ExamView - Keystone Practice (1) · ____ 5. An icicle is 12 inches long and melts at a rate of 1 4 inch per hour. a. L =12−1 4 t c. L =12−4t b. L =1 4 −12t d. t =12−1 4 L

Name: ________________________ Class: ___________________ Date: __________ ID: A

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Keystone Practice

Multiple ChoiceIdentify the choice that best completes the statement or answers the question.

Write an equation of the line with the given slope and y-intercept

____ 1. slope: 27 , y-intercept: –3

a. y = − 27 x – 3 c. y = 2

7 x + 3

b. y = 72 x – 3 d. y = 2

7 x – 3

Beach Bike Rentals charges $5.00 plus $0.20 per mile to rent a bicycle.

____ 2. Write an equation for the total cost C of renting a bicycle and riding for m miles.a. C = 5+ 0.2m c. m= 5+ 0.2Cb. C = 0.2+ 5m d. C = 5+ 2m

____ 3. What is the cost of renting a bike and riding 18 miles?a. $3.60 c. $8.60b. $41.00 d. $11.60

Write a linear equation in slope-intercept form to model the situation.

____ 4. A television repair shop charges $35 plus $20 per hour.a. C = 20+ 35h c. C = 25+ 30hb. h = 35+ 20C d. C = 35+ 20h

____ 5. An icicle is 12 inches long and melts at a rate of 14 inch per hour.

a. L = 12− 14 t c. L = 12− 4t

b. L = 14 − 12t d. t = 12−1

4 L

____ 6. The temperature is 38° and is expected to rise at a rate of 3° per hour.a. T = 3+ 38h c. T = 38− 3hb. T = 38+ 3h d. h = 38+ 3T

____ 7. A taxi driver charges $5 plus $0.30 per mile.a. C = 0.3+ 5m c. C = 5+ 0.3mb. C = 5− 0.3m d. m= 5+ 0.3C

Name: ________________________ ID: A

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Mr. Collins is constructing a fence around his property. He already has 25 sections up and plans to add 8 sections each Saturday until he is finished.

____ 8. Write an equation to find the total number of fence sections F standing after any number of Saturdays s.a. F = 25+ 8s c. F = 25− 8sb. F = 8+ 25s d. s = 25+ 8F

____ 9. Find the total number of fence sections standing after 15 Saturdays.a. 383 sections c. 145 sectionsb. 125 sections d. 105 sections

Write an equation of the line that passes through each point with the given slope.

____ 10. −3,− 4ÊËÁÁˆ¯˜̃ , m= 3

a. y = 3x + 13 c. y = −3x + 5b. y = 3x − 5 d. y = 3x + 5

Write an equation of the line that passes through the pair of points.

____ 11. −5, − 2ÊËÁÁˆ¯˜̃ , 3,− 1ÊËÁÁ

ˆ¯˜̃

a. y = 18 x + 11

8 c. y = −1

8 x – 11

8

b. y = 18 x – 11

8 d. y = 1

8 x + 8

11

Write the point-slope form of an equation for a line that passes through the point with the given slope.

____ 12. (–6, –6), m = − 47a. y – 6 = − 47 (x + 6) c. y + 6 =

4

7 (x + 6)

b. y + 6 = − 47 (x – 6) d. y + 6 = −4

7 (x + 6)

Write each equation in standard form.

____ 13. y + 6 = (x + 4)a. x + y = –2 c. x – y = 2b. y = x – 2 d. x – y = 10

____ 14. y + 3 = 25 (x + 9)

a. 2x – 5y = 33 c. y = 25 x + 3

5

b. 2x – 5y = –3 d. 2x + 5y = 3

Name: ________________________ ID: A

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Write the equation in slope-intercept form.

____ 15. y – 5 = 34 (x – 5)

a. y = 34 x – 5

4 c. y = −3

4 x + 5

4

b. y = 34 x + 5

4 d. y = 3

4 x – 3

5

Write the slope-intercept form of an equation of the line that passes through the given point and is parallel to the graph of the equation.

____ 16. (5, –1), y = − 34 x + 1

a. y = 114 x + 3

4

b. y = 43 x + 11

5

c. y = − 34 x + 11

4

d. y = − 34 x – 11

4

Write the slope-intercept form of an equation that passes through the given point and is perpendicular to the graph of the equation.

____ 17. (4, 4), 2x – y = 4a. y = 2x + 2

b. y = − 12 x + 6

c. y = 12 x + 6

d. y = 4x + 2

____ 18. (2, 2), y = − 15 x + 5

a. y = − 15 x – 2b. y = 5x – 8c. y = −5x – 8d. y = 125 x –

1

5

Name: ________________________ ID: A

4

Determine whether the graph shows a positive correlation, a negative correlation, or no correlation. If there is a positive or negative correlation, describe its meaning in the situation.

____ 19. Women in the Army

YearSource: Time Magazine, March 24, 2003

a. positive; as time goes on, more women are in the army.b. no correlationc. negative; as time goes on, fewer women are in the army.d. negative; as time goes on, more women are in the army.

____ 20. Average Cycling Speed

a. no correlationb. negative; as time passes, speed decreasesc. positive; as time passes, speed increasesd. positive; as time passes, speed decreases

Name: ________________________ ID: A

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____ 21. Video Rental Fines

a. negative; as the number of videos rented increases, the amount of fine increases.b. negative; as the number of videos rented increases, the amount of fine decreases.c. no correlationd. positive; as the number of videos rented increases, the amount of fine decreases.

____ 22. People Entering Amusement Park

Time (minutes)

a. positive; as time passes, the number of people entering decreases.b. negative; as time passes, the number of people entering decreases.c. no correlationd. positive; as time passes, the number of people entering increases.

Name: ________________________ ID: A

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____ 23. Strawberries Picked

Time (hours)

a. positive; as time passes, the number of quarts picked decreases.b. negative; as time passes, the number of quarts picked decreases.c. no correlationd. positive; as time passes, the number of quarts picked increases.

____ 24. Consumer Price Index, 1950-2002

YearSource: Bureau of Labor Statistics, U.S. Dept. of Labor

a. no correlationb. positive correlation; as time passes, the CPI increases.c. positive correlation; as time passes, the CPI decreases.d. negative correlation; as time passes, the CPI decreases.

Name: ________________________ ID: A

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____ 25. Sport Utility Vehicle Sales in the U.S.,

1991-2001

YearSource: The World Almanac, 2003

a. negative correlation; as time passes, SUV sales decrease.b. no correlationc. positive correlation; as time passes, the SUV sales decrease.d. positive correlation; as time passes, the SUV sales increase.

____ 26. Cars Passing School

a. negative; as time passes, the number of cars increases.b. negative; as time passes, the number of cars decreases.c. no correlationd. positive; as time passes, the number of cars decreases.

Name: ________________________ ID: A

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United States Birth RateYear 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001Birth Rate(per 1000) 16.7 16.3 15.9 15.5 15.2 14.8 14.7 14.5 14.6 14.5 14.7 14.5Source: National Center for Health Statistics, U.S. Dept. of Health and Human Services

____ 27. Let x represent the number of years since 1990 with x = 0 representing 1990. Let y represent the birth rate per 1000 population. Write the slope-intercept form of the equation for the line of fit using the points representing 1992 and 2000.a. y = −0.15x + 16.2 c. y = −0.15x − 15.6b. y = 0.15x + 16.2 d. x = −0.15y + 16.2

____ 28. Predict the birthrate in 2005. Round your answer to the nearest tenth, if necessary.a. 14.5 c. 15.1b. 13.1 d. 14.0

Domestic Traveler Spending in the U.S., 1987-1999

YearSource: The World Almanac, 2003

____ 29. Use the scatter plot that shows the domestic traveler spending. Use the points (1987, 235) and (1999, 446) to write the slope-intercept form of an equation for the line of fit shown in the scatter plot.a. y = −17.58x − 34,696 c. y = 17.58x − 34,696b. x = 17.58y − 34,696 d. y = 0.057x − 34,696

____ 30. Use the scatter plot that shows the domestic traveler spending. Predict the amount of spending for domestic travelers in 2010.a. about $640,000,000 c. about $640b. about $460,000,000,000 d. about $640,000,000,000

Name: ________________________ ID: A

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Strawberries Picked

____ 31. Use the scatter plot that shows the number of quarts of strawberries picked each hour. Use the points (1, 73) and (8, 41) to write the slope-intercept form of an equation for the line of fit shown in the scatter plot.a. y = 4.57x + 77.57 c. y = −0.22x + 77.57b. x = −4.67y − 77.57 d. y = −4.57x + 77.57

____ 32. Use the scatter plot that shows the number of quarts of strawberries picked each hour. Predict the number of quarts that will be picked in the tenth hour.a. about 123 quarts c. about 32 quartsb. about 45 quarts d. about 34 quarts

Average Cycling Speed

____ 33. Use the scatter plot that shows the average cycling speed as time passes. Use the points (5, 15) and (25, 10) to write the slope-intercept form of an equation for the line of fit shown in the scatter plot.a. y = −0.25x + 16.25 c. y = 0.25x + 16.25b. x = −0.25y + 16.25 d. y = −3.95x + 16.25

Name: ________________________ ID: A

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____ 34. Use the scatter plot that shows the average cycling speed as time passes. Predict the speed of the cyclist after 30 minutes.a. about 6.2 miles per hour c. about 12.3 miles per hourb. about 8.8 miles per hour d. about 10.5 miles per hour

Sport Utility Vehicle Sales in the U.S., 1991-2001Year 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001Sales(millions) 0.9 1.2 1.4 1.6 1.8 2.2 2.5 2.8 3.0 3.4 3.8Source: The World Almanac, 2003

____ 35. Let x represent the number of years since 1990. Let y represent the sport utility vehicle sales in millions. Write the slope-intercept form of the equation for the line of fit using the points representing 1992 and 2000.a. y = 0.275x + 0.65 c. y = 0.275x − 1.75b. y = − 0.275x + 0.65 d. x = 0.275y + 0.65

____ 36. Predict the number of sport utility vehicle sales in 2005.a. about 3.5 million c. about 2.4 millionb. about 4.8 million d. about 5.9 million

Use the graph below to determine the number of solutions the system has.

____ 37. x = 4

y = x + 3a. no solution c. twob. one d. infinitely many

Name: ________________________ ID: A

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____ 38. 2x = 2y − 6

y = x + 3a. no solution c. twob. one d. infinitely many

____ 39. 2x = 2y − 6

y = −x − 1a. no solution c. twob. one d. infinitely many

Graph the system of equations. Then determine whether the system has no solution, one solution, or infinitely many solutions. If the system has one solution, name it.

____ 40. y = −x + 5

y = 6x − 2a. no solution c. infinitely many

b. one solution; (4, 1) d. one solution; (1, 4)

Name: ________________________ ID: A

12

Use substitution to solve the system of equations.

____ 41. y = x + 1

8x − 4y = 0a. (1, 2) c. (2, 1)b. (0, 1) d. (–1, 0)

____ 42. −9 = x − 3y

−2x + 6 = 6ya. (3, 4) c. (–9, 0)b. infinitely many solutions d. (–3, 2)

____ 43. The length of a rectangular poster is 10 inches longer than the width. If the perimeter of the poster is 124 inches, what is the width?a. 16 inches c. 28.5 inchesb. 26 inches d. 36 inches

____ 44. The sum of two numbers is 90. Their difference is 12. What are the numbers?a. no solution c. 35 and 47b. 31 and 59 d. 39 and 51

____ 45. At a local electronics store, CDs were on sale. Some were priced at $14.00 and some at $12.00. Sabrina bought 9 CDs and spent a total of $114.00. How many $12.00 CDs did she purchase?a. 9 c. 5b. 6 d. 3

____ 46. Jordan is 3 years less than twice the age of his cousin. If their ages total 48, how old is Jordan?a. 15 c. 31b. 12 d. 17

____ 47. Dakota’s math test grade was 7 points less than his science test grade. The sum of the grades was 183%. What did Dakota get on his math test?a. 83% c. 93%b. 88% d. 95%

____ 48. Reid and Maria both play soccer. This season, Reid scored 4 less than twice the number of goals that Maria scored. The difference in the number of goals they scored was 6. How many goals did each of them score?a. Reid scored 8 and Maria scored 2.b. Reid scored 2 and Maria scored 8.c. Reid scored 16 and Maria scored 10.d. Reid scored 10 and Maria scored 16.

Name: ________________________ ID: A

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____ 49. Mrs. Davis went to a produce market to buy bananas and strawberries. She spent $8.00. If the bananas were $0.50 per pound, and the strawberries were 4 times that much, how many pounds of bananas did she buy if she bought 7 pounds of fruit altogether?a. 16 pounds c. 4 poundsb. 5 pounds d. 3 pounds

____ 50. One line segment is 5 cm more than 4 times the length of another. The difference in their lengths is 35 cm. How long are they?a. 10 cm and 40 cm c. 20 cm and 45 cmb. 20 cm and 55 cm d. 10 cm and 45 cm

Use elimination to solve the system of equations.

____ 51. −2x − 10y = 10

−3x + 10y = −10a. (0, 1) c. (–20, –5)b. (20, 5) d. (0, –1)

____ 52. −4x + 2y = −2

4x + 6y = 10a. (–2, 3) c. (–1, –1)b. (1, 1) d. (2, –3)

____ 53. −8x + 8y = −8

−8x + 4y = 8a. (–3, –4) c. (–1, 0)b. (3, 4) d. (1, 0)

____ 54. 5x − 2y = −3

4x − 2y = −6a. (–1, 1) c. (–3, –9)b. (1, –1) d. (3, 9)

____ 55. −3x − 2y = −5

7x + 6y = 1a. (–8, 7) c. (7, –8)b. (1, –1) d. (–1, 1)

Name: ________________________ ID: A

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____ 56. The cost of 3 large candles and 5 small candles is $6.40. The cost of 4 large candles and 6 small candles is $7.50. Which pair of equations can be used to determine, t, the cost of a large candle, and s, the cost of a small candle?a. 3t + 5s = 6.4

4t + 6s = 7.5

c. 3t + 5s = 6.4

t + s = 7.5b. t + s = 6.4

4t + 6s = 7.5

d. 5t + 3s = 6.4

6t + 4s = 7.5

____ 57. Isaac downloaded 7 ringtones. Each polyphonic ringtone costs $3.25, and each standard ringtone costs $1.50. If he spends a total of $21 on ringtones, find the number of polyphonic and standard ringtones he downloaded.a. 1 polyphonic, 6 standard c. 6 polyphonic, 13 standardb. 8 polyphonic, 1 standard d. 6 polyphonic, 1 standard

____ 58. Christie has a total of 15 pieces of fruit, all bananas and apples, worth $1.59. Bananas are 13 cents each and apples are 7 cents each. How many bananas and how many apples does she have?a. 6 bananas, 9 apples c. 9 bananas, 24 applesb. 9 bananas, 6 apples d. 21 bananas, 6 apples

____ 59. The admission fee of a theater is $2.50 for adults and $1.25 for children. On a certain day, 700 people went to the theater for a concert and $1375 was collected. How many children and how many adults attended the concert?a. 300 adults, 400 children c. 400 adults, 300 childrenb. 400 adults, 1100 children d. 600 adults, 100 children

____ 60. A hotel has 150 rooms. The charges for a double room and a single room are $270 per night and $150 per night respectively. On a night when the hotel was completely occupied, revenues were $33,300. Which pair of equations can be used to determine the number of double room, d, and the number of single room, s, in the hotel?a. d + s = 150

270s+ 150d = 33,300

c. d + s = 150

270d + 150s = 33,300b. d + s = 33,300

270d + 150s = 150

d. d + s = 33,300

270d + 150s = 33,300

Determine the best method to solve the system of equations. Then solve the system.

____ 61. x = 2y − 1

3x − 3y = 9a. substitution; (7,4)b. elimination using multiplication; (3,2)c. substitution; (4,7)d. elimination using multiplication; (−21,−10)

Name: ________________________ ID: A

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____ 62. −5x + 3y = −18

2x + 2y = 4a. elimination using addition; (−1,3)b. elimination using multiplication; (1,1)c. elimination using multiplication; (3, − 1)d. elimination using subtraction; (−3,1)

____ 63. x = −y

5x + 6y = −3

a. substitution; − 311 ,3

11

Ê

ËÁÁÁ

ˆ

¯˜̃˜ c. substitution; (−3, 3)

b. elimination using addition; (6, 5) d. substitution; (3, − 3)

____ 64. 2x − 5y = 8

3x − 11y = −2a. elimination using addition; (−1,− 2)

b. elimination using multiplication; −8, − 245Ê

ËÁÁÁ

ˆ

¯˜̃˜

c. elimination using multiplication; (14, 4)d. elimination using subtraction; (−1, 6)

____ 65. −4x + 5y = 9

4x − 5y = −7a. elimination using subtraction; (−2, 2)b. elimination using addition; no solutionc. substitution; (7, 7)d. elimination using addition; (0,16)

____ 66. 14 x +3

4y = 1

2x + 6y = 8a. substitution; (4,0)b. elimination using multiplication; no solution

c. substitution; − 14 , −3

4

Ê

ËÁÁÁ

ˆ

¯˜̃˜

d. elimination using multiplication; infinitely many solutions

____ 67. The sum of Jack and his father’s ages is 52. Jack’s father’s age is 2 less than 5 times Jack’s age. Find the ages of Jack and his father.a. 10, 42 c. 9, 61b. 9, 43 d. 9, 45

Name: ________________________ ID: A

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____ 68. Dylan has 15 marbles. Some are red and some are white. The number of red marbles is three more than six times the number of the white marbles. Write a system of equations that can be used to find the number of white marbles, x, and the number of red marbles, y.a. x + y = 15

y = 6x + 3

c. x − y = 15

y = 6x + 3b. x + y = 15

y = 6x − 3

d. 6x + y = 15

y = 6x + 3

____ 69. Amber and Austin were driving the same route from college to their home town. Amber left 2 hours before Austin. Amber drove at an average speed of 55 mph, and Austin averaged 75 mph per hour. After how many hours did Austin catch up with Amber?a. 10 h c. 5.5 hb. 7.5 h d. 2 h

____ 70. A gym has 2 kg and 5 kg weights. There are 10 disks in all. The total weight of 2 kg disks and 5 kg disks is equal to 29 kg. Find the number of disks of each kind in the gym.a. 5 kg disk: 17; 2 kg disk: 7 c. 5 kg disk: 3; 2 kg disk: 13b. 5 kg disk: 3; 2 kg disk: 7 d. 5 kg disk: 7; 2 kg disk: 3

____ 71. Sam’s test score is 12.5 more than Nicole’s score. The sum of twice Sam’s score and three times Nicole’s score is 195. What are Sam and Nicole’s test scores?a. Sam’s score: 46.5; Nicole’s score: 59b. Sam’s score: 21.5; Nicole’s score: 34c. Sam’s score: 34; Nicole’s score: 46.5d. Sam’s score: 46.5; Nicole’s score: 34

Name: ________________________ ID: A

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Solve the system of inequalities by graphing.

____ 72. y ≤ −x + 4

y > −2x − 4a. c.

b. d.

Name: ________________________ ID: A

18

____ 73. y ≥ −x − 4

y < −4a. c.

b. d.

Name: ________________________ ID: A

19

A business is adding a new parking lot. The length must be at least twice the width, and the perimeter must be under 800 feet.

____ 74. Make a graph showing the possible values of the length and width of the parking lot.a. c.

b. d.

The sum of two positive integers is less than 80 and their difference is more than 10.

____ 75. Write a system of inequalities to represent this situation.a. x + y ≤ 80

x − y ≥ 10

c. x + y < 80

x − y > 10b. y < x + 80

y > x − 10

d. x + y > 80

x − 10< y

____ 76. List three pairs of integers which are solutions.a. 50 and 30, 40 and 35, 45 and 30 c. 60 and 5, 44 and 34, 35 and 30b. 50 and 24, 35 and 21, 18 and 2 d. 60 and 20, 45 and 35, 36 and 22

Name: ________________________ ID: A

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A student can buy notebooks for $0.40 each and pens for $0.25 each. Ben needs to have at least 8 notebooks. He has a total of $5.00 to spend.

____ 77. Make a graph showing the number of notebooks and pens Ben can purchase.a. c.

b. d.

____ 78. Write a system of inequalities to show how many notebooks and pens Ben can buy.a. n + p ≥ 8

0.40n + 0.25p > 5.00

c. 0.40n ≥ 8

.040n + 0.25p ≤ 5.00b. 0.40n ≥ 8

n + p ≤ 5.00

d. n ≥ 8

0.40n + 0.25p ≤ 5.00

____ 79. The difference between Rosa’s age and her father’s age is less than 35. Rosa’s father is more than three times her age. Which of the following are possible ages for Rosa and her father?a. 5 and 40 c. 10 and 30b. 7 and 28 d. 14 and 38

Name: ________________________ ID: A

21

The Washington family is hosting a cookout. They decide to serve chicken and pork. They determine that they will need at most 20 pounds of meat, and they want to have at least twice as much chicken as pork.

____ 80. Write a system of inequalities for this situation.a. c + 2p ≤ 20

c ≥ 2p

c. 20< c + p

2c > pb. c + p ≤ 20

2c > p

d. c + p ≤ 20

c ≥ 2p

____ 81. Make a graph showing the amount of each type of meat that satisfies the requirements.a. c.

b. d.

____ 82. Brittany and Kaitlyn are on the swim team. At practice, they swim less than 30 laps between the two of them, and Brittany swims at least 3 more laps than Kaitlyn. List two pairs of numbers that are solutions to this system of inequalities.a. 13 and 17; 15 and 18 c. 12 and 16; 13 and 17b. 10 and 12; 12 and 15 d. 11 and 15; 13 and 16

Name: ________________________ ID: A

22

Find the mean. Round to the nearest tenth.

____ 83. {20, 21, 23, 26, 38, 39}

a. 27.8 c. 22.9b. 26.3 d. 32.7

A bin contains seven red chips, nine green chips, three yellow chips, and six blue chips. Find each probability.

____ 84. Drawing a red chip, replacing it, then drawing a blue chip

a. 42625 c.13

50

b. 7100 d.13

49

____ 85. drawing a red chip, not replacing it, then drawing a blue chip

a. 42625 c.13

50

b. 7100 d.13

49

____ 86. selecting three green chips without replacement

a. 21575 c.8

25

b. 72915625 d.64

1725

____ 87. selecting three green chips with replacement

a. 21575 c.8

25

b. 72915625 d.64

1725

____ 88. choosing a red chip, then a green chip, then a yellow chip, with replacement

a. 1925 c.189

15625

b. 1972 d.63

4600

____ 89. choosing a red chip, then a green chip, then a yellow chip, without replacement

a. 1925 c.189

15625

b. 1972 d.63

4600

____ 90. selecting two blue chips with replacement

a. 6125 c.6

25

b. 36625 d.11

29

Name: ________________________ ID: A

23

____ 91. selecting two blue chips without replacement

a. 120 c.6

25

b. 36125 d.11

29

____ 92. drawing a yellow chip, replacing it and choosing a blue chip.

a. 3100 c.9

625

b. 3200 d.18

625

____ 93. drawing a yellow chip, not replacing it and choosing a blue chip.

a. 3100 c.9

625

b. 3200 d.18

625

A standard deck of cards contains 52 cards divided evenly into four suits. The suits are hearts and diamonds which are red and clubs and spades which are black. Each suit is composed of cards numbered two through ten and a jack, queen, king, and ace.

____ 94. What is the probability of selecting a spade or a club from a standard deck of cards?

a. 152 c.1

4

b. 126 d.1

2

____ 95. What is the probability of selecting a heart or ace from a standard deck of cards?

a. 113 c.4

13

b. 14 d.17

52

____ 96. What is the probability of selecting a king or queen?

a. 113 c.1

52

b. 213 d.1

26

Name: ________________________ ID: A

24

The table lists the number of male and female students at Lakeside High School.

Lakeside High School StudentsGrade Male Female

9th 216 19310th 207 21411th 198 19712th 194 201

____ 97. What is the probability of selecting a ninth or tenth grade student?

a. 83162 c.407

805

b. 423815 d.47

180

____ 98. What is the probability of selecting a female student?

a. 12 c. 1

b. 161324 d.161

163

A coin is tossed and a spinner shown below is spun. Find each probability.

____ 99. P head and 2( )

a. 18 c.1

2

b. 116 d.5

8

____ 100. P tailand 3( )

a. 116 c.5

8

b. 12 d.1

8

____ 101. P tail and an odd number( )

a. 4 c. 14

b. 1 d. 12

Name: ________________________ ID: A

25

____ 102. P head and a multiple of 2ÊËÁÁˆ¯˜̃

a. 12 c. 1

b. 14 d. 4

____ 103. P tailand 1, 3, or 5ÊËÁÁˆ¯˜̃

a. 316 c.3

8

b. 12 d.7

8

Find the experimental probability.

____ 104. John thinks he can make 50% of the three-point shots he takes in a basketball game. He tested this by taking 47 three-point shots in practice. He made 23 of them.

a. 52% c. 46%b. 51% d. 49%

____ 105. Heads 33Tails 46

What is the experimental probability of getting heads?

a. 33% c. 42%b. 46% d. 39%

Short Answer

106. Cindy started her bank account with $400, and she deposited $50 per week. Write a linear equation in slope-intercept form to find the total amount in her account after w weeks. Then graph the equation.

107. The cost of admission to an amusement park is $9.50 plus $1.50 per ride. Write a linear equation in slope-intercept form for the amount spent if r rides are taken.

108. Anthony is reading a book with 256 pages. He reads 14 pages every day. Write a linear equation in slope-intercept form to find the number of pages left after d days.

109. The monthly telephone bill consists of $24 service charge plus $1.20 per call. Write an equation in slope-intercept form for the total monthly bill if x represents the number of calls made in a month. Then graph the equation.

Name: ________________________ ID: A

26

110. The cost, C, of joining the sports center gym includes an initial membership fee of $139 plus a $29 monthly fee. Write an equation in slope-intercept form to find the total cost for m months. Then graph the equation.

111. The table of ordered pairs shows the coordinates of the two points on the graph of a line.

x y0 64 10

Write an equation that describes the line.

112. Write an equation and describe the slope for the line that passes through 9, 22ÊËÁÁˆ¯˜̃ and 15, 36ÊËÁÁ

ˆ¯˜̃ .

113. In 1992, about 12.5 million people were using broadband internet services. In 1999, the number was 17.4 million. Write a linear equation to predict the number of people, P, who will be using broadband internet services in year t.

114. Write an equation for the line that passes through 14

,25

Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃˜̃˜̃ and

34

,75

Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃˜̃˜̃ . What is the slope?

115. A company manufactured 324,000 computers in 2002. The company’s output grows by 5,000 units per year.

Year Production (thousands)2002 3242003 3292004 334

Write a linear equation to find the company’s production, P, in year, t.

116. Write the point-slope form, slope-intercept form, and standard form of an equation for a line that passes through −1, 2ÊËÁÁ

ˆ¯˜̃ with slope 4.

117. Write the point-slope form, slope-intercept form, and standard form of an equation for a line that passes through 5, 7ÊËÁÁ

ˆ¯˜̃ with slope –9.

118. Write the point-slope form, slope-intercept form, and standard form of an equation for a line that passes

through 13

,25

Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃˜̃˜̃ with slope

38

.

Name: ________________________ ID: A

27

119. Line l passes through 15

, –37

Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃˜̃˜̃ with slope 5. Write the point-slope form, slope-intercept form, and standard

form of an equation for line l.

120. A line passes through −29

, –45

Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃˜̃˜̃ with slope

15

. Write the point-slope form, slope-intercept form, and

standard form of an equation for line l.

121. Determine whether y = 4x + 5 and y = 14

x − 2 are perpendicular. Explain.

122. Write an equation of the line that is parallel to the graph of y = −4x + 2 and passes through 2, –4ÊËÁÁˆ¯˜̃.

123. Find an equation for the line that has an x-intercept of 3 and is perpendicular to the graph of −2x + 5y = 6.

124. Write the slope-intercept form of an equation for the line that passes through −3, –2ÊËÁÁˆ¯˜̃ and is perpendicular

to the graph of the equation y = 25

x + 3.

The table shows the age of infants, t (in weeks), and the number of hours, h, they slept in a day.

Age (weeks) 3 5 8 9 11 13 15 18 19 21

Sleep (h) 15.2 14.8 14.3 14.8 14.5 13.9 13.4 13.2 13.7 13.2

125. Draw a scatter plot and determine what relationship exists, if any, in the data.

126. Suppose a child is 2 years old. Would the equation for the line of fit give a reasonable estimate of the number of hours slept in a day by a child of that age? Explain. (1 year= 52 weeks)

127. The table below shows Alex’s best time for the 200-m sprint each year.

Year 1989 1990 1991 1992 1993 1994 1995 1996

Time (s) 29.95 30.40 32.10 32.05 31.75 32.95 33.40 35.60

Draw a scatter plot and determine what relationship, if any, exists in the data.

Name: ________________________ ID: A

28

128. The graph below shows the relationship between a long-distance truck driver’s driving times and the number of miles traveled.

Is it reasonable to use the equation for line of fit to estimate the distance traveled for a driving time of 10 hours? Explain.

129. The table below shows the time in hours an investor spent researching the stock market each week and the percent gain on investments.

Time (h) 6 8 10 12 14 16 18 20

Gain (%) 23 35 36 41 44 55 47 45

Make a scatter plot and draw a line of fit for the data.

130. Year 2001 2002 2003 2004 2005 2006

Sales ($1,000) 253 242 265 270 269 275

Write an equation of the regression line in the form of y = ax+ b. Estimate the sales for 2010.

131. Game 1 2 3 4 5 6Score 85 82 83 80 78 75

Write an equation of the best-fit line in the form of y = ax+ b. Estimate the score for the 15th game.

Name: ________________________ ID: A

29

132. Year 1 2 3 4 5 6

Height (ft) 4 10 15 27 51 60

Write an equation of the regression line in the form of y = ax+ b. Estimate the height when the tree is 8 years old.

133. Month 1 2 3 4 5 6

Units Produced 275 400 612 867 1,020 1,465

Write an equation of the best-fit line in the form of y = ax+ b. Name the correlation coefficient. Round to the nearest ten-thousandth.

134. The graph below shows the annual increase in salaries of employees A and B.

If the pattern continues, will the annual salary of the two employees ever be equal? Explain.

Name: ________________________ ID: A

30

135. The graph below shows the charges for the two car rental companies.

If the pattern continues, will the rental fees for the two companies ever be equal? Explain.

136. The table below shows the number of users of broadband and dial-up Internet and the average annual increase of users for each.

Connection type Number of users (millions) Average increase per year (millions)

Broadband 8.2 2.5

Dial-Up 11.6 1.4

Graph the equations representing the number of broadband and dial-up users for any year. Estimate the solution and interpret what it means.

137. Anne planted two varieties of plants. Variety A was 14 inches tall when planted and grows 8 inches per day. Variety B was 30 inches tall when planted and grows 2 inches per day. Graph the equations that represent the height of the two varieties at any day. Assume that the rate of growth of each of the varieties remained the same. Estimate the solution and interpret what it means.

138. Sally and her sister, Laura, started their savings accounts with $250 and $300 respectively. Sally deposits $35 each week. Laura deposits $20 each week. Graph the equations representing the amount in their accounts. Estimate the solution and interpret what it means.

139. How many grams of pure silver and how many grams of an alloy that is 65% silver should be melted together to produce 56g of an alloy that is 80% silver?

140. Two trains A and B are 240 miles apart. Both start at the same time and travel toward each other. They meet 3 hours later. The speed of train A is 20 miles faster than train B. Find the speed of each train.

Name: ________________________ ID: A

31

141. The perimeter of the triangle is 61 inches. If two sides of the triangle are equal and the third side is 4 inches more than the equal sides, what is the length of the third side?

142. Scott bought a pen and received change of $4.75 in 25 coins, all dimes and quarters. How many of each kind did he receive?

143. When Katie was visiting her Grandpa’s farm, she saw the farm only raised hens and pigs. Katie counted 32 heads and 100 feet in the barnyard. How many hens and pigs were there in the barnyard?

144. The sum of two numbers is 54, and their difference is 26. What are the numbers?

145. Five times one number added to another number is 32. Three times the first number minus the other number is 8. Find the numbers.

146. To fill two new aquariums, Laura bought some saltwater fish for $2 each and some freshwater fish for $1 each. If she bought a total of 15 fish and spent a total of $23, how many fish of each kind did she buy?

147. Jack has 20 more stamps than Dylan has. Together they have 46 stamps. Find the number of stamps each has.

148. The table below shows the sales of two companies for the year 2000 and the targeted sales after 10 years.

Company Sales in 2000 (millions of dollars) Sales target for2010 (millions of dollars)

A 2.45 3.05

B 3.15 3.55

Let x represents the number of years since 2000 and y represents sales in millions of dollars. Write the system of equations to represent the sales of two companies. Then use elimination to find the solution and interpret the solution.

149. Six times a number plus five times another number equals 56. The sum of the two numbers is 10. What are the numbers?

150. The sum of the digits of a two-digit number is 8. If the digits are reversed, the new number is 10 more than twice the original number. Find the original number.

151. The graphs of 2x + 3y = 5 and 3x + y = 18 contain two of the sides of a triangle. A vertex of the triangle is at the intersection of the graphs. What are the coordinates of the vertex?

152. A boat travels 33 miles downstream in 4 hours. The return trip takes the boat 7 hours. Find the speed of the boat in still water.

Name: ________________________ ID: A

32

153. A store placed two orders with a supplier. The first order was for 12 digital cameras and 8 camcorders for a total of $7640. The second order was for 9 digital cameras and 11 camcorders for a total of $8330. Find the price of a digital camera and a camcorder.

154. Emily has a total of 20 dimes and nickels. If the dimes were nickels and nickels were dimes she would have 20 cents less than she has now. How many of each coin does she have?

155. It takes 8 turkeys and 12 chickens 10 hours to eat a certain amount of grain, while it takes 6 turkeys and 8 chickens 14 hours to eat the same amount of grain. Find the time it would take 1 turkey alone and 1 chicken alone to eat the same amount of grain.

156. Mary wants to fill a swimming pool that holds 15,000 gallons of water. If she fills from a large hose for 3 hours and a small hose for 8 hours, she can fill half the pool. The pool is completely filled if she uses both hoses together for 10 hours. How long will it take to fill the pool using each hose by itself?

157. If the length of the given rectangle is increased by 3 inches and breadth is reduced by 4 inches, then the area is reduced by 67 square inches. If the length is reduced by 1 inch and the breadth is increased by 4 inches, then the area is increased by 89 square inches. Find the length and the breadth of the rectangle.

158. Daniel’s age is 7 more than three times his daughter Lucy’s age. The difference between twice Daniel’s age and five times Lucy’s age is 24. Find the ages of Daniel and Lucy.

Use the table below that shows last week’s sales of polo shirts at a local department store.

Color Small Medium Large X-LargeWhite 8 18 15 18Blue 12 10 20 14Green 17 6 32 18

159. Suppose the department store expects a 15% increase in sales of polo shirts this week. What value of the scalar p should be used so that pN results in a matrix that estimates the number of each size and color polo shirts needed this week?

160. Patrick has $105 to spend on gifts. He must buy at least 8 gifts. He plans to buy storybooks that cost $8 or $12. How many of each book can he buy?

A radio station is giving away tickets to a play. They plan to give away tickets to seats that cost $10 or $20. They plan to give away at least 20 tickets, and the total cost of all the tickets can be no more than $300.

161. Make a graph showing how many tickets of each kind can be given away.

162. Write two ways of giving away the tickets keeping the restrictions in mind.

Name: ________________________ ID: A

33

Suppose a car dealer receives a profit of $500 for each mid-sized car m sold and $750 for each sport-utility vehicle s sold. The dealer must sell at least two mid-sized cars for each sport-utility vehicle and must earn at least $3500 per week.

163. Write a system of inequalities and make a graph representing the situation.

164. Suppose a car dealer sells 2 sport-utility vehicles. How many mid-sized cars must be sold to earn at least $3500?

Describe an unbiased way to conduct a survey based on the information given.

165. Assume you are a teacher. How can you tell whether students in your class are fully concentrating on the lesson?

166. How can a company sample the opinion of its employee regarding the personnel development training?

167. How would you determine the iron levels of tap water in homes in your neighborhood?

Identify a sample and state whether it is unbiased or biased. If unbiased, describe a biased way. If biased, describe an unbiased way.

168. A farmer tests every tenth grape tree of each row to see whether the grapes are ready to harvest.

169. A physics teacher checks readings taken by any two students in the class to ensure that each student is taking the readings correctly.

170. The height (in meters) of the basketball players on an Olympic team were: {2.1, 1.75, 1.6, 2.2, 1.8, 1.95, 1.85, 2, 1.65, 2}. Which measure of central tendency best represents the data? Justify your answer and find the measure.

171. The test scores of the students in drivers education were: {95, 90, 95, 95, 95, 90, 95, 95, 95}. Which measure of central tendency best represents the data? Justify your answer and find the measure.

172. A music teacher plans to pick 3 students out of 15 students in his music school for a music concert. How many different groups can be formed?

In an essay writing competition there are 12 participants, of those 5 are girls and the remaining are boys.

173. If all 12 participants have equal chance of placing, what is the probability that the winner is a girl and the first runner-up is a boy?

Name: ________________________ ID: A

34

174. In a shelf of a library there are 5 essay-writing books, 6 letter-writing books, and 3 essay- and letter-writing books. Ayita picks a book at random. What is the probability that she picks an essay-writing book or a letter-writing book?

175. On a survey it was found that out of 1500 people, 800 people said that they go to bed early at night, 600 people said that they go to bed late at night, and 300 people said that they sometimes go to bed early and sometimes go to bed late. What is the probability that a randomly selected member would go to bed early or late at night?

The spinner shown is spun three times.

176. Write the sample space with all possible outcomes.

177. Find the probability distribution X, where X represents the number of times the spinner lands on black for X = 0, X = 1, X = 2, and X = 3.

178. Find the probability distribution Y, where Y represents the number of times the spinner lands on gray for Y= 0, Y= 1, Y= 2, and Y= 3.

179. Make a probability histogram for the number of times the spinner lands on gray.

180. Make a probability histogram for the number of times the spinner lands on black.

181. Do all possible outcomes have an equal chance of occurring? Explain.

A video store clerk takes an inventory of the top 10 DVDs sold each week. The clerk created a probability distribution table.

Number of Top 10 DVDs Sold Each Week

0-25 26-50 51-75 76-100 101-125

Probability 0.05 0.30 0.40 0.15 0.10

182. Define a random variable and list its values.

Name: ________________________ ID: A

35

183. Show that this is a valid probability distribution.

184. In a given week, what is the probability that no more than 50 DVDs are sold?

The table shows the probability distribution of the number of persons in owner-occupied housing.

X = Number of Persons in Household

Probability

1-person 0.2032-person 0.3563-person 0.1714-person 0.1575-person 0.0726-person 0.0257-or-more person 0.016Source: U.S. Census Bureau

185. If a person was randomly selected, what is the probability that he or she lives in a household with four or fewer persons?

186. If a person was randomly selected, what is the probability that he or she lives in a household with five or more persons?

187. If a person was randomly selected, what is the probability that he or she lives in a household with three or fewer persons?

188. If a person was randomly selected, what is the probability that he or she lives in a household with two or more persons?

The table shows the probability distribution of the method of transportation workers 16 and over use to commute to work.

X = Method of Transportation Probabilitycar, truck, or van - drove alone 0.757car, truck, or van - carpooled 0.122public transportation 0.047walked 0.029other means 0.012worked at home 0.033Source: U.S. Census Bureau

189. If a person was randomly selected, what is the probability that he or she took a car, truck, or van to work?

Name: ________________________ ID: A

36

190. If a person was randomly selected, what is the probability that he or she walked to work or worked at home?

191. If a person was randomly selected, what is the probability that he or she carpooled or used public transportation?

Use the table below that shows the typing speed of the people in a community.

Typing Speed (wpm) Probability10-30 0.39131-50 0.28051-70 0.19071-90 0.139

192. Is this a valid probability distribution? Justify your answer.

193. If a person is randomly selected, what is the probability that his typing speed is more than 50 wpm?

194. If a person is randomly selected, what is the probability that his typing speed is at most 70 wpm?

Use the graph that shows the gadgets used frequently.

195. Based on the graph, in a group of 59 people, how many would you expect to say they use digital cameras?

196. Determine whether this is a valid probability distribution. Justify your answer.

Name: ________________________ ID: A

37

Crazy Cars randomly called households to determine the types of vehicles owned by residents of Claretown. The results of the survey are shown in the table.

X = Type of Vehicle Number Ownedcompact car 107sedan 357SUV 241truck 295

197. Find the experimental probability distribution for the number of each type of vehicle.

198. Based on the survey, what is the probability that a household chosen at random owns a compact car or sedan?

199. Based on the survey, what is the probability that a household chosen at random owns SUV or truck?

200. Based on the survey, what is the probability that a household chosen at random owns a sedan or SUV?

201. Based on the survey, what is the probability that a household chosen at random owns a compact car or SUV?

202. Based on the survey, what is the probability that a household chosen at random owns a compact car or truck?

203. Suppose Crazy Cars wants to order 210 more vehicles. Of those vehicles ordered, how many should be compact cars?

204. Suppose Crazy Cars wants to order 175 more vehicles. Of those vehicles ordered, how many should be SUVs?

205. What could you use to simulate the outcome of guessing on a multiple-choice test with choices A, B, C, or D?

The Dairy Stop is randomly giving samples of six flavors of ice cream.

206. What object could be used to model the possible outcomes of this situation?

207. How could you use a simulation to model the distribution of the next 50 samples?

There are six bottles of grape juice, four bottles of orange juice, and two bottles of cranberry juice.

208. What could be used for a simulation determining the probability of randomly picking any one type of fruit juice?

Name: ________________________ ID: A

38

209. What is the probability of choosing a grape juice bottle? Is your answer the theoretical or experimental probability? Explain.

210. Corey is randomly giving pizza samples to each shopper at Wilson’s Supermarket. He has cheese, pepperoni, sausage, or supreme pizza samples. What could be used to perform a simulation of this situation?

Amanda’s cat is expecting a litter of four kittens.

211. What is the theoretical probability of having four female kittens?

212. What objects could be used to perform a simulation of this situation?

213. Justin shot 25 free throws in practice and found that his experimental probability making a free throw was 60%. How many free throws did Justin make?

A medical team sent surveys to randomly selected households to determine the various health problems. The result of the survey is shown below.

Health Problems Number of PatientsObesity 32Diabetes 54Heart problems 78Eye problems 112Dental problems 96

Note: The survey result for each health problem is mutually exclusive.

214. Find the experimental probability distribution for the number of people having problem of each type.

215. Based on the survey, what is the probability that a person chosen at random is a diabetic patient or an eye patient?

216. Frances thinks she will make 60% of her serves in an upcoming tennis tournament. To test this she hit 50 serves from both sides of the court. She made 33 of the first 50 and 29 from the second. What is experimental probability that Frances will make her first serve?

217. Gloria performed a simulation by drawing a card from a standard deck. She replaced the card before she drew again. Find the experimental probability of drawing a red suit.

Suit Heart Spade Diamond ClubFrequency 6 11 9 14

Name: ________________________ ID: A

39

218. A manager of a light bulb plant randomly selected 50 light bulbs to test the failure rate. He performed the test 3 different times. Find the experimental probability of a light bulb failing. Round to the nearest tenth.

Test 1 2 3Success 48 49 46Failure 2 1 4

219. Karl rolled a die 50 times. He rolled an even number 29 times. Find the experimental probability of rolling an odd number.

220. A weather man said that there was a 30% chance of rain on Saturday. Jimmy modeled this by placing 3 red and 7 green marbles in a bag. He then chose a marble and recorded the color. He replaced the marble each time before choosing again. He chose 13 red and 34 green marbles. Find the experimental probability of it raining on Saturday. Round to the nearest percent.

Essay

221. A musician’s fan club had 35,000 members in 1999 and grew to 99,000 members by 2004.

Fan club membership

a. Explain how the slope-intercept form can be used to predict the number of members in 2007.b. Discuss how slope-intercept form is used in linear extrapolation.

Name: ________________________ ID: A

40

222. Megan wants to change her Internet Service Provider. She is considering three different plans.

Plan 1 charges a $15 monthly fee plus $0.08 per minute of use.

Plan 2 charges a $5 monthly fee plus $0.11 per minute of use.

Plan 3 charges a flat monthly fee of $49.95.

a. For each plan, write an equation that represents the monthly cost C for m minutes per month.b. Graph each of the three equations on the same coordinate axes. Label each line.c. Megan expects to use 500 minutes per month. In which plan do you think Megan should enroll? Explain.

223. a. Illustrate how you can determine whether two lines are parallel or perpendicular.b. Are the two lines graphed below parallel? Explain.c. Write an equation with a graph perpendicular to the lines graphed. Explain.

224. Average Hourly Earnings (dollars) of U.S. Production Workers, 1991-2001

Year 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001Earnings 10.32 10.57 10.83 11.12 11.43 11.82 12.28 12.78 13.24 13.76 14.32Source: Bureau of Labor Statistics, U.S. Dept. of Labor

a. Draw a scatter plot with years on the x-axis and earnings on the y-axis.b. Draw a line of fit for the data.c. Write the slope-intercept form of an equation for the line of fit.d. Predict the hourly earnings for production workers in 2005.

225. Alan used his graphing calculator to find the best-fit line of a set of data. The correlation coefficient was -0.965. Explain what that means.

Name: ________________________ ID: A

41

226. Is f(x) =x + 5 if ≤ 2

x − 3 if ≥ 2

Ï

ÌÓ

ÔÔÔÔÔÔÔÔÔÔ

a function? Explain.

227. In this example data, x is years since 1990 and y is the number of people in thousands using email or letters as the main method of communicating written information.emails usage: y = 15.2+ 2.5xletters usage: y = 43.6− 1.5x

a. Explain how graphs can be used to compare the number of people using letters to the number of people using emails.

b. Include an estimate of the year in which the number of people writing letters equaled the number of people using email. Then determine if your solution is reasonable for this problem.

228. When balancing her checkbook, Allison made an error which caused her to show a balance that was $54.00 above the actual balance. She had accidentally reversed the digits of the amount of one check. The sum of the digits of that check amount was 12.a. Write two equations to represent this situation.b. What is the best method to use to solve this system? Why?c. Solve the equations to determine the true amount of the check.

229. The total height of a building, b, and the antenna tower on top of it, t, is 425 feet. The difference in heights of the building and the antenna tower is 324 feet. The following system of equations represents the situation.b + t = 425

b − t = 324

a. Explain how to use elimination to solve a system of equations.b. Include a step-by-step solution to find the height of the antenna tower.

Name: ________________________ ID: A

42

230. A manufacturer makes both volleyballs and basketballs. Each volleyball requires 2 minutes on the forming machine, and each basketball requires 1 minute. Each volleyball requires 1 minute on the inflating machine, and each basketball requires 1.5 minutes. If the forming machine runs for 40 minutes and inflating machine runs for 25 minutes, the following system of equations can be used to determine the number of volleyballs and basketballs produced.2x + y = 40

x + 1.5y = 25

a. Explain how the system of equations can be used to plan the machine running time.b. Include a demonstration of how to solve the system of equations given in the problem.

231. a. Explain why sampling is important in doing surveys. b. Illustrate biased and unbiased way of sampling with an example. c. Which type of sampling do you think is more reasonable and why?

232. A city council conducted a random survey of home owners to see if they would support property taxes being raised to help fund the construction of a city park. The results of the survey were: 50 strongly approved, 400 approved, 150 had no opinion, 350 disapproved, 300 strongly disapproved. It was concluded that residents would approve raising the property taxes. Do you agree with the conclusion? Explain.

233. A charity randomly selected 100 donors. The mean donation amount of those donors is calculated. Identify the sample and population. Describe the sample statistic and the population parameter.

234. a. Write the number of letter groupings that can be formed using the letters of the word “POWERFUL” such that O, E, and F must be together. Does this situation represent a permutation or a combination? Explain.

b. How many 3-letter groupings can be formed using the consonants of the word “POWERFUL”? Does this situation represent a permutation or a combination? Explain.

235. Mary goes to a church every Thursday. The probability that she will go to the church on Monday is 14 and the

probability that she will meet her friend there on Monday is 12 .

a. What is the probability of meeting her friend at church on Monday?b. Are the two events independent or dependent? Explain.

236. A beauty parlor owner observed the number of times customers come to the parlor in a month.

Number of Times Number of Customers1 182 323 364 14

How could the parlor owner create a probability distribution and use it to create a frequent buyer program?

Name: ________________________ ID: A

43

237. The table below shows the observation of the experiment done by a mathematician to know whether the game meets the expectation of the gaming company.

Group Percentage of LosersA 71%B 69%C 70%

Use the information above to explain how simulations can be used in gaming business. Also give the condition in which the game can be considered as successful or failed the expectation of the company.

238. Describe how you would model an event with a 75% success rate. Explain why your model is appropriate.

ID: A

1

Keystone PracticeAnswer Section

MULTIPLE CHOICE

1. D 2. A 3. C 4. D 5. A 6. B 7. C 8. A 9. C 10. D 11. B 12. D 13. C 14. B 15. B 16. C 17. B 18. B 19. A 20. B 21. C 22. D 23. B 24. B 25. D 26. C 27. A 28. D 29. C 30. D 31. D 32. C 33. A 34. B 35. A 36. B 37. B 38. D 39. B

ID: A

2

40. D 41. A 42. D 43. B 44. D 45. B 46. C 47. B 48. C 49. C 50. D 51. D 52. B 53. A 54. D 55. C 56. A 57. D 58. B 59. C 60. C 61. A 62. C 63. D 64. C 65. B 66. D 67. B 68. A 69. C 70. B 71. D 72. C 73. A 74. A 75. C 76. B 77. C 78. D 79. B 80. D 81. A 82. D 83. A 84. A

ID: A

3

85. B 86. A 87. B 88. C 89. D 90. B 91. A 92. D 93. A 94. D 95. C 96. B 97. A 98. B 99. B 100. A 101. C 102. B 103. A 104. D 105. C

SHORT ANSWER

106. y = 50w + 400;

If a quantity changes at a constant rate over time, it can be modeled by a linear equation. The y-intercept represents a starting point, and the slope represents the rate of change.

ID: A

4

107. y = 1.5r + 9.50


108. y = −14d + 256


109. y = 1.20x + 24;


110. C = 29m+ 139;


ID: A

5

111. y = x + 6

Find the slope of the line with the slope formula. Find the y-intercept by replacing x and y with the given point and m with the slope in the slope-intercept form. Solve for b. Write the equation in slope-intercept form using the given m and the calculated b.

112. y = 73

x + 1; 73


113. P = 0.7t − 1381.9


114. y = 2x − 110

; 2


115. P = 5t − 9686


116. y − 2 = 4 x + 1( ) ; y = 4x + 6; 4x − y = −6

The linear equation y − y1 = m x− x1ÊËÁÁˆ¯˜̃ is written in point-slope form, where x1, y1

ÊËÁÁ ˆ¯

˜̃ is a given point on a

nonvertical line and m is the slope of the line.Given an equation in point-slope form, solve the equation for y to find the equation in slope-intercept form.The linear equation in standard form is given as Ax+ By = C, where A, B, and C are constants. Use Addition and Subtraction Properties of Equality to rewrite the equation in standard form.

117. y − 7 = −9 x − 5( ) ; y = −9x + 52; 9x + y = 52


ÊËÁÁ ˆ¯


nonvertical line and m is the slope of the line.Given an equation in point-slope form, solve the equation for y to find the equation in slope-intercept form.The linear equation in standard form is given as Ax+ By = C, where A, B, and C are constants. Use Addition and Subtraction Properties of Equality to rewrite the equation in standard form.

ID: A

6

118. y − 25

= 38

x − 13

Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃˜̃˜̃ ; y =

38

x + 1140

; 15x − 40y = −11


ÊËÁÁ ˆ¯


nonvertical line and m is the slope of the line.Given an equation in point-slope form, solve the equation for y to find the equation in slope-intercept form.The linear equation in standard form is given as Ax+ By = C, where A, B, and C are constants. Use Addition and Subtraction Properties of Equality to rewrite the equation in standard form. Remember that A, B, and C must be integers with a GCF of 1.

119. y + 37

= 5 x − 15

Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃˜̃˜̃ ; y = 5x −

107

; 35x − 7y = 10


ÊËÁÁ ˆ¯



120. y + 45

= 15

x + 29

Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃˜̃˜̃ ; y =

15

x − 3445

; 9x − 45y = 34


ÊËÁÁ ˆ¯



121. No; the slopes are 4 and 14

.

Two nonvertical lines are perpendicular if the slopes are opposite reciprocals of each other. 122. y = −4x + 4

Two nonvertical lines are parallel if they have the same slope. Use the given point with the slope of the parallel line in the point-slope form. Then change to the slope-intercept form.

123. y = −52

x − 3( ) or y = −52

x + 152

Two nonvertical lines are perpendicular if the slopes are opposite reciprocals of each other. Use the given point with the slope of the perpendicular line in point-slope form. Then change to slope-intercept form.

124. y = −52

x − 192

Two nonvertical lines are perpendicular if the slopes are opposite reciprocals of each other. Use the given point with the slope of the perpendicular line in point-slope form. Then change to slope-intercept form.

ID: A

7

125.

Negative correlation.

A scatter plot is a graph in which two sets of data are plotted as ordered pairs in a coordinate plane. There is a positive correlation when y increases as x increases. There is a negative correlation when y decreases as x increases. There is no correlation when x and y are not related.

126. No; using the equation would give 2.82 hrs of sleep in a day, which is not a reasonable estimate for a 2-year-old.

Write an equation for the line of fit. Use the equation to make the prediction. 127.

Positive correlation


128. No; using the equation would give –333.3 miles, which is not a reasonable estimate.

Write an equation for the line of fit. Use the equation to make the prediction.

ID: A

8

129.


If the data points do not all lie on a line, but are close to a line, you can draw a line of fit. This line describes the trend of the data.

130. y = 5.6x + 242.73; $298,730 131. y = −1.86x + 87; 59.1 132. y = 11.86x − 13.67; 81.21 feet 133. y = 230.43x − 33.33; 0.983 134. No, the graphs are parallel, so the lines will never meet, and there is no year when the annual salary will be

the same.

Since the graphs are parallel lines, there are no solutions. 135. No, the graphs are parallel, so the lines will never meet and at no distance will the rental fees be the same.

Since the graphs are parallel lines, there are no solutions.

ID: A

9

136.

3.1 years after the given year, the number of broadband and dial-up users is predicted to be the same, 15.93 million.

Graph each line. The point where the two lines intersect is the solution. Check the solution by replacing x and y in the original equations with the values in the ordered pair.

137. Sample answer: The solution 2.66, 35.33ÊËÁÁ

ˆ¯˜̃ means that 2.66 days after the plants are planted, their height are

predicted to be the same, 35.33.


ID: A

10

138. Sample answer: The solution 3.33, 366.67ÊËÁÁ

ˆ¯˜̃ means that 3.33 weeks after the initial deposit, the amount in

their savings account is predicted to be the same, $366.67.


139. 24g of pure silver and 32g of a 65% alloy

x + y = 56

x + 0.65y = 0.80 56( )

Substitute 56− y for x in the second equation and solve for y. Substitute that value into the first equation and solve for x.

140. Speed of train A: 50mph, Speed of train B: 30mph

x = y + 20

3x + 3y = 240Substitute y + 20 for x in the second equation and solve for y. Substitute that value into the first equation and solve for x.

141. 23 inches

2x + y = 61

y = 4+ xSubstitute 4+ x for y in the first equation and solve for x. Substitute that value into the second equation and solve for y.

142. 10 dimes and 15 quarters

x + y = 25

0.10x + 0.25y = 4.75Substitute 25− x for y in the second equation and solve for x. Substitute that value into the first equation and solve for y.

ID: A

11

143. 14 hens and 18 pigs

x + y = 32

2x + 4y = 100Substitute 32− x for y in the second equation and solve for x. Substitute that value into the first equation and solve for y.

144. 40, 14

x + y = 54

x − y = 26Eliminate one variable by adding the two equations. Solve for x and then substitute that value into one of the equations to find the value of y.

145. 5, 7

5x + y = 32

3x − y = 8Eliminate one variable by adding the two equations. Solve for x and then substitute that value into one of the equations to find the value of y.

146. 8 saltwater fish, 7 freshwater fish

x + y = 15

2x + y = 23Eliminate one variable by subtracting the two equations. Solve for x and then substitute that value into one of the equations to find the value of y.

147. Jack: 33 stamps; Dylan: 13 stamps

x − y = 20

x + y = 46Eliminate one variable by adding the two equations. Solve for x and then substitute that value into one of the equations to find the value of y.

148. y = 2.45+ 0.06x

y = 3.15+ 0.04x

Sample answer: The solution 35, 4.55ÊËÁÁˆ¯˜̃ means that 35 years after 2000, or in 2035, the annual sales of the

two companies A and B are predicted to be the same, 4.55 million dollars.

Eliminate one variable by subtracting the two equations. Solve for x and then substitute that value into one of the equations to find the value of y.

149. 6, 4

6x + 5y = 56

x + y = 10Eliminate the y terms by first multiplying the second equation by 5 and then subtracting the two equations. Solve for x and then substitute that value into one of the equations to find the value of y.

ID: A

12

150. 26

x + y = 8

10y + x = 10+ 2 10x + yÊËÁÁ ˆ

¯˜̃

Substitute 8− x for y in the first equation and solve for x. Substitute that value into the second equation and solve for y.

151. 7, − 3ÊËÁÁ ˆ

¯˜̃

Eliminate the x terms by first multiplying the top equation by 3 and the bottom one by 2 and then subtracting the two equations. Solve for y and then substitute that value into one of the equations to find the value of x.

152. 6.48 mph

4x + 4y = 33

7x − 7y = 33Eliminate the x terms by first multiplying the top equation by 7 and the bottom one by 4 and then subtracting the two equations. Solve for y and then substitute that value into one of the equations to find the value of x.

153. $290 digital camera, $520 camcorder

12x + 8y = 7640

9x + 11y = 8330Eliminate the y terms by first multiplying the top equation by 11 and the bottom one by 8 and then subtracting the two equations. Solve for x and then substitute that value into one of the equations to find the value of y.

154. 12 dimes, 8 nickels

x + y = 20

5x − 5y = 20Solve the first equation for one of the variables and substitute into the second equation. Solve. Substitute that value into the first equation to find the second value.

155. 140 h by a turkey, 280 h by a chicken

8x

+ 12y

= 110

6x

+ 8y

= 114

Eliminate the y terms by first multiplying the top equation by 4 and the bottom one by 6 and then subtracting the two equations. Solve for x and then substitute that value into one of the equations to find the value of y.

ID: A

13

156. 16.6 h by a large hose, 25 h by a small hose

3x

+ 8y

= 12

10x

+ 10y

= 1

Use elimination by multiplication to get the value of x and y. 157. length: 28 inches; breadth: 19 inches

x + 3( ) y − 4ÊËÁÁ ˆ

¯˜̃ = xy− 67

x − 1( ) y + 4ÊËÁÁ ˆ

¯˜̃ = xy+ 89

−4x + 3y = −55

4x − y = 93Eliminate one variable by adding the two equations. Solve for y and then substitute that value into one of the equations to find the value of x.

158. Daniel’s age: 37 years; Lucy’s age: 10 years.

x = 7+ 3y

2x − 5y = 24Substitute 7+ 3y for x in the second equation and solve for y. Substitute that value into the first equation and solve for x.

159. p = 1.15

As a decimal, 15% is 0.15. The number 1 represents the current number of polo shirts. By adding 15% or 0.15 to 1, we can determine the number of polo shirts needed for next week.

160. Sample answer: Patrick can buy 7 storybooks for $12 and 2 for $8.

x + y ≥ 8

8x + 12y ≤ 105

161. Graph the inequalities 10x + 20y ≤ 300 and x + y ≥ 20. The solution is the shaded area.

ID: A

14

162. Sample answer: They can give away 20 of the $10 tickets and 5 of the $20 tickets or 15 of the $10 tickets and 7 of the $20 tickets.

Total number of tickets given away must be greater than equal to 20 and the total cost of the tickets must be less than or equal to $300.

163. m≥ 2s

500m+ 750s ≥ 3500

Graph the inequalities m≥ 2s and 500m+ 750s ≥ 3500. The solution is the shaded area. 164. 4 cars

The number of mid-sized cars sold must be greater than or equal to twice the number of sport-utility vehicles and sum of the profit earned from car of each type must be greater than or equal to $3500.

165. Sample answer: Ask a question on the topic that you are being taught to every fifth student.

A sample is an unbiased sample if every individual or the element in the population has an equal chance of being selected.

166. Sample answer: Get a copy of the employee’s list and take the opinion of every tenth person on the list.


167. Sample answer: Take a sample of water of every twentieth house in your neighborhood.


168. unbiasedbiased way: The farmer tests all the grape trees in one row to see whether the grapes are ready to harvest.

A biased sample is one that is falsely taken to be typical of a population from which it is drawn.A sample is an unbiased sample if every individual or the element in the population has an equal chance of being selected.

ID: A

15

169. biasedunbiased way: The physics practical teacher checks readings taken by every fifth student in the class to ensure that each student is taking the readings correctly.

A biased sample is one that is falsely taken to be typical of a population from which it is drawn.A sample is an unbiased sample if every individual or the element in the population has an equal chance of being selected.

170. Sample answer: Mean would be the best because there no outliers. The mean is 1.89 m. 171. Sample answer: Mode would be the best because there are many repeated numbers. The mode is 95. 172. 455

The number of combinations of n objects taken r at a time is the quotient of n! and (n − r)! r!.

173. 35132 ≈ 27%

Simplify 5C1 ×

7C112× 11 to get the answer.

174. 47

Use the formula P Aor B( ) = P A( ) + P B( ) − P AandB( ) to solve. 175. 1115

Use the formula P Aor B( ) = P A( ) + P B( ) − P AandB( ) to solve. 176. BBB, BBG, BGB, BGG, GBB, GBG, GGB, GGG

177. P(X = 0) = 827

P(X = 1) = 1227

P(X = 2) = 627

P(X = 3) = 127

Determine which combinations contain 0, 1, 2, or 3 spins that land on black. Multiply to determine the probability of spinning and landing on black for each combination.

178. P(Y = 0) = 127

P(Y = 1) = 627

P(Y = 2) = 1227

P(Y = 3) = 827

Determine which combinations contain 0, 1, 2, or 3 spins that land on gray. Multiply to determine the probability of spinning and landing on gray for each combination.

ID: A

16

179.

180. 181. Answers may vary. Sample Answer: No, it is more probable to land on gray since it is two-thirds of the

spinner. 182. Let X = the number of DVDs.

X = 25, 50, 75, 100, 125

A random variable is a variable whose value is the numerical outcome of a random event. In this problem, the random variable is the number of DVDs.

183. 0.05+ 0.30+ 0.40+ 0.15+ 0.10= 1.00

A valid probability distribution should have a sum of 1.00. 184. 0.05+ 0.30= 0.35

The probability of an event is equal to the sum of the individual probabilities. 185. 0.157+ 0.171+ 0.356+ 0.203= 0.887

The probability of the event is equal to the sum of the individual probabilities. 186. 0.072+ 0.025+ 0.016= 0.113

The probability of the event is equal to the sum of the individual probabilities. 187. 0.203+ 0.356+ 0.171= 0.73

The probability of the event is equal to the sum of the individual probabilities.

ID: A

17

188. 0.356+ 0.171+ 0.157+ 0.072+ 0.025+ 0.016= 0.797

The probability of the event is equal to the sum of the individual probabilities. 189. 0.757+ 0.122= 0.879



The probability of the event is equal to the sum of the individual probabilities. 192. Yes; 0.391+ 0.280+ 0.190+ 0.139= 1

A probability distribution is valid if the probabilities of all outcomes add up to 1. 193. 0.329

The probability of an event is equal to the sum of the individual probabilities. 194. 0.861

The probability of an event is equal to the sum of the individual probabilities. 195. 11

Find 19.1% of 59. 196. No; 0.282+ 0.191+ 0.134+ 0.071+ 0.236= 0.914. The sum of the probabilities does not equal 1.

A probability distribution is valid if the probabilities of all outcomes add up to 1. 197. P(compact car) = 0.107

P(sedan) = 0.357P(SUV) = 0.241P(truck) = 0.295

What is the total number of vehicles? Divide the number of each vehicle by the total to determine the probability of each vehicle.

198. 0.107+ 0.357= 0.464




The probability of the event is equal to the sum of the individual probabilities.

ID: A

18

202. 0.107+ 0.295= 0.402

The probability of the event is equal to the sum of the individual probabilities. 203. 0.107× 210≈ 23

The probability of the event is equal to the sum of the individual probabilities. 204. 0.241× 175≈ 43

The probability of the event is equal to the sum of the individual probabilities. 205. Answers may vary.

Sample Answer: Spinner divided into four equal sections or four different colored marbles in a bag. 206. Answers may vary.

Sample Answer: A die could be used since it has six sides that could correspond to the six ice cream flavors. 207. Answers may vary.

Sample Answer: A die could be used since it has six sides that could correspond to the six ice cream flavors. Roll the die fifty times.

208. Answers may vary.

Sample Answer: You could use a special spinner that was divided into three sections where 12 represents

grape juice, 13 represents orange juice, and 1

6 represents cranberry juice.

209. The theoretical probability is 12 or 50%.

If a simulation was performed, the experimental probability could be determined. 210. A spinner divided into four equal sections with each section representing a different type of pizza could be

used to simulate the outcomes.

211. The theoretical probability is 116 or ≈ 6%. 212. Answers may vary.

Sample Answer: Four coins could be used where each coin represents a kitten. Let heads represent females, and tails represents males.

213. Justin made 25× 0.60, or 15 free throws. 214. P ObesityÊ

ËÁÁ ˆ

¯˜̃ = 0.086

P Diabetes( ) = 0.145

P Heart problemsÊËÁÁˆ¯˜̃ = 0.210

P Eye problemsÊËÁÁ ˆ

¯˜̃ = 0.301

P DentalproblemÊËÁÁ ˆ

¯˜̃ = 0.258

experimentalprobability=frequency of an outcome

totalnumber of trials 215. 0.45 or 45%

The probability of the event is equal to the sum of the individual probabilities. 216. 62%

62÷ 100= 0.62

ID: A

19

217. 37.5%15÷ 40= 0.375

218. 4.7%

7÷ 150= 0.04666 219. 42%

21÷ 50= 0.42 220. 28%

13÷ 47= 0.2765

ID: A

20

ESSAY

221. Sample answer:a. You can use the slope-intercept form of the equation to find the y-value for any requested x-value. The

number of members in the fan club in 2007 will be 137,400.b. Linear extrapolation is when you use a linear equation to predict values that are outside of the given points

on the graph.

Find the slope of the line with the slope formula. Find the y-intercept by replacing x and y with the given point and m with the slope in the slope-intercept form. Solve for b. Write the equation in slope-intercept form using the given m and the calculated b.Linear extrapolation is using a linear equation to predict values that are beyond the range of the data.

Assessment RubricLevel 3 Superior*Shows thorough understanding of concepts.*Uses appropriate strategies.*Computation is correct.*Written explanation is exemplary.*Diagram/table/chart is accurate (as applicable).*Goes beyond requirements of problem.

Level 2 Satisfactory*Shows understanding of concepts.*Uses appropriate strategies.*Computation is mostly correct.*Written explanation is effective.*Diagram/table/chart is mostly accurate (as applicable).*Satisfies all requirements of problem.

Level 1 Nearly Satisfactory*Shows understanding of most concepts.*May not use appropriate strategies.*Computation is mostly correct.*Written explanation is satisfactory.*Diagram/table/chart is mostly accurate (as applicable).*Satisfies most of the requirements of problem.

Level 0 Unsatisfactory*Shows little or no understanding of the concept.*May not use appropriate strategies.*Computation is incorrect.*Written explanation is not satisfactory.*Diagram/table/chart is not accurate (as applicable).*Does not satisfy requirements of problem.

ID: A

21

222. Sample Answer

a. Plan 1: C = 15+ 0.08mPlan 2: C = 5+ 0.11mPlan 3: C = 49.95

b.

c. Megan should enroll in Plan 3. The graph shows that at 500 minutes, she would be paying $49.95 for Plan 3, about $60 for Plan 2, and about $55 for Plan 1.




ID: A

22


ID: A

23

223. a. Sample answer: If two equations have the same slope, then the lines are parallel. If the product of their slopes equals –1, then the lines are perpendicular, except for horizontal and vertical lines.

b. Yes, the lines are parallel as the slopes are equal.

c. The graph of y = 85

x is perpendicular to the graph of y = −58

x + 15

and y = −58

x + 3 because the slopes are

negative reciprocals of each other.

Two nonvertical lines are parallel if they have the same slope.Two nonvertical lines are perpendicular if the slopes are opposite reciprocals of each other.





ID: A

24

224. Sample Answer

a. and b.Average Hourly Earnings (dollars) of U.S.

Production Workers, 1991-2001

Year

c. Using (1992, 10.57) and (2000, 13.76), the slope of the line is: m= 13.76− 10.572000− 1992 =3.19

8 ≈ 0.4.Find b using one of the points.

13.76= 0.4 * 2000+ b

13.76= 800+ b

−786.24= bThe equation for the line of fit is y = 0.4x − 786.24

d. y = 0.4x − 786.24

y = 0.4(2005)− 786.24

y = 15.76

Hourly earnings in 2005 should be about $15.76.



ID: A

25


Level 0 Unsatisfactory*Shows little or no understanding of the concept.*May not use appropriate strategies.*Computation is incorrect.*Written explanation is not satisfactory.*Diagram/table/chart is not accurate (as applicable).

*Does not satisfy requirements of problem.

ID: A

26

225. The correlation coefficient measures the how closely the best-fit line is modeling the data. The closer it is to 1 or -1, the more closely it models the data. The best-fit line is a good model for the data because -0.965 is very close to -1. The fact that it is negative means that there is a negative correlation.





ID: A

27

226. No it is not a function. A function has to have a unique y value for every x value. If x is 2, y would be either 2+ 5 = 7 or 2− 3 = −1.


Level 2 Satisfactory*Shows understanding of concepts.*Uses appropriate strategies.*Computation is mostly correct.*Written explanation is effective.*Diagram/table/chart is mostly accurate (as applicable)

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ExamView - Keystone Practice (1) · ____ 5. An icicle is 12 inches long and melts at a rate of 1 4 inch per hour. a. L =12−1 4 t c. L =12−4t b. L =1 4 −12t d. t =12−1 4 L