for 5 hours per day. The manufacturer does not want more than 3% of the CD players returned as defective within the warranty period. What is the longest warranty period (in months) that will satisfy that criterion?

(Assume that there are 31 days in each month.)

B) 50 months C) 53 months D) 48 months A) 58 months

18)

19) The ages of people randomly surveyed on a college campus are summarized in the bar graph.

19)

What age occurs most frequently?

A) 18 years B) 22 years

C) 26 years

D) 23 and 24 years

20) Assume that math SAT scores are normally distributed with a mean of 500 and a standard deviation of 100. If you scored 560, what percentage of those taking the test scored below you?

A) 72.6% B) 70.1% C) 68.8% D) 66.7%

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20)

21) Assume that the mean length of a human pregnancy is 268 days with a standard deviation of 9 days. What percentage of human pregnancies do we expect to last no more than 260 days?

A) 31.3% B) 29.6% C) 18.7% D) 20.4%

21)

22) Assume that in your earth science class you have earned the following test scores: 91, 94, 89, 92; and only one test remains. If you need a mean score of 90 to earn a ʺAʺ, then what minimum score must you obtain on the last test?

A) 86 B) 91 C) 90 D) 84

22)

23) If you score an 80 on an examination that has a mean score of 73 and a standard deviation of 5, to what percentile does your score correspond?

A) 89th B) 90th C) 88th D) 91st

23)

24) Assume that among the members of a menʹs gym, the distribution of body weights has a mean of 188 pounds and a standard deviation of 7. If 267 men belong to the gym, how many of them do you expect to be over 200 pounds?

D) About 11 or 12 A) About 12 or 13 B) About 10 or 11 C) About 13 or 14

24)

Solve the problem. Assume that the given distribution is normal.

25) Due to random variations in the operation of an automatic hot chocolate machine, not every cup is filled with the same amount of hot chocolate. Assume that the mean amount dispensed is 12 ounces with a standard deviation of 0.7 ounces. What percentage of the cups should have more than 12.7 ounces of hot chocolate?

B) 34% C) 32% D) 16% A) 25% Solve the problem. Round to the nearest hundredth, if necessary.

26) The following data gives the number of applicants that applied for a job at a given company each month of 1999: 62, 70, 68, 75, 83, 78, 80, 85, 82, 68, 66, 62. What is the median of the data?

B) 72.5 A) There is no median.

C) 70 D) 75 27) Assume that the professor in a class assigns grades based on the following: A: scores which are 1.5 or more standard deviations above the mean.

B: scores which are between 0.5 and 1.5 standard deviations above the mean.

C: scores which are between 0.5 standard deviations below the mean and 0.5 standard deviations above the mean.

D: scores which are between 0.5 and 1.5 standard deviations below the mean.

F: scores which are 1.5 or more standard deviations below the mean.

25)

26)

27)

The scores in the class are 85, 78, 95, 81, 70, 88, 84, 90, 68, 74. What grade does the person earning the 84 get?

B) A C) C D) D A) B 28) The following data gives the number of applicants that applied for a job at a given company each month of 1999: 64, 67, 96, 77, 78, 84, 87, 89, 90, 96, 72, 64. What is the mode of the data?

A) There is no mode.

B) 64 C) 96 D) 96 and 64

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28)

State what kind of correlation, if any, the scatterplot indicates.

29)

29)

y 20 18 16 14 12 10 8 6 4 2 1 2 3 4 5 6 7 8 9 10 11 12

x

A) positive correlation C) negative correlation

B) significant positive correlation D) no correlation

30)

30) y 10 9 8 7 6 5 4 3 2 1 10 20 30 40 50 60 70 80 90 100110

A) positive correlation C) significant negative correlation

x

B) no correlation D) negative correlation

This double-bar graph shows the number of male (M) and female (F) athletes at a university over a four -year period.

Answer the question.

YEAR 31) Which year had the smallest number of female athletes?

A) 1988 B) 1989 C) 1986

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31) D) 1987

32) Which year had the greatest number of female athletes?

A) 1989 B) 1986 C) 1987

D) 1988

33) Which year had the smallest number of male athletes?

A) 1986 B) 1987 C) 1989

D) 1988

34) Which year had the greatest number of male athletes?

A) 1987 B) 1986 C) 1989

D) 1988

Use a table to find a z-score that fits the given conditions. Interpolate if necessary.

35) 22% of the area under the standard normal curve is below the score.

A) -0.77 B) -0.58 C) -0.81

32)

33)

34)

35) D) -0.61

Use a table to find the percentage of the area under the standard normal curve between the two values. Round your answer to the nearest tenth.

36) z = 0 and z = 1.12 36) A) 36.4% B) 34.6% C) 38.9% D) 36.9% Use the table below to determine whether we can be 95% or 99% confident that there is significant linear correlation between x and y. n α = 0.05 α = 0.01 4 0.950 0.999 5 0.878 0.959 6 0.811 0.917 7 0.754 0.875 8 0.707 0.834 9 0.666 0.798 10 0.632 0.765 11 0.602 0.735 12 0.576 0.708 13 0.553 0.684 14 0.532 0.661 15 0.514 0.641 16 0.497 0.623 17 0.482 0.606 18 0.468 0.590 19 0.456 0.575 20 0.444 0.561 37) (5, 14), (5, 9), (19, 9), (22, 5) 37) A) We can be 99% confident.

B) neither C) We can be 95% confident.

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SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Construct the specified histogram.

38) The weights (in ounces) of 38 tomatoes are shown below. Construct a histogram to represent the data. Use 8 classes with a class width of 0.2 and begin with a lower class boundary of 1.95.

2.1 3.3 2.0 2.8 3.4 3.5 2.7 3.1 3.0 2.4 2.6 2.9 2.0 2.8 3.3 3.4 2.7 2.1 2.5 2.8 2.3 3.0 3.3 2.6 2.0 3.5 3.1 2.0 2.9 3.2 3.4 2.2 2.5 2.5 2.9 2.8 3.0 3.2

38)

39) In a survey, 20 people were asked how many magazines they had purchased during the previous year. The results are shown below. Construct a histogram to represent the data.

Use 4 classes with a class width of 10 and begin with a lower class boundary of -0.5.

6 15 3 36 25 18 12 18 5 30 24 7 0 22 33 24 19 4 12 9

39)

40) During the quality control process at a manufacturing plant, 142 finished items are randomly selected and weighed. The results are summarized in the frequency table below.

Construct a relative-frequency histogram corresponding to the frequency table.

40)

Weight (g) Frequency 0.35 - 0.44 32 0.45 - 0.54 82 0.55 - 0.64 17 0.65 - 0.74 11

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41) In a survey, 26 voters were asked their age. The results are shown below. Construct a histogram to represent the data. Use 5 classes.

43 56 28 63 67 66 52 48 37 51 40 60 62 66 45 21 35 49 32 53 61 53 69 31 48 59

41)

42) The frequency table below shows the number of days off in a given year for 30 police detectives.

42)

Days off Frequency 0-1 10 2-3 1 4-5 7 6-7 7 8-9 1 10 or more 4 Construct a relative-frequency histogram.

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43) The students in Mrs. Loganʹs Spanish class received the following scores on a test.

Construct a histogram to represent the data. Use 4 classes with a class width of 10 and begin with a lower class boundary of 59.5 75 94 87 83 78 72 65 75 82 78 97 72 87 94 72 83 87 95 85 97 69

43)

44) In a survey, 20 voters were asked their age. The results are summarized in the frequency table below. Construct a histogram corresponding to the frequency table.

44)

AGE OF NUMBER OF VOTER VOTERS 20-29 5 30-39 5 40-49 6 50-59 0 60-69 4

Solve the problem.

45) A researcher is comparing two different drugs to determine which is more effective at lowering cholesterol. The following data represent, for each drug, the drop in cholesterol over a three-month period for comparable patients. Represent the two sets of data on a single stem-and-leaf display. Which drug, if either, seems to be more effective?

Drug B: 32, 28, 25, 45, 36, 21, 24, 47, Drug A: 10, 34, 26, 30, 17, 18, 23, 49, 31, 10, 55, 25, 25, 46, 22, 19 34, 12, 29, 53, 15, 45, 16, 17

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45)

Answer Key Testname: CHAPTER 14 EXAM A

1) D 2) D 3) B 4) A 5) B 6) C 7) B 8) A 9) B 10) A 11) A 12) C 13) B 14) B 15) A 16) D 17) C 18) C 19) A 20) A 21) C 22) D 23) D 24) D 25) D 26) B 27) C 28) D 29) A 30) B 31) C 32) D 33) A 34) C 35) A 36) D 37) B

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Answer Key Testname: CHAPTER 14 EXAM A

38)

39)

40)

41)

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Answer Key Testname: CHAPTER 14 EXAM A

42) 43)

44)

45)

Drug A Drug B 98700 1 2567 65532 2 14589 410 3 246 96 4 557 5 5 3 Neither drug seems to be more effective than the other.

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Chapter 14 Exam B Name___________________________________

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Calculate the linear correlation coefficient.

1) (5, 14), (5, 9), (19, 9), (22, 5) Construct a bar graph as requested.

2) Students in Mr. Masonʹs classes collected items from different countries. The data show how many of each item one class collected. Construct a bar graph for the frequency data.

1)

2)

Stamps, 9 Postcards, 11 Coins, 7 Books, 13 3) The table lists winners of the Wimbledon womenʹs singles title for the years 1976 -1995.

Construct a bar graph for the frequency data.

Winner

Frequency

C. Evert V. Wade M. Navratilova C. Martinez S. Graf E. Goolagong

2 1 9 1 6 1

3)

Relative frequency 0.10 0.05 0.45 0.05 0.30 0.05

Construct a box-and-whisker plot for the given data.

4) The weekly salaries (in dollars) of 24 randomly selected employees of a company are shown below.

4)

310 320 450 460 470 500 520 540 580 600 650 700 710 840 870 900 1000 1200 1250 1300 1400 1720 2500 3700 5) The normal monthly precipitation (in inches) for August is listed for 20 different U.S. cities.

0.4 1.0 1.5 1.6 2.0 2.2 2.4 2.7 3.4 3.4 3.5 3.6 3.6 3.7 3.7 3.9 4.1 4.2 4.2 7.0

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5)

6) The highest temperatures ever recorded (in °F) in 32 different U.S. states are shown below.

6)

100 100 105 105 106 106 107 107 109 110 110 112 112 112 114 114 114 115 116 117 118 118 118 118 118 119 120 121 122 125 128 134 Construct the specified histogram.

7) The frequency table below shows the number of days off in a given year for 30 police detectives.

7)

Days off Frequency 0-1 10 2-3 1 4-5 7 6-7 7 8-9 1 10 or more 4 Construct a histogram.

8) The weights (in ounces) of 38 tomatoes are shown below. Construct a histogram to represent the data. Use 8 classes with a class width of 0.2 and begin with a lower class boundary of 1.95.

2.1 3.3 2.0 2.8 3.4 3.5 2.7 3.1 3.0 2.4 2.6 2.9 2.0 2.8 3.3 3.4 2.7 2.1 2.5 2.8 2.3 3.0 3.3 2.6 2.0 3.5 3.1 2.0 2.9 3.2 3.4 2.2 2.5 2.5 2.9 2.8 3.0 3.2

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8)

9) In a survey, 20 voters were asked their age. The results are summarized in the frequency table below. Construct a histogram corresponding to the frequency table.

9)

AGE OF NUMBER OF VOTER VOTERS 20-29 5 30-39 5 40-49 6 50-59 0 60-69 4

Find the line of best fit for the data.

10) (12, 54), (14, 53), (16, 55), (18, 54), (20, 56) Find the mean and standard deviation of the given data. Round to the nearest tenth, if necessary.

11) The following are the heights, in inches, of a group of college students: 72, 68, 62, 64, 66, 74, 70, 60, 63, 67, 69, 67 12) The office manager at an accounting firm counted the number of employees that were in the coffee room each hour during the work week. The results are summarized in the following bar graph.

Find the mean, median, and mode for the given distribution.

13) 7, 5, 2, 8, 11, 7, 7, 5, 8, 11, 7, 2, 13, 8, 7, 7, 2, 5, 8, 7 14) 8, 7, 4, 10, 12, 8, 8, 7, 10, 12, 8, 4, 14, 10, 8, 8, 4, 7, 10, 8

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10)

11)

12)

13) 14)

Find the missing value.

15) 119 = mean 13 = standard deviation ______ = raw score -0.62 = z-score

15)

16) 70 = mean 9 = standard deviation 82 = raw score ______ = z-score

16)

Find the range for the set of data given.

17) 6 16 2 14 12

17)

18) 78 149 27 100 174

18)

19) 25 40 19 50 57

19)

Find the standard deviation. Round to one more place than the data.

20) 16, 10, 19, 9, 11, 8, 13, 7, 6

20)

21) 38, 38, 62, 21, 89, 72, 32, 39, 82

21)

22) 291, 296, 102, 266, 163, 236, 260, 115, 240

22)

Solve the problem.

23) A tennis promoter is comparing two brands of tennis ball to determine which one gives a faster serve. The following data represent the top speeds (in mph) clocked by comparable players using each ball. Represent the two sets of data on a single stem -and-leaf display.

Which ball, if either, seems to give a faster serve?

Ball A: 68, 76, 94, 74, 93, 70, 71, 86, Ball B: 66, 86, 84, 92, 96, 89, 73, 71, 66, 92, 64, 62, 76, 85, 83, 69 91, 67, 87, 93, 73, 89, 93, 69

23)

24) Assume that math SAT scores are normally distributed with a mean of 500 and a standard deviation of 100. If you scored 560, what percentage of those taking the test scored below you?

24)

25) Assume that the distribution of wait times spent by women in a restroom line at a sporting event is 6.4 minutes with a standard deviation of 1.5 minutes. For this distribution, find a raw score that corresponds to a z-score of 2.1.

25)

26) Assume that in a 31-day month you begin with a $40 balance due on your credit card, charge an item for $50 on the 15th and an item for $120 on the 20th of the month. What is your average daily balance on your credit card for this month?

26)

27) If you score an 80 on an examination that has a mean score of 73 and a standard deviation of 5, to what percentile does your score correspond?

27)

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28) The ages of people randomly surveyed on a college campus are summarized in the bar

28)

graph.

How many people were 25 years old or older?

29) A tennis promoter is comparing two brands of tennis ball to determine which one gives a faster serve. The following data represent the top speeds (in mph) clocked by comparable players using each ball. Represent the two sets of data on a single stem -and-leaf display.

Which ball, if either, seems to give a faster serve?

Ball B: 94, 94, 63, 74, 79, 61, 62, 75, Ball A: 86, 62, 61, 85, 91, 89, 94, 96, 75, 71, 92, 90, 70, 84, 82, 69 82, 70, 72, 87, 69, 67, 88, 66

29)

30) Assume that in your psychology class you have earned the following test scores: 95, 82, 60, 73; and only one test remains. If you need a mean score of 80 to earn a ʺBʺ, then what minimum score must you obtain on the last test?

30)

Solve the problem. Assume that the given distribution is normal.

31) Assume that a distribution has a mean of 21 and a standard deviation of 7. What percentage of the values in the distribution do we expect to fall between 14 and 21?

31)

32) Assume that a distribution has a mean of 21 and a standard deviation of 4. What percentage of the values in the distribution do we expect to fall between 21 and 29?

32)

33) Assume that a distribution has a mean of 26 and a standard deviation of 7. What percentage of the values in the distribution do we expect to fall below 12?

33)

Solve the problem. Round to the nearest hundredth, if necessary.

34) Assume that the professor in a class assigns grades based on the following: A: scores which are 1.5 or more standard deviations above the mean.

B: scores which are between 0.5 and 1.5 standard deviations above the mean.

C: scores which are between 0.5 standard deviations below the mean and 0.5 standard deviations above the mean.

D: scores which are between 0.5 and 1.5 standard deviations below the mean.

F: scores which are 1.5 or more standard deviations below the mean.

The scores in the class are 85, 78, 95, 81, 70, 88, 84, 90, 68, 74. What grade does the person earning the 84 get?

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34)

35) The following data gives the number of applicants that applied for a job at a given company each month of 1999: 64, 68, 95, 76, 79, 81, 86, 88, 90, 95, 75, 64. What is the mode of the data?

35)

36) Suppose for a given month that the mean daily closing price (all numbers in dollars) for Expensive, Inc. common stock was 101.7 with a standard deviation of 11.2. For Cheap, Inc. stock, the mean daily closing price was 94.3 with a standard deviation of 7.5. Which stock was more volatile (i.e., had a greater coefficient of variation)?

36)

State what kind of correlation, if any, the scatterplot indicates.

37)

37)

y 20 18 16 14 12 10 8 6 4 2 1 2 3 4 5 6 7 8 9 10 11 12

x

38)

38) y 10 9 8 7 6 5 4 3 2 1 10 20 30 40 50 60 70 80 90 100110 x

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This double-bar graph shows the number of male (M) and female (F) athletes at a university over a four -year period.

Answer the question.

YEAR 39) How many students were involved in athletics in 1989?

39)

40) What is the only year in which the number of female athletes declined from its previous value?

40)

41) Has the total number of students involved in athletics increased each year?

41)

42) What percentage of all students involved in athletics in 1986 was female? (Round to the nearest percent.)

42)

Use a table to find a z-score that fits the given conditions. Interpolate if necessary.

43) 48% of the area under the standard normal curve is above the score.

43)

Use the table below to determine whether we can be 95% or 99% confident that there is significant linear correlation between x and y. n α = 0.05 α = 0.01 4 0.950 0.999 5 0.878 0.959 6 0.811 0.917 7 0.754 0.875 8 0.707 0.834 9 0.666 0.798 10 0.632 0.765 11 0.602 0.735 12 0.576 0.708 13 0.553 0.684 14 0.532 0.661 15 0.514 0.641 16 0.497 0.623 17 0.482 0.606 18 0.468 0.590 19 0.456 0.575 20 0.444 0.561 44) (4, 5), (6, 7), (8, 9), (10, 10), (11, 12) 44)

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45) (3, 12), (3, 7), (15, 7), (19, 3)

45)

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Answer Key Testname: CHAPTER 14 EXAM B

1) -0.76 2)

Collected Items from Foreign Countries

3)

4)

5)

6)

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Answer Key Testname: CHAPTER 14 EXAM B

7) 8)

9)

10) y = 0.25x + 50.4 11) Mean = 66.8, standard deviation = 4.1 12) Mean = 3.8, standard deviation = 2.6 13) Mean = 6.85, median = 7, mode = 7 14) Mean = 8.35, median = 8, mode = 8 15) 110.94 16) 1.333 17) 14 18) 147 19) 38 Copyright © 2022 Pearson Education, Inc.

Answer Key Testname: CHAPTER 14 EXAM B

20) 4.3 21) 24.2 22) 73.6 23) Ball A 98642 66410 653 432

Ball B 6 679 7 133 8 46799 9 12336

Ball B seems to give a faster serve.

24) 72.6% 25) 9.55 26) $113.87 27) 91st 28) 3 people 29) Ball A Ball B 921 6 123679 510 7 02459 96542 8 278 64210 9 44 Ball A seems to give a faster serve.

30) 90 31) 34% 32) 47.5% 33) 2.5% 34) C 35) 95 and 64 36) Expensive, Inc. 37) significant positive correlation 38) no correlation 39) 800 40) 1989 41) Yes. 42) 43% 43) 0.05 44) We can be 99% confident.

45) neither

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