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Chapter 0 Pretest
Determine whether you need an estimate or an exact answer. Then solve.
1. SHOPPING Addison paid $1.29 for gum and $0.89 for a package of notebook paper. She gave the cashier a $5 bill.
If the tax was $0.14, how much change should Addison receive?
SOLUTION: This problem requires an exact answer. To find how much change Addison should receive, find the sum of the things
she bought and the tax and subtract that from the amount she gave the cashier.
5 – (1.29 + 0.89 + 0.14) = 2.68
So, Addison should receive $2.68 in change.
2. DISTANCE Luis rode his bike 1.2 miles to his friend’s house, then 0.7 mile to the video store, then 1.9 miles to the
library. If he rode the same route back home, about how far did he travel in all?
SOLUTION: Because the question asks “about how far,” this problem requires an estimate. Round each of the distances Luis
rode on his bike to the nearest mile. Then find the sum.
1.2 ≈ 1
0.7 ≈ 1
1.9 ≈ 2
1+1+2=4
Because Luis rode about 4 miles and then back the same route, multiply 4 by 2 to find the total distance.
4 × 2 = 8
So, Luis rode about 8 miles in all.
Find each sum or difference.
3. 20 + (–7)
SOLUTION: 20 has greater absolute value, so the sum is positive.
4. –15 + 6
SOLUTION: –15 has greater absolute value, so the sum is negative.
5. –9 – 22
SOLUTION: Both numbers are negative, so the sum is negative.
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Chapter 0 Pretest
5. –9 – 22
SOLUTION: Both numbers are negative, so the sum is negative.
6. 18.4 – (–3.2)
SOLUTION: To subtract –32, add its inverse.
7. 23.1 + (–9.81)
SOLUTION: 12.1 has greater absolute value, so the sum is positive.
8. –5.6 + (–30.7)
SOLUTION: Both numbers are negative, so the sum is negative.
Find each product or quotient.
9. 11(–8)
SOLUTION: The product of two integers with different signs is negative.
11(–8) = –88
10. –15(–2)
SOLUTION: The product of two integers with the same sign is positive.
–15(–2) = 30
11. 63 ÷ (–9)
SOLUTION: The Manual
quotient
of twobyintegers
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63 ÷ (–9) = –7
12. –22 ÷ 11
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10. –15(–2)
SOLUTION: Chapter
0 Pretest
The product
of two integers with the same sign is positive.
–15(–2) = 30
11. 63 ÷ (–9)
SOLUTION: The quotient of two integers with different signs is negative.
63 ÷ (–9) = –7
12. –22 ÷ 11
SOLUTION: The quotient of two integers with different signs is negative.
–22 ÷ 11 = –2
Replace each ▒ with <, >, or = to make a true sentence.
13. ▒ SOLUTION: To compare the fractions, write both fractions with a common denominator.
So,
<
.
14. 0.15 ▒ SOLUTION: To compare these numbers, write
as a decimal.
0.15 > 0.125
So, 0.15 >
15. Order 0.5,
.
, –0.2, and
from least to greatest.
SOLUTION: To order these numbers from least to greatest, write the fractions as decimals.
The Manual
decimals
in order
from least
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greatest are –0.2,
,
, 0.5.
to greatest are –0.2,
,
, 0.5. So, the numbers in order from least toPage 3
0.15 > 0.125
Chapter
0 Pretest
So, 0.15
> .
15. Order 0.5,
, –0.2, and
from least to greatest.
SOLUTION: To order these numbers from least to greatest, write the fractions as decimals.
The decimals in order from least to greatest are –0.2,
greatest are –0.2,
,
,
, 0.5. So, the numbers in order from least to
, 0.5.
Find each sum or difference. Write in simplest form.
16. +
SOLUTION: 17. –
SOLUTION: 18. +
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Chapter 0 Pretest
18. +
SOLUTION: 19. SOLUTION: Find each product or quotient.
20. 2.4(–0.7)
SOLUTION: The product of two numbers with different signs is negative.
2.4(–0.7) = –1.68
21. –40.5 ÷ (–8.1)
SOLUTION: The quotient of two numbers with the same sign is positive.
–40.5 ÷ (–8.1) = 5
Name the reciprocal of each number.
22. SOLUTION: The product of a number and its reciprocal is 1. So,
is the reciprocal of
.
23. SOLUTION: The product of a number and its reciprocal is 1. So,
is the reciprocal of
.
Find each product or quotient. Write in simplest form.
24. ÷ SOLUTION: eSolutions Manual - Powered by Cognero
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SOLUTION: Chapter
0 Pretest
The product
of a number and its reciprocal is 1. So,
is the reciprocal of
.
Find each product or quotient. Write in simplest form.
24. ÷ SOLUTION: 25. •
SOLUTION: 26. ÷ SOLUTION: To divide, multiply by the reciprocal. Write each mixed number as an improper fraction.
27. • SOLUTION: 28. ÷ SOLUTION: eSolutions Manual - Powered by Cognero
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Chapter 0 Pretest
28. ÷ SOLUTION: 29. • SOLUTION: Express each percent as a fraction in simplest form.
30. 20%
SOLUTION: 31. 7.5%
SOLUTION: Use the percent proportion to find each number.
32. 18 is what percent of 72?
SOLUTION: The part is 18 and the base is 72. Let p represent the percent.
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Chapter 0 Pretest
Use the percent proportion to find each number.
32. 18 is what percent of 72?
SOLUTION: The part is 18 and the base is 72. Let p represent the percent.
So, 18 is 25% of 72.
33. 35 is what percent of 200?
SOLUTION: The part is 35 and the base is 200. Let p represent the percent.
So, 35 is 17.5% of 200.
34. 24 is 60% of what number?
SOLUTION: The part is 24 and the percent is 60. Let b represent the base.
So, 24 is 60% of 40.
35. TEST SCORES James answered 14 items correctly on a 16-item quiz. What percent did he answer correctly?
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SOLUTION: To find the percent that James answered correctly, find what percent 14 is of 16. The part is 14 and the base is 16.
Chapter
0 Pretest
So, 24 is 60% of 40.
35. TEST SCORES James answered 14 items correctly on a 16-item quiz. What percent did he answer correctly?
SOLUTION: To find the percent that James answered correctly, find what percent 14 is of 16. The part is 14 and the base is 16.
Let p represent the percent.
So, James answered 87.5% of the items correctly.
36. BASKETBALL Emily made 75% of the baskets that she attempted. If she made 9 baskets, how many attempts
did she make?
SOLUTION: To find the number of attempts Emily made, find what number 9 is 75% of. The part is 9 and the percent is 75. Let b
represent the base.
So, Emily made 12 attempts.
Find the perimeter and area of each figure.
37. SOLUTION: So, the perimeter is 36 inches.
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Chapter
0 Pretest
So, Emily made 12 attempts.
Find the perimeter and area of each figure.
37. SOLUTION: So, the perimeter is 36 inches.
So, the area is 81 square inches.
38. SOLUTION: So, the perimeter is 48 centimeters.
So, the area is 96 square centimeters.
39. A parallelogram has side lengths of 7 inches and 11 inches. Find the perimeter.
SOLUTION: To find the perimeter, find the sum of the sides of the parallelogram.
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Chapter
0 Pretest
So, the area is 96 square centimeters.
39. A parallelogram has side lengths of 7 inches and 11 inches. Find the perimeter.
SOLUTION: To find the perimeter, find the sum of the sides of the parallelogram.
So, the perimeter is 36 inches.
40. GARDENS Find the perimeter of the garden.
SOLUTION: So, the perimeter of the garden is 23 meters.
Find the circumference and area of each circle. Round to the nearest tenth.
41. SOLUTION: So, the circumference is approximately 12.6 meters.
So, the area is approximately 12 square meters.
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Chapter
0 Pretest
So, the
area is approximately 12 square meters.
42. SOLUTION: So, the circumference is approximately 50.3 centimeters.
So, the area is approximately 201.1 square centimeters.
43. BIRDS The floor of a birdcage is a circle with a circumference of about 47.1 inches. What is the diameter of the
birdcage floor? Round to the nearest inch.
SOLUTION: To find the diameter of the birdcage floor, solve the formula for the circumference of a circle for r.
So, the diameter is approximately 15 inches.
Find the volume and surface area of each rectangular prism given the measurements.
44. l = 3 cm, w = 1 cm, h = 3 cm
SOLUTION: So, the volume is 9 cubic centimeters.
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So, the surface area is 30 square centimeters.
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Chapter
0 Pretest
So, the diameter is approximately 15 inches.
Find the volume and surface area of each rectangular prism given the measurements.
44. l = 3 cm, w = 1 cm, h = 3 cm
SOLUTION: So, the volume is 9 cubic centimeters.
So, the surface area is 30 square centimeters.
45. l = 6 ft, w = 2 ft, h = 5 ft
SOLUTION: So, the volume is 60 cubic feet.
So, the surface area is 104 square feet.
46. Find the volume and surface area of the rectangular prism.
SOLUTION: So, the volume is 30 cubic inches.
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Chapter
0 Pretest
So, the surface area is 104 square feet.
46. Find the volume and surface area of the rectangular prism.
SOLUTION: So, the volume is 30 cubic inches.
So, the surface area is 63 square centimeters.
One pencil is randomly selected from a case containing 3 red, 4 green, 2 black, and 6 blue pencils. Find
each probability.
47. P(green)
SOLUTION: The number of possible outcomes is 3 + 4 + 2 + 6, or 15.
probability =
P(green) =
48. P(red or blue)
SOLUTION: The number of possible outcomes is 3 + 4 + 2 + 6, or 15.
probability =
P(red or blue) =
= 49. Use a tree diagram to find the sample space for the event a die is rolled, and a coin is tossed. State the number of
possible outcomes.
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probability =
Chapter
P(red0orPretest
blue) =
= 49. Use a tree diagram to find the sample space for the event a die is rolled, and a coin is tossed. State the number of
possible outcomes.
SOLUTION: The tree diagram shows that there are 12 possible outcomes.
One coin is randomly selected from a jar containing 20 pennies, 15 nickels, 3 dimes, and 12 quarters.
Find the odds of each outcome. Write in simplest form.
50. a penny
SOLUTION: There are 50 possible outcomes; 20 are successes and 30 are failures. So, the odds of selecting a penny are 20:30 or 2:3.
51. a penny or nickel
SOLUTION: There are 50 possible outcomes; 35 are successes and 15 are failures. So, the odds of selecting a penny or a nickel
are 7:3 or 7:3.
52. A coin is tossed 50 times. The results are shown in the table. Find the experimental probability of heads. Write as a
fraction in simplest form.
SOLUTION: probability =
The number of possible outcomes is 22 + 28, or 50.
So, the experimental probability of a coin landing heads up is
or .
Find the mean, median, and mode for each set of data.
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53. {10,Manual
SOLUTION: Page 15
probability =
The number of possible outcomes is 22 + 28, or 50.
Chapter
0 Pretest
So, the
experimental probability of a coin landing heads up is
or .
Find the mean, median, and mode for each set of data.
53. {10, 11, 18, 24, 30}
SOLUTION: So, the mean is 18.6.
The numbers are already in numerical order. The median, or middle number, is 18.
Because all of the numbers appear only once in the set of data, there is no mode.
54. {4, 8, 9, 9, 10, 14, 16}
SOLUTION: So, the mean is 10.
The numbers are already in numerical order. The median, or middle number, is 9.
The number 9 appears most often, so the mode is 9.
55. Find the range, median, lower quartile, and upper quartile for {16, 19, 21, 24, 25, 31, 35}.
SOLUTION: So, the range is 19.
The numbers are already in numerical order. {16, 19, 21, 24, 25, 31, 35} Since there is an odd number of values, the
median or Q2 is the middle value. So, Q2 is 24. Q1 is the median of the lower half of the data set. The lower half is {16, 19, 21}. Since there is an odd number of
values, the median is the middle valuer or 19. So, 19 is the lower quartile.
Q3 is the median of the upper half of the data set. The upper half is {25, 31, 35}. Since there is an odd number of
values, the median is the middle valuer or 31. So, the upper quartile is 31.
56. SCHOOL Devonte’s scores on his first four Spanish tests are 92, 85, 90, and 92. What test score must Devonte
earn on the fifth test so that the mean will be exactly 90?
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SOLUTION: Let x be the score Devonte must earn on the fifth test so that the mean will be exactly 90.
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values, the median is the middle valuer or 19. So, 19 is the lower quartile.
Q3 is0the
median of the upper half of the data set. The upper half is {25, 31, 35}. Since there is an odd number of
Chapter
Pretest
values, the median is the middle valuer or 31. So, the upper quartile is 31.
56. SCHOOL Devonte’s scores on his first four Spanish tests are 92, 85, 90, and 92. What test score must Devonte
earn on the fifth test so that the mean will be exactly 90?
SOLUTION: Let x be the score Devonte must earn on the fifth test so that the mean will be exactly 90.
So, Devonte must earn a score of 91on his fifth test.
57. MUSIC The table shows the results of a survey in which students were asked to choose which of four instruments
they would like to learn. Make a bar graph of the data.
SOLUTION: Draw a bar to represent each instrument. The vertical scale is the number of students who chose each instrument.
The horizontal scale identifies the instrument chosen.
58. Make a double box-and-whisker plot of the data.
A: 42, 50, 38, 59, 50, 44, 46, 62, 47, 35, 55, 56
B: 47, 49, 48, 49, 40, 54, 56, 42, 57, 45, 45, 46
SOLUTION: Put data
A-into
L1 and
data B into L2 on your graphing calculator. Turn the stat plots on, choose a suitable window
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and graph the box-and-whisker plots. Chapter 0 Pretest
58. Make a double box-and-whisker plot of the data.
A: 42, 50, 38, 59, 50, 44, 46, 62, 47, 35, 55, 56
B: 47, 49, 48, 49, 40, 54, 56, 42, 57, 45, 45, 46
SOLUTION: Put data A into L1 and data B into L2 on your graphing calculator. Turn the stat plots on, choose a suitable window
and graph the box-and-whisker plots. 59. EXPENSES The table shows how Dylan spent his money at the fair. Make a circle graph of the data.
SOLUTION: How
Ratio
Spent
rides
Degrees for
Section of Graph
food
games
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