Test Bank for Discovering Mathematics A Quantitative Reasoning Approach, 2nd Edition by Richard N. A

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TEST BANK FOR Discovering Mathematics A Quantitative Reasoning Approach, 2nd Edition by Richard N. Aufmann Chapter 1-11

chapter 1 Enter the appropriate value to answer the question or solve the problem.

1. What is the missing number in the sequence below? , , , ? , , ...

2. Use inductive reasoning to predict the most probable next letter in the list. . . . , H, I, M, N, R, S, . . .

3. In a chess tournament, each player played a game in the first round. The losers dropped out. This process continued until a winner was declared. The winner of the tournament played 12 games. How many people were in the tournament?

Indicate the answer choice that best completes the statement or answers the question.

4. Use deductive reasoning to determine the number that will always be produced from the following procedure. Pick a number. Add 10 to the number and multiply the sum by 4. Subtract 8 and then decrease this difference by 4 times the original number. a. Let n be the original number (add 10) (multiply by 4) (substract 8) (decrease by 4 times original number) (final number)

b. Let n be the original number (add 10) (multiply by 4)

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(substract 8) (decrease by 4 times original number) (final number) c. Let n be the original number (add 10) (multiply by 4) (substract 8) (decrease by 4 times original number) (final number) d. Let n be the original number (add 10) (multiply by 4) (substract 8) (decrease by 4 times original number) (final number) e. Let n be the original number (add 10) (multiply by 4) (substract 8) (decrease by 4 times original number) (final number)

5. Look at the pie chart and determine which of the film genres is the least popular?

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a. Comedy b. Fiction c. Horror d. Drama 6. The student wants to read a book of 346 pages. How many pages should he read per day to finish the book in a week? a. 30 b. 40 c. 50 d. 65 7. Suppose 79 points are placed around a circle. A line segment is drawn between each pair of points. How many line segments are drawn? a. 6,162 b. 6,241 c. 3,160 d. 79 e. 3,081 8. The four teams (Cheetahs, Ostriches, Antelopes, and Gazelles) took part in a sports tournament. Each team has a uniform of a certain color (red, yellow, green, and blue). From the following clues, determine which team has which color.

1. During one of the matches, Gazelles cheered on the yellow team and the green team cheered on Ostriches.

2. Anthelopes won the match against the yellow team.

3. In the match between Ostriches and Cheetahs, the blue team won. a. Cheetahs – blue, Ostriches – yellow, Antelopes – red, and Gazelles – green b. Cheetahs – yellow, Ostriches – blue, Antelopes – green, and Gazelles – red c. Cheetahs – green, Ostriches – blue, Antelopes – yellow, and Gazelles – red d. Cheetahs – blue, Ostriches – yellow, Antelopes – green, and Gazelles – red 9. Sam, John, and Peter want to rent a house at the seaside for 2 weeks. They chose a house that costs $10 per day. How much will each of the friends pay? a. About $35. b. About $50. c. About $85. d. About $70.

10. Find the sixth term in the pattern.

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... a. 40 b. 12 c. 11 d. 13 11. The pie chart shows clothes sales of an online store. Which of the following statements is correct?

a. Trouser sales are the largest. b. Dress and skirt sales are about the same. c. Accessory sales are the smallest. d. All statements are correct.

12. Three sons of a miller must divide a mill, a donkey and a cat. Selling them is not an option for the brothers. Which methods can they use to divide the inheritance fairly? Assume that all three brothers consider the value of the mill to be higher than that of the donkey, and the value of the donkey to be higher than that of the cat. a. Lone Divider–Chooser Method for More than Two Players, Method of Sealed Bids b. Method of Adjusted Winner, Method of Sealed Bids, Knaster Inheritance Procedure c. Method of Sealed Bids, Knaster Inheritance Procedure d. Lone Divider–Chooser Method for More than Two Players, Method of Adjusted Winner, Knaster Inheritance Procedure 13. Which of the equalities is incorrect? a. b. c. d. All equalities are correct.

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14. The parking accommodates 130,000 cars. What area does it occupy if one car occupies about 7 square meters? a. 1 square mile b. 1 square kilometer c. 13,000,000,000 square feet d. 13,000,000 square kilometers 15. Use the table and the Knaster inheritance procedure to distribute the antique chest among four siblings.

Bids for the chest

Will $360

Mary $240

George $1200

Anna $840

a. Will gets the chest and pays $225, Mary gets $195, George gets $765, Anna gets $345. b. Will gets $225, Mary gets $195, George gets the chest and pays $765, Anna gets $345. c. Will gets $225, Mary gets the chest and pays $195, George gets $765, Anna gets $345. d. Will gets $225, Mary gets $195, George gets $765, Anna gets the chest and pays $345.

16. If two ladders are placed end to end, their combined height is 42.5 feet. One ladder is 6.5 feet shorter than the other ladder. What are the heights of the two ladders? a. 18 feet and 24.5 feet b. 21.25 feet and 27.75 feet c. 24.5 feet and 31 feet d. 18 feet and 11.5 feet e. 42.5 feet and 36 feet 17. Write the number 98,000,000 in scientific notation. a. b. c. d.

18. 8 players submit sealed bids for each item. According to the Knaster inheritance procedure, which value does the player submitting the highest bid place into a joint account? a.

of the value of the object.

b. The bid he submits multiplied by 8.

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of the value of the object.

d. The bid he submits divided by 8.

19. A parking lot contains a total of 64 cars and motorcycles. There are a total of 228 tires (not counting spare tires) in the lot. Assuming each car has 4 tires and each motorcycle has 2 tires, determine how many cars and how many motorcycles are in the parking lot. a. 50 motorcycles and 14 cars b. 14 motorcycles and 50 cars c. 32 motorcycles and 32 cars d. 6 motorcycles and 58 cars e. 20 motorcycles and 44 cars 20. What of the following fair division methods can be applied only for two players? a. Divider–Chooser Method, Lone Divider–Chooser Method b. Divider–Chooser Method, Method of Adjusted Winner c. Method of Adjusted Winner, Knaster Inheritance Procedure d. Method of Sealed Bids, Method of Adjusted Winner 21. Use the pattern to make a conjecture. Then, use the conjecture to find the next product.

a. The product of a number consisting of

and 8 consists of

,

and . The next product is

. b. The product of a number consisting of n c. The product of a number consisting of d. The product of a number consisting of n

and 8 consists of , n and 8 consists of and 8 consists of ,

and 2. The next product is ,n

and . The next product is

. .

and . The next product is

.

22. What is the 78th decimal digit in the decimal representation of

?

a. 6

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b. 3 c. 4 d. 7 e. 5 23. Using the map below, determine the number of direct routes (no backtracking) from point A to point B if you want to pass by point D.

a. 3 b. 6 c. 5 d. 4 e. 7 24. How many digits does it take in total to number a book from page 44 to page 383? a. 1,958 b. 339 c. 964 d. 1,963 e. 73,536 25. What number is not expressed in scientific notation?

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a. b. c. d. All numbers are in scientific notation.

26. A number is divisible by 6 if the sum of the digits of the number is divisible by 3 and the number is even. Which statement is correct about the conclusion that can be made? a. Deductive reasoning can be used to determine that 156,090 is divisible by 6. b. Inductive reasoning can be used to determine that 156,090 is not divisible by 6. c. Inductive reasoning can be used to determine that 156,090 is divisible by 6. d. Deductive reasoning can be used to determine that 156,090 is not divisible by 6.

27. Alisa reads in a geometry book that two intersecting lines will lie in the same plane. Which statement is correct about the conclusion Alisa can make? a. She can use deductive reasoning to conclude that if she considers two intersecting lines in space, the lines will not lie in the same plane. b. She can use deductive reasoning to conclude that if she considers two intersecting lines in space, the lines will lie in the same plane. c. She can use deductive reasoning to conclude that if she considers three intersecting lines in space, the lines will lie in the same plane. d. She can use deductive reasoning to conclude that if she considers three intersecting lines in space, the lines will not lie in the same plane.

28. Which choice gives an example that supports the conjecture, and a counterexample that shows the conjecture is false?

For any real number , a. b. c. d.

.

, but , but , but , but

29. Three siblings decide to divide the family bakery. Selling the bakery is not an option for them. Which methods can they use to divide the bakery fairly? a. Divider–Chooser Method for Two Players, Lone Divider–Chooser Method for More than Two Players

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b. Method of Adjusted Winner, Method of Sealed Bids, Knaster Inheritance Procedure c. Method of Sealed Bids, Knaster Inheritance Procedure d. Lone Divider–Chooser Method for More than Two Players, Knaster Inheritance Procedure 30. Suppose a candlestick, watch, and porcelain service are to be divided among three people. The table shows the values (unknown to the others) that each person assigns for each item. Find a fair division of the items.

Candlestick Player 1 $800 $700 Player 2 $400 Player 3

Watch $400 $600 $400

Porcelain service $600 $400 $500

a. Player 1 – Candlestick, Player 2 – Watch, Player 3 – Porcelain service b. Player 1 – Porcelain service, Player 2 – Watch, Player 3 – Candlestick c. Player 1 – Watch, Player 2 – Candlestick, Player 3 – Porcelain service d. Player 1 – Porcelain service, Player 2 – Candlestick, Player 3 – Watch 31. Each of the four ships, Blue Miracle, Liberty, The High Seas, and Horizon Chaser, has a different type (yacht, sailboat, bulk carrier, or tanker). From the following clues, determine the type of each ship.

1. Liberty is not a tanker.

2. Blue Miracle and The High Seas can pass through the Suez Canal, and the bulk carrier and the tanker can not pass.

3. Blue Miracle is faster than the yacht. a. Blue Miracle is a bulk carrier, Liberty is a yacht, The High Seas is a sailboat, and Horizon Chaser is a tanker. b. Blue Miracle is a yacht, Liberty is a bulk carrier, The High Seas is a tanker, and Horizon Chaser is a sailboat. c. Blue Miracle is a sailboat, Liberty is a bulk carrier, The High Seas is a yacht, and Horizon Chaser is a tanker. d. Blue Miracle is a sailboat, Liberty is a bulk carrier, The High Seas is a tanker, and Horizon Chaser is a yacht.

32. Rachel and Rebecca need to divide 5 dishes. They decided to use the adjusted winner method, and the table shows the points they assigned to each item. Which division is not fair?

Bowl Cup Pan Teapot Plate

Rachel 16 8 12 12 12

Rebecca 20 4 20 12 4

a. Rachel - the cup, the teapot, the plate, and 22.2% of the value of the bowl; Rebecca - the pan and 77.8% of the value of the bowl b. Rachel - the cup, the teapot, the plate, and 22.2% of the value of the pan; Rebecca – the bowl and 77.8% of the value of the pan

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c. Rachel - the cup, the teapot, the plate, and 25% of the value of the pan; Rebecca – the bowl and 75% of the value of the pan d. Rachel - the cup, the teapot, the plate, and 25% of the value of the bowl; Rebecca – the pan and 75% of the value of the bowl 33. The line graph shows a number of clients of a company at the beginning of each year from 2011 to 2015. Which year was the growth of clients the largest?

a. 2011 b. 2012 c. 2013 d. 2014 34. Elia, Asmara, Cameron, and Deepal are riding bicycles one after another. Two of them are wearing red helmets and the other two are wearing green ones. They can only look ahead during the ride. From the following clues, determine the colors of the cyclists' helmets.

1. Deepal is riding first.

2. Cameron sees twice as many green helmets as red ones.

3. Elia sees no green helmets. a. Elia – red, Asmara – green, Cameron – red, Deepal – green b. Elia – green, Asmara – green, Cameron – red, Deepal – red

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c. Elia – green, Asmara – green, Cameron – green, Deepal – red d. Elia – red, Asmara – green, Cameron – red, Deepal – green 35. Three items will be divided among three people. The bids for each of the items are given in the table. Find a fair division of the items.

Item 1 Item 2 Item 3

Sonya $210 $90 $120

Bob $120 $180 $120

Michelle $120 $150 $150

a. Sonya gets Item 1 and pays $70 into a joint account, Bob gets Item 3 and pays $30 into a joint account, Michelle gets Item 2 and $70 from a joint account. b. Sonya gets Item 1 and $30 from a joint account, Bob gets Item 2 and $30 from a joint account, Michelle gets Item 3 and pays $30 into a joint account. c. Sonya gets Item 1 and pays $69.90 into a joint account, Bob gets Item 2 and pays $39.90 into a joint account, Michelle gets Item 3 and pays $9.90 into a joint account. d. Sonya gets Item 1 and pays $30 into a joint account, Bob gets Item 2 and makes no additional payments, Michelle gets Item 3 and $30 from a joint account.

36. Morris Mouse can easily find his way through the maze from the entrance A to the exit B. However, he only receives food if he finds the exit without going west or south. (North is towards the top of the page.) How many different paths can he take through the maze to receive food? (Note: Different paths have at least one distinct section. See the diagram for an example.)

a. 252 b. 15,120 c. 30,240 d. none of these 37. Use the graph below, which shows the average number of weekly viewers of a 30-minute television program (in millions of viewers) from 2000 to 2006.

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Find the change in the average number of weekly viewers from 2000 to 2006. a. –5 million b. no change c. 5 million d. –10 million e. 10 million 38. Divide a box with sweets among 7 students. If each student gets a fair share, in the student’s opinion, he has a value that is at least _____ of the total value of all sweets as assigned by that student. a. 7 % b. 0.07 c. 93 % d.

39. Determine the units digit of

.

a. 0 b. 6 c. 4 d. 2

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e. 8 40. Use inductive reasoning to predict the most probable next number in the given list. , ? a. –4 b. –20 c. –22 d. –26 e. –15 41. Alex and Dani won a car in the lottery. Which methods can they use to divide the prize fairly? a. Method of Adjusted Winner, Method of Sealed Bids, Knaster Inheritance Procedure b. Lone Divider–Chooser Method for More than Two Players, Method of Sealed Bids, Knaster Inheritance Procedure c. Divider–Chooser Method for Two Players, Method of Adjusted Winner, Method of Sealed Bids d. Divider–Chooser Method for Two Players, Method of Adjusted Winner, Knaster Inheritance Procedure 42. Following the pattern shown in the number sequence below, what is the missing number?

You may find it helpful to list perfect squares or cubes beneath the sequence terms to try to see how they may relate to the sequence.

a. 232 b. 36 c. 216 d. 34 e. 214 43. Use inductive reasoning to decide whether the conclusion for the following argument is correct. Pick any counting number. Multiply the number by 5. Subtract 2.5 from the product. Divide the difference by the sum of the original number and 2. The resulting number is 5. a. The conclusion is correct. b. The conclusion is incorrect. c. There is not enough information to determine the validity of the conclusion.

44. Each art collector got 10 coins and was offered to distribute them between the art objects to evaluate them. The table shows the distribution. Which division is not fair?

Vase

Sculpture

Painting

Jewelry

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Collector 1 Collector 2 Collector 3 Collector 4

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3 2 4 1

1 3 1 2

3 2 4 3

Date:

3 3 1 4

a. Collector 1 – Vase, Collector 2 – Sculpture, Collector 3 – Painting, Collector 4 – Jewelry b. Collector 1 – Jewelry, Collector 2 – Vase, Collector 3 – Painting, Collector 4 - Sculpture c. Collector 1 – Painting, Collector 2 – Sculpture, Collector 3 – Vase, Collector 4 – Jewelry d. Collector 1 – Jewelry, Collector 2 – Sculpture, Collector 3 – Vase, Collector 4 – Painting 45. Paul and Frank need to divide devices. They use the adjusted winner method, and the table shows the points they assigned to each item. The value of which device should be divided equally to make a fair division?

Smartphone Tablet Laptop Power bank

Paul 12 12 16 8

Frank 20 12 24 4

a. The smartphone b. The tablet c. The laptop d. None of them 46. Write the number 0.000000049 in scientific notation. a. b. c. d.

47. On three examinations, a student received scores of 75, 81, and 79. What score will the student need on the fourth examination to have an average of 83? a. 79 b. 78 c. 97 d. 83 e. 82

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48. Find a counterexample to show that the conjecture is a false statement.

For any real number ,

.

a. choose b. choose c. choose d. choose e. choose

49. Change the number

from scientific notation to standard form.

a. 0.00573 b. 0.573 c. 573 d. 5730 50. The farmer harvested 71 baskets of oranges. What approximate number of oranges does he have if the smallest amount in one basket is 126 oranges and the largest is 144 oranges? a. 5,000 b. 10,000 c. 15,000 d. 20,000 51. Use inductive reasoning to predict the most probable next number in the given list. , ? a. 1296 b. 343 c. 307 d. 2401 e. 341 52. Three boys are in three different rooms. Ernest always tells the truth. Barry sometimes tells the truth. Mario never tells the truth. Use the statements made by the person in each room to tell who is in each of the rooms.

Room 1 The guy in Room 2 is Mario.

Room 2 I’m Barry.

Room 3 The guy in Room 2 is Ernest.

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a. Room 1 - Mario; Room 2 - Barry; Room 3 - Ernest b. Room 1 - Ernest; Room 2 - Mario; Room 3 - Barry c. Room 1 - Barry; Room 2 - Ernest; Room 3 - Mario d. Room 1 - Mario; Room 2 - Ernest; Room 3 - Barry 53. Use inductive reasoning to help complete the table. Round your answer to two decimal places, if necessary.

Number of sides of a regular polygon

4

5

6

7

Interior angle measure

90

108

120

128.57

8 13

a. 140, 152.31 b. 135, 292.5 c. 135, 152.31 d. 140, 292.5 54. Some furniture will be divided among three people. The bids for each of the items are given in the table. Find a fair division of the items and determine the values of additional payments.

Ottoman Armchair Sideboard Coffee table

Lina $50 $50 $70 $40

Victor $10 $80 $20 $40

Barbara $20 $70 $30 $60

a. Lina gets ottoman and sideboard and pays $23.33 into a joint account; Victor gets armchair and pays $3.33 into a joint account; Barbara gets coffee table and gets $26.67 from a joint account. b. Lina gets ottoman and sideboard and gets $23.33 from a joint account; Victor gets armchair and gets $3.33 from a joint account; Barbara gets coffee table and pays $26.67 into a joint account. c. Lina gets ottoman and sideboard and pays $26.67 into a joint account; Victor gets armchair and pays $3.33 into a joint account; Barbara gets coffee table and gets $23.33 from a joint account. d. This furniture set cannot be fairly divided.

55. The UCSB has 9 squads of badminton players. The UCI team has 5 squads. Every squad from UCSB must play every squad from UCI at least once. What is the least number of games that must be played? a. 14 b. 45 c. 20 d. 48

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56. Four entrepreneurs decide to divide the assets in an IT startup using the divider–chooser method. Guang is chosen as the divider. The bids for each of the partners are shown in the following table. Determine the disposition of the shares.

S1 15% 15% 25% 40%

S2 35% 20% 25% 15%

S3 40% 15% 25% 20%

S4 10% 50% 25% 25%

Tola Kaino Guang Shakti a. (Tola – S2, Kaino – S4, Guang – S3, Shakti – S1) or (Tola – S3, Kaino – S4, Guang – S2, Shakti – S1) b. (Tola – S3, Kaino – S4, Guang – S2, Shakti – S1) or (Tola – S2, Kaino – S3, Guang – S2, Shakti – S1) c. Tola – S2, Kaino – S1, Guang – S3, Shakti – S4 d. The divider–chooser method is not applicable here.

57. Find a counterexample to show that the conjecture is a false statement.

For any real number

,

.

a. choose b. choose c. choose d. choose e. choose 58. Use the table and the Knaster inheritance procedure to distribute the picture among three siblings.

Bids for the picture

Tony $1350

Lora $5400

Simon $2430

a. Each person gets $3060. b. Tony gets $1710, Lora pays $2340, Simon gets $630. c. Tony gets $630, Lora gets the picture and pays $1620, Simon gets $990. d. Tony gets the picture and pays $1350 to Lora and Simon.

59. A baseball team has won more than 95% (but less than 100%) of its games in a season.What is the least possible number of games that the team could have played in the season? a. 20 b. 21 c. 22 d. 23 e. 24

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60. Lin, Angel, and Sasha want to divide a cake worth $24 that is one-half chocolate icing and one-half strawberry icing using the divider–chooser method. Lin values chocolate icing at $16 and the strawberry icing at $8. Angel values both halves at $12, whereas Sasha values the strawberry icing at $6 and the chocolate icing at $18. Lin is selected as the divider and cuts the cake into three pieces as shown in the following figure. Determine the fair division of the cake.

a.

b.

c.

61. One kilogram of cookies contains about 40 units. The energy value of cookies is 395 calories per 100 grams. How many calories does one cookie have? a. 90 b. 100 c. 80 d. 140 62. Use the data in the table and inductive reasoning to answer the question.

Cube edge length

Weight of water inside cube (water fills entire cube)

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1 cm 2 cm 3 cm 4 cm

Date:

1g 8g 27 g 64 g

If a cube is filled with water and the weight of the water is 216 grams, what is the edge length of the cube? a. 72 b. 36 c. 6 d. 5 63. The bar graph shows the results of a bowling game for four players. Which player is the best?

a. Player 1 b. Player 2 c. Player 3 d. Player 4 64. Which is a valid conclusion based on the following information? An equilateral triangle has three congruent sides.

Given:

is equilateral.

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a. b.

has a measure between and

.

are collinear.

c. B is the midpoint of d.

and

Date:

.

has three congruent sides.

65. David and Nick were roommates in a dormitory and after graduation need to divide 5 vinyl records. They decided to use the adjusted winner method, and the table shows the points they assigned to each record. Which division is fair?

David Nick 5 5 The Beatles 2 1 Frank Sinatra 3 5 Michael Jackson 5 3 Rolling Stones 3 1 Elvis Presley a. David - The Beatles, Rolling Stones; Nick - Frank Sinatra, Michael Jackson, Elvis Presley b. David - Rolling Stones, Elvis Presley; Nick - The Beatles, Frank Sinatra, Michael Jackson c. David - Frank Sinatra, Rolling Stones, Elvis Presley; Nick - The Beatles, Michael Jackson d. David - Frank Sinatra, Rolling Stones; Nick - The Beatles, Michael Jackson, Elvis Presley 66. How many boxes of pizza does the courier carry over a year if he works three days a week and carries from 11 to 21 boxes per day? a. 500 b. 2,500 c. 8,000 d. 5,500 67. Which two numbers should come next in the sequence? ... a. 37, 41 b. 33, 37 c. 34, 38 d. 33, 30 68. Three partners are dividing the assets of a business into three shares, S1, S2, and S3, using the lone divider-chooser method for more than two players. Partner 1 is chosen as the divider; Partner 2 and Partner 3 are the choosers. The value each partner has assigned to a share is shown in the following table. Determine the fair division of the assets.

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S1 Partner 1

33

S2 %

33

Date:

S3 %

Partner 2 35% 35% Partner 3 30% 35% a. Partner 1 – S2, Partner 2 – S1, Partner 3 – S3

33

%

30% 35%

b. Partner 1 – S1, Partner 2 – S2, Partner 3 – S3 c. Partner 1 – S3, Partner 2 – S1, Partner 3 – S2 d. Partner 1 – S2, Partner 2 – S3, Partner 3 – S1

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Answer Key 1.

2. W 3. 2048 4. c 5. d 6. c 7. e 8. b 9. b 10. d 11. d 12. c 13. a 14. b 15. b 16. a 17. c 18. c 19. b 20. b

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21. d 22. b 23. d 24. c 25. d 26. a 27. b 28. d 29. c 30. a 31. c 32. b 33. c 34. b 35. d 36. a 37. c 38. d 39. d 40. e 41. a

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42. e 43. b 44. b 45. d 46. d 47. c 48. d 49. a 50. b 51. b 52. b 53. c 54. a 55. b 56. a 57. e 58. c 59. b 60. a 61. b 62. c

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63. b 64. d 65. c 66. b 67. c 68. a

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chapter 2

Enter the appropriate value to answer the question or solve the problem.

1. Tell whether each of the following statements is true or false.

2. Find the number of subsets of the set

3. Find

if

4. If

,

.

and

, and

find

.

5. Draw two Venn diagrams to determine whether the following expressions are equal for all sets A and B. and 6. The circles contain the members of sets D, E, and F, as indicated. Designate the area that shows

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.

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chapter 2

7. Use the roster method to write the set of the odd natural numbers less than 15.

8. Is

equivalent to

? Back up your answer with truth tables.

9. Construct a truth table for

.

Indicate the answer choice that best completes the statement or answers the question.

10. If

and

, is A a subset of B?

a. Yes b. No 11. Use

notation to indicate which of the sets E and F is a subset of the other.

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chapter 2

a. b. c. d. e.

12. Survey analysis In a survey of the dining preferences of 110 dormitory students at the end of the spring semester, the following facts were discovered about Adam’s Lunch (AL), Pizza Tower (PT), and the Dining Hall (DH).

27 liked AL but not PT 13 liked AL only 43 liked AL 41 liked PT 59 liked DH 4 liked PT and AL but not DH 13 liked PT and DH How many liked PT or DH? a. 57 b. 9 c. 33 d. 48 e. 87 13. Identify the sets: The even natural numbers that are less than 14. a. {0, 2, 4, 6, 8, 10, 12} b. {2, 4, 6, 8, 10, 12} c. {2, 4, 6, 8, 10, 12, 14} d. {0, 2, 4, 6, 8, 10, 12, 14} 14. Given

and

, which of the following statements is true?

a. b. c. d.

15. Identify the sets : Copyright Cengage Learning. Powered by Cognero.

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chapter 2 The integers greater than –6 and less than 2. a. {-6, -5, -4, -3, -2, -1, 0, 1} b. {-5, -4, -3, -2, -1, 0, 1} c. {-5, -4, -3, -2, -1, 0, 1, 2} d. {-6, -5, -4, -3, -2, -1, 0, 1, 2} 16. If

, and

find

.

a. 1 b. 2 c. 4 d. 5 17. Write a description of the set

.

a. The set of all integers between 8 and 13. b. The set of all integers between 9 and 12. c. The set of all real numbers between 8 and 13. d. The set of all real numbers between 9 and 12. e. The set of all rational numbers between 9 and 12.

18. Use Venn diagrams to determine which (if any) of the following expressions are equal for all sets A, B and C.

a. b. c. none are equale d. all are equale e.

19. Use the graph below, which shows the average number of weekly viewers of a 30-minute television program (in millions of viewers) from 2000 to 2006.

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List the set of years such that the average number of weekly viewers decreased from the previous year. a. {2004, 2005, 2006} b. {2004, 2006} c. {2003, 2004, 2005, 2006} d. null set e. {2004} 20. Indicate whether the following sets are equal.

a. b.

21. Given the sets and which are false.

,

, and

, tell which of the following statements are true

a. a. False b. True c. False d. True Copyright Cengage Learning. Powered by Cognero.

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chapter 2 b. a. False b. False c. False d. False c. a. True b. True c. True d. True d. a. True b. False c. True d. False 22. How many rows should the truth table for 3 simple propositions contain if it is supposed to be in standard form? a. 8 b. 9 c. 7 d. 3 23. Job growth The number of jobs in 2000, the number projected in 2025, and the projected annual growth rate for jobs in some cities are shown in the table below. Consider the following sets.

A = set of cities with at least 2,000,000 jobs in 2000 or in 2025 B = set of cities with at least 1,500,000 jobs in 2000 C = set of cities with projected annual growth rate of at least 2.5% Cities Jobs in 2000 (thousands) O (Orlando) 1539 M (Myrtle Beach) 133 A (Atlanta) 2715 P (Phoenix) 1953 D (Denver) 233

Projected Jobs in 2025 (thousands) 1923 256 4893 3723 524

Annual Rates of Increase (%) 0.89 2.65 2.38 2.61 3.29

Which of the following statements is true? a. A is a subset of B. b. B is a subset of A. c. A is a subset of C. d. B is a subset of C. e. C is a subset of A. 24. Choose the right premise for the given statement and conclusion.

Appeal to Popularity Fallacy This medicine helped my mother to cure a migraine, so it will help you.

Conclusion: The medicine will help you. a. Premise: My mum cured a migraine. b. Premise: My mum had a migraine.

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chapter 2 c. Premise: The medicine helped my mother to cure a migraine. d. Premise: My mum took a medicine.

25. A large soft drink company conducted a poll of 1,000 families to determine how many had seen its television and newspaper advertisements. The results are shown in the diagram.

U = the set of families polled T = the set of families who saw the television ad N = the set of families who saw the newspaper ad

Based on the facts in the diagram, which is a valid conclusion? a. 538 families saw neither the television ad nor the newspaper ad. b. Only 226 saw the television ad. c. 279 families saw at least 1 of the ads. d. 83 families saw both the television ad and the newspaper ad.

26. Identify a quantifier in the following categorical statement.

At least one kid enjoyed the show. a. enjoyed b. kid c. the show d. At least one 27. Survey analysis In a survey of the dining preferences of 110 dormitory students at the end of the spring semester, the following facts were discovered about Adam’s Lunch (AL), Pizza Tower (PT), and the Dining Hall (DH).

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chapter 2 27 liked AL but not PT 13 liked AL only 43 liked AL 41 liked PT 59 liked DH 4 liked PT and AL but not DH 13 liked PT and DH How many liked all three? a. 61 b. 41 c. 28 d. 31 e. 4 28. If

,

, and

find

.

a. b. c. d.

29. Find a subset of the set

.

a. The set of even whole numbers. b. c. d. e. The set of positive real numbers between 10 and 4000.

30. Find the number of subsets of the given set.

a. 31 b. 29 c. 32 d. 35 31. Let

,

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, and

. Find

.

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a. b. c. d. e.

32. Choose the Venn diagram that correctly represents the following sets a.

b.

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chapter 2 c.

d.

33. Choose the right conclusion for the given statement and premise.

Appeal to Emotion Fallacy To become a happy family, it is necessary to buy a house in this neighborhood.

Premise: A family wants to be happy. a. Conclusion: You should buy a house. b. Conclusion: A happy family should have a house. c. Conclusion: Every happy family has a house in this neighborhood. d. Conclusion: It should buy a house in this neighborhood.

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chapter 2 34. Advertising Suppose that a survey of 100 advertisers in U.S. News, These Times, and World found the following.

21 advertised in all three 24 advertised in These Times and U.S. News 57 advertised in World and U.S. News 23 advertised in World and These Times 51 advertised in These Times 64 advertised in U.S. News 65 advertised in World Which is the correct Venn diagram representing this information? a.

b.

c.

d.

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chapter 2 e.

35. Determine which of the following three propositions are equivalent.

(a) (b) (c)

a. (a) and (b) b. (a) and (c) c. (b) and (c) d. all three are equivalent 36. Choose the right conclusion for the given statement and premise.

Straw Man Fallacy My dad said when he was little he could not play basketball. I did not know that my dad was bad at sports.

Premise: Dad could not play basketball when he was little. a. Conclusion: Dad cannot play basketball. b. Conclusion: Dad can play basketball. c. Conclusion: Dad was bad at sports. d. Conclusion: Dad is bad at sports.

37. Identify the converse of the conditional proposition.

If it is appropriate, then I eat out.

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a. If I eat out, then it is appropriate. b. If it is appropriate, then I do not eat out. c. If it is not appropriate, then I do not eat out. d. If I do not eat out, then it is not appropriate.

38. Assume that

and that U is the universal set of natural numbers less than 11. Find a.

.

b. c. d. e.

39. Survey analysis In a survey of the dining preferences of 110 dormitory students at the end of the spring semester, the following facts were discovered about Adam’s Lunch (AL), Pizza Tower (PT), and the Dining Hall (DH).

15 liked AL but not PT 10 liked AL only 23 liked AL 42 liked PT 48 liked DH 4 liked PT and AL but not DH 25 liked PT and DH How many liked only DH? a. 23 b. 34 c. 9 d. 25 e. 14 40. Choose the right conclusion for the given statement and premise.

Black-or-White (False Dilemma) Fallacy We must follow a map or we will get lost.

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chapter 2 Premise: Either we follow a map or we get lost. a. Conclusion: We will not get lost if we follow a map. b. Conclusion: We must always follow a map. c. Conclusion: A map will not let us get lost. d. Conclusion: We will get lost.

41. Determine which sentence is a proposition. a. Was George Boole born in Lincoln, England? b. Was George Boole a mathematician? c. George Boole was the best mathematician of his time. d. George Boole was born in 1815.

42. Find

if the universal set

a. b. c. d. e.

43. Use an Euler diagram to determine whether the argument is valid or invalid.

All divers have permits.

Lan is a diver.

Lan has a permit.

a. Valid b. Invalid 44. Assume that

and that U is the universal set of natural numbers less than 11. Find Copyright Cengage Learning. Powered by Cognero.

.

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a. b. c. d. e.

45. Find

, the intersection of sets A and B.

a. b. c. d. e.

46. Choose the right premise for the given statement and conclusion.

Appeal to Authority Fallacy My dad said if I ate a lot of sweets, my teeth would fall out.

Conclusion: The teeth will fall out because of sweets. a. Premise: Dad said eating too many sweets would lead to tooth loss. b. Premise: Dad said that my teeth would fall out. c. Premise: Dad said that I couldn’t eat too many sweets. d. Premise: I eat a lot of sweets.

47. Given that set A has 35 elements, set B has 12 elements, and set C has 7 elements, determine the maximum possible number of elements in and the minimum possible number of elements in . a. maximum: 35 minimum: 7 b. maximum: 40 minimum: 30

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chapter 2 c. maximum: 54 minimum: 35 d. maximum: 54 minimum: 7 e. maximum: 35 minimum: 12 48. Which could be the negation of a conditional proposition? a. I complete my project and I will not be able to submit it in the science fair. b. I cannot go to France in the summer. c. I join the French club or I cannot go to France in the summer. d. I complete my project or I will not be able to submit it in the science fair.

49. Form the negation of the following categorical statement.

Some T-shirts are made of cotton. a. Some T-shirts are made of cotton. b. No T-shirts are made of cotton. c. Every T-shirt is made of cotton. d. Most T-shirts are made of cotton.

50. Write the symbolic proposition

in words using , ,

and

as defined below.

: I want a hamburger. : I want a steak. : I want to go to a restaurant. : I want to go to a park. a. I do not want a steak, and I want a hamburger. b. I want a steak, and I do not want a hamburger. c. I want to go to a restaurant, and I do not want a steak. d. I do not want to go to a restaurant, and I want a steak. e. I do not want to go to a park, and I do not want to go to a restaurant.

51. National health care Suppose that the table below summarizes the opinions of various groups on the issue of national health care.

Whites Opinion

Rep.

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Nonwhites Dem.

Rep.

Dem.

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chapter 2 Favor Oppose Total

150 100 250

250 100 350

70 120 190

100 110 210

570 430 1000

Identify the number of individuals in the set of Whites or those who oppose national health care. a. 600 b. 430 c. 830 d. 350 e. 230 52. Find the cardinality of the set

.

a. 310 b. 10 c. 160 d. 5 e. 40 53. Use the following propositions to construct a disjunction.

This month is June.

Next month is not August. a. This month is June and next month is not August. b. This month is June or next month is not August. c. Either this month is not June or next month is not August. d. If this month is not June then next month is August.

54. Use

notation to indicate which set is a subset of the other.

a. b. c. d. e.

55. The Venn diagram displays the results of a survey of 119 families regarding kitchen appliances.

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chapter 2 M represents the number of families with a microwave.

P represents the number of families with a pasta maker.

W represents the number of families with a dishwasher.

U represents all the families surveyed.

How many families have a microwave and a dishwasher?

a. 51 b. 8 c. 43 d. 37 56. Choose the right type of fallacy for the given statement, premise and conclusion.

If you keep eating sweets, you will gain excess weight that can lead to heart problems.

Premise: Excess weight can lead to heart problems.

Conclusion: Eating sweets can lead to heart problems. a. Post Hoc (False Cause) Fallacy b. Appeal to Common Practice Fallacy c. Slippery Slope Fallacy d. Appeal to Emotion Fallacy Copyright Cengage Learning. Powered by Cognero.

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chapter 2 57. Assume that

and that U is the universal set of natural numbers less than 11. Find a.

.

b. c. d. e.

58. Determine a true proposition. a.

or 15 is a prime number.

b. and

is an irrational number.

c. 0 is a natural number and 0 is a whole number. d. or e.

and

59. Which Venn diagrams represent

?

a.

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b.

c.

d.

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60. Let

,

,

, and

. Find

. a. b. c. d. e.

61. Choose the right type of fallacy for the given statement, premise, and conclusion.

My friend’s dog became cleverer after their trip to the mountains. Therefore, I should take my dog to the mountains.

Premise: Trip to mountains makes dogs cleverer.

Conclusion: I should take my dog to the mountains to make it cleverer. a. Circular Reasoning b. Hasty Generalization Fallacy c. Slippery Slope Fallacy d. Red Herring Fallacy 62. Use

or

to indicate whether the given object is an element of the given set.

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a. b.

63. Ms. Teller surveyed the 37 students in her class about their families. 29 students have a brother or a sister, 15 students have a brother, and 7 students have both a brother and a sister. How many students have only a sister? a. 17 b. 19 c. 21 d. 15 64. Find the negation of the quantified proposition below. Then determine the negation’s truth value.

All boys like math. a. No boys like math.; True b. Some boys don't like math.; True c. Some boys don't like math.; False d. No boy like math.; False 65. Which is the antecedent of the following conditional proposition?

If a number is a perfect square then it has a square root that is an integer. a. The square root of a number is not an integer. b. A number is a perfect square. c. If a number is a perfect square then it has a square root that is an integer. d. The square root of a number is an integer.

66. Study the information given below. If a valid conclusion is given, select that conclusion.

All beachcombers are swimmers.

All swimmers wear swimsuits.

John is wearing a swimsuit. a. Therefore John cannot swim. b. Therefore John is a beachcomber. c. Therefore John can swim. d. no valid conclusion given 67. Let B.

and

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. If

, determine the relationship between sets A and

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chapter 2 a. A is a subset of B. b. B is the complement of A. c. B is an element of A. d. B is not a subset of A. e. B is a subset of A. 68. Find all the subsets of the set

.

a. b. c. d.

69. Use an Euler diagram and all of the premises in the following argument to determine a valid conclusion for the argument.

All olympians are Texans.

No Texans are farmers. a. No farmers are olympians. b. All Texans are olympians. c. No farmers are Texans. d. All olympians are farmers. e. No olympians are farmers.

70. Form the negation of the following categorical statement.

All rovers successfully landed on Venus. a. At least one rover did not successfully land on Venus. b. No rovers successfully landed on Venus. c. Most rovers successfully landed on Venus. d. Some rovers successfully landed on Venus.

71. If

, and

find

.

a. 10 b. 12 c. 42 d. 24 72. Choose the right premise for the given statement and conclusion.

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Ad Hominem (Personal Attack) Fallacy My physics teacher has not made any significant discoveries, so what can he teach us?

Conclusion: My teacher cannot educate us. a. Premise: The physics teacher has not made any significant discoveries. b. Premise: The physics teacher cannot teach us. c. Premise: The physics teacher cannot make any significant discovery. d. Premise: The physics teacher cannot educate kids.

73. Determine which of the following propositions are true. (a) If 4 > 2, then –4 < 1. (b) If > 2, then . (c) If 1 is odd, then 4 is even. a. (a) b. (b) c. (c) d. (a) and (c) e. (a) and (b) 74. Determine a sentence that is a proposition. a. How many odd integers are there between 36 and 119? b. Be sure to round your answers to the nearest . c. If

is a number, then

is even.

d. Natural numbers are better than whole numbers. e. Please work the first 23 problems for homework.

75. Choose the right type of fallacy for the given statement, premise, and conclusion.

Wife: I need a new coat for this season.

Husband: Last year it was not so cold at this time.

Premise: Last year it was not so cold at this time.

Conclusion: Therefore, you do not need a new coat. a. Circular Reasoning b. Hasty Generalization Fallacy c. Slippery Slope Fallacy Copyright Cengage Learning. Powered by Cognero.

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chapter 2 d. Red Herring Fallacy 76. Choose the right premise for the given statement and conclusion.

Red Herring Fallacy Employee: I would like to request a salary increase.

Director: There is no vacant position to promote you.

Conclusion: The director cannot increase the salary. a. Premise: There is no vacant position for promotion. b. Premise: The director cannot promote you. c. Premise: There is no position with a higher salary. d. Premise: The director cannot increase your salary.

77. Assume that

and that U is the universal set of natural numbers less than 11. Find

.

a. b. c. d. e.

78. Choose the right conclusion for the given statement and premise.

Appeal to Common Practice Fallacy Everyone has seen this movie, so you should watch it as well.

Premise: Everyone has seen this movie. a. Conclusion: You should watch the movie. b. Conclusion: You do not have a reason to watch the movie. c. Conclusion: You can watch the movie. d. Conclusion: You have watched the movie.

79. Choose the right premise for the given statement and conclusion.

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Appeal to Ignorance Fallacy There is no evidence that the man is innocent, so he must be guilty.

Conclusion: The man is guilty. a. Premise: The man is not innocent. b. Premise: There is no evidence of his innocence. c. Premise: The man cannot prove his innocence. d. Premise: The man must prove his innocence.

80. Determine whether

for all sets A, B, and C.

a. Yes, by the Commutative property of intersection. b. Yes, by the Associative property of intersection. c. Yes, by the Associative property of union. d. No, 81. Let

and

. Find

.

a. b. c. d. e.

82. Determine which of the following three propositions are equivalent. (a) (b) (c)

a. (a) and (b) b. (a) and (c) c. (b) and (c) d. all three are equivalent 83. Find

, the union of sets A and B.

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and a. b. c. d. e.

84. Find the number of subsets of the set of all vowels in the alphabet. a. 128 b. 5 c. 32 d. 25 85. Which shows an equivalent proposition?

If Abe auditions for the part, he will act in the school play. a. Abe does not audition for the part and he will not act in the school play. b. Abe does not audition for the part or he would act in the school play. c. If Abe does not audition for the part, he will not act in the school play. d. Abe does not audition for the part.

86. National health care Suppose that the table below summarizes the opinions of various groups on the issue of national health care.

Whites Opinion Favor Oppose Total

Rep. 100 200 300

Nonwhites Dem. 250 50 300

Rep. 90 90 180

Dem. 80 140 220

Total 520 480 1000

Identify the number of individuals in the set of Whites who oppose national health care. a. 480 b. 600 c. 250 d. 450 e. 700 Copyright Cengage Learning. Powered by Cognero.

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87. Job growth The number of jobs in 2000, the number projected in 2025, and the projected annual growth rate for jobs in some cities are shown in the table below. Consider the following sets.

A = set of cities with at least 2,000,000 jobs in 2000 or in 2025 B = set of cities with at least 1,500,000 jobs in 2000 C = set of cities with projected annual growth rate of at least 2.5% Cities Jobs in 2000 (thousands) O (Orlando) 1098 M (Myrtle Beach) 133 A (Atlanta) 2715 P (Phoenix) 1953 D (Denver) 233

Projected Jobs in 2025 (thousands) 2207 256 4893 3675 420

Choose the correct verbal description of

.

Annual Rates of Increase (%) 2.83 2.65 2.38 2.56 2.38

a. The set of cities with at least 2,000,000 jobs in 2000 or 2025 and projected annual growth rates of at least 2.5%. b. The set of cities with at least 2,000,000 jobs in 2000 or 2025 and projected annual growth rates of less than 2.5%. c. The set of cities with at least 2,000,000 jobs in 2000 or 2025 or projected annual growth rates of at least 2.5%. d. The set of cities with at least 1,500,000 jobs in 2000 and projected annual growth rates of at least 2.5%. e. The set of cities with at least 1,500,000 jobs in 2000 or projected annual growth rates of at least 2.5%.

88. Let

,

, and

. Find

.

a. b. c. d. e.

89. Is

if

and

?

a. Yes b. No 90. Which is the consequent of the following conditional proposition?

If two numbers are both odd, then the sum of the numbers is odd. a. The sum of two numbers is even. b. The sum of two numbers is odd.

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chapter 2 c. If two numbers are both odd, then the sum of the numbers is odd. d. Two numbers are odd.

91. Find the intersection of the following sets.

a. b. c. d. none of these 92. Write the converse of the given proposition.

a. b. c. d. e.

93. Identify a quantifier in the following categorical statement.

Some apples are blue. a. apples b. Some c. blue d. are 94. Assume that

and that U is the universal set of natural numbers less than 11. Find

.

a. b.

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95. Determine a true proposition. a.

or 15 is a prime number.

b. and

is an irrational number.

c. 0 is a natural number and 0 is a whole number. d. or e.

and

96. Which shows a truth table that has been completed correctly? a.

T T F F

T F T F

T F F T

T T T T

T T F F

T F T F

F T F T

F T F F

T T F F

T F T F

T F T F

T F T T

T T F

T F T

F F F

T T T

b.

c.

d.

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chapter 2 F

F

F

F

97. Assume that

and that

is the universal set of natural numbers less than 11. Find

.

a. {2, 4, 6, 8, 9, 10} b. {1, 3, 5, 7} c. {1, 3, 5, 7, 11} d. {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} e. {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11} 98. Find the cardinality of the set

.

a. 57 b. 29 c. 30 d. 5 e. 191 99. Choose the right type of fallacy for the given statement, premise and conclusion.

I follow the rules from the book because that is what the book says.

Premise: The book says to follow its rules.

Conclusion: I follow the rules from the book. a. Circular Reasoning b. Appeal to Common Practice Fallacy c. Slippery Slope Fallacy d. Red Herring Fallacy 100. If

, and

find

.

a. 14 b. 17 c. 50 d. 29 101. Use

or

to indicate whether the given object is an element of the given set.

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a. 5 b. 5 102. Identify a quantifier in the following categorical statement.

None of the cars have a hydrogen engine. a. hydrogen b. the cars c. engine d. None of 103. Which compound proposition is true? a. a triangle has 2 sides and b.

and a triangle has 2 sides

c.

and a triangle has 3 sides

d.

and a triangle has 3 sides

104. An Italian food restaurant claims that with the choices of toppings that they offer on their pizzas, you can order about 32768 different types of pizza. How many toppings do they offer? a. 32768 b. 15 c. 17 d. 16 e. 19 105. Determine whether propositions , , and each need to be true or false to make the proposition below true.

a.

: true : true : false b. : false : false : false c. : false : true : true Copyright Cengage Learning. Powered by Cognero.

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chapter 2 d. : false : true : false e. : true : false : true 106. Use the roster method to write the set of integers

that satisfy

.

a. b. c. d. e.

107. Choose the right conclusion for the given statement and premise.

Post Hoc (False Cause) Fallacy Yesterday it was raining, and today my car has broken down. Therefore, the rain caused the damage.

Premise: Yesterday it was raining, and today my car has broken down. a. Conclusion: The rain was strong enough to break the car. b. Conclusion: The car can break down because of rain. c. Conclusion: The rain caused the damage. d. Conclusion: The car broke down yesterday.

108. Select a valid conclusion for the following argument.

All turtles have shells.

Some pets are turtles. a. Some pets have shells. b. No turtles have shells. c. No pets are turtles. d. All pets are turtles.

109. Let

and

. Find

.

a. b. c.

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110. Use Venn diagrams to determine which (if any) of the following expressions are equal for all sets A and B.

a. b. c. d. all are equal e.

111. How many subsets of seven elements are contained in the set

?

a. 70 b. 56 c. 8 d. 28 112. Use an Euler diagram to determine whether the argument is valid or invalid.

No detectives are memoirs.

Some memoirs are non-fiction.

No detectives are non-fiction.

a. Valid b. Invalid Copyright Cengage Learning. Powered by Cognero.

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chapter 2 113. Use De Morgan’s laws to choose an equivalent form of the following sentence. It is not true that penguins and bears live in the Antarctic. a. Penguins do not live in the Antarctic. b. Bears do not live in the Antarctic. c. It is not true that penguins or bears live in the Antarctic. d. Penguins do not live in the Antarctic or bears do not live in the Antarctic.

114. Choose the right type of fallacy for the given statement, premise, and conclusion.

You must have excellent grades at school or you will not succeed in life.

Premise: Either you will have excellent grades at school or you will not succeed in life.

Conclusion: Having excellent grades at school will make you successful in life. a. Circular Reasoning b. Appeal to Ignorance Fallacy c. Appeal to Popularity Fallacy d. Black-or-White (False Dilemma) Fallacy

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chapter 2 Answer Key 1. a. False b. True 2. 64 3.

4. 32

5.

equal

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chapter 2

6.

7. {1, 3, 5, 7, 9, 11, 13} 8. Yes T T F F

T F T F

F F F T

T T F F

T F T F

F F F T

9.

T T F F T F F T T F F` T F T T T Copyright Cengage Learning. Powered by Cognero.

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chapter 2 F T T F F T T T F F T T F T T T

10. a 11. b 12. e 13. b 14. b 15. b 16. b 17. a 18. c 19. b 20. a 21. a 22. a 23. a 24. c 25. d 26. d 27. e 28. a Copyright Cengage Learning. Powered by Cognero.

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29. c 30. c 31. b 32. a 33. d 34. b 35. a 36. c 37. a 38. a 39. e 40. a 41. d 42. e 43. a 44. c 45. e 46. a 47. c 48. a 49. b Copyright Cengage Learning. Powered by Cognero.

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50. b 51. c 52. d 53. b 54. a 55. a 56. c 57. b 58. e 59. b 60. d 61. b 62. a 63. c 64. b 65. b 66. d 67. e 68. a 69. e 70. a Copyright Cengage Learning. Powered by Cognero.

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71. b 72. a 73. d 74. c 75. d 76. a 77. d 78. a 79. b 80. b 81. d 82. a 83. c 84. c 85. b 86. c 87. a 88. a 89. b 90. b 91. a Copyright Cengage Learning. Powered by Cognero.

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92. b 93. b 94. c 95. d 96. b 97. b 98. b 99. d 100. b 101. b 102. d 103. c 104. b 105. d 106. d 107. c 108. a 109. c 110. c 111. c 112. b Copyright Cengage Learning. Powered by Cognero.

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chapter 2

113. d 114. d

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chapter 3

Enter the appropriate value to answer the question or solve the problem.

1. In 1999 the circulation of a local newspaper was 51,000. In 2000 its circulation was 65,220. What percent increase is this? Round your answer to tenth percent.

2. A van travels 350 miles on 12 gallons of gas. At that rate, how much gas will it need to travel 480 miles? Round your answer to the nearest gallon.

Indicate the answer choice that best completes the statement or answers the question.

3. The ratios of comments, likes, and views for a Youtube video are 1:6:100, in that order. If a video has got 665,000 views, how many comments and likes does it have? a. 6,650 comments, 39,900 likes b. 6,215 comments, 37,290 likes c. 6,652 comments, 53,200 likes d. 6,650 comments, 53,200 likes 4. The value z varies directly as x and inversely as the square of y. The value function z.

when

and

. Find the

a. b. c. d.

5. Express 86 km/h in miles per hour. a. 138.46 mph b. 53.42 mph c. 2.31 mph d. 3,205 mph 6. Second Newton’s law. The force applied to the body varies directly as the body’s acceleration. If for somebody the force applied is 128 N when the body has an acceleration of

, what will it be if the body has an acceleration of

?

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chapter 3 a.

N

b.

N

c.

N

d.

N

7. For the right triangle shown below, the sides a, b, and c are in the ratio of 3:4:5, in that order. If side b has a length of 20 centimeters, what are the lengths of sides a and c?

a. b. c. d.

8. A used appliance store estimates that the value of an oven-range combination decreases by 43% in the first year of use.

If the original price of a one-year-old oven-range combination was $1500, how much value will this store probably say the appliance lost? Round your answer to two decimal places. a. $34.88 b. $645.00 c. $855.00 d. $1457.00 9. At 58 kilometers per hour, how far can you travel in 4.5 hours? Round your answer to one decimal place. a. 232.0 km b. 292.5 km c. 277.5 km d. 261.0 km Copyright Cengage Learning. Powered by Cognero.

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10. As of 2022, there have been 103,436,829 confirmed cases of COVID-19 in USA. Given that the United States population that year was 338,289,857 people, find the rate per 1,000. Round to the nearest whole number. a. 305 per 1,000 population b. 3,057 per 1,000 population c. 30 per 1,000 population d. 3,270 per 1,000 population 11. During the soccer season, Susan scored goals on 6% of the shots she took. If she scored 30 goals, how many shots did she take? a. 180 b. 18 c. 500 d. 50

12. Convert

into a percent.

a. 24% b. 60% c. 48% d. 42% e. 72% 13. Convert 744 megameters to gigameters. a. 74.4 Gg b. 7.44 Gg c. 0.744 Gg d. 0.0744 Gg 14. Convert 0.064 oz to milligrams. a. 181.44 mg b. 1,814.4 mg c. 2.26 mg d. 0.23 mg 15. Maegan bought a new small car and drove 2000 miles in the first 10 months. At the same rate, how many miles will Maegan drive in 3 years?

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chapter 3 a. 9,600 b. 4,800 c. 7,200 d. 10,800 e. 14,400 16. A car, which costs 33,000 U.S. dollars, sells in the EU for 37,620 euros including 10% import tax. Find the exchange rate per U.S. dollars for Euros. Round your answer to three decimal places. a. 0.877 b. 0.965 c. 0.797 d. 1.140 17. Calculate the total weight in tons for 7000 cartons of juice weighting 9 ounces each. Round your answer to three decimal places. a. 19.6875 tons b. 39.375 tons c. 1.96875 tons d. 3.9375 tons 18. Electric field strength. An electric field strength for the field of one-point charge varies jointly as the charge and inversely as the square of the distance to the point charge. The electric field strength is

for the electric field of a

point with a charge of 10 C and distance to point 4 m. What will it be for the point with a charge of 23 C and distance to point 12 m? a. b. c. d.

19. Convert 54% into a fraction. a. b.

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chapter 3 c. d. e.

20. Potential energy of a linear spring. The potential energy of a linear spring is directly proportional to the square of the spring displacement. If a spring has a potential energy of 160 Joules with a displacement of 4 meters, what will it be for a displacement of 12 meters? a.

Joules

b.

Joules

c.

Joules

d.

Joules

21. Bob wants to find the best buy on laundry soap. Brand A costs $6.03 for 37 ounces. He has a coupon for $0.50 off the regular price of Brand B, which costs $7.21 for 46 ounces. Brand C costs $5.16 for 30 ounces. Which of these is the best buy? a. Brand B b. Brand A c. Brand C d. Either brand B or brand A; they cost the same per ounce.

22. If the price of a barrel of oil in Canada is 90 CAD, what should be the exchange rate of CAD per USD so that a barrel of oil costs 26% less in U.S. dollars? Round your answer to three decimal places. a. CAD/USD = 0.740 b. CAD/USD = 1.351 c. CAD/USD = 0.840 d. CAD/USD = 0.640 23. Work. In physics, the work W done by a constant force on a point that moves in a straight line varies directly as the point displacement s. If the work becomes 238 J for a displacement of 14 meters, what is the work for a displacement of 20 meters? a.

J

b.

J

c.

J

d.

J

24. Convert 63 oz to kilograms.

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a. 1.79 kg b. 2,222.22 kg c. 0.06 kg d. 2.22 kg 25. Convert 0.76 micrograms to nanograms. a. 0.00076 ng b. 0.076 ng c. 7.6 ng d. 760 ng 26. A lamppost is 15 feet high and casts a 25-foot shadow at noon. At the same time, a cell-phone tower next to the lamppost casts a 86-foot shadow. Which proportion can be used to find the height, H, of the cell-phone tower? a. b. c. d.

27. A racer completed a lap in 51.2 seconds on the first try. On the second try, the racer completed the lap in 43.9 seconds. What is the percent decrease in the lap time? a. 16.6% b. 14.3% c. 0.14% d. 0.17% 28. You have a choice of paying an apartment rental cost of $1950/month, $400/week, or $90/day. Which paying choice would you take? Assume that there are 30 days in a month. a. $1950/month b. $400/week c. $90/day 29. Convert 8940 mL to gallons.

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a. 2,358.84 gal b. 33.88 gal c. 2.36 gal d. 302,082.6 gal 30. The force of static friction. The force of static friction is directly proportional to the normal force on an object.

Assume that the force of static friction for a given object is 8 N when the normal force on that object is 16 N. What would the force of static friction be if the normal force becomes 30 N? a.

N

b.

N

c.

N

d.

N

31. Find the weight in pounds of 5-kilogram luggage. a. 110 lb b. 23 lb c. 2 lb d. 11 lb 32. Convert 22.5% into a decimal. a. 4.5 b. 0.0225 c. 2.25 d. 0.45 e. 0.225 33. Newton’s law of universal gravitation. The force interacting along the line intersecting two mass points is inversely proportional to the square of the distance between them. Suppose that for two particular mass points, the force was 10 N when the distance between the points was 3 meters. What will the force be if the distance between the points becomes 14 meters? a.

N

b.

N

c.

N

d.

N

34. Density. A density of a substance is inversely proportional to the volume of a substance. If for some substance the Copyright Cengage Learning. Powered by Cognero.

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density is

when the volume of the substance is

, what will it be if the substance have volume

?

a. b. c. d.

35. The water level in a reservoir went down by 2.5 meters from the initial 4 meters level in 40 minutes. Identify which fraction represents a rate and which one represents a ratio. a. (2.5/4) and (4-2.5)/40 are both ratios. b. (2.5/4) is a rate and (4-2.5)/40 is a ratio. c. (2.5/4) and (4-2.5)/40 are both rates. d. (2.5/4) is a ratio and (4-2.5)/40 is a rate.

36. The value F varies jointly as n, square of m, and cube of p, and function F.

when

,

, and

. Find the

a. b. c. d.

37. A clothing consignment store purchased a coat for $18.00 and then sold it for $30.60. Find the percent of increase.

Round your answer to tenth percent. a. 41.2% b. 70.0% c. 170.0% d. 58.8% 38. Convert 53 yd to feet. a. 17.67 ft b. 5.3 ft Copyright Cengage Learning. Powered by Cognero.

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chapter 3 c. 159 ft d. 53 ft 39. Jamie bought a pair of shoes priced at $39.00. If the sales tax rate in Jamie’s state is 8%, which is the total price of the shoes? a. 45.52 b. 46.21 c. 32.76 d. none of these 40. Wavelength. In physics, a wave is a disturbance that transfers energy through matter or space. A wavelength depends directly on the period of wave. The scientist has a mechanical wave of length 672 m with a period of 48 s. If the period becomes equal to 22 seconds, what will the length of the wave be equal to? a.

m

b.

m

c.

m

d.

m

41. Solve:

.

a. 1 b. 9 c. 14 d. 2 42. Find the length in feet of 32-m fence. a. 104.96 ft b. 9.76 ft c. 29.36 ft d. 34.88 ft 43. Convert 9463 cc to liters. a. 946.3 L b. 94.63 L c. 9.463 L d. 0.9463 L Copyright Cengage Learning. Powered by Cognero.

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44. Convert 244 picograms to nanograms. a. 0.244 ng b. 24.4 ng c. 2440 ng d. 244000 ng 45. Which of the following capacities is equal to 17 quarts? a. 34 gal b. 34 pt c. 68 pt d. 68 gal 46. A train travelled the first 300 km of a 550 km distance in 3 hours. Identify which fraction represents a rate and which one represents a ratio. a. 300/550 is a ratio and 300/3 is a rate. b. 300/550 and 300/3 are both rates. c. 300/550 is a rate and 300/3 is a ratio. d. 300/550 and 300/3 are both ratios.

47. Centripetal acceleration. In circular motion, a centripetal acceleration of a point is inversely proportional to the radius of the circle along which the point moves provided the speed does not change. Let the centripetal acceleration for some moving point be

when the radius of the circle is 3meters. What will the acceleration be if the point moves

along the circle of radius 8meters? a. b. c. d.

48. L is directionally proportional to the cube of x, and

when

. Find the function L.

a. b.

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chapter 3 c. d.

49. Convert 5 ft to centimeters. a. 152.44 cm b. 1.52 cm c. 16.4 cm d. 0.16 cm 50. Theresa made 32 of 50 free throws at basketball practice. Which percent did she make? Round your answer to tenth percent. a. 44.8% b. 72.4% c. 64% d. 83.1% 51. If 1,230,000 adults out of 4,000,000 were unemployed, find the unemployment rate per 100,000. Round to the nearest whole number. a. 307500 b. 3075 c. 30750 d. 3075000 52. A personal meal plan consists of fruits, milk, meat dishes, vegetable dishes, and grain dishes. Their ratios are 2:2:3:5:5, in that order. If a total of 25.5 servings are needed per day, how many servings of each are needed? Round your answers to the nearest tenth. a. 51:51:76.5:127.5:127.5 b. 2:2:3:5:5 c. 3:3:4.5:7.5:7.5 d. 3:3:6.5:7.5:9.5 53. The distance between two planets is 53,000,000,000 m. Describe this distance in gigameters. a. 53 Gm b. 0.053 Gm c. 53,000 Gm d. 530 Gm

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chapter 3 54. Three people put their money together to buy lottery tickets. The first person put in $10, the second person put in $25, and the third person put in $40. One of their tickets was a winning ticket. If they won $4.8 million, what was the first person's share of the winnings? Round answer to the nearest dollar. a. $1,600,000 b. $2,560,000 c. $342,857 d. $640,000 e. $738,462 55. An astronaut who weighs 177 pounds on Earth would weigh 52 pounds on the Theta Space Station. If a piece of equipment weighed 2231 pounds on Earth, what would it weigh on the Theta Space Station? Round your answer to the nearest pound. a. 647 lb b. 619 lb c. 655 lb d. 665 lb 56. Ohm’s law. By Ohm’s law, the current through a conductor between two points is directly proportional to the voltage across the two points. If the current becomes 2.5 A for a voltage of 10 V, what is the current for a voltage of 45 V? a.

A

b.

A

c.

A

d.

A

57. Over the course of two hockey seasons, a star hockey player scored 48 goals while playing in 73 games. Which of the following expresses his scoring rate as a unit rate rounded to the thousandths place? Round your answer to three decimal places. a. 0.822 goals per game b. 0.526 goals per game c. 0.658 goals per game d. 0.669 goals per game

58. Solve the equation

. Round any approximate values to the nearest hundredth.

a. 2.50 b. 10.00 c. 0.32 Copyright Cengage Learning. Powered by Cognero.

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chapter 3 d. 0.10 e. 0.40 59. Convert 0.68 petameters to terameters. a. 0.068 Tm b. 6.8 Tm c. 68 Tm d. 680 Tm

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chapter 3 Answer Key 1. 27.9 2. 16 3. a 4. d 5. b 6. c 7. d 8. b 9. d 10. a 11. c 12. b 13. c 14. b 15. c 16. b 17. c 18. a 19. d 20. c

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chapter 3 21. a 22. a 23. c 24. a 25. d 26. c 27. b 28. b 29. c 30. b 31. d 32. e 33. d 34. b 35. d 36. b 37. b 38. c 39. d 40. c 41. d Copyright Cengage Learning. Powered by Cognero.

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chapter 3 42. a 43. c 44. a 45. b 46. a 47. a 48. c 49. a 50. c 51. a 52. c 53. a 54. d 55. c 56. d 57. c 58. a 59. d

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chapter 4

Indicate the answer choice that best completes the statement or answers the question.

1. What lump sum should be deposited in an account that will earn at an annual rate of 8%, compounded quarterly, to grow to $130,000 for retirement in 30 years? a. $12,075.99 b. $12,919.05 c. $12,264.15 d. $38,235.29 e. $11,887.64

Enter the appropriate value to answer the question or solve the problem.

2. A couple want to buy a house priced at $150,200. Last year, the property tax and fire insurance bills were $2,194 and $800, respectively. Neither is expected to increase significantly in the coming year. If the couple can qualify for a 25-year conventional mortgage at 6.5% annual interest, what is the total monthly bill they should expect for the mortgage, property tax, and fire insurance?

3. Teesha left $5,000 in an account that paid 8% interest compounded annually. How much interest was earned in 4 years?

Indicate the answer choice that best completes the statement or answers the question.

4. Jolene has the option of a 7-year unsubsidized student loan of $48,000 at an annual interest rate of 5.65%. She starts her repayments 4 years after graduation or of a 6-year PLUS Loan of $48,000 at an annual interest rate of 5.55% to attend law school for her 3 years, and she starts making payments 3 years after obtaining the loan. Determine the difference between the interest paid of the given options. a. $5,136 b. $14,988 c. $144 d. $2856 5. A mutual fund has total assets of $10,000,000 and total liabilities of $200,000. There are 4,000,000 shares outstanding.

Find the net asset value of the mutual fund to the nearest cent, if necessary. a. $2.45 b. $20.00 c. $3.55 d. $0.05 e. $1.50 Copyright Cengage Learning. Powered by Cognero.

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chapter 4 6. In 2022, an intern's salary was $8000 per month, while the consumer price index (CPI) was 292.7. Calculate the equivalent salary in constant 2009 year dollars if the CPI in 2009 was 214.5. a. $5276 b. $10917 c. $5863 d. $9825 7. A purchaser obtains a 8-year auto loan at an annual interest rate of 3.92% compounded monthly. Calculate the monthly car payment if the total car cost is 17,610, including tax and license, and the purchaser makes a 25% down payment. a. $4,314.45 b. $214 c. $160.5 d. $172.79 8. Suppose the net capitalized cost of a car is $15,000, trade-in is $4,900, and the down payment is 5%. Then what is the negotiated price of the car? a. $15,995 b. $9,350 c. $20,145 d. $20,650 9. A cattleman purchases six refrigeration units for $55,000 and makes a down payment of 30%. The remainder is financed for 7 years at an annual interest rate of 3.4% compounded quarterly. Find the quarterly payment for this loan. a. $1,550.92 b. $1,537.85 c. $411.27 d. $1,499.92 10. Jack received a 4.1% nonsubsidized 7-year student loan for $16,000. If Jack qualifies for an income-adjusted repayment plan of $175 per month assuming he graduates in 5 years, how many months will it take him to repay the loan? a. 109.8 b. 138.46 c. 137.86 d. 137.52 11. Calculate the effective annual rate for an investment that earns 7% interest compounded quarterly. Round to the nearest hundredth of a percent.

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chapter 4 a. 7.19% b. 7.16% c. 7.23% d. 7.12% e. 7.00% 12. Calculate the simple interest due on a three-month loan of $1000 if the interest rate is 1.6% per month. a. $48.00 b. $4,800.00 c. $192.00 d. $4.00 e. $1048.00 13. Calculate the consumer price index (CPI) if a market basket of consumer goods and services cost $52,471 in 2021.

Suppose that the market basket cost $19,362 during the base period of 1982-85. The CPI for the base period is 100. a. 230.4 b. 295.4 c. 257.0 d. 271 14. Calculate the annual percentage yield of an investment that earns 7.50% interest compounded quarterly? a. 7.71% b. 7.69% c. 30.00% d. 67.32% 15. A purchaser obtains a 3-year auto loan at an annual interest rate of 6.69% compounded monthly. Calculate the monthly car payment if the total car cost is 24,440, including tax and license. a. $13,625.3 b. $751.18 c. $8,237.67 d. $994.62 16. What is the simple interest for a principal of $620 invested at a rate of 9% for 3 years? a. $167.40 b. $206.67 c. $502.20 d. $452.60 Copyright Cengage Learning. Powered by Cognero.

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chapter 4

17. Use the portion of the stock table shown below to answer the questions that follow. Round dollar amounts to the nearest cent when necessary.

YTD %CHG

52HI

Week LO

STOCK

DIV

YLD %

VOL 100s

CLOSE

NET CHG

–2.8

39.05

19.15

A1

0.49

1.9

978

26.33

–0.13

2.1

49.80

32.56

B1

...

1,243

37.13

0.34

If you have $2,817.31, how many shares of A1 can you purchase at its closing price? a. 107 b. 76 c. 72 d. 57 e. 147 18. Use the portion of the stock table shown below to answer the questions that follow. Round dollar amounts to the nearest cent, if necessary.

YTD %CHG

52HI

Week LO

STOCK

DIV

YLD %

VOL 100s

CLOSE

NET CHG

–0.5

39.02

22.94

A1

0.49

1.8

935

27.24

–0.4

5.5

45.38

33.12

B1

...

821

38.81

–0.17

If you purchased 375 shares of B1 stock at $41.02, what would the loss be if the shares were sold at the closing price indicated in the table.

a. $828.75 b. $5,167.50 c. $2.21 d. $1,635.00 e. $–2,062.50 19. What is the effective annual interest rate of an investment that pays 6.1% annual interest, compounded quarterly?

Round to the nearest hundredth of a percent. a. 6.24% b. 6.22% Copyright Cengage Learning. Powered by Cognero.

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chapter 4 c. 6.27% d. 6.19% e. 6.10% 20. Suppose you purchase a set of living room furniture for $1,300. You pay 10% down and sign a contract to repay the balance in 12 equal monthly payments. The finance charge on the balance is 5% simple interest. Estimate the annual percentage rate (APR) to the nearest tenth of a percent. a. 9.2% b. 4.6% c. 10.0% d. 20.0% 21. A student sets up an investment program and invests $130 at the end of each month into an account that earns an annual interest rate of 3% compounded monthly. Find the value of the investment after 7 years. a. $12,164.79 b. $12,134.45 c. $12,498.48 d. $64,294.79 22. If $12,000 had been invested in the Fictious Fund on June 30, 1994, then on June 30, 2006 the investment would have been worth $90,156.74. What interest rate compounded annually would this investment have earned? Round to the nearest hundredth of a percent. a. 18.30% b. 62.61% c. 54.28% d. 16.81% e. 54.27% 23. Yan has $8671.44 in credit card debt. The annual interest rate on the unpaid balance is 16.5% compounded monthly. If Yan wants to pay off this credit card debt in 2 years and makes no additional purchases, what are the monthly payments? a. $1468.37 b. $361.31 c. $490.65 d. $426.66 24. Determine the finance charge for a credit card that has the given average daily balance and interest rate.

Average daily balance: $836.20; monthly interest rate: 4%. Round your answer to the nearest hundredth percent. a. 33.45% Copyright Cengage Learning. Powered by Cognero.

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chapter 4 b. 25.00% c. 5.00% d. 66.90% 25. Inflation If inflation causes the cost of automobiles to increase by 2.5% each year, what should a car cost today if it cost $18,000 8 years ago? a. $21,931.25 b. $18,000.00 c. $21,600.00 d. $18,450.00 e. $26,594.20 26. $39,000 are received by a student through the PLUS program to complete his last three years of music academy. If the annual interest rate for a 9-year loan is 2.1% and the student begins repayment of the loan 3 years after graduation, what is the student’s monthly payment? a. $445.82 b. $446.6 c. $421.61 d. $420.88 27. A homeowner has been paying a monthly mortgage payment of $898.33 on a 30-year loan at a fixed annual interest rate of 6.25%. After making payments for 9 years, the homeowner must sell the house and move to another state for a new job. What is the payoff for the mortgage? Round your answer to the nearest cent. a. $125,898.78 b. $252,020.35 c. $145,900.00 d. $62,870.57 28. A house has been sold for $162,500. The mortgage company requires a 25% down payment and charges a loan origination fee of 1.5 points in addition to $600 in other fees. Find the total of the down payment and the closing costs.

Round your answer to the nearest cent. a. $43,053.13 b. $43,062.50 c. $43,068.50 d. $40,631.00 29. Ebenezer has $1212.18 in credit card debt and the annual interest rate is 20% compounded monthly. He decides to use the option that allows deferred credit card payments for 1 year, during which the interest on the card debt continues to accrue, but there are no late payment penalties. After this year, he wants to start repayment and pay off the credit card debt Copyright Cengage Learning. Powered by Cognero.

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chapter 4 in 18 months without making any additional purchases. What will be his minimum monthly payment? Round your answer to the nearest dollar. a. $96 b. $79 c. $103 d. $63 30. Jenny received a 3.5% nonsubsidized 10-year student loan for $27,000. Assuming she graduates in 2 years, determine Jenny’s monthly payment on the loan. a. $285.68 b. $284.85 c. $276.02 d. $119.17 31. A couple plans to invest money for their child's college education. What principal must be deposited by the parents when their child turns 6 in order to have $35,000 when the child reaches the age of 18? Assume the money earns 4% interest, compounded quarterly. a. $21,709.11 b. $21,860.90 c. $23,648.65 d. $56,427.91 e. $21,674.71 32. A stock pays an annual dividend of $1.31 per share. Calculate the dividends paid to a shareholder who has 1,975 shares of the company's stock. a. $2,587.25 b. $1,507.63 c. $1,975.00 d. $4,562.25 e. $20,758.35 33. Calculate the purchasing power of $10,000 in 30 years using an annual inflation rate of 4%. Round to the nearest cent. a. $3,083.19 b. $3,047.82 c. $4,545.45 d. $3,017.96 e. $3,029.95 Copyright Cengage Learning. Powered by Cognero.

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chapter 4 34. Jim wants to pay off the loan for his bass guitar immediately after he has made 18 payments. If his quarterly payment is $27.56 on a 5-year loan at an annual percentage rate of 2.4%, what is the payoff amount? a. $54.96 b. $55.94 c. $54.63 d. $4,565.94 35. Assume that the manufacturer’s suggested retail price of a car is $33,300 and its residual value is 53%. The purchaser negotiates a price of $28,800. Find the average monthly finance charge of the car if he made a $2,400 down payment, the annual interest rate is 3.3%, and there is no trade-in. a. $60.57 b. $24.63 c. $57.29 d. $66.75 36. Find the future value if $2,700 is invested for 9 years at an annual rate of 7% compounded quarterly. a. $5,042.00 b. $6,804.00 c. $3,156.27 d. $4,963.84 e. $5,015.22 37. What is the effective annual interest rate of an investment that pays 7.7% annual interest, compounded quarterly?

Round to the nearest hundredth of a percent. a. 7.93% b. 7.90% c. 7.98% d. 7.85% e. 7.70% 38. You have saved $15,000 for a down payment on a house. Your bank requires a minimum down payment of 5%.

What is the maximum price you can offer for a home in order to have enough money for the down payment? Round to the nearest dollar. a. $300,000 b. $75,000 c. $115,000 d. $3,000,000 e. $1,425,000 Copyright Cengage Learning. Powered by Cognero.

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39. Lia obtains a loan for $9,400. How much money does she actually receive assuming a loan fee of 1.142%? a. $8,326.52 b. $9,389.27 c. $9,346.33 d. $9,292.65 40. Suppose the manufacturer’s suggested retail price of a car is $18,000. What is the percentage of the residual value if the dealer thinks the car will be worth $7,500 at the end of the lease period? a. 24% b. 41.67% c. 58.33% d. 14% 41. Calculate the simple interest earned when Round to the nearest cent.

,

% and

days using the ordinary method.

a. $207.78 b. $11,204.93 c. $74,800.00 d. $204.93 e. $11,207.78 42. Kate invests $12,000 into an investment that earns an annual interest rate of 6.9% (the nominal rate). The current rate of inflation is 2.5%. How much will the investment increase in 1 year? Round your answer to the nearest cent. a. $528.00 b. $521.48 c. $515.12 d. $493.92 43. Jenny wants to pay off the loan for her bike immediately after she has made 81 payments. If her monthly payment is $177.05 on a 7-year loan at an annual percentage rate of 5%, what is the payoff amount? a. $42,140.1 b. $553.09 c. $528.95 d. $526.75 44. The table below estimates the incomes and expenses of a college student. Find the balance of the given table, which is the difference of total income and total expenses.

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Incomes Source Part-time job Student loans Scholarships Income from savings Other income

Amount ($) 8900 10000 15000 19000 2000

School expenses Source Amount ($) Tuition 25000 Books 1250 Insurance 750 Student activity fee 125 Lab fees 380 Supplies 250

Living Expenses Amount ($) 8

Source Rent Utilities Cell phone plan Internet Credit card Food Insurance Entertainment Transportation Personal expenses Miscellaneous

6

5 2 1 5

a. -$5305 b. -$3805 c. $3805 d. $7195 45. Assume you are thinking of buying a house currently priced at $197,000. If housing prices rise at an annual inflation rate of 5%, estimate the purchase price of a similar house if you wait 6 years before committing yourself to buying one. a. $263,998.84 b. $264,943.10 c. $265,756.50 d. $265,428.16 46. The face value on a bond is $10,000. It has a 20-year maturity and a 3% coupon. What is the annual interest paid to the bondholder? a. $300.00 b. $6,000.00 c. $16,000.00 d. $800.00 e. $18,061.11 47. Suppose you purchase a home and secure a loan for $390,000. If the bank charges a fee of 4 points, what is the charge for points? a. $15,600.00 b. $97,500.00 Copyright Cengage Learning. Powered by Cognero.

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chapter 4 c. $975.00 d. $4,140.00 e. $4,000.00 48. A bank is offering 20-year home loan rates of 5.5% with 1 point or 5.1% with 1.5 points. If a borrower chooses the second option for a loan of $210,000, how many months will it take to recoup the additional cost in points? Round up to the nearest month. a. 25 b. 45 c. 42 d. 23 49. Ben has the option of a 9-year nonsubsidized student loan of $12,000 at an annual interest rate of 2.95% or a 9-year nonsubsidized loan of $10,000 at an annual interest rate of 2.25%. Assuming he graduates in 4 years, determine the difference between the interest paid of the given options. a. 516 b. 1,677 c. 1,932 d. 966 50. Suppose a fitness trainer wants to have $150,000 in 8 years to own a new gym. How much does the trainer need to invest at the end of each week into an account that earns 3.7% interest compounded weekly? a. $309.75 b. $309.97 c. $298.91 d. $79.34 51. Eric received a 0.59% nonsubsidized 15-year student loan for $29,000 to attend space academy. Assuming he graduates in 4 years and possible income-adjusted repayment plan of $585 per month, how many months will it take him to repay the loan? a. 51.37 b. 51.35 c. 51.4 d. 50.2 52. Susan bought a 4-month $1,200 certificate of deposit. At the end of 4 months, she received $98 simple interest. Find the annual rate of simple interest paid. Round your answer to the nearest percent. a. 25% b. 2% Copyright Cengage Learning. Powered by Cognero.

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chapter 4 c. 37% d. 74% 53. Suppose you want a 35-year, fixed-rate mortgage loan in the amount of $146,900. If the lowest fixed annual interest rate you can find is 7%, find the monthly mortgage payment. a. $938.48 b. $1,878.23 c. $67.62 d. $2,819.24 54. A nurse had $1361.25 in credit card debt. The annual interest rate on the unpaid balance was 11% compounded monthly. If the nurse has paid off this credit card debt in 3 years without making any additional purchases, what is the sum of all the payments? a. $1604.36 b. $1510.99 c. $1973.36 d. $1439.57 55. Ivan has the option of a 13-year nonsubsidized student loan of $10,000 at an annual interest rate of 3.1% to attend law school for him 3 years. He starts making payments 4 years after obtaining the loan or 12-year PLUS Loan of $10,000 to attend law school for him 3 years at an annual interest rate of 3%, and he starts his repayments 3 years after graduation.

Determine the difference between the interest paid of the first and the second given options. a. $1,270 b. $560 c. $30 d. $340 56. A person purchased a used car for $10,000. The car was exploited for 5 years and was driven 7,000 miles. If it depreciates by 15% per year, what is the cost, in dollars per 100 miles, of depreciation? a. $4.29 b. $85.71 c. $428.57 d. $3,000,000 57. $4,500 is invested for 15 months at an annual simple interest rate of 12%. How much interest will be earned? Round your answer to the nearest cent, if necessary. a. $675.00 b. $5,175.00 c. $5,228.25 Copyright Cengage Learning. Powered by Cognero.

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chapter 4 d. $724.36 e. $1,350.00 58. Suppose a musician wants to have $100,000 in 7 years to start a band and buy a ball room for rehearsals, musical instruments, and sound equipment. How much does the musician need to invest at the beginning of each quarter into an account that earns 3.2% interest compounded quarterly? a. $3,175.16 b. $3,200.56 c. $3,101.31 d. $634.94 59. Suppose when you are 51 years old, the yearly statement you get from the Social Security Administration estimates that your monthly payment at age 71 will be $620. If inflation stays constant at 4%, what will be the purchasing power of that $620? a. $282.96 b. $12,358.80 c. $299.00 d. $529.98 60. Calculate the simple interest rate when

,

and

months. Round to the nearest hundredth.

a. 6.67% b. 0.07% c. 0.56% d. 2.00% e. 3.33% 61. A purchaser obtains a 9-year auto loan at an annual interest rate of 1.23 % compounded monthly. Calculate the monthly car payment if the total car cost is 20,210, the sales tax is 8.19%, the registration and license fee is 3.1%, and the purchaser makes a 25% down payment. a. $170.66 b. $220.1 c. $148.33 d. $175.45 62. Suppose a car cost is $5,000 after 5 years of exploitation. Evaluate its initial cost if it depreciates by 12% per year. a. $12,500 b. $8,333.33 c. $5,681.82 Copyright Cengage Learning. Powered by Cognero.

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chapter 4 d. $84.75 63. Suppose a new car is purchased for $17,000. Evaluate its depreciation percentage per year if after 3 years its cost is $7,800. a. 0.18% b. 54.12% c. 18.04% d. 15.29% 64. The manufacturer of engine oils and lubricants leases the rights to produce a group of high-speed lubricants from Oil Corporation. The lease agreement calls for a payment of $50,000 at the end of each quarter for 4 years. If the current interest rate is 5% compounded quarterly, find the present value of payments. a. $3,319,972.7 b. $757,065.34 c. $730,027.3 d. $721,014.61 65. Evaluate the cost of one gallon of fuel if the EPA rating of the car is 23 mpg and it costs about $20 per 110 miles driven for fuel. a. $95.65 b. $4.18 c. $126.5 d. $0.18 66. A programmer purchases a new garage for $50,000 and makes a down payment of 20%. The remainder is financed for 3 year at an annual interest rate of 5.4% compounded quarterly. The quarterly payment for this loan is $3,633.02.

Calculate the amount of interest paid over a 3-year term of the loan. a. $3,015.56 b. $3,596.24 c. $1,362.68 d. $32,490.04 67. Suppose an entrepreneur wants to have $23,000 in 14 years to start a new business. How much does the entrepreneur need to invest at the end of each quarter into an account that earns 5.5% interest compounded quarterly? a. $275.37 b. $271.63 c. $261.01 d. $145.2 Copyright Cengage Learning. Powered by Cognero.

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68. If $7,500 is invested at an annual rate of 11.5% compounded continuously, find the future value after years. Round to the nearest cent. a. $14,117.33 b. $13,991.94 c. $14,074.88 d. $12,243.75 e. $7,968.93 69. If you purchase a home for $405,000 with a down payment of 8%, what is the amount of the down payment and the mortgage amount? a. down payment: $32,400 mortgage amount: $372,600 b. down payment: $50,625 mortgage amount: $354,375 c. down payment: $34,992 mortgage amount: $402,408 d. down payment: $32,400 mortgage amount: $405,000 e. down payment: $34,992 mortgage amount: $405,000 70. A mutual fund has total assets of $25,000,000 and total liabilities of $200,000. There are 4,500,000 shares outstanding. If you invest $2,500 in this fund, how many shares will you purchase? Round to the nearest integer. a. $454 b. $1,800 c. $6 d. $80 e. $10,000 71. Kim has money in a savings account that earns an annual interest rate of 2.8%, compounded monthly. What is the effective rate of interest on Kim's account? Round to the nearest hundredth of a percent. a. 2.84% b. 2.82% c. 2.80% d. 2.83% e. 2.60% Copyright Cengage Learning. Powered by Cognero.

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chapter 4 72. A credit card had a balance of $919.59 due on October 31. The next due date was November 30. The following table shows purchases and payments made during that time. Calculate the finance charge if the interest rate for the period is 1.1%.

Date Purchase or Payment ($) Date Purchase or Payment ($) 11/3 50.84 11/15 155.87 11/4 30.48 11/17 177.14 11/5 158.94 11/18 119.83 11/7 -550.00 11/19 122.81 11/10 24.92 11/24 141.41 11/11 131.39 11/25 182.01 11/12 136.85 11/26 -800.00 a. $10.12 b. $11.96 c. $11.62 d. $13.42 73. Suppose a baker wants to have $16,000,000 in 9 years to open a new bakery in the center of a city. How much does the baker need to invest at the beginning of each month into an account that earns 5.5% interest compounded monthly? a. $108,840.4 b. $114,826.62 c. $114,302.73 d. $44,548.27 74. An accountant purchases a new accountant software for $750 and makes a down payment of 20%. The remainder is financed for 3 years at an annual interest rate of 2% compounded weekly. Find the weekly payment for this loan. a. $3.89 b. $3.96 c. $3.96 d. $0.24 75. The price of an item in 2004 was $1.3. Use an inflation rate of 6% to calculate its price in 2020. Round to the nearest cent. a. $3.30 b. $3.37 c. $3.35 d. $3.39 e. $3.93 76. What is the simple interest to the nearest cent on a credit card balance of $1,300.00 at 12% interest for 3 months?

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a. $39.00 b. $1,300.03 c. $3,900.00 d. $468.00 77. Calculate the present value when nearest cent.

,

compounded quarterly, and

years. Round to the

a. $7,568.15 b. $7,768.63 c. $13,200.00 d. $8,157.10 e. $143,892.50 78. Calculate the future value when cent.

,

compounded monthly, and

years. Round to the nearest

a. $7,045.56 b. $6,525.00 c. $8,804.90 d. $4,671.30 e. $11,488.36 79. Andre De Quadros bought a $5,000, 9-month certificate of deposit (CD) that would earn 8.5% annual simple interest.

What is the value of the CD when it matures? a. $5,318.75 b. $8,825.00 c. $5,329.13 d. $5,327.93 e. $5,106.25 80. Christy obtained a 11-year subsidized student loan of $13,000 at an annual interest rate of 3%. If Christy qualifies for an income-adjusted repayment plan of $196.5 per month, how many months will it take her to repay the loan? a. 72.21 b. 69.41 c. 72.41 d. 72.05 81. A student purchases a new laptop for $6,500 and makes a down payment of 13%. The remainder is financed for 2 Copyright Cengage Learning. Powered by Cognero.

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chapter 4 years at an annual interest rate of 2.4% compounded monthly. The monthly payment for this loan is $241.56. Calculate the amount of interest paid over a 2-year term of the loan. a. $130.92 b. $142.44 c. $6.6 d. $5,370.84 82. John cares about environment and decided to change his car from gasoline to electric. Moreover, electric cars are more fuel-efficient. His old gasoline car needed 3.6 gallons of gasoline per 100 mile, and a new electric car will need 28 kilowatt-hours (kWh) for the same distance. Evaluate John’s profit during the first year of exploitation of the electric car if electricity costs $0.17 per kWh and gasoline costs $3.25 per gallon. John has driven 2,700 miles. a. $444.42 b. $83.16 c. $18,738 d. $187.38 83. Josh borrows $6,080 through the PLUS program to complete his last two years of medical school. If the current annual interest rate for a 12-year loan is 2.88% and Josh begins repayment of the loan 3 years after graduation, what is Josh’s monthly payment? a. $54.31 b. $57.05 c. $57.19 d. $54.18 84. What interest will be earned if $5,300 is invested for 3 years at an annual rate of 11% compounded monthly? a. $7,361.06 b. $5,447.09 c. $5,859.60 d. $7,049.00 e. $12,974.07 85. Sandra received a 8-year PLUS Loan of $15,000 to attend war academy for her last 4 years. If the current interest rate is 1.1% and she starts her repayments 5 years after graduation, what are her monthly payments? a. $170.33 b. $179.46 c. $179.3 d. $170.48 Copyright Cengage Learning. Powered by Cognero.

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chapter 4 86. How much money should be invested in an account that earns 8% interest, compounded quarterly, in order to have $10,000 in 4 years? Round to the nearest cent. a. $7,284.46 b. $7,350.30 c. $7,575.76 d. $13,727.86 e. $7,269.21 87. Suppose that a bond with a par value of $1000 has coupon of 3.1%. If the current rate of inflation is 2%, what is the real rate of return on the investment? a. 1.08% b. 0.37% c. 1.10% d. 0.33% 88. John received a 5-year subsidized student loan of $18,000 at an annual interest rate of 5.1%. Assuming John graduates in 4 years, determine John’s monthly payment on the loan. a. $339.07 b. $340.51 c. $323.98 d. $98.25 89. A prospective homeowner knows that the monthly mortgage payment on a house that is for sale will be $711.2. The current owner says that the annual property tax bill for the upcoming year has been set at $2,429 and will not be reassessed until next year. Fire insurance is supposed to be the same as last year, $1,300. What would be the prospective homeowner’s total monthly costs for the mortgage, property tax, and insurance bills? Round your answer to the nearest cent. a. $1,021.95 b. $878.80 c. $1,561.68 d. $913.62 90. If $1,390 is invested in an account which earns 9% interest compounded annually, which will be the balance of the account at the end of 13 years? a. $4,261.47 b. $4,365.54 c. $4,459.06 d. $4,420.87 Copyright Cengage Learning. Powered by Cognero.

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chapter 4 91. Suppose you obtain a mortgage loan of $115,000 at an annual interest rate of 7.0%. How much less is the interest paid over the life of a 20-year loan than over the life of a 25-year loan? Round your answer to the nearest cent. a. $29,856.32 b. $128,838.82 c. $98,982.51 d. $23,639.31 e. $18,911.45 92. The maturity value of a four-month loan of $2,000 is $2,054. Find the simple annual interest rate to the nearest hundredth. a. 8.10% b. 7.89% c. 2.43% d. 97.37% e. 2.70% 93. Leon received an 10-year PLUS Loan of $18,000 to attend law school for her last 3 years. If the current interest rate is 3.59% and he starts his repayments 3 years after graduation, what are his monthly payments? a. $64.8 b. $65 c. $216.61 d. $217.26 94. Suppose you purchase a home and obtain a 25-year loan of $190,000 at an annual interest rate of 5%. Find the amount of interest that will be paid on the loan over the 25 years. Round your answer to the nearest cent. a. $143,216.32 b. $333,216.32 c. $237,500.00 d. $453,407.44 e. $471,445.19 95. What is the effective annual interest rate of an investment that pays 7% annual interest, compounded daily, assuming a 365-day year? Round your answer to two decimal places. a. 7.25% b. 7.19% c. 7.00% d. 7.12% Copyright Cengage Learning. Powered by Cognero.

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chapter 4 96. The manufacturer of a motorcycle leases the rights to the brake system technology from Motorcycle Corporation. The lease agreement calls for a payment of $80,000 at the beginning of each month for 6 years. If the current interest rate is 4.1% compounded monthly, find the present value of payments. a. $5,098,533.08 b. $5,115,953.06 c. $5,307,572.93 d. $18,378,681.08 97. What is the payoff amount for a loan with monthly payments of $353.39, immediately after 22 payments have been made, if the original contract was for 3 years at an annual interest rate of 7.3%? a. $4,729 b. $11,394 c. $2,415 d. $3,534 e. $1,060 98. A 5-year subsidized student loan of $3,000 at an annual interest rate of 6.9% was borrowed by Jacob. Assuming that Jacob qualifies for an income-adjusted repayment plan of $330 per month, how many months will it take him to repay the loan? a. 9.25 b. 9.31 c. 9.36 d. 6.36 99. Suppose you purchase a home and obtain a 25-year fixed-rate loan of $235,000 at an annual interest rate of 5.5%. Of the second month's mortgage payment, how much is applied to the principal? a. $367.70 b. $366.02 c. $1,075.41 d. $1,077.08 e. $1,443.11 100. Assume that the manufacturer’s suggested retail price of a car is $31,500 and its residual value is 55%. The purchaser leases the car for 1 years and negotiates a price of $28,600. Find the average monthly depreciation of the car if he made a $2,500 down payment and there is no trade-in. a. $8,775 b. $864.17 c. $731.25 Copyright Cengage Learning. Powered by Cognero.

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chapter 4 d. $972.92 101. Calculate the future value of $4,000 earning 5% interest, compounded quarterly, for 12 years. Round to the nearest cent. a. $7,261.42 b. $7,234.90 c. $2,203.43 d. $7,183.43 e. $6,400.00 102. A purchaser can afford a monthly payment of $250 for a car. What amount can he spend if he can obtain a 9-year loan at an annual interest rate of 1.28%? a. $2,343.71 b. $2,238.05 c. $25,012.16 d. $25,490.01 103. If you decide to make monthly payments of $180 (and make no additional charges on the account) on a credit card debt of $2592.44, assuming the annual interest rate of 20.5%, it will take approximately 17 months to repay the debt.

What minimum monthly payment will reduce the repayment time to 12 months? Round your answer to the nearest dollar. a. $224 b. $255 c. $196 d. $245 104. A company has declared an annual dividend of $0.73 per share. The stock is trading at $21.00. Find the dividend yield. Round to one decimal place. a. 3.5% b. 5.0% c. 29.0% d. 3.0% e. 2.0% 105. A man purchases a new car for $6,500 and makes a down payment of 25%. The remainder is financed for 8 years at an annual interest rate of 5.9% compounded monthly. Find the monthly payment for this loan. a. $60.27 b. $63.52 c. $63.83 d. $38.19 Copyright Cengage Learning. Powered by Cognero.

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106. A credit card bill due on April 5 showed a balance of $265. The card holder forgot to pay the bill until the 20th of the month, but paid the full amount of $265 at that time. In the mean time, the card was used to make purchases of $125 on the 10th of the month and $72 on the 20th of the month. What was the average daily balance for the billing period? Round to the nearest cent. a. $355.44 b. $101.93 c. $176.87 d. $195.80 107. Use the formula and months.

to calculate the maturity value of the simple interest loan when

,

a. $4,255.30 b. $70,560.00 c. $55.30 d. $9,730.00 e. $4,863.60 108. Assume that the manufacturer’s suggested retail price of a car is $21,900 and its residual value is 52%. The purchaser leases the car for 15 months and negotiates a price of $19,200. Find the monthly lease payment of the car if he made a $1,600 down payment, the annual interest rate is 8.6%, and there is no trade-in. a. $455.57 b. $518.01 c. $138.38 d. $621.28 109. Calculate the compound amount using the compound amount formula when semiannually, and years. Round to the nearest cent.

,

compounded

a. $8,793.90 b. $6,076.00 c. $4,962.15 d. $8,584.25 e. $11,593.90 110. A startup founder had a credit card bill of $8914.76 at the end of September. If the minimum monthly payment is the greater of $300 or 4.5% of the credit card bill, what is the minimum monthly payment for September? Round your answer to the nearest cent. a. $300 Copyright Cengage Learning. Powered by Cognero.

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chapter 4 b. $401.16 c. $387.66 d. $414.66 111. Use the portion of the stock table shown below to answer the questions that follow. Round dollar amounts to the nearest cent when necessary.

YTD %CHG

52HI

Week LO

STOCK

4.6

32.93

19.25

A1

0.9

46.67

32.85

B1

DIV

YLD %

VOL 100s

CLOSE

NET CHG

0.99

3.5

984

28.04

–0.1

...

1,334

39.82

–0.2

(i) If you own 690 shares of A1, what dividend do you receive this year? (ii) What was the price of a share of stock B1 at the close of the trading day yesterday? a. $683.10 $39.62 b. $683.10 $27.94 c. $69.00 $27.94 d. $69.00 $40.02 e. $683.10 $40.02 112. $20,000 are borrowed by Frank through the PLUS program to attend his last two years of police academy. If the current annual interest rate for a 9-year loan is 2.05% and Frank starts repayment of the loan 2 years after graduation, what is Frank’s monthly payment? a. $210.91 b. $211.27 c. $219.22 d. $219.59 113. An unpaid credit card bill for $947 had a due date of June 12. A purchase of $369 was made on June 15, and $188 was charged on June 29. A payment of $1000 was made on June 18 and another payment of $400 was made on July 3.

Calculate the finance charge due on July 12 based on the average daily balance and an annual interest rate of 11%.

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chapter 4 a. $412.47 b. $372.92 c. $3.73 d. $3.98

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chapter 4 Answer Key 1. a 2. $1,263.66 3. $1,802.44 Note: This question includes a decimal places requirement.

4. a 5. a 6. c 7. c 8. d 9. a 10. b 11. a 12. a 13. d 14. a 15. b 16. a 17. a 18. a 19. a 20. a Copyright Cengage Learning. Powered by Cognero.

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chapter 4 21. b 22. a 23. d 24. a 25. a 26. b 27. a 28. a 29. a 30. a 31. a 32. a 33. a 34. c 35. a 36. a 37. a 38. a 39. d 40. b 41. d Copyright Cengage Learning. Powered by Cognero.

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chapter 4 42. c 43. d 44. b 45. a 46. a 47. a 48. d 49. a 50. b 51. c 52. a 53. a 54. a 55. b 56. c 57. a 58. a 59. a 60. a 61. a 62. a Copyright Cengage Learning. Powered by Cognero.

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chapter 4 63. c 64. d 65. b 66. b 67. a 68. a 69. a 70. a 71. a 72. b 73. c 74. c 75. a 76. a 77. a 78. a 79. a 80. c 81. b 82. d 83. c Copyright Cengage Learning. Powered by Cognero.

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chapter 4 84. a 85. b 86. a 87. a 88. b 89. a 90. a 91. a 92. a 93. d 94. a 95. a 96. b 97. a 98. c 99. a 100. c 101. a 102. d 103. d 104. a Copyright Cengage Learning. Powered by Cognero.

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chapter 4 105. c 106. a 107. a 108. b 109. a 110. b 111. e 112. d 113. c

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chapter 5

Enter the appropriate value to answer the question or solve the problem.

1. Use the slope and y-intercept to sketch the graph of the equation.

Indicate the answer choice that best completes the statement or answers the question.

2. Find the x- and y-intercepts of

.

a. x-intercept: y-intercept: b. x-intercept: y-intercept: c. x-intercept: y-intercept: d. x-intercept: y-intercept: 3. Sketch the graph of the function.

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chapter 5 a.

b.

c.

d.

2

4. One ball is thrown vertically upward from the ground and its height as a function of time is given by h1(t) = 20t - 4.9t .

2 The second ball is dropped from a 65-m-high cliff and its height as a function of time is given by h2(t) = 65 - 4.9t . Time t Copyright Cengage Learning. Powered by Cognero.

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chapter 5 is measured in seconds, and heights h1 and h2 are measured in meters. Determine the height difference between the two balls at time t = 1.1 s. a. Δh = 16.1 m b. Δh = 59.1 m c. Δh = 37.6 m d. Δh = 43.0 m 5. The ordered pairs

,

and

are solutions of the same linear equation. Find n.

a. b. c. d. e.

6. Find a slope-intercept form of equation for the line that passes through the given point and has the given slope. , a. b. c. d.

7. Given that

x y

–2

–1

complete the table and sketch the graph of the equation.

0

1

2

a.

b. x –2 y 1

–1 –2

0 –3

1 –2

2 1

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x y

–2 –1

–1 2

0 3

1 2

2 –1

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chapter 5

c.

d. x –2 y 1

–1 –2

0 –3

1 –2

2 1

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x y

–2 –1

–1 –2

0 3

1 –2

2 –1

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chapter 5

8. If f is a linear function for which

and

, find

.

a. b. c. d. e.

9. Find the intercepts of the following function.

a. x-intercept: 10 y-intercept: –14 Copyright Cengage Learning. Powered by Cognero.

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chapter 5 b. x-intercept: –14 y-intercept: 10 c. x-intercept: –2 y-intercept: 2 d. x-intercept: 14 y-intercept: –10 e. x-intercept: 5 y-intercept: –7 10. Depreciation Suppose the cost of a business property is $720,000 and a company wants to use a straight-line depreciation schedule for a period of 360 months. If y is the value of this property after x months, then the company’s depreciation schedule will be the equation of a line through and . Write the equation of this depreciation schedule. a. b. c. d. e.

11. If which

are the coordinates of a point on a line that has slope –3, what is the y-coordinate of the point on the line at

a. b. c. d. e.

12. Find the intercepts of the following function. Round your answer to one decimal, if necessary.

a. x-intercept: –10.5 y-intercept: 21 b. x-intercept: 21 y-intercept: 42 c. x-intercept: –42 y-intercept: 10.5 d. x-intercept: –21 y-intercept: 2 e. x-intercept: 10.5 Copyright Cengage Learning. Powered by Cognero.

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chapter 5 y-intercept: –21 13. A city council passed an ordinance that states that the slope of a wheelchair ramp in public buildings must not exceed (i.e., one inch rise for every 13 inches of length). A wheelchair ramp for a particular building must be 18 inches high.

What is the minimum length of this ramp so that it meets the city's requirements? Round approximate values to one decimal place. a. 18 feet b. 1.4 inches c. 19.5 feet d. 234 feet e. 1.4 feet 14. The distance d, in miles, a forest fire ranger can see from an observation tower is a function of the height h, in feet, of the tower above level ground and is given by . Find the distance a ranger can see whose eye level is 20 feet above level ground. Round approximate values to the nearest tenth of a mile. a. 880 b. 9.1 c. 9.8 d. 14.7 e. 7.8 15. Graph the linear equation by finding the x- and y-intercepts.

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chapter 5 a.

b.

c.

d.

16. Graph the function Copyright Cengage Learning. Powered by Cognero.

.

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chapter 5 a.

b.

c.

d.

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chapter 5 e.

17. Marijuana use Suppose the percent of U.S. high school seniors from 1975 to 2001 who used marijuana can be modeled by percent where x is the number of years past 1975. Choose the correct interpretation the slope in this equation as a rate of change.

Round your answer to three decimal places, if necessary. a. The percentage of U.S. high school seniors who used marijuana increased at a rate of 0.198% per year. b. The percentage of U.S. high school seniors who used marijuana decreased at a rate of 19.8% per year. c. The percentage of U.S. high school seniors who used marijuana decreased at a rate of 0.198% per year. d. The percentage of U.S. high school seniors who used marijuana increased at a rate of 19.8% per year. e. The percentage of U.S. high school seniors who used marijuana decreased at a rate of 1.98% per year.

18. Find the x- and y-intercepts of

.

a. x-intercept is 2; y-intercept is b. x-intercept is

; y-intercept is

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chapter 5 c. x-intercept is

; y-intercept is 2

d. x-intercept is

; y-intercept is

19. The following graph shows the process of charging a battery over time. What is the average rate of change of charge capacity between 1 hour and 1.5 hours after the start of the process?

a. 0.6 Ah/hr b. 1.2 Ah/hr c. 0.2 Ah/hr d. 1.92 Ah/hr 20. Find the slope of the line passing through the pair of points. , a. b. c. 0 d. Undefined Copyright Cengage Learning. Powered by Cognero.

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chapter 5

21. The graph shows the current through an inductor as a function of time.

What is the average rate of change of the current in the interval between 3 seconds and 7 seconds? a. –4.50 A/s b. –1.5 A/s c. –6.00 A/s d. –2.00 A/s 22. Choose the correct graph of the line with the given slope and y-intercept. slope:

y-intercept: –1

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chapter 5 a.

b.

c.

d.

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chapter 5 e.

23. Find the slope-intercept form of the equation of the line passing through the points. , a. b. c. d.

24. Draw a line through all the points with a y-coordinate of 1.

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chapter 5 a.

b.

c.

d.

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chapter 5 e.

25. Find the slope of the line passing through the given pair of points. and a. b. 1 c. –8 d. –6 e. The slope is undefined.

26. Identify the x- and y-intercepts of the graph of the equation.

a. x-intercept: y-intercept:

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chapter 5 b. x-intercept: y-intercept:

c. x-intercept: y-intercept:

d. x-intercept: y-intercept: 27. The cost of a school banquet is $75 plus $14 for each person attending. Identify the linear function that models this problem. What is the cost for 65 people? a.

; $4889

b.

; $985

c.

; $1115

d.

; $5785

28. Graph the line that passes through the point

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and has slope

.

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chapter 5 a.

b.

c.

d.

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chapter 5 e.

29. Find the slope of the line passing through the given pair of points. and a. 15 b. c. –3 d. e. The slope is undefined.

30. The velocity of a model rocket launched vertically upward changes with time as follows: v(t) = 35 - 7.7t, where t is in seconds and v is in meters per second. Find the average rate of change of the rocket's velocity between t1 = 0.8 s and t2 = 1.4 s. a. –4.62 m/s2 b. –3.30 m/s2 c. –7.70 m/s2 d. –2.10 m/s2 Copyright Cengage Learning. Powered by Cognero.

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chapter 5 31. Evaluate the function below for the given value. ; a. –48 b. 6 c. 96 d. 60 e. –6 32. Find the slope of the line.

a. b. c. d.

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chapter 5 Answer Key

1.

2. d 3. c 4. d 5. a 6. c 7. c 8. c 9. d 10. c 11. e Copyright Cengage Learning. Powered by Cognero.

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chapter 5

12. a 13. c 14. c 15. d 16. d 17. c 18. a 19. b 20. d 21. a 22. d 23. c 24. c 25. b 26. c 27. b 28. e 29. c 30. c 31. a 32. a Copyright Cengage Learning. Powered by Cognero.

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chapter 5

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chapter 6

Enter the appropriate value to answer the question or solve the problem.

1. Solve for x.

Indicate the answer choice that best completes the statement or answers the question.

2. Chemists measure the acidity of an aqueous solution using pH. The pH is

where pH is a measure of the hydrogen ion concentration Find the pH of a solution if

measured in moles of hydrogen per liter of a solution.

. Round your answer to one decimal place, if necessary.

a. 8.8 b. 7.3 c. 8.3 d. –8.8 3. Find the x-intercepts of the graph of the quadratic function

.

a. b. c. d.

4. Let Q represents a mass of radioactive radium present after t years is

(in grams), whose half-life is 1,599 years. The quantity of radium

. Determine the quantity present after 200 years. Round to the nearest hundredth of

a gram, if necessary. a. 0 g b. 0.31 g c. 0.92 g d. 4.58 g e. 5 g Copyright Cengage Learning. Powered by Cognero.

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chapter 6 5. The following graph depicts the mass a radioactive material with initial mass of 32 mg decaying exponentially over time. Determine the half-life of the material.

a. 32 hr b. 24 hr c. 16 hr d. 8 hr 6. Determine the x-intercept(s) of the quadratic function

.

a. b. c. d. e. no x-intercept(s) 7. A credit union client deposits $1290 in an account earning 10% annual interest, compounded quarterly. What will the balance of the account be at the end of 10 years? Use the formula , where A is the account balance, P is the principal originally invested, r is the interest rate per compounding period as a decimal, and n is the total number of compounding periods. Round your answer to the nearest dollar. a. $3,464 Copyright Cengage Learning. Powered by Cognero.

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chapter 6 b. $58,384 c. $7,987 d. $4,546 8. Find the minimum or maximum value of the quadratic function below. State whether the value is a minimum or maximum.

a. ; maximum b. ; maximum c. ; minimum d. ; minimum

9. Determine the x-intercept(s) of the quadratic function

.

a. b. c. d. e. no x-intercept(s) 10. Solve the equation by using the quadratic formula. Give real solutions only.

a.

b.

c.

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chapter 6 d.

e. No real solutions.

11. Determine the vertex of the graph of the quadratic function.

a. b. c. d. e.

12. An arrow is shot upward and outward from a top a 85-foot cliff, with an initial velocity of 144 feet per second. The height of the arrow t seconds after launch is given by the equation reached by the arrow. Round to the nearest foot.

. Find the greatest altitude

a. 85 ft b. 527 ft c. 258.5 ft d. 517 ft

13. Use the Richter scale equation

, where M is the magnitude of an earthquake, I is the intensity of the

shock waves, and is the measure of the intensity of a zero-level earthquake. An earthquake occurred that measured 7 on the Richter scale. Find the intensity of the earthquake in terms of . Round to the nearest whole number. a. b. c. d.

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chapter 6 e.

14. The pH of an acidic solution is a measure of the concentration of the acid particles in the solution, with smaller values of the pH indicating higher acid concentration. In a laboratory experiment, the pH of a certain acid solution is changed by dissolving over-the-counter antacid tablets into the solution. In this experiment, the pH changes according to the equation , where x is the number of grams of antacid added to the solution. What is the pH of the solution after the addition of 0.2 grams of antacid tablet? Round your answer to two decimal places. a. 4.41 b. 3.98 c. 0.12 d. 4.285 e. 4.53

15. Richter scale Use the formula

. In October 2004, an earthquake measuring 6.8 on the Richter scale

occurred in Japan. The largest quake in Japan since 1990 was one in 1993 that registered 7.7. How many times more severe was the 1993 shock than the one in 2004 on the Richter scale?

a. 0.5 times as severe b. 5.6 times as severe c. 7.9 times as severe d. 8.9 times as severe e. 17.2 times as severe 16. Identify the value of the function

at

. Round to 3 decimal places.

a. 2.332 b. 2.832 c. 3.332 d. 3.832 e. 5.371 17. Find the vertex of the graph of

.

a.

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chapter 6 b. c. d.

18. Find the x-intercepts of the graph of the quadratic function a.

.

,

b.

,

c.

,

d.

,

19. Find the x-intercepts of the graph of the quadratic function

.

a. b. c. d.

20. Solve using the quadratic formula:

.

a. , b. , c. , Copyright Cengage Learning. Powered by Cognero.

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chapter 6 d. ,

21. Moe estimates that the cost, C, to his company (in thousands of dollars) of producing x boxes of his computer chips . How many boxes should Moe’s company produce to pay the

can be modeled by minimum cost per box? a. 10,000 b. 50 c. 16,200 d. 2,500 e. None of these 22. Find the vertex of the graph of

.

a. b. c. d.

23. Modeling Personal income Total personal income in the United States (in billions of dollars) for selected years from 1960 to 2002 is given in the following table.

Year Personal Income

1960 411.7

1970 836.1

1980 2,285.7

1990 4,791.6

2000 8,406.6

2002 8,929.1

Source: Bureau of Economic Analysis, U.S. Department of Commerce These data can be modeled by an exponential function. Write the equation of this function, with x as the number of years past 1960.

If this model is accurate, what will be the total U.S. personal income in 2010? Round your answer to the nearest cent. a. $12,511.59 billion b. $12,567.61 billion c. $12,130.93 billion d. $18,466.61 billion Copyright Cengage Learning. Powered by Cognero.

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chapter 6 e. $13,185.43 billion 24. Profit The daily profit from the sale of a product is given by maximizes profit? Round your answer to the nearest whole number.

dollars. What level of production

a. production level of 170 units b. production level of –170 units c. production level of 6 units d. production level of 624 units e. production level of 164 units 25. Decibel readings Use the fact that the loudness of sound (in decibels) perceived by the human ear depends on intensity levels according to loudness when I is 10,000 times

where

is the threshold of hearing for the average human ear. Find the

.

a. 4 b. 40 c. 5 d. 400 e. 1,000 26. Determine which of the following is a quadratic function.

I. II. III. IV. a. II, III b. II c. II, IV d. I

27. The height,

, of a punted rugby ball is given by

where x is the horizontal distance in

feet from the point where the ball is punted. How far, horizontally, is the ball from the kicker when it is at its highest point?

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chapter 6 a. 19 feet b. 24 feet c. 22 feet d. 41 feet e. 29 feet 28. Modeling Consumer Price Index The consumer price index (CPI) is calculated by averaging the prices of various items after assigning a weight to each item. The following table gives the consumer price indexes for selected years from 1940 through 2002, reflecting buying patterns of all urban consumers, with x representing years past 1900. Find an exponential regression equation for these data. Round coefficients in equation to three decimal places, if necessary.

Year 1940 1950 1960 1970

Consumer Price Index 14 24.1 29.6 38.8

Year 1980 1990 2000 2002

Consumer Price Index 82.4 130.7 172.2 179.9

Source: U.S. Bureau of the Census a. b. c. d. e.

29. A farmer has 336 feet of fencing and wants to build two identical pens for his prize-winning pigs. The pens will be arranged as shown. Determine the dimensions of a pen that will maximize its area.

a. b. c. d.

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chapter 6 e.

30. Determine whether the function’s vertex is a maximum point or a minimum point and find the coordinates of this point. Round your answer to two decimal places, if necessary.

a. vertex:

, a minimum point

b. vertex:

, a maximum point

c. vertex:

, a minimum point

d. vertex:

, a maximum point

e. vertex:

, a maximum point

31. Profit The daily profit from the sale of a product is given by possible profit? Round your answer to the nearest dollar.

dollars. What is the maximum

a. $805 b. $1276 c. $354 d. $5 e. $90 32. Early in the 1900s, an airplane manufacturer was able to increase the time its planes could stay aloft by constantly refining its techniques. Use a graphing utility to determine which exponential equation best models the data. Assume x is the number of years after 1910 and y is the time aloft in hours.

Years after 1910 Time aloft

1 2 3 4 5 6 0.93 1.5 2.8 3.5 4.3 5.2

a. b. c. d.

33. On Day 0, there are 40000 cases of a virus infection. The virus spreads at a rate of about 12% per week. Find an exponential growth model for the spread of the virus, and use it to determine the day when the number of infections will double. a. Day 7 b. Day 9 Copyright Cengage Learning. Powered by Cognero.

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chapter 6 c. Day 62 d. Day 43 34. A free neutron striking a uranium atom splits apart its nucleus, releasing energy. This process of nuclear fission also produces 2 or 3 free neutrons that strike other uranium atoms, causing a nuclear chain reaction. Suppose that uranium is bombarded with 60 free neutrons and on average 2.5 free neutrons are released in each fission event. Find the exponential growth model for the system and predict the number of free neutrons after 6 generations of fission events have occurred.

Round your answer to the nearest whole number. a. 14648 b. 110296 c. 150 d. 5859 35. If $4,000 is invested with an interest rate of 9%, compounded continuously, determine the amount of money in the account after 2 years. Use the formula . Round your answer to the nearest cent. a. $4,788.87 b. $5,733.32 c. $5,239.86 d. $29,556.22 36. The hydrogen ion concentration of a drilling mud is raised to 0.0000000001 mole per liter. What is the pH of the mud? a. 10 b. 11 c. 9 d. 8.5 37. Use a graphing utility to approximate the solutions to

a.

,

b.

,

c.

,

d.

,

e.

. Round your answers to two decimal places.

,

38. Find the x-intercepts of the graph of the quadratic function

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.

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chapter 6 a. b. c. d.

39. Iodine-131 is an isotope that is used to study the functioning of the thyroid gland. This isotope has a half-life (time required for half the material to erode) of approximately 7 days. If a patient is given an injection that contains 7 micrograms of iodine-131, what will be the iodine level in the patient after 5 days? Use the function , where A is the amount of the isotope, in micrograms, in the patient after t days. Round to the nearest tenth. a. 3.0 micrograms b. 4.3 micrograms c. 5.1 micrograms d. 5.9 micrograms e. 6.7 micrograms 40. Find the vertex of the graph of the equation.

Round your answer to 4 decimal places, if necessary. a. b. c. d. e.

41. The percent of light that will pass through a material is given by the formula , where P is the percent of light passing through the material (in fractions), k is a constant that depends on the material, and d is the thickness of the material in centimeters. The constant k for a piece of tinted glass is 0.5. How thick (in centimeters) is a piece of this glass that allows 25% of the light incident to the glass to pass through it? Round to the nearest hundredth of a centimeter.

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chapter 6 a. 2.77 b. 1.2 c. 2.8 d. 6.44 e. 1.66 42. Determine if the vertex of the graph of the equation is a maximum or minimum point.

a. vertex is at a maximum point b. vertex is at a minimum point c. has no vertex 43. pH levels Use the following information. Chemists use the pH (hydrogen potential) of a solution to measure its acidity or basicity. The pH is given by the formula

where is the concentration of hydrogen ions in moles per liter.

What value of is associated with pH level 12? a. b. c. d. e.

44. Solve

using the quadratic formula.

a.

b.

c.

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chapter 6 d.

e.

45. An insect population in a controlled laboratory environment is increasing exponentially. Two days after the population was established, there are 300 insects, and after 2 more days, there are 900 insects. How many insects will there be 6 days after the population was established? a. 2,700 b. 8,100 c. 1,200 d. 2,780 46. Determine the vertex of the graph of the quadratic function

.

a. b. c. d. e.

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chapter 6 Answer Key 1. 10,000,000 2. c 3. b 4. d 5. c 6. a 7. a 8. a 9. e 10. e 11. e 12. d 13. a 14. e 15. c 16. a 17. a 18. d 19. d 20. c

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chapter 6 21. a 22. b 23. d 24. d 25. b 26. c 27. a 28. a 29. a 30. a 31. c 32. b 33. d 34. a 35. a 36. a 37. c 38. a 39. b 40. d 41. b Copyright Cengage Learning. Powered by Cognero.

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chapter 6 42. b 43. d 44. d 45. a 46. d

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chapter 7

Enter the appropriate value to answer the question or solve the problem.

1. Six math books and four literature books are on a shelf. How many ways can they be arranged if the math books are kept together and the literature books are kept together?

2. Evaluate the expression.

Indicate the answer choice that best completes the statement or answers the question.

3. Gambling A game of cards is played with a hand that consists of 2 cards dealt from a deck of 42 cards. How many different hands of cards are possible? a. 861 b. 1,722 c. 84 d. 1,764 e. 2 4. A coin was thrown 9 times. What is tail expectation? a. 4.5 b. 9 c. 18 d. 7 5. A shooter has 12 bullets. What is his expectation of hits if the probability of hit of each shoot is 0.4? a. 4.8 b. 9.6 c. 30 d. 4 6. Eight balls of the same size but different colors — two greens, two whites, two reds, and two blues — are placed in a box and a blindfolded person chooses three balls. List the elements of the event that these three balls all have different colors. a. {GWRB} b. {GWR, GWB, WRB, GRB} c. {GWR, WRB} d. {GWR, WRB, GB} Copyright Cengage Learning. Powered by Cognero.

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chapter 7

7. A granny wrote letters to 5 grandchildren and signed 5 addresses on the envelopes. She put the letters in the envelopes randomly. How many grandchildren will get the correct letter on the average? a. 1 b. 0.2 c. 0.8 d. 1.25 8. One ball is drawn at random from a bag containing 20 red (R) balls and 13 white (W) balls. What is the probability that the ball is green (G)? a. b. c. d. e.

9. A bag of marbles contains 8 blue, 8 green, 6 red, 7 yellow, and 3 black marbles. If you reach in the bag and draw one marble at random, what is the probability that you will draw a yellow marble? a. b. c. d.

10. Evaluate:

.

a. b. c.

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chapter 7 d. 120 11. Find the expectation of a dice with 6 sides. The sides are numerated from 1 to 6 consistently. a. 3.5 b. 0.167 c. 1 d. 21 12. Committiees In how many ways can a committee consisting of 7 men and 7 women be selected from a group consisting of 22 men and 19 women? a. 220,932 b. 8,593,371,072 c. 218,285,374,622,515,000 d. 1,113,497,280 e. 859,592,148 13. The odds against a particular candidate winning an election are estimated to be 11 to 15. If those odds are accurate, what is the probability that that candidate will win the election? a. b. c. d.

14. If

, evaluate

.

a. 6 b. 720 c. 24 d. 5,040 e. 120 15. How many different seven-letter arrangements can be made from the letters in the word AVERAGE? a. 1,260 b. 2,520 c. 3,780 Copyright Cengage Learning. Powered by Cognero.

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chapter 7 d. 630 16. The odds against winning $5 in a lottery game are 190 to 3. What is the probability of winning? a. b. c. d. e.

17. Two regular six-sided dice are tossed. Compute the probability of rolling a 10. a. b. c. d. e.

18. A player throws a dart at a target. Depending on what area of the target the dart hits, the player can get 1, 5, 10, 25, or 50 points. If the dart misses the target, the player loses 15 points. The probability of gaining/losing a certain number of points in one throw for this particular player is shown in the table.

Points Probability -15 0.01 1 0.26 5 0.25 10 0.2 25 0.25 50 0.03 What is the expectation for the player's throw? Round your answer to two decimal places. a. 11.26 points per throw b. 11.11 points per throw c. 11.41 points per throw d. 10.96 points per throw Copyright Cengage Learning. Powered by Cognero.

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chapter 7 19. Tom received a bag of candies as a gift. It is known that one half of the candies is made of dark chocolate, and the other half is made of white chocolate. Among the dark chocolates, 5 pieces contain almonds, and the rest contain hazelnuts. Among the white chocolates, 5 pieces contain hazelnuts, and the rest contain almonds. There are 26 candies in total and they all have the same wrapper. What is the probability that a randomly selected candy will be made of white chocolate or contain hazelnuts? a. b. c. d. 1 20. A fortune teller uses a deck consisting of 78 cards, one of which is unique and named The Fool. If she has already drawn 2 cards and none of them are The Fool, what is the probability that the next card will also be not The Fool? a. b. c. d.

21. How many candy boxes can be compounded from 15 candies of 5 sorts? a. 3,876 b. 15,504 c. 10,897,286,400 d. 20,274,183,401,472,000 22. Lunch menu consists of a sandwich, a desert, and a drink. How many variants of lunch can be made if a person can choose from 4 sandwiches, 7 deserts, and 3 drinks? a. 84 b. 14 c. 30 d. 252 23. A win-win lottery is organized. There are 160 wins, 20 of them are $100, 60 of them are $30, and 80 of them are $30.

What is the average gain for a person who bought one ticket? a. 38.75 b. 1 Copyright Cengage Learning. Powered by Cognero.

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chapter 7 c. 121.25 d. 53.333 24. How many ways exist to encage 5 animals in 11 cages if all of them should be in different cages? a. 55,440 b. 332,640 c. 120 d. 524,160 25. There are 10 people who play frisbee golf in a league. In how many ways can the 10 people be divided into two teams of 5 people. a. 252 b. 504 c. 756 d. 126 e. 120 26. There are three traffic lights on the road. The probability that a car will stop at any of them is 0.6. Find the expectation that the car will drive through all of them. a. 0.912 b. 1.8 c. 0.064 d. 0.2 27. The data in the table describes occupants of an apartment complex.

Age 0-18 19-30 31-50 50+ Total

Male 133 203 297 338 971

Female 181 173 268 253 875

Total 314 376 565 591 1,846

Compute the probability that an occupant chosen at random will be a female between 0 and 50 years of age. a. b.

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chapter 7 c. d. e.

28. There are 14 patients in Dr. Ziglar's waiting room. Dr. Ziglar can see 6 patients before lunch. In how many different orders can Dr. Ziglar see 6 of the patients before lunch? a. 3,003 b. 121,080,960 c. 84 d. 6 e. 2,162,160 29. Mary, in addition to the regular five pence coins, has several defective five pence coins with two tails. There are five regular coins and one defective coin in her pocket, and 10 regular and two defective coins in her purse. Consider three successive events: A) first, Mary randomly picks one regular coin from the pocket, B) next, Mary randomly picks one regular coin from the purse, C) next, Mary randomly picks one two-tailed coin from the purse.

Choose the correct statement. a. Events A and B are dependent. b. Events B and C are dependent. c. Events A and C are dependent. d. There are no two dependent events.

30. Two students need to pass the exam. The probability that the first student will pass it is 0.5, and the probability that the second student will pass it is 0.5. Find the expectation of passing the exam. a. 1 b. 0.25 c. 2 d. 0.5

31. Evaluate:

.

a. 420 b. 84 c.

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chapter 7 d.

32. If a pair of dice, one green and one red, is rolled, what is the probability that the sum of the two dice is a number between 3 and 4, inclusive? a. b. c. d. e.

33. A box contains 3 red balls, 6 white balls, and 7 black balls. Two balls are drawn at random from the box with replacement of the first before the second is drawn. What is the probability of getting a red (R) ball on the first draw and a white (W) ball on the second? a. b. c. d. e.

34. Evaluate

.

a. 40,320 b. 120 c. 6 d. 720 e. 24 35. How many ways to form a queue from 12 people exist?

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a. 479,001,600 b. 78 c. 132 d. 144 36. There are 5 black keys in one piano octave. How many different 5-keys chords can be played on the synthesizer of 2 octaves, using only black keys? a. 252 b. 1,077,167,364,120,210,000,000 c. 30,240 d. 15,120 37. There are 5 roads to the top of the mountain. How many ways to climb and come down from the mountain exist if the tourist should take different ways? a. 20 b. 25 c. 60 d. 12 38. The fur color of Labrador Retrievers is determined by a dominant allele B, corresponding to black fur, and a recessive allele b, corresponding to brown fur. If two Labrador Retrievers, one of genotype Bb and the other of genotype Bb, have offspring, compute the probability of one of the offspring having black fur. Hint: Draw a Punnett square. a. 0.5 b. 0.75 c. 0 d. 1 39. There are 3 entrances and 3 exits in the labyrinth. In how many ways can it be passed if there are two routes between each entrance and each exit? a. 18 b. 9 c. 36 d. 12 40. Evaluate:

.

a. 2 b. 6 Copyright Cengage Learning. Powered by Cognero.

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chapter 7 c. 24 d. 1

41. If the probability that an event will occur is what are the odds against the event occurring? a. b. c. d. e.

42. A committee is to consist of three members. If there are six men and five women available to serve on the committee, how many different committees can be formed? a. 165 b. 20 c. 10 d. 33 43. A deck consists of 52 usual cards and two Jokers. If you pull 5 cards from this deck (without replacing them), what is the probability that at least one of the cards is Joker? a. 0.822 b. 0.217 c. 0.178 d. 0.172 44. A company of 10 people, 5 boys and 5 girls, decided to go to the cinema. How many ways to seat them in one row exist if any two boys and any two girls should not seat beside each other?

a. 28,800 b. 14,400 c. 3,628,800 d. 50 45. 11 boxers participated in the competition. Each boxer had one fight with each of the opponents. How many fights were held in the competition? a. 55 b. 66 c. 3,628,800 Copyright Cengage Learning. Powered by Cognero.

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chapter 7 d. 110 46. The table below shows the employment status of individuals living in a particular town by age group.

0-17 18-50 51+

Full-time Part-time Unemployed 33 155 376 320 68 29 431 154 192

If a person in this town is selected at random, what is the probability that the individual is unemployed, given that he or she is over 51 years old? a. b. c. d. e.

47. Two regular six-sided dice are tossed three times in succession. Compute the probability of rollng a sum of at most 8 on all three tosses. a. b. c. d. e.

48. Compute the conditional probability answer to two decimal places.

given

,

and

. Round your

a. 0.41 b. 0.45 c. 0.22 d. 0.52 Copyright Cengage Learning. Powered by Cognero.

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chapter 7

49. If the probability of rain this afternoon is 0.32, what is the probability that it will not rain this afternoon? a. 0.68 b. 0.16 c. 0.84 d. 0.32 50. Evaluate:

.

a. 56 b. 504 c. 7 d. 5,040 51. How many 3-digit numbers can be formed from odd digits? a. 125 b. 60 c. 15 d. 120 52. Evaluate the expression.

a. b. c. d. 0 53. The publisher decided to publish a new book. He is going to sell one copy for $20. Assume that the cost of publishing is $65,000 for 1,000 copies and $275,000 for 5,000 copies. The probability of selling 1,000 copies is 0.8 and of selling 5,000 copies is 0.2. Find the publisher’s expected profit. a. –71,000 b. 36,000 c. 1,800 Copyright Cengage Learning. Powered by Cognero.

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chapter 7 d. –220,000 54. Two eight-sided dice are thrown. Given that one of the dice shows a three, what is the probability that the sum on the two dice is four? a. 0 b. c. d.

55. In December, in Nowhere town, if it snows one day, there is a 58% chance that it will snow the next day. If it does not snow on a given day, there is a 20% chance that it will snow the following day. If there is no precipitation on December 1st, what is the probability that it will snow on the next three days and not snow on the fourth day. Round your answer to five decimal places. a. 0.06728 b. 0.03902 c. 0.02826 d. 0.01346 56. Find the probability for the experiment of selecting one card from a 52 playing cards such that the card is a 10 or higher (aces are low). a. b. c. d. e.

57. The table shows the number of black and colored cars with manual and automatic transmission in a rental service's park.

Black Colored Total Manual 20 16 36 Automatic 24 28 52 Total 44 44 88 Copyright Cengage Learning. Powered by Cognero.

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chapter 7 If you booked a car with manual transmission, what is the probability that it will be black? a.

P(black|manual) = b. c. d.

P(black|manual) = P(black|manual) = P(black|manual) =

58. In a week, a coffee shop has sold different drinks, which are listed in the table below. If an order from the list is selected at random, compute the probability its price is higher than $3.

Type of Coffee Price of a cup ($) Number of orders Black 2.7 1000 Latte 3.8 790 Cappuccino 3.5 450 Americano 2.6 470 Espresso 2.3 310 Macchiato 2.7 120 Mocha 3.9 50 a. 0.20 b. 0.60 c. 0.80 d. 0.40 59. In a batch of 70 fortune cookies, two cookies were mistakenly left without predictions. If 10 cookies are randomly selected from the batch, what is the probability that at least one is empty? Round your answer to three decimal places. a. 0.733 b. 0.636 c. 0.364 d. 0.267 60. A coin is tossed 5 times. What are the odds against the coin showing heads all five times? a. 32 to 1 b. 1 to 31 c. 33 to 1 d. 31 to 1 e. 1 to 32 61. In order to assign examination questions to students randomly, cards are used. The cards with 12 questions on them are laid out on a desk face down. A student picks one card and takes it. Determine whether the event that she picks a Copyright Cengage Learning. Powered by Cognero.

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chapter 7 question with an odd number and the event that she picks one of the first 6 questions are independent. a. The events are independent. b. The events are dependent.

62. Two regular six-sided dice are tossed. Compute the probability of rolling a sum of at most 2. a. b. c. d. e.

63. Evaluate

.

a. 55,440 b. 7,920 c. 990 d. 462 e. 330

64. Evaluate

.

a. b. c. 5,005 d. e.

65. The Countess wants to insure her $200,000 worth of jewelry against theft for a year. The insurance company estimates the chance of theft to be 0.1% and offers a 1-year policy for $398, which guarantees reimbursement of the full cost of the jewelry in the event of theft. What is the company's expectation? Round your answer to the nearest cent. a. $197.20 b. $197.60 Copyright Cengage Learning. Powered by Cognero.

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chapter 7 c. $198.00 d. $200.40 66. A panel of contest judges is to consist of thirteen women and seven men. A list of potential judges includes fourteen women and nine men. How many different panels could be created from this list? a. 504 b. 468 c. 126 d. 98 67. If you roll a single fair die and count the number of dots on top, what is the probability of getting a number less than 5 on a single throw? a. b. c. d. e.

68. Jane and her friends are playing a board game. To win on her last step, Jane must roll at least 15 using one 20-sided dice (the dice with 20 sides numbered from 1 to 20 and having an equal probability of being rolled). What is the probability of losing? a. b. c. d.

69. A purse contains 11 red, 19 blue, 22 yellow, and 48 green beads. Find the probability that one bead drawn at random will be red or green. a. b. c.

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chapter 7 d.

70. List the elements of the sample space for the following experiment.

A month is selected from the months that have exactly 31 days. a. February b. January, March, April, May, June, July, August, September, October, November, December c. January, March, May, July, August, October, December d. April, June, September, November e. January, March, May, July, August, October 71. A student needs to have 6 exams in 11 days. In how many ways can this be done if it is known that one of the exams will be taken in the last day? a. 181,440 b. 332,640 c. 55,440 d. 8,910,720 72. Two regular six-sided dice are tossed. Compute the probability of rollng a 4 or doubles. a. b. c. d. e.

73. How many sets from pens and pencils can be compounded if one set consists of 12 things? a. 4,096 b. 132 c. 479,001,600 d. 66 74. You and 2 friends all have tickets for seats in the same row at a concert. How many different ways can you sit in the assigned seats?

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chapter 7 a. 1 b. 6 c. 2 d. 24 75. A bag contains 2 nickels, 6 dimes, and 9 quarters. If you draw 3 coins at random from the bag, without replacement, what is the probability that you will get a nickel (N), a quarter (Q), and a nickel (N), in that order? a. b. c. d. e.

76. A student group consists of 21 people, 7 of them are girls and 14 of them are boys. How many ways exist to choose a pair of the same-sex people? a. 112 b. 210 c. 98 d. 322

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chapter 7 Answer Key 1. 34,560 2. 45 3. a 4. a 5. a 6. b 7. a 8. a 9. c 10. a 11. a 12. b 13. c 14. c 15. a 16. b 17. d 18. b 19. c 20. d

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chapter 7 21. a 22. a 23. a 24. a 25. a 26. a 27. c 28. e 29. b 30. a 31. a 32. e 33. a 34. e 35. a 36. a 37. a 38. b 39. a 40. b 41. a Copyright Cengage Learning. Powered by Cognero.

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chapter 7 42. a 43. c 44. a 45. a 46. e 47. a 48. a 49. a 50. a 51. a 52. b 53. a 54. d 55. c 56. d 57. b 58. d 59. d 60. d 61. a 62. a Copyright Cengage Learning. Powered by Cognero.

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chapter 7 63. a 64. b 65. c 66. a 67. c 68. a 69. b 70. c 71. a 72. a 73. a 74. b 75. d 76. a

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chapter 8

Enter the appropriate value to answer the question or solve the problem.

1. The scores for a standardized reading test are found to be normally distributed with a mean of 290 and a standard deviation of 39. If the test is given to 450 students, how many are expected to have scores between 290 and 329?

2. The Jackson triplets, Jenny, John, and James, are in different algebra classes at City High. On their final exams, Jenny scored 76 on a test with a mean of 69 and a standard deviation of 10; John scored 79 on a test with a mean of 74 and a standard deviation of 10; and James scored 74 on a test with a mean of 67 and a standard deviation of 8. Who had the best score?

Indicate the answer choice that best completes the statement or answers the question.

3. Tom has a mean score of 73 on the first three tests in class. What is the highest grade Tom can get if there is only one more 100-point test and all the tests are equally weighted. The teacher rounds final grades to the nearest integer. a. 87 b. 82 c. 77 d. 79 e. 80 4. A data set has a mean of

and a standard deviation of 17. Find the z-score of

.

a. b. c. d. e.

5. For the standard normal distribution, find the probability that a value is greater than 2. Round your answer to three decimal places, if necessary. a. 0.477 b. 0.523 c. 0.954 d. 0.023 e. 0.977 6. Mark typed an average of 69 words per minute on the first 500 words of his 1000 word essay. Because of fatigue he was only able to type 53 words per minute on the remaining 500 words. What was Mark's average words per minute on Copyright Cengage Learning. Powered by Cognero.

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chapter 8 his entire essay? Round any approximate answers to the nearest integer. a. 61 b. 60 c. 69 d. 53 e. 32 7. The median salary of the 1,714 teachers in a large public school district is $39,800. If the 74th percentile of the salaries is $46,500, find the percent of teachers whose salary is between $39,800 and $46,500. a. 74% b. 24% c. 76% d. 26% 8. In a normal distribution, what percent of the data lie within 1 standard deviation of the mean? Round your answer to one decimal place. a. 34.1% b. 47.7% c. 95.4% d. 68.2 % e. 84.1% 9. Find the mean, the median, and all the modes for the pay rates in the given frequency distribution. Round your answers to two decimal places.

Hourly pay rates for employees 8.00 11.50 16.00 21.00

Frequency 4 26 8 2

a. Mean: $18.37 Median: $13.75 Mode: $11.50 b. Mean: $14.13 Median: $13.75 Mode: $16.00 Copyright Cengage Learning. Powered by Cognero.

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chapter 8 c. Mean: $12.53 Median: $11.50 Mode: $11.50 d. Mean: $12.53 Median: $13.75 Mode: $16.00 e. Mean: $14.13 Median: $13.75 Mode: $11.50 10. Given the sample data below, use the defining formula to compute the sample variance. Round your answer to two decimal places, if necessary.

27, 19, 26, 27, 14, 22 a. 4.79 b. 27 c. 22.92 d. 27.5 e. 5.24 11. The table below displays the population density of six cities alongside corresponding crime rates within these cities.

Population density (per square kilometer) 200 400 500 650 700 850 Crime rate (incidents per 1000 people) 7 5 11 14 14 18 Find the linear correlation coefficient for this dataset. Round your answer to three decimal places. a. 0.914 b. 0.823 c. 0.997 d. 0.686 12. So far in art class, a student’s quiz scores are 87%, 89%, 81%, and 76%. What score does the student need on the fifth quiz to have a mean quiz score of 85%? All the quizzes have equal weights. Round your answer to the nearest whole number. a. 84% b. 83% c. 91% d. 92% 13. Find the range of the set of numbers given.

2, 9, 4, 2, 7, 3, 8 Copyright Cengage Learning. Powered by Cognero.

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a. 4 b. 2 c. 7 d. 5 e. 8 14. A population is normally distributed with a mean of 35 and a standard deviation of 8. What percent of the data are less than 41? Round your answer to one decimal place. a. 77.3% b. 27.3% c. 72.7% d. 22.7% e. 45.4% 15. Find the mean, the median, and the mode, if any, for the given data. Round noninteger means to the nearest tenth.

93, 98, 81, 77, 111, 76, 93, 68 a. Mean:87.8 Median: 81 Mode: none b. Mean:87.8 Median: 93 Mode: none c. Mean:87.8 Median: 87 Mode: none d. Mean:87.8 Median: 93 Mode: 93 e. Mean: 87.1 Median: 87 Mode: 93 16. Statistical Abstracts, (117th ed.), reports average travel time to work for commuters in the New England states to be (to the nearest minute): 17

21

16 26 17

21

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chapter 8 What is the median of these commuting times? Round your answer to one decimal place, if necessary. a. 17 b. 19 c. 16.8 d. 21 e. 0 17. The lifetime of a disposable water filter is normally distributed with mean gal and standard deviation gal. What is the probability that a filter selected at random will last from 40 gal to 58 gal? Round your answer to three decimal places. a. 0.192 b. 0.286 c. 0.669 d. 0.714 e. 0.477 18. For the standard normal distribution, find the probability that a value lies between the z-scores of . Round your answer to three decimal places, if necessary.

and

a. 0.192 b. 0.268 c. 0.651 d. 0.232 e. 0.46 19. Find the range, the standard deviation, and the variance for the given samples. Round noninteger results to the nearest tenth.

92, 68, 56, 73, 88, 68, 73 a. range: 36 standart deviation: 12.4 variance: 153 b. range: 19 standart deviation: 14.8 variance: 220.3 c. range: 19 standart deviation: 8.7 variance:75 d. range: 36 standart deviation: 278.8 Copyright Cengage Learning. Powered by Cognero.

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chapter 8 variance: 278.8 e. range: 36 standart deviation: 18.6 variance:344.3 20. Find the mode of the set of scores.

6, 10, 10, 7, 6, 12, 10, 5 a. 10 b. 8.25 c. 6 d. 8 e. 7 21. Braking distance is the distance a vehicle travels from the moment the driver applies the brakes to the moment the vehicle comes to a complete stop. Many factors, such as the type of a vehicle, road conditions, the efficiency of the braking system, tire quality, and several others influence braking distance. However, it is predominantly determined by the speed of the vehicle. The table below presents data on cars' speeds and their corresponding braking distances, collected from different but similar types of vehicles.

Car speed (km/h) 60 70 80 90 100 110 Braking distance (m) 14 23 24 32 42 49 Find the linear correlation coefficient for the given data. Round your answer to three decimal places. a. 0.779 b. 0.867 c. 0.916 d. 0.985 22. Bev and Dawn have been comparing their investment portfolios for several years. Bev claims that her portfolio of only stocks has a better record than Dawn's portfolio that is 70% stocks and 30% bonds. Let be a random variable representing the annual percent return for Bev's portfolio and let be a random variable representing the annual return on Dawn's portfolio. Use this information to calculate the coefficient of variation for Dawn's portfolio. Round your answer to two decimal places.

22 30

16 10

19 21

20 6

26 1

–2 –3

31 9

34 –1

–2 19

10 –10

a. 66.77% b. 149.78% c. 71.02% d. 142.09% e. 140.8%

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chapter 8 23. Construct a box-and-whisker plot for the math test results for a class of 15 students, which are as follows: 90, 90, 60, 69, 80, 85, 88, 73, 71, 70, 66, 90, 86, 84, 73 a.

b.

c.

d.

24. The light bulbs produced by a generic manufacturer have a stated average life of 1,994 hours. Assume that the lifetimes of the bulbs are normally distributed with a standard deviation of 132 hours. Find the probability that a light bulb from this manufacturer will last longer than 2225 hours. Round your answer to three decimal places. a. 0.960 b. 0.920 c. 0.040 d. 0.460 e. 0.540 Copyright Cengage Learning. Powered by Cognero.

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chapter 8 25. The duration of routine operations in a certain hospital has approximately a normal distribution with an average of 156 minutes and a standard deviation of 14 minutes. What percentage of operations last less than 177 minutes? Round your answer to one decimal place. a. 56.7% b. 6.7% c. 93.3% d. 86.6% 26. Find the mean of the set of sample data.

76, 68, 96, 80, 86, 68, 72 a. 76 b. 78 c. 28 d. 80 e. 68 27. The lengths of a certain species of fish were found to be normally distributed. The mean length is 74 cm with a standard deviation of 10 cm. In a school of 460 of these fish, about how many would be longer than 51 cm? Use the Empirical Rule. a. 21 b. 459 c. 38 d. 449 28. A person's weight is influenced by various factors, with one of the primary determinants being height. The table below displays the heights and weights of eight individuals.

Height (cm) 153 161 166 172 174 181 185 189 Weight (kg) 50 56 62 64 73 75 82 89 To analyze this relationship, treat height as the independent variable and weight as the dependent variable, and determine the linear regression equation. Round the slope and y-intercept to three significant figures. a. y = 1.43x + 99.9 b. y = 1.06x - 114 c. y = 1.06x - 99.9 d. y = 1.43x + 114 29. Find the median of the set of scores.

48, 62, 62, 98, 76, 88, 70

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chapter 8 a. 98 b. 72 c. 62 d. 70 e. 50 30. The price of a home is linked to its total area. The agency released data on homes currently available for sale. The table below shows their respective prices and areas.

Home Price ($) 150000 180000 190000 220000 230000 250000 270000 300000 2

100 110 120 130 140 150 160 170 Home Area (m ) Treat the area as the independent variable and price as the dependent variable and find the linear regression equation.

Round the slope and y-intercept to the nearest whole number. a. y = 2012x + 47307 b. y = 47857x + 2012 c. y = 2362x - 47307 d. y = 2012x - 47857 31. Thirteen students took a test, and their results are as follows: 85, 59, 78, 71, 95, 89, 91, 65, 62, 83, 80, 87, 74. Find the quartiles for the data. a. Q1 = 65, Q2 = 80, Q3 = 89 b. Q1 = 59, Q2 = 80, Q3 = 95 c. Q1 = 71, Q2 = 80, Q3 = 87 d. Q1 = 68, Q2 = 80, Q3 = 88 32. A random sample of 1000 oranges showed that the mean amount of juice per orange was 9.5 fluid ounces, with a standard deviation of 1.7 fluid ounces. If the z-score for a particular orange was –0.5, how much juice was produced by this orange? Round approximate values to the nearest tenth of a fluid ounce. a. 9.0 fluid ounces b. 10.0 fluid ounces c. 8.7 fluid ounces d. 10.4 fluid ounces e. 10.7 fluid ounces 33. What is the G.P.A. for a student who earned the grades shown below? The grades are based on a 4.0 point maximum scale, with

,

,

,

Class

Credits

Phys 150C

4

Phys Lab 160C

2

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,

, etc. Round your answer to two decimal places.

Grade

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chapter 8 Math 210A Hist 220A

9 2

a. 2.19 b. 4.25 c. 3.00 d. 9.33 34. Find the mean of the scores.

4, 3, 4, 1, 0, 6 a. 3.5 b. 3 c. 4 d. 2.5 e. 6 35. The rate of a car's gasoline consumption is influenced by its driving speed. The table below illustrates gasoline consumption, measured in liters per hour, at various driving speeds specified in kilometers per hour.

Driving speed (km/h) 40 50 60 70 80 90 100 110 Gasoline consumption (liter/hour) 1.0 1.1 1.4 1.5 1.8 2.0 2.2 2.4 Find the equation of a linear regression line for the data where driving speed is the independent variable and gasoline consumption is the dependent variable. Round the slope and y-intercept to three decimal places. a. y = 0.021x + 0.121 b. y = 0.021x + 0.198 c. y = 0.121x + 0.021 d. y = 0.024x + 0.121 36. Systolic blood pressure for a group of women is normally distributed, with a mean of 112 and a standard deviation of 14. Find the probability that a woman selected at random has blood pressure greater than 140. Round your answer to four decimal places. a. 0.4773 b. 0.9773 c. 0.0227 d. 0.5227 e. 0.9546 37. Find the average price per item for an order that consists of the following catalog items. Round your answer to two decimal places.

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chapter 8 Price Per Item $10 $15 $17 $20

Number of items 4 1 9 6

a. $22.72 b. $16.40 c. $3.00 d. $3.20 38. The number of patients coming into a hospital’s emergency clinic between midnight and 6:00 A.M. was recorded each day for several days. Use the median procedure for finding quartiles to find the first, second, and third quartiles ( , , and ) for the data.

Number of Patients (midnight - 6:00 A.M.) 9 11 15 17 8 23 18 11 24 11 8 9

20 16 20 a.

,

b. c. d.

21 13

, ,

,

, ,

,

,

39. Bev and Dawn have been comparing their investment portfolios for several years. Bev claims that her portfolio of only stocks has a better record than Dawn's portfolio that is 50% stocks and 50% bonds. Let be a random variable representing the annual percent return for Bev's portfolio and let be a random variable representing the annual return on Dawn's portfolio. Use this information to calculate the coefficient of variation for Dawn's portfolio. Round your answer to two decimal places.

7 24

34 26

8 6

10 30

11 18

35 –3

14 15

14 15

–2 20

33 17

a. 174.15% b. 57.42% c. 78.99% d. 54.48% e. 126.6% 40. The table below displays the ages and incomes of employees within one of the departments of a specific company.

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chapter 8 Age (in years) 26 31 38 47 51 55 58 63 Income (in thousands of dollars) 42 51 60 62 65 70 73 79 Find the linear correlation coefficient for the given dataset. Round your answer to three decimal places. a. 0.804 b. -0.980 c. 0.980 d. 0.882 e. -0.804 f. -0.882 41. A race car made six laps on a race track. The time it took to complete each lap is given in the table below.

Lap # 1 2 3 4 5 6 Time (min:sec) 2:25 2:24 2:39 2:15 2:27 2:30 Find the population standard deviation of the set of data. Calculate the standard deviation in seconds and round it to one decimal place. a. 51.6 b. 7.2 c. 24.0 d. 5.0 42. The table below provides daily air temperatures alongside sales of ice cream for each respective day, recorded at a specific ice cream shop. o 20 23 25 28 32 34 Temperature ( C) Number of ice creams 107 115 176 238 318 343 Treat temperature as the independent variable and the number of ice creams as the dependent variable and find the linear regression equation for the given data. Round the slope to one decimal place and the y-intercept to the nearest whole number. a. y = 18.5x - 284 b. y = 18.5x - 161 c. y = 23.2x - 284 d. y = 23.2x - 161 43. Demographers conducted a study on the population of a small village, categorizing it into the following age groups: 020 years, 20-40 years, 40-60 years, 60-80 years, and 80-100 years. The data they obtained is shown in the graph below.

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chapter 8

Find the population weighted variance of the set of data. Round your answer to one decimal place.

Hint: For each age category, assign a midpoint and calculate the weighted mean. a. 896.4 b. 22.3 c. 496.5 d. 351.6 44. Eight athletes competed in a 100 meter sprint. Each athlete's time is given in the table below.

Athlete # 1 2 3 4 5 6 7 Time in seconds 9.86 9.80 9.85 9.73 9.65 9.77 9.87

8 9.83

Find the range of this set of data. a. 0.03 b. 9.80 c. 0.22 d. 0.07 45. The table below shows average monthly temperatures for a specific city over the course of a year.

Month o

Temperature ( C)

January

February

March

April

May

June

July

August

12

15

18

21

24

30

31

32

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September October November D

27

22

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Find the sample standard deviation of the set of data. Round your answer to one decimal place. a. 7.0 b. 10.8 c. 20.0 d. 7.3 46. The life expectancy of a fluorescent tube is normally distributed with a mean of 6,400 hours and a standard deviation of 600 hours. Find the probability that a tube lasts for more than 7,600 hours. Use the Empirical Rule. a. 0.8410 b. 0.4770 c. 0.5230 d. 0.1590 47. The following daily temperatures were recorded at three-hour intervals. Find the midrange of the data. Round your answer to one decimal place, if necessary.

53o, 61o, 64o, 67o, 70o, 67o, 65o, 63o, 62o a. 57.5o b. 66o c. 17o d. 61.5o e. 9o 48. In a company, Tom's salary of $75,920 is greater than the salaries of 27 out of 46 employees. Find the percentile for Tom's salary, rounded to the nearest percent. a. 41 b. 59 c. 61 d. 27 49. The following is a list of the ages of employees at Hammer's Inc. Find the mean and the sample standard deviation of the ages of the employees. Round noninteger results to the nearest tenth.

23 55

28 49

36 39

39 36

45 49

48 23

49 36

55 28

a. mean: 47.9 standart deviation: 12.8 Copyright Cengage Learning. Powered by Cognero.

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chapter 8 b. mean: 358.9 standart deviation: 95.7 c. mean: 39.9 standart deviation: 10.6 d. mean: 27.9 standart deviation: 7.4 e. mean: 29.9 standart deviation: 8 50. Find the mode(s) of the scores.

18, 19, 16, 16, 11, 15, 11, 14 a. 11 b. 15, 16 c. 15 d. 16 e. 11, 16 51. The following table shows how the range of a toy paper airplane depends on its launch speed. Find the linear regression equation and the linear correlation coefficient r for this data and predict the range for a speed of 5 m/s. Round the coefficients to three decimal places.

Speed (m/s) - X 1 1.5 2 2.5 3 3.5 4 4.5 Range (m) - Y 5 7 8 11 17 19 22 24 a. y = 6.538x - 3,387, r = -0.951, Range(5 m/s) = 27.152 m b. y = 3.454x + 8.350, r = 0.951, Range(5 m/s) = 25.625 m c. y = 5.881x - 2.048, r = 0.987, Range(5 m/s) = 27.357 m d. y = 5.138x + 2.723, r = -0.987, Range(5 m/s) = 28.341 m 52. There is a noticeable relationship between leading an active lifestyle, which includes regular exercise, and the occurrence of sickness. The table below displays daily exercise duration for six individuals alongside the number of sick days they experienced in a month.

Daily exercise in minutes 60 45 30 20 10 0 Number of sick days in a month 1 1 3 3 3 7 Calculate the linear correlation coefficient for this dataset. Round your answer to three decimal places. a. –0.731 b. –0.859 c. –0.945 d. –0.645 53. A professor grades students on two tests, three quizzes, and a final examination. Each test counts the same as three quizzes and the final examination counts the same as two tests. Maegan has test scores of 85 and 97. Maegan's quiz scores are 88, 76, and 84. Her final examination score is 94. Use the weighted mean formula to find Maegan's average for the Copyright Cengage Learning. Powered by Cognero.

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chapter 8 course. The professor rounds averages to the nearest integer. a. 87 b. 91 c. 89 d. 88 e. 67 54. The following table shows how the weight of an average person in a given sample of population depends on the height of this person. Find the linear regression equation and the linear correlation coefficient r for this data. Round the coefficients to three decimal places.

Height (cm) - X 160 165 170 175 180 185 190 195 Weight (kg) - Y 50 54 62 72 78 82 85 90 a. y = 0.812x – 65, r = 0.781 b. y = 1.193 x –140, r = 0.986 c. y = 1.314x – 152, r = 0.876 d. y = 1.014x – 132, r = -0.482 55. Find the variance of the set of sample data.

97, 76, 91, 54, 95, 51 a. 425.07 b. 83.5 c. 20.62 d. 464 e. 77.33 56. For the standard normal distribution, find the probability that a value is greater than 0.5. Round your answer to three decimal places, if necessary. a. 0.191 b. 0.809 c. 0.382 d. 0.691 e. 0.309 57. The employees of a small business were surveyed to find the time they normally spend commuting to work, one-way.

The times, in minutes, are shown in the table below. Use the median procedure for finding quartiles to find the first, second, and third quartiles ( , , and ) for the data.

19

One Way Time to Work (minutes) 18 19 18

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chapter 8 30 31 37 14

18 38 37

a.

,

b.

,

c.

,

d.

,

28 25 25

19 19 30

25 19 25

, , , ,

58. A certain model of automobile has its gas mileage (in miles per gallon, or mpg) normally distributed, with a mean of 12 mpg and a standard deviation of 4 mpg. Find the probability that a car selected at random has gas mileage less than 2 mpg. Round your answer to four decimal places. a. 0.0062 b. 0.5062 c. 0.4938 d. 0.9938 e. 0.9876 59. You know that 146 of the 199 students that took a test scored lower than 84 on test. What percentile does the score of 84 represent? a. 27 b. 73 c. 84 d. 16

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chapter 8 Answer Key 1. 153 2. James 3. e 4. a 5. d 6. b 7. b 8. d 9. c 10. d 11. a 12. d 13. c 14. a 15. e 16. b 17. b 18. b 19. a 20. a

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chapter 8 21. d 22. b 23. a 24. c 25. c 26. b 27. d 28. b 29. d 30. d 31. d 32. c 33. a 34. b 35. a 36. c 37. b 38. b 39. b 40. c 41. b Copyright Cengage Learning. Powered by Cognero.

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chapter 8 42. a 43. c 44. c 45. d 46. d 47. d 48. b 49. c 50. e 51. c 52. b 53. b 54. b 55. a 56. e 57. c 58. a 59. b

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chapter 9

Enter the appropriate value to answer the question or solve the problem.

1. Consider a fictional country with a population of 430,012 that is divided into 5 provinces, as shown in the table below.

The country's constitution provides for 13 representatives to the lower house of the legislature. These representatives are allocated on the basis of province population. Use the Jefferson Apportionment Plan to find the number of representatives for each province by completing the table. Use modified standard divisor 30,000. Round values in the Quotient column to the nearest hundredth.

Province Kennebec South Bay North Island Lakeland Montbleu

Population 60,712 38,816 94,967 167,245 68,272

Quotient Number of Representatives

2. Charter High School just opened this year. Its first class voted for the school's mascot. The members of the class narrowed the choices to Rams, Tigers, and Eagles. They then voted for the first, second, and third preferences. The outcome of the voting is given below.

Mascot Preference Table Ranking Rams 2 1 2 3 Tigers 1 2 3 1 Eagles 3 3 1 2 Number of Voters 25 86 32 28 Using the plurality method, which mascot, if any, is the winner? Explain.

3. A grant and a newly passed levy will allow a county to buy 13 new fire trucks for its fire precincts. The new trucks are going to be allotted to the precincts based on the number of times each precinct had to respond to calls in the last six months. Use the Hamilton Apportionment Plan and the table below to determine the number of fire trucks each precinct will receive.

District D-1 D-2-1 D-2-2 D-3 D-4-1 D-4-2

Number of Calls 47 73 100 64 170 95

4. A local zoo has asked 27 people to rank their preferences for the four names shown below in the table. The zoo will use the pairwise comparison voting method to pick a winning name that will be given to a newborn baby tiger. Use the given Copyright Cengage Learning. Powered by Cognero.

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chapter 9 information to complete a head-to-head comparison table and determine the winning name.

Rankings for Tiger Cub Name Apollo 1 4 2 1 3 Bengal 4 1 3 3 2 King 3 2 4 2 1 Prince 2 3 1 4 4 Number of voters: 4 4 8 5 6

5. Suppose that three candidates for office were ranked by voters as as shown in the table below. Use the Borda count method to determine the winner and then show that this method violates the majority criterion.

Ahmad Bennett Oelker Number of ballots

Candidate Rankings 2 1 2 1 3 3 3 1 2 1 1 2 3 3 2 17 17 31 10 11

Indicate the answer choice that best completes the statement or answers the question.

6. A group of college students was surveyed to determine their favorite class among History, Mathematics, and Art. The students ranked the classes in order of preference, and the results are shown below. (a) Using plurality voting, which class is the students' favorite? (b) Did that class recieve a majority vote?

History Mathematics Art Number of Students:

1 2 3 15

1 3 2 37

Rankings 2 2 1 3 3 1 13 34

3 1 2 11

3 2 1 25

a. (a) History (b) No b. (a) History (b) Yes c. (a) Art (b) No d. (a) Art (b) Yes e. (a) Math (b) No Copyright Cengage Learning. Powered by Cognero.

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7. A university system has a total of 40 new computers to distribute to each of its three campuses. After preregistration, the enrollment at each of the campuses was the value shown in second column of the table below together with the apportionment of the computers in the third column according to the Hamilton method. Final enrollment at each of the campuses is shown in the fourth column of the table with the percent increase in enrollment over the preregistration values in the fifth column. Determine whether a population paradox will occur in the reapportionment of the computers according to final enrollments. If it does, which campus loses a computer in the reapportionment?

Campus A B C

Preregistration Apportionment of 40Computers Enrollment Based on Preregistration Enrollment 356 4 1,050 10 2,600 26

Final Enrollment 366 1077 2615

% Increase in Final Enrollment Over Preregistration Enrollment 2.81% 2.57% 0.58%

a. The paradox will occur and Campus A will lose a computer. b. The paradox will occur and Campus B will lose a computer. c. The paradox will occur and Campus C will lose a computer. d. The paradox will occur and Campus A and Campus C will each lose a computer. e. The paradox will not occur.

8. Three computer games have been selected as the finalists in an annual game award. Gamers who took part in the vote have ranked them in order of preference. The results are given in the following preference schedule.

Rankings Game A 1 2 2 3 3 1 Game B 2 1 3 2 1 3 Game C 3 3 1 1 2 2 Number of voters: 397 357 274 235 212 166 If the plurality method of voting is used to distribute prizes, which game is the second-place winner and by how many votes does it lose to the first-place winner? a. Game C is in second place, 54 votes behind first place. b. Game C is in second place, 6 votes behind first place. c. Game A is in second place, 54 votes behind first place. d. Game A is in second place, 6 votes behind first place.

9. A project team must select an activity for a corporate event. The project manager offered four different options, and the team members ranked them in order of preference, as shown in the following table.

Rankings Bowling 1 4 4 3 1 4 Kart racing 3 3 2 1 2 2 Paintball 4 2 1 2 3 3 Board games 2 1 3 4 4 1 Number of voters: 5 4 4 3 2 2 Using the plurality with elimination method, what is the preferable activity? a. Bowling Copyright Cengage Learning. Powered by Cognero.

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chapter 9 b. Kart racing c. Paintball d. Board games 10. Suppose that a government is composed of six political parties, A, B, C, D, E, and F. The voting system for this government is {64: 40, 32, 16, 15, 15, 8}. Determine the Banzhaf power index for B and E. a.

BPI(B) = BPI(E) = b.

BPI(B) = BPI(E) =

c.

BPI(B) = BPI(E) =

d.

BPI(B) = BPI(E) =

11. Consider the following weighted voting scheme where the voters in the order listed are A, B, C, D, and E and . For what values of q is there at least one dummy?

a.

,

, or

b. c. d.

or

e.

or

12. Suppose the stock in a company was initially held by three people, A, B, and C. The voting system for this company was {44: 36, 23, 29}. Then, a fourth person D with 17 votes was added. The voting system became {53: 36, 25, 29, 17}.

Use Banzhaf power index to determine how did the voting powers of A, B, and C change after the addition of D. a. A, B, and C lost voting power. b. A and B gained more voting power, while C lost it. c. A gained more voting power, while B and C lost it. d. The voting powers of A, B, and C did not change.

13. State A and state B are each candidates for an extra congressional representative. The relative unfairness of Copyright Cengage Learning. Powered by Cognero.

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chapter 9 apportionment for state A is approximately 0.34, whereas for state B it is about 0.335. According to the apportionment principle, which of the two states should receive a new representative? Explain why. a. State B, because it has the smaller relative unfairness b. State A, because it has the smaller relative unfairness. c. State A, because it has the larger relative unfairness. d. State B, because it has the larger relative unfairness.

14. Calculate, if possible, the Banzhaf power index for each voter. Suppose the voters in the order listed are A, B and C.

a.

b.

c.

d.

e.

15. Calculate the average constituency of a state with a population of 18,820 if it has 7 representatives. a. 2688.57 b. 2688 c. 2689 d. 2687.57 16. Identify the name given to the fair voting attribute described below. If candidate A wins an election, then candidate A will also win the election if the only change in the voters' preferences is that supporters of a different candidate change their votes to support candidate A. a. Majority criterion b. Monotonicity criterion Copyright Cengage Learning. Powered by Cognero.

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chapter 9 c. Condorcet criterion d. Independence of irrelevant alternatives 17. A company has four outlet stores. The number of customers at each outlet is shown in the table below and the company has a total of 100 sales associates to assign to the four stores. Use the Webster method of apportionment to determine how many sales associates should be sent to each outlet using 24.26 as the modified standard divisor.

Outlet Store A B C D

Number of Customers per Day 319 559 697 841

a.

Outlet Store Number of Sales Associates A 13 B 23 C 28 D 34

b.

Outlet Store Number of Sales Associates A 13 B 23 C 30 D 34

c.

Outlet Store Number of Sales Associates A 13 B 23 C 28 D 36

d.

Outlet Store Number of Sales Associates A 13 B 23 C 29 Copyright Cengage Learning. Powered by Cognero.

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chapter 9 D

35

e.

Outlet Store Number of Sales Associates A 12 B 25 C 30 D 34

18. A city library system comprised of 4 different libraries dispersed throughout the city allots a certain number of computers for each library to use to keep track of its books and to check books in and out of the library. Given the current computer setup below, use the Huntington-Hill Apportionment Principle to determine which library should receive a new computer recently purchased by the city for library use.

City Libraries Current Number of Computers Current Number of Books Library A 21 256,000 Library B 15 121,000 Library C 20 213,000 Library D 19 488,000

a. Library A b. Library B c. Library C d. Library D 19. A correctional facility firm has hired a total of 112 new prison guards to send to its four correctional facilities. The number of inmates at each of the facilities is listed in the table below together with its apportionment according to the Hamilton method. If the firm decides at the last minute to hire one more guard, determine whether the Alabama paradox will occur in the reapportionment of the guards. If it does, which facility loses a guard in the reapportionment?

Prison Facility A B C D

Number of Inmates 25 256 185 309

Apportionment of 112 guards 5 37 26 44

a. The paradox will occur and County A will lose a guard. b. The paradox will occur and County B will lose a guard. c. The paradox will occur and County C will lose a guard.

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chapter 9 d. The paradox will occur and County D will lose a guard. e. The paradox will not occur.

20. The table that follows shows the enrollment at two campuses of a university and the number of computer stations for each campus. The number of computer stations was apportioned according to the Hamilton method. A new computer station is to be set up at one of the campuses. Find the relative unfairness of apportionment for each campus, and use the apportionment principle to determine which campus should receive the new computer station. Round your answer to four decimal places.

Campus A B

Enrollment 1,010 940

Apportionment of 44 Computer Stations 23 21

a. relative unfairness of apportionment is 0.0153 if Campus A receives the computer station relative unfairness of apportionment is 0.0151 if Campus B receives the computer station Campus B should receive the new computer station. b. relative unfairness of apportionment is 0.0153 if Campus A receives the computer station relative unfairness of apportionment is 0.0151 if Campus B receives the computer station Campus A should receive the new computer station. c. relative unfairness of apportionment is 0.0151 if Campus A receives the computer station relative unfairness of apportionment is 0.0153 if Campus B receives the computer station Campus A should receive the new computer station. d. relative unfairness of apportionment is 0.0151 if Campus A receives the computer station relative unfairness of apportionment is 0.0153 if Campus B receives the computer station Campus B should receive the new computer station. e. relative unfairness of apportionment is 0.0153 if Campus A receives the computer station relative unfairness of apportionment is 0.0153 if Campus B receives the computer station Campus A should receive the new computer station.

21. Calculate, if possible, the Banzhaf power index for each voter. Suppose the voters in the order listed are A, B, C, and D.

a.

b.

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chapter 9 c.

d.

e.

22. There are 14 students in a class. One student proposed himself for the position of the class president. Other students must vote and either accept or reject his candidacy. Each student has one vote, and a majority is required to pass a measure. On the voting day, two students are on sick leave. How does their absence affect the power of the other students' votes? a. BPI of each voter does not change. b.

BPI of each voter increases by . c. d. e.

BPI of each voter decreases by

.

BPI of each voter increases by

.

BPI of each voter decreases by

.

23. Which is an example of a veto power voting system? a. b. c. d.

24. Determine which candidate will win using the Borda count method.

Franco

1

Rankings for Club President 4 2 1

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chapter 9 Jurdan Tarshikov Vansaghi Number of voters:

4 3 2

1 2 3

3 4 1

3 2 4

2 1 4

7

13

5

4

11

a. Franco b. Jurdan c. Tarshikov d. Vansaghi 25. Consider the two fictional city wards in the table below. They have experienced the largest population gain of all the wards in the city, so one of them will receive an additional seat on the city council. Find the absolute unfairness of the apportionment if the Southwest ward gets the council seat. Round all intermediate calculations and the answer to the nearest whole number.

Ward Southwest West

Population 31,269 30,834

Current Number of Representatives 5 6

a. 73 b. 76 c. 77 d. 80 26. Use the plurality with elimination method to determine which name a new store will be given.

All Tools Tool World Tooling Around Town of Tools Number of ballots:

Rankings for New Store Name 1 4 2 1 3 4 1 3 3 2 3 2 4 2 1 2 3 1 4 4 15 56 77 56 51

a. All Tools b. Tool World c. Tooling Around d. Town of Tools 27. Identify any dictator and all dummies in the following weighted voting scheme. Suppose the voters in the order listed are A, B, C, D, and E. Copyright Cengage Learning. Powered by Cognero.

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a. A is a dictator, and B, C, D, and E are dummies. b. There is no dictator, and C, D, and E are dummies. c. There is no dictator, and B, C, D, and E are dummies. d. A is a dictator, and C, D, and E are dummies. e. A is a dictator, and D and E are dummies.

28. The stock in Company 1 was held by two people, A and B. The voting system for this company was {4: 5, 2}. The stock in Company 2 was held by C and D. The voting system for this company was {3: 4, 2}. The two companies merged and the voting system for A, B, C, and D became {7: 5, 2, 4, 2}. Determine the Banzhaf power indices of D before and after the merger. a. before: BPI(D) = 0; after: BPI(D) = 0.17 b. before: BPI(D) = 0; after: BPI(D) = 0.15 c. before: BPI(D) = 0.33; after: BPI(D) = 0.15 d. before: BPI(D) = 0; after: BPI(D) = 0.25 e. before: BPI(D) = 0; after: BPI(D) = 0.23 29. A home bakery asked its customers to rank five varieties of pies in order of preference. The results are shown in the following table.

Rankings Apple pie 4 5 2 3 5 3 Blueberry pie 1 2 5 4 4 1 Cherry pie 3 1 4 2 2 5 Peach pie 5 2 3 1 1 4 Strawberry pie 2 3 1 5 3 2 Number of voters: 14 12 10 9 9 6 Using the Borda count method, which pies should come in first and second place? a. 1st place: Blueberry pie 2nd place: Peach pie b. 1st place: Strawberry pie 2nd place: Cherry pie c. 1st place: Blueberry pie 2nd place: Cherry pie d. 1st place: Strawberry pie 2nd place: Peach pie 30. Identify the following weighted voting system.

a. one person, one vote Copyright Cengage Learning. Powered by Cognero.

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chapter 9 b. dictatorship c. null system d. veto power system

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chapter 9 Answer Key 1.

Province

Population

Kennebec

60,712

2

South Bay

38,816

1

North Island

94,967

3

Lakeland

167,245

5

Montbleu

68,272

2

Quotient

Number of Representatives

2. Using the plurality method, the winner is the mascot with the most first-place votes. In this case, Rams win with 86 first-place votes.

3.

District Number of Calls D-1 47 D-2-1 73 D-2-2 100 D-3 64 D-4-1 170 D-4-2 95

4. versus Apollo Bengal King Prince

Number of Trucks 1 2 2 2 4 2

Apollo X X X X

Bengal Apollo X X X

King Apollo King X X

Prince Apollo Bengal King X

winner is Apollo 5. Ahmad received a total of 188 points, Bennett received a total of 180 points, and Oelker received a total of 148 points.

Ahmad, therefore, wins the election using the Borda count method, however Bennett actually received the majority of the first-place votes

, so the majority criterion is violated.

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6. c 7. a 8. d 9. c 10. a 11. d 12. c 13. a 14. e 15. c 16. b 17. d 18. d 19. a 20. a 21. c 22. b 23. d 24. c 25. a 26. b Copyright Cengage Learning. Powered by Cognero.

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27. b 28. a 29. b 30. c

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chapter 10

Enter the appropriate value to answer the question or solve the problem.

1. Use the Edge-Picking Algorithm to find a Hamiltonian circuit in the weighted graph shown below. Give the path and its total weight.

2. The table below shows all the nonstop airline flights available between five cities. Draw a graph to represent the information, where each vertex represents a city and each nonstop flight between two cities is represented by an edge.

Ashton Lakeview Carson Oroville Wilton

Ashton Lakeview — yes yes — yes no no yes yes no

Carson Oroville Wilton yes no yes no yes no — yes yes yes — no yes no —

3. Find a Hamiltonian circuit on the graph below, beginning with vertex F.

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chapter 10

Indicate the answer choice that best completes the statement or answers the question.

4. Find an Eulerian circuit of the graph.

a. A-B-C-D-E-F-G-F-E-D-C-B-A b. C-A-B-D-F-E-G-F-E-B-C c. C-A-B-C-D-B-E-G-F-E-D-F-C d. D-B-A-C-D-E-G-F-C-D-B-E-D 5. To complete a quest in a computer game, the player's character must deliver four scrolls to four different castles and return to the outpost where he started the quest. Time to complete is limited. The table below shows how much time in seconds it takes to move between game locations.

Outpost Castle A Castle B Castle C Castle D Outpost 90 60 180 120 Castle A 90 120 250 150 Castle B 60 120 180 210 Castle C 180 250 180 270 Castle D 120 150 210 270 Use the edge-picking algorithm to find the optimal route that travels through each castle only once. Determine the time to complete the quest using this route. a. 780 seconds b. 750 seconds c. 660 seconds d. 540 seconds 6. Find a Hamiltonian circuit starting at vertex E for the given weighted graph and find the sum of the weights along the path.

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a. E-F-G-B-D-C-A: The total weight of the circuit is 32. b. E-F-A-B-G-D-C-E: The total weight of the circuit is 40. c. E-D-B-G-F-A-C-E: The total weight of the circuit is 40. d. E-F-A-B-D-G-E: The total weight of the circuit is 33.

7. The table below contains estimated travel times for ordered taxi rides. Use graph coloring to find the minimum number of taxi cabs that can serve these orders.

Passenger # Departure Time Arrival Time 1 15:10 15:20 2 15:15 15:34 3 15:30 15:49 4 15:00 15:17 5 15:45 16:00 6 15:25 15:41 a. At least 3 taxi cabs are required. b. At least 2 taxi cabs are required. c. At least 4 taxi cabs are required. d. At least 5 taxi cabs are required.

8. Find an Eulerian path of the graph.

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a. D-A-C-B-D-C-E-D-F-E b. E-C-A-D-F-E-D-B-C-E c. C-A-D-B-D-E-F-D-C-E d. D-C-B-D-A-C-D-E-F-D 9. What edges should be added to the graph to make it Eulerian?

a. AE, BF b. AF c. AC, DF d. AE, BF, AF Copyright Cengage Learning. Powered by Cognero.

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10. Represent the map by a graph and find a coloring of the graph that uses the lowest possible number of colors.

a.

b.

c.

d.

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11. Consider a database of a bookstore that consists of the tables Authors, Books, Clients, and Orders. The table Books has a reference to the table Authors, the table Orders has references to the tables Books and Clients. Draw a graph that represents connections in the database. Determine the number of vertices and edges in the graph. Determine whether the graph is Eulerian. a. 3 vertices, 4 edges, Eulerian b. 4 vertices, 3 edges, Eulerian c. 3 vertices, 4 edges, not Eulerian d. 4 vertices, 3 edges, not Eulerian 12. Represent the map as a graph and find the coloring of the graph using the least possible number of colors.

a.

b.

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d.

13. Represent the following land map as a graph.

a.

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chapter 10 b.

c.

d.

14. Determine (by trial and error) the chromatic number of the graph.

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a. 4 b. 5 c. 6 d. 3 15. If a planar drawing of a graph has 12 edges and 6 vertices, how many faces does the graph have? a. 18 b. 8 c. 30 d. 3 16. Which of the following graphs are equivalent?

a. I, II, & III b. I & II c. II & III d. I & III 17. Is it possible to make the graph Eulerian by adding or deleting only one edge?

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a. Yes, by deleting one of the edges from the vertex A. b. Yes, by deleting one of the edges from the vertex B. c. Yes, by adding the edge AB. d. No, it is not possible.

18. Find a graph that shows that the given graph is planar.

a.

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b.

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d.

e.

19. Consider the given graph. (a) Determine the number of vertices of the graph. (b) Determine whether the graph is connected.

a. (a) 6 verticles (b) not connected b. (a) 14 verticles (b) connected c. (a) 6 verticles (b) connected d. (a) 14 verticles (b) not connected e. (a) 10 verticles (b) connected 20. A pizza deliveryman needs to deliver pizza to points A, B, and C starting from point D and returning back at the end Copyright Cengage Learning. Powered by Cognero.

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chapter 10 of the trip. The distances between the points are shown in the following graph. Find the shortest route for the deliveryman to follow.

a. D-C-A-B-D b. D-B-A-C-D c. D-B-C-A-D d. D-A-B-C-D 21. Find an Eulerian circuit of the graph if it is possible. If it is not, find an Eulerian path of the graph.

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a. path B-C-E-G-D-E-B-D-F-H-G-F-A b. circuit A-B-C-E-D-G-H-F-A c. path B-C-E-G-D-E-B-D-F-H-G-F-A-B d. circuit B-C-E-G-D-E-B-D-F-H-G-F-A-B 22. Which, if any, of the following graphs are equivalent?

Graph I

Graph II

Graph III

a. I and II are equivalent b. II and III are equivalent c. I and III are equivalent d. all are equivalent e. none are equivalent 23. Which graph is Eulerian?

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chapter 10 a.

b.

c.

d.

24. Find a graph that shows that the given graph is planar.

a.

b.

c.

d.

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e.

25. Consider the given graph. (a) Determine the number of vertices of the graph. (b) Determine whether the graph is connected.

a. (a) 4 verticles (b) not connected b. (a) 0 verticles (b) connected c. (a) 0 verticles (b) not connected d. (a) 4 verticles (b) connected e. (a) 2 verticles (b) connected 26. A Local Dance Association holds competitions in seven disciplines. Some judges serve on juries of more than one Copyright Cengage Learning. Powered by Cognero.

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chapter 10 discipline. An "X" in the following table indicates that the two competitions share a judge, and thus cannot be held on the same day.

Tap dance Smooth dance Latin dance Folk dance Ballet Street dance Cheerleading Tap dance X X X Smooth dance X X Latin dance X X Folk dance X X X Ballet X X Street dance X X X Cheerleading X X X Use graph coloring to design the competition schedule with the fewest days possible. a. day 1: Tap dance and Street dance day 2: Smooth dance, Ballet, and Cheerleading day 3: Latin dance and Folk dance b. day 1: Tap dance, Latin dance, Folk dance day 2: Smooth dance and Street dance day 3: Ballet and Cheerleading c. day 1: Tap dance, Latin dance, Ballet, and Cheerleading day 2: Smooth dance, Folk dance, and Street dance d. day 1: Tap dance, Latin dance, and Ballet day 2: Smooth dance and Street dance day 3: Folk dance and Cheerleading 27. Determine which graph is nonplanar and indicate whether it contains a Utilities Graph or

Graph I

Graph II

as a subgraph.

Graph III

a. II is nonplanar; it contains b. III is nonplanar; it contains c. I is nonplanar; it contains a Utilities Graph d. II is nonplanar; it contains e. III is nonplanar; it contains a Utilities Graph 28. Consider the original land map shown below.

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Now suppose that parcels J and K are merged. Determine the chromatic numbers of the graphs representing the original and the modified maps. a. The original map is represented by a 5-colorable graph. The modified map is represented by a 4-colorable graph. b. Both the original and modified maps are represented by 3-colorable graphs. c. The original map is represented by a 4-colorable graph. The modified map is represented by a 3colorable graph. d. Both the original and modified maps are represented by 4-colorable graphs.

29. Consider the given graph. (a) Determine the number of vertices of the graph. (b) Determine whether the graph is connected.

a. (a) 7 verticles (b) connected b. (a) 7 verticles (b) not connected c. (a) 8 verticles (b) not connected d. (a) 8 verticles (b) connected e. (a) 10 verticles Copyright Cengage Learning. Powered by Cognero.

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chapter 10 (b) not connected 30. Find a graph that shows that the given graph is planar.

a.

b.

c.

d.

e.

31. Determine which graph is nonplanar and indicate whether it contains a Utilities Graph or

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as a subgraph.

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chapter 10

Graph I

Graph II

Graph III

a. II is nonplanar; it contains b. III is nonplanar; it contains c. I is nonplanar; it contains d. II is nonplanar; it contains a Utilities Graph e. III is nonplanar; it contains a Utilities Graph 32. Determine the chromatic number of the graph.

a. 2 b. 3 c. 4 d. 5 33. If a planar drawing of a graph has 9 vertices and 8 faces, how many edges does the graph have? a. 16 b. 19 c. 39 d. 15

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chapter 10 34. Find a graph that shows that the given graph is planar.

a.

b.

c.

d.

e.

35. If a planar drawing of a graph has 52 faces and 67 edges, how many vertices are there in the graph? a. 121 b. 119 c. 117 d. 17 e. 15 f. 13 Copyright Cengage Learning. Powered by Cognero.

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36. Use the Greedy Algorithm to find a Hamiltonian circuit starting at vertex D in the weighted graph shown below.

a.

, with total weight of

b.

, with total weight of

c.

, with total weight of

d.

, with total weight of

37. Consider the graph shown and five different paths.

1. A-C-B-E-D-F-A 2. B-C-D-F-C-A-F-E-D-A-E-B 3. A-D-E-A-F-E-B-C-D-F-C-A 4. B-C-F-A-E-D-B 5. F-C-B-E-D-A-F Which of the paths 1-5, if any, is the correct Hamiltonian circuit? a. 2 and 3 b. 1, 4, and 5 c. only 4 d. 1 and 5 Copyright Cengage Learning. Powered by Cognero.

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38. Find two different Hamiltonian circuits starting from vertex F for the given weighted graph and calculate the sums of the weights along these paths.

a. 1) F-H-J-I-G-E-C-D-A-B-F: The total weight is 96.

2) F-J-H-B-A-C-D-I-G-E-F: The total weight is 78. b. 1) F-H-B-J-G-E-C-A-D-I: The total weight is 103.

2) F-J-I-G-D-A-B-C-E-F: The total weight is 83. c. 1) F-E-C-B-A-D-G-I-J-H-F: The total weight is 99.

2) F-H-B-A-C-D-I-J-G-E-F: The total weight is 91. d. 1) F-E-C-A-B-H-J-I-D-G-E-F: The total weight is 102.

2) F-E-G-I-D-A-C-B-H-J-F: The total weight is 91.

39. Darla heard from her friend that the presence of a fish tank attracts wealth and helps the flow of positive energy. She also heard that 7 is the luckiest number. So, she decided to buy seven different types of aquarium fish. But it soon became clear that not all species are compatible and can live in the same aquarium.

Species A is incompatible with E and G. Species B is incompatible with D and F. Species C is incompatible with D, F, and G. Species D is incompatible with B, C, and E. Species E is incompatible with A and D. Species F is incompatible with B, C, and G. Species G is incompatible with A, C, and F. Use graph coloring to determine the minimum number of aquariums to safely house all the fish species. a. 4 Copyright Cengage Learning. Powered by Cognero.

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chapter 10 b. 3 c. 2 d. 5 40. Determine which graph is nonplanar and indicate whether it contains a Utilities Graph or

Graph I

Graph II

as a subgraph.

Graph III

a. II is nonplanar; it contains b. III is nonplanar; it contains c. I is nonplanar; it contains a Utilities Graph d. II is nonplanar; it contains a Utilities Graph e. III is nonplanar; it contains a Utilities Graph 41. How many edges does a complete graph of 5 vertices contain? a. 15 b. 10 c. 120 d. 24 42. Suppose you are at the library and you need to visit the computer lab, the food court, the administration building, and the campus police before returning to the library. The distances (in yards) between each of the places that you wish to visit are listed in the table below. Find the distance you will travel if you use the Greedy Algorithm to find a short route that starts and ends at the library.

Library

Computer Lab

Food Court

Admin Building

Campus Police

Library

—

320

200

265

565

Computer Lab

320

—

150

140

390

Food Court

200

150

—

110

530

Admin Building

265

140

110

—

261

Campus Police

565

390

530

261

—

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a. 821 yds b. 1,406 yds c. 1,311 yds d. 1,405 yds e. 890 yds 43. A company representative needs to visit 5 cities in South East Asia starting from and then returning to Bangkok. The cities and the distances between them in kilometers are shown in the following table. Find an efficient route for the representative to follow.

Ho Chi Minh Bangkok Singapore Manila Guangzhou Hanoi City Bangkok 1430 760 2210 1700 980 Singapore 1430 1100 2400 2620 2200 Ho Chi Minh 760 1100 1610 1530 1140 City Manila 2210 2400 1610 1250 1760 Guangzhou 1700 2620 1530 1250 800 Hanoi 980 2200 1140 1760 800 a. Bangkok - Ho Chi Minh City - Singapore - Hanoi - Guangzhou - Manila b. Bangkok - Hanoi - Guangzhou - Manila - Ho Chi Minh City - Singapore - Bangkok c. Bangkok - Ho Chi Minh City - Singapore - Hanoi - Guangzhou - Manila - Bangkok d. Bangkok - Singapore - Ho Chi Minh City - Manila - Guangzhou - Hanoi - Bangkok 44. Harry, Jerry, Larry and Terry are going on vacation to Sintra, Portugal. They compiled a list of selected castles and palaces and noted who wanted to visit which places.

Pena Palace Harry, Jerry, Larry, Terry Moorish Castle Harry, Terry Monserrate Palace Jerry, Larry Quinta da Regaleira Jerry, Terry Sintra National Palace Harry, Larry A whole day is allotted for each place. What is the minimum duration of vacation in days so that everyone has time to visit all the planned places? a. 5 b. 4 c. 2 d. 3

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chapter 10 Answer Key 1.

;

2.

3. Answers may vary. Sample answer: F-D-A-C-E-B-F 4. c 5. b 6. b 7. a 8. a 9. b 10. b 11. d 12. b 13. a

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chapter 10 14. a 15. b 16. b 17. c 18. b 19. c 20. d 21. d 22. d 23. b 24. b 25. d 26. a 27. d 28. c 29. b 30. a 31. c 32. a 33. d 34. c Copyright Cengage Learning. Powered by Cognero.

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chapter 10 35. d 36. a 37. d 38. c 39. b 40. e 41. b 42. d 43. b 44. d

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chapter 11

Enter the appropriate value to answer the question or solve the problem.

1. Find the supplement of a

angle.

2. In the figure shown,

. Find the measure of

3. If

find

and

.

.

4. A lamppost is 12 feet high and casts a 21-foot shadow. At the same time of day, a flagpole directly behind the lamppost casts a 29-foot shadow.

H

Write a proportion that can be used to find the height, H, of the flagpole.

5. A square wheat field is watered by a center pivot irrigation system with a radius of 27 feet. To the nearest square foot, find the area of the field that will not be irrigated.

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6. Use a protractor to measure the angle to the nearest degree. State whether the angle is acute, obtuse, or right.

7. Find the values of x, y, and z, suppose

,

, and

.

Indicate the answer choice that best completes the statement or answers the question.

8. In the figure below, , BD measures The figure is not drawn to scale.

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, AE measures

, and CD measures

. Find the length of

.

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chapter 11

a. b. c. d. e.

9. Find the surface area, suppose, that

,

.

a. b. c. d.

10. Two walls are in the shape of a trapezoid with bases that measure (labeled a in the figure), and (labeled b in the figure) and a height of (labeled h in the figure). You wish to wallpaper the two walls. One roll of wallpaper will cover

. How many rolls of wallpaper should you purchase?

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a. 156 rolls b. 9 rolls c. 16 rolls d. 1 rolls 11. Suppose you wish to tile a floor that measures should you purchase for the job?

by

. How many square tiles that measure

on a side

a. 160 tiles b. 320 tiles c. 36 tiles d. 80 tiles e. 18 tiles 12. What length of binding is needed to bind a circular rug that is 28 inches in diameter? Round to the nearest tenth of an inch. a. 175.9 inches b. 88 inches c. 2463 inches d. 615.8 inches e. 44 inches 13. Find the perimeter of the larger triangle given that it is similar to the smaller triangle where the vertical sides of each triangle correspond as do the horizontal sides. The triangles are not drawn to scale.

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chapter 11 a. b. c. d. e.

14. The width of a rectangle is

. If the area is

, what is the length of the rectangle?

a. b. c. 16 d. 5 e. 10 15. Consider the square fractal shown in the figure below.

Find the similarity dimension of this fractal. Round your answer to the nearest ten-thousandth. a. 0.6931 b. 0.5000 c. 1.3863 d. 2.0000 16. A can of paint will cover has a height of

of surface. How many cans of paint will have to be purchased to paint a cylinder that

and radius of

?

a. 10 b. 11 c. 27 d. 44 Copyright Cengage Learning. Powered by Cognero.

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chapter 11 e. 45 17. Determine whether the two triangles are congruent. If they are, state by what theorem they are congruent. The triangles are not to scale.

a. not congruent b. congruent by AAS c. congruent by SAS d. congruent by SSS e. congruent by AAA 18. Determine whether the two triangles are congruent. If they are, state by what theorem they are congruent. The triangles are not to scale.

a. congruent by ASA b. congruent by SAS c. congruent by SSS d. congruent by AAS e. not congruent 19. When the horizontal distance AB is 6 feet, the height of the loading dock, BC, is 2 feet, and BD is 9 feet. What is the height of the loading dock, DE? Round your answer to the nearest feet.

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a. 3 ft b. 45 ft c. 5 ft d. 3 ft 20. The walls of a room that is long, wide, and high are being painted. There are 2 doors in the room, each measuring by , and there are 5 windows in the room, each measuring by . At a cost of per square foot, find the cost of painting the walls of the room. Round to the nearest cent, if necessary. a. b. c. d. e.

21. Use an iterative process to draw stage 4 of the fractal with the given initiator (stage 0) and the given generator (stage

1).

a.

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chapter 11 b.

c.

d.

22. Find the value of , suppose

.

a. b. c. d.

23. Plot the points in the city circle with center

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and radius

blocks.

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chapter 11 a.

b.

c.

d.

e.

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chapter 11

24. The distance between two planets is 49,000,000,000 m. Describe this distance in gigameters. a. 49 Gm b. 0.049 Gm c. 49,000 Gm d. 490 Gm 25. A fish tank is 29 inches tall and has a base that is 13 inches by 22 inches. You want to fill the tank to a depth of 27 inches. How much water will it take? a. b. c. d.

26. Use a calculator to evaluate

. Round your answer to two decimal places.

a. 0.46 b. -0.52 c. 0.48 d. 2.09 e. -1.11 27. A thermos is in the shape of a cylinder with a hemispherical cap. The height of the whole thermos (both cylinder and cap) is 21.9 centimeters, while the diameter of the cap is 8.1 centimeters. Which is the volume of the thermos, including the cap? Use . Round your answer to two decimal places. a. b. c. d.

28. A forest observation tower is tall. From its top, a ranger spots a campfire below at an angle of depression of . How far is the fire from the foot of the observation tower? Round your answer to the nearest foot. a.

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chapter 11 b. c. d. e.

29. A square table has a perimeter of

. Find the length of each edge of the table.

a. b. c. d. e.

30. Suppose you have a circular garden with radius . How much greater is the area of the garden if you increase the radius to ? Round to the nearest tenth of a square foot. a. b. c. d. e.

31. Find the ratio of the lengths of corresponding sides for the similar triangles below. Express the ratio with the lengths from the smaller triangle in the numerator. The triangles are not drawn to scale.

a.

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chapter 11 b. c. d. e.

32. Find the volume of a sphere with radius hundredth of a cubic centimeter.

. Use the exact value for

and round your answer to the nearest

a. b. c. d. e.

33. Find the surface area. Suppose, that

,

, and

.

a. b. c. d.

34. Convert

to radian measure. Find the exact answer then round it to the nearest ten-thousandth.

a. b.

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chapter 11 c. d. e.

35. Plot the points in the city circle with center

and radius

blocks.

a.

b.

c.

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chapter 11 d.

e.

36. The area of a spherical polygon of

sides on a sphere of radius is given by

where is the sum of the measures of the angles of the polygon in degrees. Use the formula to find the area of a spherical quadrilateral with angles of , , , and on the Earth, which has a radius of 1980 miles. Round to the nearest 10,000 square miles. a. b. c. d.

37. Convert 0.057 oz to milligrams. a. 161.595 mg b. 1,615.95 mg c. 2.01 mg d. 0.2 mg 38. Consider the fractal shown in the figure below.

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Find the similarity dimension of this fractal. Round your answer to the nearest ten-thousandth. a. 1.0986 b. 1.4650 c. 0.6826 d. 1.6094 39. Find the length in feet of 15-m fence. a. 49.2 ft b. 4.57 ft c. 13.76 ft d. 16.35 ft 40. The side of a cube measures

. Find the surface area of the cube.

a. b. c. d. e.

41. Convert 54 yd to feet. a. 18 ft b. 5.4 ft c. 162 ft d. 54 ft 42. Find the area of a spherical triangle with angles of nearest hundredth.

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,

,

on a sphere with a radius of 3 meters. Round to the

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chapter 11 a. b. c. d.

43. The slant height of a cone is

, and its base has a radius of its base is

. Find the exact surface area of the cone.

a. b. c. d. e.

44. The height of a regular square pyramid is pyramid?

, and the length of a side of its base is

. What is the volume of the

a. b. c. d. e.

45. Find the complement of a

angle.

a. b. c. d.

46. Find the perimeter and the area of the given rectangle. Suppose, that necessarily drawn to scale.

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,

. Note that the rectangle is not

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a. perimeter: area: b. perimeter: area: c. perimeter: area: d. perimeter: area: e. perimeter: area: 47. A wheel on an automobile has a radius of 21 inches. How many feet does the automobile travel when wheel makes 22 revolutions? Round to the nearest hundredth of a foot. a. 120.95 feet b. 211.66 feet c. 30479.73 feet d. 241.9 feet e. 2902.83 feet 48. Determine whether the two triangles are congruent. If they are, state by what theorem they are congruent. The triangles are not to scale.

a. not congruent b. congruent by AAA Copyright Cengage Learning. Powered by Cognero.

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chapter 11 c. congruent by ASA d. congruent by SAS 49. If

and

then QR.

a. 88 b. 44 c. 27 d. 20 50. A triangle has a

angle and a

angle. What is the measure of the third angle?

a. b. c. d. e.

51. Find (if possible) the supplement of

.

a. b. c. d. e. not possible 52. Find the value of , suppose

,

.

a. 61 Copyright Cengage Learning. Powered by Cognero.

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chapter 11 b. 154 c. 145 d. 119 53. For the pair of similar triangles, find the value of b.

a. b. c. d.

54. Find the volume of the pyramid, suppose, that necessary.

and

. Round your answer to 1 decimal place, if

a.

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chapter 11 b. c. d.

55. Wall-to-wall carpeting is to be installed in a rectangular room that is long and wide. The edges of the carpet are to be held down by tack strips. How many feet of tack-strip material are needed? a. b. c. d. e.

56. The height of a cylinder is

, and a radius of its base is

. Find the exact volume of the cylinder.

a. b. c. d. e.

57. Calculate the circumference of the circle, suppose that

. Use

.

a. b. c. d.

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chapter 11 58. Find the exact value of below.

given that the hypotenuse has length

while a side has the length shown in the figure

a.

b. c. d. e.

59. Find the surface area of a sphere with radius square centimeter.

. Use the exact value for

. Round to the nearest hundredth of a

a. b. c. d. e.

60. Find the perimeter of a right triangle with legs of length

and

.

a. b. c. d. e.

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chapter 11

61. Convert 0.72 petameters to terameters. a. 0.072 Tm b. 7.2 Tm c. 72 Tm d. 720 Tm 62. Convert 8646 mL to gallons. a. 2,281.27 gal b. 32.77 gal c. 22.81 gal d. 292,148.34 gal 63. Which is the measure of

, suppose

?

a. b. c. d. none of these 64. The distance around the equator of Earth is about 40,074 kilometers. Which is the equatorial diameter of Earth? Use . Round your answer to the nearest kilometer. a. 6396 km b. 12,749 km c. 6381 km d. 12,762 km 65. Plot the points in the city circle with center

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and radius

blocks.

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chapter 11 a.

b.

c.

d.

e.

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chapter 11

66. Determine whether the two triangles are congruent. If they are, state by what theorem they are congruent. The triangles are not to scale.

a. congruent by SSS b. congruent by SSA c. congruent by SAS d. congruent by AAA e. not congruent 67. Given

. Use a calculator to find

to the nearest tenth.

a. b. c. d. e.

68. Find the area of the circle, suppose that

. Use

.

a. b. c. d.

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chapter 11 69. There are three triangles. Triangle ABC has the sides of 6, 12, and 9. Triangle DEF has the sides of 12, 15, and 24.

Triangle GHI has the sides of 8, 6, and 4. Determine which of the triangles are similar.

a. All three triangles are similar. b. Triangles ABC and DEF are similar. c. Triangles DEF and GHI are similar. d. Triangles ABC and GHI are similar. e. There are no pairs of similar triangles.

70. Find the perimeter and the area of the given parallelogram if parallelogram is not necessarily drawn to scale.

,

, and

. Note that the

long and

wide. What is the area

a. perimeter: area: b. perimeter: area: c. perimeter: area: d. perimeter: area: e. perimeter: area: 71. A path that is of the path?

wide is built around a rectangular garden. The garden is

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a. b. c. d. e.

72. The slant height of a regular square pyramid is area of the pyramid?

, and the length of a side of its base is

. What is the surface

a. b. c. d. e.

73. Convert

to degree measure.

a. b.

c. d. e.

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chapter 11

74. The formula

can be used to convert the Euclidean distance between points

to city distance where

represents the slope of the line segment

the city distance between

and

Given

and slope of

and , find

.

a. b. c. d. e.

75. A guy wire whose grounded end is from the post it supports makes an angle of with the ground. If the wire is attached to the top of the post, find the height of the post to the nearest tenth of a foot, if necessary. a. b. c. d. e.

76. Given

. Use a calculator to find

to the nearest tenth.

a. b. c. d. e.

77. Find the volume of the sphere. Suppose, that

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. Use

. Round your answer to the nearest tenth place.

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a. b. c. d.

78. Determine whether the two triangles are congruent. If they are, state by what theorem they are congruent. The triangles are not to scale.

a. congruent by SAS b. congruent by SSS c. congruent by ASA d. congruent by SSA e. not congruent 79. Find the perimeter of a triangle with sides 10 inches, 8 inches, and 11 inches in length. a. b. c. d.

80. Given the following initiator (stage 0) and generator (stage 1), use an iterative process to draw stage 2 of the fractal: Stage 0: Stage 1: a. Stage 2: b. Stage 2: c. Stage 2: Copyright Cengage Learning. Powered by Cognero.

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chapter 11 d. Stage 2: e. Stage 2: 81. Given that

and

, find the value of .

a. 11 b. 99 c. –7 d. 9 e. –0.57 82. A furniture store has a loading ramp that is long and its upper end is between the ramp and the ground to the nearest tenth of a degree.

above its lower end. Find the angle

a. b. c. d. e.

83. Given

, find the exact value of

.

a. b.

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chapter 11 c. d.

e.

84. If

and

, determine the value of B.

a. b. c. d. e.

85. Convert 788 megameters to gigameters. a. 78.8 Gg b. 7.88 Gg c. 0.788 Gg d. 0.0788 Gg 86. Find the similarity dimension of the fractal, which is defined by the following iterative process.

1. Start with a square. (Stage 0) 2. a.) At each convex corner of the previous stage, place another square, centered at that corner. Each added square should have half the side length of the square from the previous stage. b.)Take the union of the previous image with the collection of smaller squares placed in this way. (Stage 1) 3. Repeat step 2. (Stages 2 and 3)

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1.

a. 1.584 b. 2 c. 3 d. 1.5 87. Convert 87 oz to kilograms. a. 2.47 kg b. 3,068.78 kg c. 0.09 kg d. 3.07 kg 88. Use an iterative process to draw stage 2 of the fractal with the given initiator (stage 0) and the given generator (stage 1).

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chapter 11 a.

b.

c.

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chapter 11 d.

89. Convert 19 ft to centimeters. a. 579.27 cm b. 5.79 cm c. 62.32 cm d. 0.62 cm 90. Each day, a can factory produces 4656 metal cans of a certain size. Each of those cans is 16.2 centimeters tall and has a diameter of 13 centimeters. If waste created during the manufacturing process is ignored, how many square centimeters of sheet metal does the factory use per day to make the cans? Use . Round the answer to the nearest thousand. a. b. c. d.

91. Use a calculator to estimate the value of

. Round to the nearest ten-thousandth.

a. 1.4605 b. 0.5650 c. 0.8251 d. 0.5828 e. 1.3945 92. Suppose that on a sphere with a radius of 2.2 meters there is a triangle with angles 90 , 90 , and 50 . Find the area of this spherical triangle. Round your answer to the nearest hundredth of a square meter.

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chapter 11 a. 15.21 m2 b. 1.92 m2 c. 1.34 m2 d. 4.22 m2 93. Plot the points in the city circle with center

and radius

blocks.

a.

b.

c.

d.

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chapter 11 e.

94. Two ladders are leaning against a wall at the same angle as shown. How long is the shorter ladder? Suppose, that , , and .

a. 22 b. 48 c. 18 d. 28 e. none of these 95. Given that

,

and

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, find the value of x.

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chapter 11

a. 24 b. –60 c. 6 d. 60 e. 60 96. Given the points P(–3, –4) and Q(5, –2) find the city distance dC(P, Q) and Euclidean distance dE(P, Q) between these points. Assume that both dC(P, Q) and dE(P, Q) are measured in blocks. Round approximate results to the nearest tenth of a block. a. dC(P, Q) = 8.2, dE(P, Q) = 10.0 b. dC(P, Q) = 10.0, dE(P, Q) = 68.0 c. dC(P, Q) = –10.0, dE(P, Q) = 8.2 d. dC(P, Q) = 10.0, dE(P, Q) = 8.2 97. Use an iterative process to draw stage 2 of the fractal with the given initiator (stage 0) and the given generator (stage

1).

a.

b.

c.

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chapter 11 d.

98. In triangle ABC, the measure of than . Find the measure of .

is two times the measure of

. The measure of

is thirty degrees more

a. b. c. d.

99. Convert 798 picograms to nanograms. a. 0.798 ng b. 79.8 ng c. 7980 ng d. 798000 ng 100. An observer is feet from a hot air balloon before it lifts off. Determine the angle of elevation, , when the balloon reaches a height of feet. State your answer in degrees and round to one decimal place. a. b. c. d. e.

101. Given that

and

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, find

.

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a. b. c. d. e.

102. Determine whether the two triangles are congruent. If they are, state by what theorem they are congruent. The triangles are not to scale.

a. not congruent b. congruent by AAA c. congruent by SSS d. congruent by ASA e. congruent by SSA 103. Find the Euclidean distance and the city distance between the points to one decimal place.

and

. Round approximate results

a. Euclidean distance: city distance:

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chapter 11 b. Euclidean distance: city distance:

c. Euclidean distance: city distance:

d. Euclidean distance: city distance:

e. Euclidean distance: city distance:

104. The maximum weight a given container can hold is 20 tons. How many laptops could it hold if the weight of one packaged laptop is 10 pounds? Round your answer to whole number. a. 200 b. 4000 c. 2000 d. 400 105. Kim is standing on the rim of a canyon and her friend, Karl, is standing on the floor of the canyon (see figure). Karl carefully paced off his distance from the canyon escarpment and reported to Kim via radio that the distance was approximately . Using a simple plastic protractor, Kim estimates that Karl's position lies at from the vertical, relative to the edge of the cliff. Estimate the height of the canyon escarpment, , to the nearest foot. [Assume that the points corresponding to the cliff face, the cliff base, and Karl's position form a right triangle.]

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a. b. c. d. e.

106. Consider the fractal shown in the figure below.

Find the similarity dimension of this fractal. Round your answer to the nearest ten-thousandth. a. 0.6826 b. 1.6094 c. 1.4650 Copyright Cengage Learning. Powered by Cognero.

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chapter 11 d. 1.0986 107. Which of the following capacities is equal to 5 quarts? a. 10 gal b. 10 pt c. 20 pt d. 20 gal 108. Find the length of the third side of the triangle below.

a. b. c. d. e.

109. Express 22 km/h in miles per hour. a. 35.42 mph b. 13.66 mph c. 0.59 mph d. 820 mph 110. Find the surface area of the cylinder exactly, suppose, that

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,

.

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chapter 11

a. b. c. d.

111. Given the following initiator (stage 0) and generator (stage 1), use an iterative process to draw stage 2 of the fractal: Stage 0: Stage 1: a. Stage 2: b. Stage 2: c. Stage 2: d. Stage 2: e. Stage 2: 112. The triangles below are similar. Find the value of . Round your answer to the nearest whole number.

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chapter 11

a. 27 b. 64 c. 63 d. 60 113. Find the volume of a sphere that has a diameter of 6 centimeters. Use 3.14 for nearest hundredth.

and round your answer to the

a. b. c. d.

114. Find the height of the flagpole given that the shadows being cast by each object occurs at exactly the same time of day. The figures are not drawn to scale.

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chapter 11

a. b. c. d. e.

115. Find the weight in pounds of 7-kilogram luggage. a. 154 lb b. 32 lb c. 3 lb d. 15.4 lb 116. Convert 0.6 micrograms to nanograms. a. 0.0006 ng b. 0.06 ng c. 6 ng d. 600 ng 117. Convert 5151 cc to liters. a. 515.1 L b. 51.51 L c. 5.151 L d. 0.5151 L 118. Given

, BC is half the length of AB, and CD is half the length of BC, find the length of AD.

a. 42 b. 48 c. 36 d. 72 119. Find the volume of the cylinder. Suppose, that places.

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,

. Use

. Round your answer to 2 decimal

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chapter 11

a. b. c. d.

120. How much wood is needed to make a crate that is open top?

long,

wide, and

high if the crate is to have an

a. b. c. d. e.

121. Consider the circle fractal shown in the figure below.

Find the similarity dimension of this fractal. Round your answer to the nearest ten-thousandth. Note that the ratio of the radii of the larger circle and any of the three smaller circles inscribed in it is:

.

a. 1.4311 b. 0.6987 Copyright Cengage Learning. Powered by Cognero.

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chapter 11 c. 1.0986 d. 0.7677 122. Find the area. Suppose, that

,

, and

.

a. b. c. d.

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chapter 11 Answer Key 1.

2.

3.

4. Answers may vary. Sample answer:

5.

6. The angle is an obtuse angle with a measure of 96 .

7.

8. e 9. c 10. c 11. d 12. b 13. b 14. d 15. d 16. b Copyright Cengage Learning. Powered by Cognero.

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chapter 11 17. a 18. a 19. c 20. d 21. d 22. b 23. b 24. a 25. c 26. d 27. c 28. d 29. b 30. e 31. c 32. e 33. d 34. c 35. b 36. a 37. b Copyright Cengage Learning. Powered by Cognero.

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chapter 11 38. b 39. a 40. a 41. b 42. c 43. d 44. b 45. d 46. b 47. d 48. c 49. d 50. c 51. b 52. d 53. a 54. c 55. e 56. d 57. b 58. c Copyright Cengage Learning. Powered by Cognero.

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chapter 11 59. e 60. b 61. d 62. c 63. a 64. d 65. b 66. a 67. a 68. b 69. d 70. a 71. a 72. b 73. e 74. e 75. e 76. b 77. d 78. a 79. a Copyright Cengage Learning. Powered by Cognero.

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chapter 11 80. d 81. d 82. b 83. b 84. d 85. c 86. b 87. a 88. c 89. a 90. b 91. b 92. d 93. b 94. e 95. a 96. d 97. a 98. c 99. a 100. b Copyright Cengage Learning. Powered by Cognero.

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chapter 11 101. a 102. a 103. d 104. b 105. b 106. c 107. b 108. c 109. b 110. b 111. d 112. d 113. d 114. a 115. d 116. d 117. c 118. a 119. b 120. c 121. a Copyright Cengage Learning. Powered by Cognero.

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chapter 11 122. a

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Page 292