Selected Answers and Solutions R1 Selected Answers and Solutions For Homework Help, go to Hotmath.com Go to Hotmath.com for step-by-step solutions of most odd-numbered exercises free of charge. Chapter 1 Multiply and Divide Decimals Page 24 Chapter 1 Are You Ready? 1. 300 3. 672 5. 2,820 7. $92 9. 774 mi 11. 34 13. 41 Pages 27–29 Lesson 1-1A 1. 6 × 4 = 24 3. 60 × 30 = 1,800 5. 14 × 3 = 42 7. about $8 9. 10 × 3 = 30 11 11 Sample answer: Round 17.5 to 20, and round 8.4 to 8. 20 × 8 = 160 13. 30 × 80 = 2,400 15. 40 × 5 = 200 17. 70 × 2 = 140 19. about 90 21. His estimate is not reasonable. He rounded $15.75 to $20. If he rounded $15.75 to $16, the estimate would be $48 for the three books. 23. no; 70 25. yes 27 27 More; her wage and hours worked were rounded up, so the actual total is less than the estimate. 29. 35 × 8 = 280; 40 × 8 = 320; Rounding to the ones gives an estimate closer to the actual product. 31. 59 × 6 = 354; 60 × 6 = 360; Rounding to the ones gives an estimate closer to the actual product. 33. about 10 yards 35. no; 90.8 × 3.1 ≈ 90 × 3 ≈ 270 37. about $12 39. B 41. yes; 4 × $3.69 ≈ 4 × $4 = $16 43. G Pages 34–35 Lesson 1-1C 1. 16.2 3. 1.56 5. 0.45 7. 1.17 9 9 Multiply 12 times $4.89, 17 times $4.72, and 15 times $5.09. Add the three products to find that they spent $215.27 for gas. 11. 8.5 13. 3.6 15. 19.2 17. 1.5 19. 0.084 21. 1.485 23. 8,850 m; 8.85 rounds to 9 and 9 × 1,000 = 9,000 25 25 134.6°F; 1,346 × 10 = 13,460. Since 13.46 has 2 decimal places, 13.46 × 10 = 134.60. 27. Sample answer: I bought three ice cream cones for $1.59 each. How much money did I spend? 3 × 1.59 = $4.77 29. The product of 123 × 47 is 5,781. The product of 123 × 0.47 is 57.81, which is one-hundredth the size of the whole number product. The second factor is one-hundredth the size of the whole number factor. 31. 12.12 33. H Pages 39–41 Lesson 1-1E 1. 0.3 3. 29.87127 5 5 Sample answer: Multiply 52 × 21 to get 1,092. Two decimal places in the first factor and one decimal place in the second factor produce three decimal places in the product. 0.52 × 2.1 = 1.092 7. 3.645 9. 0.0848 11. 0.28 13. 1.48 15. 7.154 17. 0.186 19. 166.992 21. 0.0224 23 23 Estimate. 46.93 × 1.8 ≈ 45 × 2 = 90 46.93 2 decimal places × 1.8 1 decimal place 37544 + 4693 84.474 3 decimal places So, the giraffe could run 84.474 feet in 1.8 seconds. Since 84.474 ≈ 90, the answer is reasonable. 25. 75.2452 27. 20.48512 29. 2.0646 31. 6.5745 33. 30.39 in 2 ; Since 3.1 × 6.9 = 21.39 and 3(6.1 - 3.1) = 9, the area of the figure is 21.39 + 9 or 30.39 in 2 . 35 35 $5.76; Each price is about $1. He bought about 6 pounds of fruit. 6 × 1 = 6 ≈ $5.76 37. Sample answer: If a = 1.5 and b = 0.2, then ab = 0.3, which is less than 1; if a = 1.5 and b = 0.8, then ab = 1.2, which is not less than 1. 39. Sample answer: 0.1 × 0.6 41. always; 0.3 × 0.5 = 0.15; 0.75 × 0.6 = 0.45 43. 0.75 45. 2.7348 47. D 49. 12.15 51. 134.4 53a. Sample answer: about 75,000 mi 53b. Sample answer: about 1,000 mi 55. 65 57. 400 Pages 43–46 Lesson 1-2A Sample answers given. 1. 25 ÷ 5 = 5 3. 1,000 ÷ 40 = 25 5 5 Sample answer: Divide 3 by 1. She can make about 3 smoothies. 7. 54 ÷ 9 = 6 9. 46 ÷ 23 = 2 11. 120 ÷ 20 = 6 13. about $10; $38.04 ÷ 4 ≈ $40 ÷ 4 = $10 15. no; 3 17. no; 4 19a. 5; 100 × 5 = 500 19b. 10 21 21 Sample answer: Each cow produces about 6 gallons of milk per day. The answer is reasonable because 54 is close to 53 pounds, and 54 divided by 9 is 6. 23. about $22 25. about $100 27. 300 ÷ 50 = 6; 6.42 29. 2,000 ÷ 25 = 80; 74.65 31 31 Her answer is reasonable because $474.72 is close to $480, and $480 divided by the 12 months in a year is $40. 33. Sample answer: Mrs. Fisher bought 2.75 lb of apples. The apples cost $1.79 per pound. About how much did she pay for the apples? about $6 35. Sample answer: 160.23 ÷ 6.54 37. A 39. I 41a. 93.6 lb 41b. 438.178 lb 41c. 241.198 lb 43. 320 45. 2,500 Pages 52–53 Lesson 1-2C 1. 0.9 3. 1.4 5. 0.6 7. 0.49 9. 13.1
39
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Selected Answers and Solutions R1
Selected Answers and Solutions
For Homework Help, go to Hotmath.com
Go to Hotmath.com for
step-by-step solutions of most odd-numbered exercises free of charge.
140 19. about 90 21. His estimate is not reasonable. He rounded $15.75 to $20. If he rounded $15.75 to $16, the estimate would be $48 for the three books. 23. no; 70 25. yes
2727 More; her wage and hours worked were
rounded up, so the actual total is less than the estimate.
29. 35 × 8 = 280; 40 × 8 = 320; Rounding to the ones gives an estimate closer to the actual product. 31. 59 × 6 = 354; 60 × 6 = 360; Rounding to the ones gives an estimate closer to the actual product. 33. about 10 yards 35. no; 90.8 × 3.1 ≈ 90 × 3 ≈ 270 37. about $12 39. B 41. yes; 4 × $3.69 ≈ 4 × $4 = $16 43. G
Pages 34–35 Lesson 1-1C
1. 16.2 3. 1.56 5. 0.45 7. 1.17
99 Multiply 12 times $4.89, 17 times $4.72, and 15
times $5.09. Add the three products to fi nd that they spent $215.27 for gas. 11. 8.5 13. 3.6 15. 19.2 17. 1.5 19. 0.084 21. 1.485 23. 8,850 m; 8.85 rounds to 9 and 9 × 1,000 = 9,000
2525 134.6°F; 1,346 × 10 = 13,460. Since 13.46 has 2
decimal places, 13.46 × 10 = 134.60. 27. Sample answer: I bought three ice cream cones for $1.59 each. How much money did I spend? 3 × 1.59 = $4.77 29. The product of 123 × 47 is 5,781. The product of 123 × 0.47 is 57.81, which is one-hundredth the size of the whole number product. The second factor is one-hundredth the size of the whole number factor. 31. 12.12 33. H
Pages 39–41 Lesson 1-1E
1. 0.3 3. 29.87127
55 Sample answer: Multiply 52 × 21 to get 1,092.
Two decimal places in the fi rst factor and one decimal place in the second factor produce three decimal places in the product. 0.52 × 2.1 = 1.092
46.93 2 decimal places× 1.8 1 decimal place 37544+ 4693
84.474 3 decimal placesSo, the giraffe could run 84.474 feet in 1.8 seconds. Since 84.474 ≈ 90, the answer is reasonable.25. 75.2452 27. 20.48512 29. 2.0646 31. 6.5745 33. 30.39 in2; Since 3.1 × 6.9 = 21.39 and 3(6.1 - 3.1) = 9, the area of the fi gure is 21.39 + 9 or 30.39 in2.
3535 $5.76; Each price is about $1. He bought about
6 pounds of fruit. 6 × 1 = 6 ≈ $5.76 37. Sample answer: If a = 1.5 and b = 0.2, then ab = 0.3, which is less than 1; if a = 1.5 and b = 0.8, then ab = 1.2, which is not less than 1. 39. Sample answer: 0.1 × 0.6 41. always; 0.3 × 0.5 = 0.15; 0.75 × 0.6 = 0.45 43. 0.75 45. 2.7348 47. D 49. 12.15 51. 134.4 53a. Sample answer: about 75,000 mi 53b. Sample answer: about 1,000 mi 55. 65 57. 400
6 gallons of milk per day. The answer is reasonable because 54 is close to 53 pounds, and 54 divided by 9 is 6.23. about $22 25. about $100 27. 300 ÷ 50 = 6; 6.42 29. 2,000 ÷ 25 = 80; 74.65
3131 Her answer is reasonable because $474.72 is
close to $480, and $480 divided by the 12 months in a year is $40. 33. Sample answer: Mrs. Fisher bought 2.75 lb of apples. The apples cost $1.79 per pound. About how much did she pay for the apples? about $6 35. Sample answer: 160.23 ÷ 6.54 37. A 39. I 41a. 93.6 lb 41b. 438.178 lb 41c. 241.198 lb 43. 320 45. 2,500
2323 22.8 ft; Sample answer: area = length × width,
so to fi nd the width, divide the area by the length. 752.4 ÷ 33 = 22.8, so the deck is 22.8 feet wide.25. 1.42 thousand yards; 4.26 ÷ 3 = 1.42 27. 422; 0.422; 42.2; 0.0422; 4.22; 0.00422; Sample answer: You can fi rst mentally divide 96 by 3, which is 32. Since 0.0096 has four decimal places, place four decimal places in the quotient, 32. So, 0.0096 ÷ 3 = 0.0032. 29. Less than; the fi rst number in the dividend, 2, is less than the divisor, 3. 31. 62.46 33. B 35. Sample answer: 100 37. 13.68 39. 2.592
Pages 58–60 Lesson 1-2E
1. 12.3 3. 1.5
55 Move both decimal points four places to the
right after annexing three zeros to the dividend. Then divide. 2500.0024. � ������������������������������ 0.6000.
red, divide 0.2 by 0.09. 0.0220.09 � ����������������������� 0.20 -18 20 -18 0 Respondents chose silver 2.2 times more than they chose red. 35b. To fi nd how many more chose silver or black than red, add the amount of silver and black to get 0.34. Then divide by the number who chose red, 0.09, to get 3.8. Respondents chose silver or black 3.8 times more than they chose red. 39. 24 41. Sample answer: If a < 1 and b < 1, then a ÷ b < 1. If a = 0.08 and b = 0.2, then a ÷ b = 0.4, which is less than 1. If a = 0.8 and b = 0.02, then a ÷ b = 40, which is not less than 1. 43. Sample answer: How many times more people live in India
than in Indonesia? Round to the nearest tenth. 4.8 45. I 47. $2; Because $11.18 is close to 10, and 10 is a multiple of 5, the estimate $10 ÷ 5 = $2 is reasonable. 49. 102.465 51. 91.64
together four times to equal 0.0625.37. 3.2 × 3.2 × 3.2; 32.768 39. 6.5 × 6.5; 42.25 41. Sample answer: 502 43. Sample answer: Exponential form is a short way to write repeated multiplication of a common factor such as 5 × 5 × 5 × 5 = 54. 45. 145 47. 10 49. 11 51. 90 ft by 90 ft
zeros to 0.5 to rewrite it as 0.5000, and then move the decimal point three places to the right; 0.5 × 1,000 = 500.15. 95,300 17. 28,600,000 19. 0.003 21. 0.87 23. 3.46 25. 0.002 27. 0.00045
2929 Sample answer: First, fi nd the amount of
decrease: 6,500 × 0.01 = 65. Then, subtract the amount of decrease from the original number of tickets sold: 6,500 - 65 = 6,435. There were 6,435 tickets sold during the second week. 31. Dwayne moved the decimal point the wrong direction; 0.60 × 1,000 = 600. 33. Multiply 3 by the number. Move the decimal point of the product one place to the left; 7.5. 35. B 37. 8 × 8 × 8; 512 39. 1 × 1 × 1 × 1 × 1 × 1 × 1 × 1 × 1 × 1; 1
Pages 72–73 Lesson 1-3C
1. 2.68 3. 0.00052 5. 6,254
77 Sample answer: 1,400 Aby cats is 0.01 times the
number of Labrador retriever dogs. To fi nd the number of dogs, divide the number of Aby cats by 0.01; 1,400 ÷ 0.01. Since there are two numbers to the right of the decimal point in 0.01, move the decimal point in 1,400 two places to the right; 1,400 ÷ 0.01 = 140,000. There are 140,000 registered Labrador retriever dogs. 9. 7.28 11. 0.295 13. 0.00082 15. 64,650 17. 8,160 19. 49.1 21. 18.5 weeks
0.1 pound of candies; 2.5 ÷ 0.1 = 25. Keisha can fi ll 25 party favor bags.25. 420 27. 150 29. The divisor 0.0001 has 4 decimal places, so move the decimal point of 0.01 four places to the right: 0.01 ÷ 0.0001 = 100. 31a. 10; decimal point moved 1 place to the right 31b. 100; decimal point moved 2 places to the right 31c. 0.001; decimal point moved 3 places to the left 33. C 35. F 37. 41,217 39. 114 41. 0.45
Pages 74–75 Lesson 1-3D PSI
1. Sample answer: Checking on an answer for the distance to a planet; the distance is so large, an exact answer is not needed. 3. $100 is enough5. 270 ft 7a. 2009 7b. 2010
99 Two numbers that multiply to give 48 are 6
and 8, but they are only two digits apart. John needs a number smaller than 6 and another larger than 8, and they need to be even in order to give an even product. Four times twelve is 48 and 4 and 12 are eight digits apart. 11. 5 magnets and 7 keychains
Altogether, it took Jeffrey 5 hours to make the trip to his sister’s.
Pages 107–110 Lesson 2-2B
1. 1 _ 16
3. 8 5. 1 _ 4
77 Sample answer: Juanita spent 1 _ 2 of 3 _
4 of her
allowance on earphones. Multiply to fi nd 1 _ 2 of
3 _
4 ; 1 _
2 × 3 _
4 = 3 _
8 . She spent 3 _
8 of her allowance on new
earphones.
9. 3 _ 32
11. 6 _ 35
1313 2 _ 3 × 4 = 2 _
3 × 4 _
1 = 8 _
3 or 2 2 _
3
15. 4 1 _ 8 17. 3 _
7 19. 1 _
3 21. Nyemi: 138; Luke: 69;
Natalie: 23 23. $462 25. 1 _ 24
27. 3 _ 16
29a. 15 3 _ 4 min
29b. 42 min; If 1 _ 5 of the time is spent on instruction,
then 4 _ 5 of the 7 _
8 -hr class is not. So, 4 _
5 ×
7 _
8 = 7 _
10 . 7 _
10 ×
60 min = 42 min 31. 1 _ 2 c; 3 _
4 ×
2 _
3 =
3 × 2 _
4 × 3 =
1 _
2
3333 3 _ 10
; If the homerooms share a bulletin board,
then they each have 1 _ 2 of the board. Since
Homeroom 101 uses 3 _ 5 of their half, they use
3 _ 5 ×
1 _
2 or 3 _
10 of the whole board.
35a. true 35b. false; 4 9 _ 10
× 9 _
10 = 4 41
_ 100
35c. true
37. The fraction a _ b × b _ c × c _
d × d _ e can be simplifi ed
before multiplying by crossing out the factors that appear in both a numerator and a denominator. The factors that can be crossed out are b, c, and d. Thus, the only factors remaining are a in the numerator and e in the denominator, or a _ e .
39. C 41. H 43. 30 minutes 45. 40 _
3 or 13 1 _
3
47. 120 in2 49. Sample answer: 2 _ 3 × 18 = 12
51. 6 lb
Pages 113–115 Lesson 2-2D
1. 1 3 _ 16
3. 4 9 _ 10
5. 9
77 Sample answer: Multiply the amount of fl our
for one batch of waffl es by 1 1 _ 2 to fi nd how much
fl our Chun needs for his larger batch.
2 1 _ 4 cups × 1 1 _
2 = 9 _
4 × 3 _
2
= 27 _
8
= 3 3 _ 8
Chun needs 3 3 _ 8 cups of flour to make the waffle
recipe.
9. 2 1 _ 8 11. 1 1 _
2 13. 17
_ 20
15. 10 2 _ 15
17. 12 3 _ 4 19. 19 1 _
2
2121 Sample answer: Use the distance formula,
distance = rate × time, and the given information to answer the question.
d = r × t
= 3 7 _ 10
× 2 1 _ 2
= 37 _
10 × 5 _
2
= 37 _
4
= 9 1 _ 4
The distance the carp travels is 9 1 _ 4 miles.
23. 3 _ 5
2525 1 _ 7 × 5 5 _
6 × 1 1 _
4 =
1 _
7 × 35
_ 6 × 5 _
4 Write the mixed numbers
as improper fractions. 5
= 1 _
7 × 35
_ 6 × 5 _
4 Divide 7 and 35 by
their GCF, 7. 1
= 25
_ 24
Multiply the numerators and multiply the denominators.
= 1 1 _ 24
Simplify.
27a. about 69 27 _
40 million mi 27b. about 139 7 _
20
million mi 27c. about 487 29 _
40 million mi 27d. about
882 11 _
20 million mi 29. 2 1 _
3
3131 bc = 3 1 _ 2 × 1 3 _
4 Substitute.
= 7 _
2 ×
7 _
4 Write the mixed numbers as
improper fractions.
= 49
_ 8 Multiply the numerators and
multiply the denominators. = 6 1 _
8 Simplify.
33. Sample answer: 1 1 _ 5 × 1 1 _
2 = 1 4 _
5 35. B; The
product must be greater than 2 _ 3 and less than 2 1 _
2 .
37. D 39. 15 _
28 41. 3 _
20 43. 28 45. 15 47. 38
_ 2 or 19 1 _
2
Pages 122–123 Lesson 2-3B
1. 3 _ 2 3. 5 _
2 5. 6 7. 2 1 _
2
99 110 horses; Sample answer: Divide the total
amount of hay on hand by the amount each horse needs per day to find the number of horses that can
be fed each day. The expression is 44 bales divided
into pieces that are 5 _ 6 foot each, use division.
8 ÷ 5 _ 6 =
8 _
1 ×
6 _
5 Multiply by the reciprocal of 5 _ 6 .
= 48
_ 5 Multiply the numerators and
multiply the denominators. = 9 3 _
5 Simplify.
There will be 9 whole pieces to use for the steps
with 3 _ 5 foot left over.
29. Sample answer: Multiplication is repeated addition. Multiplication and division are inverse operations. Multiplication is commutative and associative; division is not. 31. I 33. 5 1 _
24 35. 23 1 _
3
Pages 128–129 Lesson 2-3D
1. 1 _ 2 3. 1 _
24 5. 9 _
10
77 Sample answer: Area = base × height, so
base = area ÷ height. Divide the area by one
measurement to find the other. 3 _ 4 ÷ 1 =
3 _
4 foot
9. 3 _ 4 11. 1 _
12 13. 7 _
24 15. 1 _
24 17. 2 _
5 19. 5 _
12
2121 2 T-shirts; Sample answer: Use the table to fi nd
the amount of orange dye available, then divide
that amount by the 3 _ 8 cup needed for each shirt.
3 _ 4 cup of orange dye ÷ 3 _
8 cup for each shirt
3 _ 4 ÷
3 _
8 =
3 _
4 ×
8 _
3 Multiply by the reciprocal of 3 _ 8 .
= 24
_ 12
or 2 Simplify.
23. 8 _ 9 25. 4 _
3 or 1 1 _
3 27. Sample answer: 1 _
2 ÷ 3 _
5
29a. c _ b ; When the numerators are the same, the
quotient is a fraction of the denominators. 29b. a _
c ; When the denominators are the same, the
quotient is a fraction of the numerators. 31. D33. Yes; the shelf can hold 24 ÷ 3 _
8 or 64 cases.
35. 24 1 _ 2 37. 4
Pages 131–133 Lesson 2-3E
1. 7 3. 6
55 Sample answer: Divide the dough Jay has,
10 1 _ 2 inches, by the amount needed for each slice,
3 _ 8 inch.
10 1 _ 2 ÷
3 _
8 =
21 _
2 ÷
3 _
8
Write the mixed numbers as improper fractions.
= 21
_ 2 ×
8 _
3 Multiply by the reciprocal of 3 _ 8 .
7 4
= 21
_ 2 ×
8 _
3
Divide 21 and 3 by their GCF, 3. Divide 2 and 8 by their GCF, 2.
1 1
= 28
_ 1 or 28 slices Simplify.
7. 5 _ 12
9. 2 2 _ 3 11. 39 13. 4 1 _
26
1515 3 3 _ 4 ÷ 5 5 _
8 =
15 _
4 ÷
45 _
8
Write the mixed numbers as improper fractions.
= 15
_ 4 ×
8 _
45 Multiply by the reciprocal of 45 _ 8 .
1 2
= 15
_ 4 ×
8 _
45 Divide 15 and 45 by their GCF, 15.
Divide 4 and 8 by their GCF, 4.1 3
= 2 _
3 Simplify.
17. 2 2 _ 5 19. 13 1 _
2 ÷ 2 1 _
4 ; 6 photos
2121 Sample answer: The distance around the
kitchen, 24 2 _ 3 feet, needs to be divided by the amount
of border in each strip, 1 3 _ 4 feet.
24 2 _ 3 ÷ 1 3 _
4 =
74 _
3 ÷
7 _
4 Write the mixed numbers as
improper fractions.=
74 _
3 ×
4 _
7 Multiply by the reciprocal of 7 _ 4 .
= 296
_ 21
or 14 2 _ 21
Multiply and simplify.
They will need to have 15 strips and there will be some left over.23. Sample answer: 8 2 _
3 ÷ 3 1 _
4 25. less than;
Sample answer: Since 3 5 _ 8 > 2 2 _
5 , the quotient of
5 1 _ 6 ÷ 3 5 _
8 < 5 1 _
6 ÷ 2 2 _
5 . The expression 5 1 _
6 ÷ 3 5 _
8
represents 5 1 _ 6 being divided into a greater number
mystery. 15. 1 _ 5 , 1 to 5, or 1:5; One out of every fi ve
articles of clothing Ramona packed was a pair of jeans. 17. 24, 40
1919 a. 5 _ 16
; The Rangers have made 5 Stanley Cup
fi nal appearances for every 16 appearances made by the Canadiens.
19b. 23 _
17 ; The Maple Leafs have made 23 Stanley
Cup appearances to every 17 Bruins’ appearances.
21. 21, 24 23. 1 _ 3 ; 1:3; or 1 to 3 25. 15
27. Sample answer:
29. If the fraction is in simplest form, the GCF of the numerator and denominator is 1, and the ratio is simplifi ed. 31. G 33. D
Pages 160–162 Lesson 3-1D
1. 11 points
_ 1 quarter
3. $3 _
1 case 5. $8
77 Divide the numerator and denominator by 8 to
make the denominator 1; 40.8 gallons
_ 8 containers
÷ 8 _ 8 =
5.1 gal _
1 container
9. 60 words _
1 min 11. $0.50
_ 1 bottle
13. 340 trees; Multiply
17 by 20. 15. Mr. Brown’s homeroom sold 3 subscriptions per student while Mrs. Garcia’s homeroom sold 3.5 subscriptions per student. So, Mrs. Garcia’s homeroom sold more subscriptions. 17. Divide the time by the number of laps. Evans drove the fastest at 2.3 seconds per lap. 19a. California: 223 people/sq mi; Florida: 278.3 people/sq mi; Iowa: 53.1 people/sq mi; New Jersey: 996.3 people/sq mi; Wyoming: 5.3 people/sq mi 19b. The higher the population density, the more people in a smaller space, if the population was distributed evenly across the state.
19c. Population Density
Peop
le p
er S
quar
e M
ile
State
Calif
orni
aFl
orid
a
Iow
a
Wyo
min
g
New
Jers
ey
0
200
400
600
800
1000
2121 a. The unit rate, miles in one hour, is 2,144
_ 8 , or
268 _
1 , or 268 miles per hour.
21b. To fi nd the time, divide the distance by the rate; 560 ÷ 268 ≈ 2.09. It would take a little over two hours to travel from Columbus to New York City.
23. 32 tickets 25. B 27. $14 per CD
Pages 166–168 Lesson 3-2A
1. $28 3. 15 tsp 5. 8 pounds
77
AmericanDollars
270 27 9
Mexican Pesos
3,000 300 100
÷10
÷10
÷3
÷3
He will have $9 left.9. 3 balls 11. 285 mi 13. If 20 lb ≈ 9 kg, then 60 lb is about 27 kg. Since half of 60 is 30, a 30 lb dog weighs half of 27 kg or 27 ÷ 2, which is 13.5 kg.
1515 a. People Served 24
Liters of Soda 4
Pints of Sherbet 2
Cups of Ice 6
15b.
Number of
People
Litersof
Soda
Pintsof
Sherbet
Cups of Ice
Steps
24 4 2 6 Original amounts
12 2 1 3 To find the ingredients for 12 people, divide each item by 2.
36 6 3 9 To find the ingredients for 36 people, multiply each item by 3.
18 3 1.5 4.5 To find the ingredients for 18 people, divide each item by 2.
2 L soda, 1 pt sherbet, 3 c ice; 6 L soda, 3 pt sherbet, 9 c ice 15c. 3 L soda, 1.5 pt sherbet, 4.5 c ice; Since 18 is half of 36, half the recipe that serves 36 people will serve 18 people. 6 L ÷ 2 = 3 L, 3 pt ÷ 2 = 1.5 pt, and 9 c ÷ 2 = 4.5 c.17. No; if 5 girls and 5 boys are added, there would be 15 girls and 13 boys in the class. Using the ratio table below, you can see that there should be 12 boys for 15 girls.
1. Sample answer: Use this strategy when the change between events is the same.
33 The pattern in this exercise is the step number
multiplied by 5. So, step number 7 multiplied by 5 equals 35. 5. 60 mph 7. 1, 5, 10, 10, 5, 1 9. 25 11. 2 adults, 2 senior citizens 13. Sample answer: Suppose the doctor says you should walk every day, starting with 1 block. After every 2 days, increase the amount by 2 blocks. How many blocks would you be walking after 2 weeks? First fi nd the number of 2-day periods in 2 weeks. There are 7 increases. You start with 1 and each increase is 2, so 1 + 7(2) = 1 + 14 = 15 blocks.
Pages 175–177 Lesson 3-3A
1. no; Since the unit rates, $8 _
1 wk and
$7.43 _
1 wk , are not
the same, the rates are not equivalent.
33 yes; Since 3 h · 3 _
$12 · 3 = 9 h
_ $36
, the fractions are
equivalent; 3 h _
$12 = 9 h
_ $36
. Also, the ratios both
simplify to equal 1 _ 4 , so they are equivalent to each
other.
5. no; Micah’s unit rate is 25 push-ups
__ 1 min
and Eduardo’s
unit rate is 26 push-ups
__ 1 min
. 7. no; Since the unit rates,
4 points _
1 game and
6 points _
1 game , are not the same, the rates are
not equivalent.
99 First fi nd the unit rate for each.
$3 _
6 bagels =
3 ÷ 6 _
6 ÷ 6
= $0.50 _
1 bagel
So, the unit rate is $0.50
_ 1 bagel
.
$9 _
24 bagels =
9 ÷ 24 _
24 ÷ 24
= $0.38 _
1 bagel
So, the unit rate is $0.38
_ 1 bagel
.
Since the rates do not have the same unit rate, they are not equivalent.
11. yes; Since 15 computers · 3
__ 45 students · 3
= 45 computers
__ 135 students
, the
fractions are equivalent; 15 computers
__ 45 students
= 45 computers
__ 135 students
.
13. no; Since 16 students
_ 28 students
≠ 240 students
__ 560 students
, the ratios
are not equivalent.
1515 no; Kiera did 6 problems
_ 30 minutes
or 1 problem
_ 5 minutes
, and
Heath did 18 problems
__ 40 minutes
or 9 problems
_ 20 minutes
. Heath took
less time to do each problem. 17a. Super Saver: $0.21 per can; Shop Smart: $0.19 per can; Price Busters: $0.25 per can 17b. They should purchase the cans of lemonade from Shop Smart. At Shop Smart, the cost per can is the
cheapest. 19. Sample answers: 10 _
14 and 15
_ 21
21. $10 23. about 1,200 miles
Pages 183–185 Lesson 3-3C
1. 170 3. 90 cookies
55 120 gallons
_ 4 days
= �
_ 28 days
Write equivalent ratios.
= 120 × 7 _
4 × 7
Since 4 times 7 is 28, multiply 120 by 7.
= 840 _
28
A Clydesdale will drink 840 gallons of water in 28 days.7. $30 9. 2 min
1111 Sample answer: Since there were 20 students
who responded to the original survey and 3 of them favored science, set up equivalent ratios to fi nd the number who would favor science out of 400 students.
3 science _
20 students = �
__ 400 students
Write equivalent ratios.
= 3 × 20 _
20 × 20
Since 20 times 20 is 400, multiply 3 by 20.
= 60 _
400
Therefore, 60 students could be expected to favor science out of 400 students surveyed. 13. 28 DVDs 17. Elisa did not set up the equivalent ratios in the
correct order. She should have set it up as 1 _ 12
= x _ 276
.
There are 23 teachers at the preschool. 19. 15 people
21. C 23. 27 25. yes; Since the unit rates are the
same, 1 poster
_ 3 students
, the rates are equivalent;
12 posters
_ 36 students
= 21 posters
_ 63 students
. 27. $75 29. $2.40 per
hot dog 31. 2 _ 9 , 2 to 9, or 2:9; Every 2 out of 9 shoes
sold last week were running shoes.
Pages 188–191 Chapter Study Guide and Review
1. false; division 3. true 5. false; ratio 7. true
part as it is and change the fraction part to a fraction with a denominator of 10, 100, or 1,000. Mercury:
87 24 _
25 = 87
24 × 4 _
25 × 4
Rewrite the fraction to have a denominator of 100.
= 87 96 _
100 Multiply.
= 87.96 Read 87.96 as eighty-seven and ninety-six hundredths.
Venus:
224 7 _ 10
= 224.7 Read 224.7 as two hundred twenty-four and seven tenths.
Mars:
686 49 _
50 = 686
49 × 2 _
50 × 2 Rewrite the fraction to have a
denominator of 100. = 686 98
_ 100
Multiply.
= 686.98 Read 686.98 as six hundred eighty-six and ninety-eight hundredths.
27. 1 _ 4 , 0.25 29. Sample answer: 7 _
12 = 0.58
− 3 31. C
33. 0.333… or 0. −
3 35. 0.8181… or 0. −−
81
Pages 212–213 Lesson 4-2B
1. 3 _ 20
3. 33 _
100 5. 3 _
4 7. 23
_ 50
9. 7 _ 50
1111 Write the percent number as a fraction with a
denominator of 100 and then simplify the fraction if necessary.
2% = 2 _
100 Definition of percent
= 1 _ 50
Divide the numerator and denominator by the GCF, 2.
13. 1 _ 5 15. 43
_ 50
17. 1 _ 25
19. 18 _
25 21. 7 _
25 23. 27
_ 50
2525 Eighty-two percent of the students use the
Internet at home, so 100% - 82%, or 18%, use the Internet elsewhere.
18% = 18 _
100 Definition of percent
= 9 _ 50
Divide the numerator and denominator by the GCF, 2.
27. Sample answer: 11 _
20 = 55
_ 100
or 55%, 3 _ 5 = 60
_ 100
or
60%, 7 _
10 = 70
_ 100
or 70% 29. Sample answer: I received
a 95% on my science test. What fraction of the
problems did I get correct? 19 _
20 31. H 33. 0.75
35. 73 _
100 37. 11 7 _
50
Pages 215–217 Chapter 4-2C
1. 25%
33 3 _ 20
= 3 × 5 _
20 × 5 = 15
_ 100
or 15%
5. 90% 7. 30% 9. 30% 11. 44% 13. 72%
1515 Two sections out of the 10 sections are shaded.
Write 2 out of 10 as a fraction, 2 _ 10
. Since 10 × 10 gives
a denominator of 100, multiply both the numerator
and denominator by 10 and write the fraction as 20 _
100 .
Write the fraction as a percent, 20%. 17. 70% 19. 90% 21. 70% 23. 36%
2525 From the tally marks, you know that 20 students
were surveyed, 16 did not prefer uniforms, and 4 students preferred uniforms. Write each preference as a fraction with a denominator of 100 and then write that fraction as a percent.
16 _
20 = 16 × 5
_ 20 × 5
= 80 _
100
= 80%
4 _ 20
= 4 × 5 _
20 × 5
= 20 _
100
= 20% The sum of the percents, 80% + 20%, is equal to 100%.
0.9% = 0.009 Write 0.9% as a decimal. 0.9% of 1,000 = 0.009 × 1,000 Write the multiplication
problem. = 919. 336 21. 0.45
2323 Find 20% of $42. 20% = 0.2 Write 20% as a decimal.20% of 42 = 0.2 × 42 Write the multiplication problem. = 8.4The amount off during this sale was $8.40.25. 95 27a.
Test NumberCorrect Score Total
Math 68 80% 85
Science 63 90% 70
27b. science 27c. 48 29. Yes; 16% of 40 is 6.4 and 40% of 16 is 6.4. 31. Sample answer: Any number that can be written as a fraction can be expressed as a decimal or a percent. 33. About 135 cars; round 28% to 0.3 and multiply by 450. 35. Sample
answer: $30 37. = 39. 3 1 _ 4 , 3 1 _
3 , 5 3 _
4 41. 8%
43. 252%
Pages 252–253 Lesson 4-4E PSI
1. Sample answer: when there is a way to solve the problem in which you can arrive at the answer by using simpler numbers 3. $5 5. 400 pieces 7. 6 mi
99 Sample answer: To fi nd the amount of tax,
multiply the tax rate times the cost of the item. 6.75% × $350 = 0.0675 × 350 Write 6.75% as a decimal.
= 23.63 Multiply.She will pay about $23.63 in tax.11. 4.5 times 13. 21 stickers
33. Sample answer: They prescribe the order to use to simplify expressions containing more than one operation. It ensures that there is only one correct answer. 35. G 37. Sample answer: He should have multiplied 5 and 3 before adding 3 and 9; 24.
pay is 77% of what he earns. (100% - 23% is 77%.)0.77(13.50h)
= 0.77(13.50 × 40) Replace h with 40.= 0.77(540) Multiply 13.50 by 40.= 415.8 Multiply 0.77 by 540.
His earnings will be $415.80 after taxes. 47. yes; 30 49. B 51. I 53. 9d and 2d are like terms. 55. 9k and 3k are like terms. 57. 4c and 3c are like terms. 59. 14x, 7x, and 3x are like terms.
Pages 284–285 Lesson 5-1D
1. m = money Elliot saved; 4m3. = the length of the box; − 4
5. d = cost of one drink; 3d + 3.507. a = the number of apples; 4a
99 t represents Tracey’s age. Less than means to
subtract. Therefore, t - 6 represents six years less than her age.11. p = the number of points the Panthers scored; 1 _
3 p
or p ÷ 3 13. j = the cost of James’s dinner; j - 5
1515 s represents the number of members in the
Senate. The number of representatives in the House of Representatives is defi ned by 4s + 35.17. Sample answer: She is indicating a number less than 5; 5 - n is the correct expression. 19. Sample answer: 7 more songs, 2 fewer songs, 4 times the songs, and half the number of songs. 21a.
1. Sample answer: Using the act it out strategy, it is easier to determine the reasonableness of an answer.
33
Team 1 Team 2 Team 3 Team 4
Student1
Student2
Student3
Student4
Student5
Student6
Student7
Student8
Student9
Student10
Nate
Nate will be on Team 3.5. 5 students 7. 6 9. about 5 times 11. 120 words
Pages 291–293 Lesson 5-2A
1. yes; Associative Property
33 72 - (63 - 8) (72 - 63) - 8 72 - (55) (9) - 8 17 ≠ 1 no; The fi rst expression is equal to 17 and the second is equal to 1. 5. no; The fi rst expression is equal to 16 and the second is equal to 4. 7. Sample answer: (12 + 24) + 6 and 12 + (24 + 6) 9. yes; Associative Property 11. no; The fi rst expression is equal to 11 and the second is equal to 21. 13. yes; Associative Property 15. no; The fi rst expression is equal to 9 and the
nssecond is equal to 1. 17. no; The fi rst expression is
equal to 32, not 0. 19. (4 1 _ 2 + 5 1 _
2 ) + 6 = 16 in.
2121 75,000 · 5 and 5 · 75,000; Use the Commutative
Property that states the order of the numbers does not change the product when multiplying. So, 75,000 people times 5 days and 5 days times 75,000 people both have the same product. 23. y + 5 25. b + 4 27. 8n 29. 36w 31. 36k
3333 17 + x = 3 + 17 Write the original equation.
17 + x = 17 + 3 Commutative Property of Additionx = 3
35. 0 37. False; using the order of operations, (18 + 35) · 4 = 212 and 18 + 35 · 4 = 158. 39. Sample answer: For each operation the identity elements are numbers that combine with other numbers without changing the value of the other numbers. The additive identity is zero (0). The multiplicative identity is one (1). 41a. (2 × 7) × 6 and 2 × (7 × 6) 41b. $84; Sample answer: I knew that 6 × 7 = 42 and double 42 is 84. 43. Identity Property of Addition 45. Identity Property of Addition 47. Identity Property of Multiplication
= 21 + 5.6 Multiply mentally within the parentheses.
= 26.6 Add.
1313 Distance is equal to rate multiplied by time.
Therefore, a coyote can run 43(6) miles in 6 hours and a rabbit can run 35(6) miles in 6 hours. The difference between the two distances can be written 43(6) - 35(6). Rewrite the expression using the Distributive Property: (43 - 35) × 6. Simplify within the parentheses: 8 × 6 equals 48. Therefore, a coyote can run 48 miles farther in 6 hours than a rabbit can. 15. 6x + 66 17. 4x + 8 19. 0.37; Sample answer: 0.1(3.7) = 0.1(3) + 0.1(0.7) = 0.3 + 0.07 = 0.37 21. Sample answer: The friend did not multiply 5 and 2. The expression 5(x + 2) = 5x + 10. 23. F25. 8 days 27. b = price of a book; b × 3 29. 4
Pages 302–305 Chapter Study Guide and Review
1. true 3. false; equivalent 5. false; seven times x 7. 30 9. 7 11. 3 × 5 + 7; 22 motorcycles 13. 54 15. 26 17. 456 19. 144 tiles 21. c represents the cost of renting a video game; c + 3 23. m represents the amount of memory that is music;
m + 0.5 25. 25 s 27. no; The fi rst expression is
equal to 8 and the second is equal to 1 _ 8 . 29. no;
The fi rst expression is equal to 17, not 1. 31. 14 +
Try 45. 700 - d = 665 700 - 45 � 665 655 ≠ 665Try 40. 700 - d = 665 700 - 40 � 665 660 ≠ 665Try 35. 700 - d = 665 700 - 35 � 665 665 = 665Therefore, there are 35 fewer students this year.37. Sample answer: m + 8 = 13 39. True; m + 8 is not equal to any specifi c value, so there are no restrictions placed upon the value of m. 41. Sample answer: Curtis has 12 more baseball cards than Juan. Curtis and Juan have a total of 30 baseball cards. Solve the equation a + 12 = 30 to fi nd the number of baseball cards that Juan has. 43. 7 45. 4 × 14 = 56; Each side is 14 units.
Pages 318–319 Lesson 6-1B PSI
1. Sample answer: Start with the answer that you found and then work forward to see if you arrive at the number you were given in the problem. 3. 6:55 a.m.
55 To use the work backward strategy, begin with the
fi nal answer and do the opposite of each operation
R01_R39_EM_SelAns_895129.indd R12R01_R39_EM_SelAns_895129.indd R12 1/19/10 8:46 AM1/19/10 8:46 AM
Selected Answers and Solutions R13
Selected Answers and Solutions
For Homework Help, go to Hotmath.com
but in reverse order. 18 was the fi nal answer. Six had been added to it, so subtract 6 from 18 and get 12. The original value had been multiplied by 4, so divide 12 by 4 to fi nd the original value. It was 3. 7. 127 pictures 9. 17 rungs 11. 8 13. 37 spaces
Pages 324–326 Lesson 6-1D
1. 2
33 Solution:
c + 3 = 6 Write the equation. - 3 = - 3 Subtract 3 from each side.c = 3Check: c + 3 = 6 Write the equation.3 + 3 6 Replace c with 3. 6 = 6 The equation is true.5. x + 7 = 19; 12 m 7. 3 9. 7 11. 2 13. 5 15. 5
1717 The length of a Black Mamba plus 22 inches is
118 inches. Let � represent the length of a Black Mamba.� + 22 = 118 - 22 - 22
� = 96So, a Black Mamba is 96 inches. 19. 15.4 = x + 4.9; 10.5 ft 21. 0.3
2323 Solution:
7.8 = x + 1.5 Write the equation.- 1.5 = - 1.5 Subtract 1.5 from each side. 6.3 = xCheck:7.8 = x + 1.5 Write the equation.7.8 6.3 + 1.5 Replace x with 6.3.7.8 = 7.8 The equation is true.25. 1 _
2 27. Sample answers: 56 = 44 + x; 36 = 24 + m
29. Sample answer: Nicholas added $5 to his savings account. He now has $87. How much money did he originally have? 31. G 33a. 15 + b = 24; b = 9 33b. Sample answer: Wes could have had 3 land on the board for 3 points and 2 went through the hole for 6 points. 35. 8 37. 3
Pages 330–331 Chapter 6-1F
1. 14 3. 12 5. s - 20 = 45; 65 min 7. 6
99 Solution:
1 = g - 3 Write the equation.+ 3 = + 3 Add 3 to both sides. 4 = gCheck:1 = g - 3 Write the equation.1 4 - 3 Replace g with 4.1 = 1 The equation is true.11. 9 13. 15 = v - 12; 27 votes 15. 21 17. 3.4
19. 1 21. 10 _
9 or 1 1 _
9
2323 x represents the amount she gave the cashier.x - (24 + 13 + 16 + 3) = 4 x - 56 = 4 Add the amounts in the parentheses. + 56 = + 56 Add 56 to both sides. x = 60 Alejandra gave the cashier $60.25. Sample answer: I have d dollars. After paying my sister $32, I have $64 left. How much money did I have to start with? 27. H 29. 3:05 p.m.
Pages 337–338 Lesson 6-2B
1. 3 3. 2 5. 18x = 90; 5; To check, multiply 18 by 5. The result should be 90. 7. 4 9. 3
1111 Solution:
4g = 24 Write the original equation.4g
_ 4 = 24
_ 4 Divide both sides by 4.
g = 6Check: 4g = 24 Write the original equation. 4(6) 24 Replace g with 6. 24 = 24 The equation is true.13. 2 15. 4e = 58; $14.50 17. 2 19. 9 21. 1 _
2
2323 a. p = the number of points Blanda scored
each year.26p = 2,002 Write the original equation.26p
_ 26
= 2,002
_ 26
Divide both sides by 26.
p = 77 George Blanda averaged 77 points each year.23b. p = the number of points Johnson scored each year.16p = 1,736 Write the original equation.16p
_ 16
= 1,736
_ 16
Divide both sides by 16.
p = 108.5Norm Johnson averaged 108.5 points each year.25. 4b = 7; The solution for the other equations is 4. 27. Sample answer: Jacob bought four T-shirts for $24 at a souvenir shop. How much did each T-shirt cost? 29. I 31. 5 33. 7 35. 500 min.
Dividing by 3 is the same as multiplying by 1 _ 3 .
35. A 37. H 39. 10 41. a - 3 = 11; 14 yr
43. 21 45. $29
Pages 348–351 Lesson 6-3B
1. 4
33 Solution:
9k - 4 = 32 Write the original equation. + 4 = + 4 Add 4 to each side of the equation. 9k = 36 Simplify.
9k _ 9 =
36 _
9 Divide both sides by 9.
k = 4 Simplify.Check: 9k - 4 = 32 Write the original equation. 9(4) - 4 � 32 Substitute 4 for k. 36 - 4 = 32 Simplify. 32 = 32 This equation is true.5. 7 7. 18x - 9 = 171; 10 h 9. 8 11. 7 13. 515. 15x + 89 = 149; 4 wk 17. 3.1 19. 1.98 21. 4.2
2323 games + shoes = total cost
g represents the number of games, so $3.00g is the
cost of g games.3.00g + 3.50 = 15.50 Write the original equation. - 3.50 = - 3.50 Subtract 3.50 from each side. 3.00g = 12.00 Simplify.
3.00g
_ 3.00
= 12.00
_ 3.00
Divide each side by 3.00.
g = 4You can bowl 4 games.
2525 current temp + increase = new temp
h represents the number of hours, so 2.5h is the increase during those hours. 62.8 + 2.5x = 75.3 Write the original equation.- 62.8 = - 62.8 Subtract 62.8 from each side. 2.5x = 12.5 Simplify.
2.5x _ 2.5
= 12.5
_ 2.5
Divide each side by 2.5.
x = 5It will take 5 hours for the temperature to reach 75.3 degrees.27. 45 29a. Sample answer: Anita had $15 and spent all of it on 2 bracelets and a necklace. If the necklace was $7, how much were each of the bracelets?29b. $15
x x 7
29c. $4 29d. Only one number makes a true sentence when it replaces the variable. 31. Sample answer: Five more than three times a number is 29. 33. Addition; since the variable is being multiplied fi rst and added second, the opposite would be to undo addition and then undo multiplication. 35. 12 represents the cost per hour, x represents the unknown number of hours, 35 represents the fl at rate, and 95 represents the total spent. 37. C 39. add 8; divide by 3 41. 77 43. 45 45. 56 47. x - 3 = 14; x = 17 inches 49. 18 51. 31 53. 15
3 units to the right. You do not need to move any units up or down. Draw a dot and label it M.
6–13. y
xO
123456789
1 2 3 4 5 6 7
Q
M
R
L
N
PA
B
1515 a. (5, 20), (5 1 _ 4 , 21) , (5 1 _
2 , 22) , (5 3 _
4 , 23)
15b. The points appear to fall on a line.
y
x
161718192021222324
5 6
(5, 20)(5 , 21)1
4
(5 , 22)12
(5 , 23)34
17. Sample answer: Laureen earned $7 an hour tutoring. Make a table showing the relationship between the number of hours she tutors and the amount of money she earns.
Hours AmountEarned ($)
1 7
2 14
3 21
19. Sample answer: The point (3, 2) is 3 units to the right of the origin on the x-axis and 2 units up the y-axis. The point (2, 3) is 2 units to the right on the x-axis and 3 units up the y-axis. 21. D
1. multiply the position number by 2; 2n; 30 3. 2x + 1
55 Position Add 9 Value of Term
3 3 + 9 12
4 4 + 9 13
5 5 + 9 14
6 6 + 9 15
n n + 9 n + 9
Add 9 to the position number; n + 9;therefore, the twelfth term is 21.7. multiply the position number by 5; 5n; 60 9. Sample answer: This is a geometric sequence. Each term is found by multiplying the previous term by 3; 486, 1,458, 4,37411a. The amount increases by $8. 11b. 8x + 5 13. add 12; 52, 64 15. add 2.4; 11.1, 13.5
19b. The equation for the money spent t on lunch for d days is y = 5x. 21a. y = x · x or y = x2
21b. y
xO
2
4
6
8
1 3 5 7 9 102 4 6 8
10
1
3
5
7
9
21c. No; the graph is curved; it does not form a line.
25. y = x _ 2 - 3 27. C 29. Sample answer: The
graph could represent the growth of a tree.
Pages 391–393 Chapter 7-1F
1a. t = 3n 1b. Number of Lunches, n
1 2 3
Total Cost ($), t 3 6 9
1c. y
xO
2
4
6
8
1 3 5 7 9 102 4 6 8
10
1
3
5
7
9
(1, 3)
(2, 6)
(3, 9)
1d. The graph is a line because each ticket costs $3.
33 a. Use v = 400d because 400 multiplied by the
number of days will give you the total amount of vegetation eaten.
3b. Number of Days, d 1 2 3
Pounds Eaten, v 400 800 1,200
3c. y
x
400
800
1200
1 2 3
200
600
1000
1400(3, 1,200)
(2, 800)
(1, 400)
Number of Days
Poun
ds E
aten
3d. The graph is a line because with each day, the amount of vegetation increases by 400.5a. Music Man: t = 45n; Road Tunes: t = 35n; where t represents the total cost and n represents the number of hours 5b. The Music Man; The Music Man charges more.
9. straight line; Sample answers: (0, 0), (1, 1), and (2, 2) 11. Sample answer: Cable Company A charges a $50 start-up fee and $60 a month. Cable Company B doesn’t charge a start-up fee, but charges $70 a month. You could use a graph to see how many months it would take before Company A would become cheaper. 13. c = 25 + 2m 15. p = 2m + 5s17.
Feet Yards
3 1
6 2
9 3
12 4
3n n ; 12 ft
Pages 398–399 Lesson 7-2B
1. 7 3. no 5. Friday and Saturday 7. 8 9. 0
1111 t - 7 < 10 Write the inequality. 28 - 7 < 10 Replace t with 28. 13 < 10 Simplify.Since 13 is not less than 10, 28 is not a solution.13. no
1515 Month Number
of Texts t > 55True or
False
January 56 56 > 55 True
February 57 57 > 55 True
March 55 55 > 55 False
April 51 51 > 55 False
She went over her limit of text messages in January and February.
17. true; 112 _
8 + 2 ≥ 15 + 4(2) - 7, so 16 ≥ 16 19. A
21a. h = 5w
21b. Weeks(w)
Hours (h)
1 5
2 10
3 15
21c. y
x
3
6
9
12
1 2 3 4 5
15
(1, 5)
(2, 10)
(3, 15)
Hour
sWeeks
Pages 400–401 Lesson 7-2C PSI
1. Sample answer: when you are trying to fi nd the solution of an equation 3. 5 problems worth 2 points each and 2 problems worth 4 points each5. 8 quarters, 1 dime, 1 nickel, and 5 pennies 7. Sample answer: 7 and 13
99 Use the guess, check, and revise strategy for this
exercise. Remember to use the order of operations. 3 × 4 + 6 ÷ 1 = 18; (3 × 4) + (6 ÷ 1) = 12 + 6 = 18
11. 31 students;
40
? 9
3rd grading period
13. Sample answer: The sum of four coins is thirty-two cents. What are the coins? To solve this problem, choose any four coins and fi nd their sum. Then check to see if the sum is thirty-two. If not, choose another four coins and check the answer. Repeat this process. The answer is a quarter, a nickel, and two pennies.
nsThen 3x is the number of pounds gained each month. 163 + 3x > 178 Write the inequality.-163 -163 Subtract 163 from both sides. 3x > 15 Simplify.
3x _ 3 >
15 _
3 Divide both sides by 3.
x > 5It will take him greater than 5 months.23. Sample answer: 2x + 2 ≥ 1625. x ≥ 3
2 30 1 4 5 627. 42529. f > 3
2 30 1 4 5 6
31. x ≥ 3 2 30 1 4 5 6
33. C and I or G and L
Pages 421–422 Lesson 7-3B
1. 15 3. 245.
5-5 -4 3 421-3 -2 -1 0
7. 5 9. 28 11. 45
1313 Spending money means a loss, so the integer
would be -25. 15. -217.
12-12 -8 84-4 0
19.
-10-12-14 -8 -6 4 6 8 102-4 -2 0
21. 12 14-12 -8 84-4 0
23. 18 25. 25
2727 ⎪-15⎥ + ⎪-6⎥ = 15 + ⎪-6⎥ Absolute value of -15 is 15.= 15 + 6 Absolute value of -6 is 6.= 21 Add.
29. 30 31. -3 33. 14
3535 The absolute value of -230°F is 230. The
absolute value of 70°F is 70. 70 < 230, so 70°F has the lower absolute value.37. Never; distance cannot be negative. 39. Absolute value is distance and distance cannot be negative. 41. F 43. x < -5
-8 -7 -6 -5 -4 -3 -2
Pages 425–427 Lesson 7-3C
1. H 3. B 5. (0, -2); none 7. gym
9–11. y
xO
21
345
21 3 4 5-5-4-3-2-1-1-2-3-4-5
(-3, 3)
(2, 1)
(0, -1)
13. U 15. S 17. J
1919 The coordinates for point C are (5, 0). Since the
point lies on the x-axis, it is not in any of the quadrants. 21. (3, -5); IV 23. (5, 4); I
24–29.
O
21
345
21 3 4 5-5-4-3 -1-1-2-3-4-5
-2
(-1.5, 2.5)
(5, -2)
(1, 2)
(-4, -1)
(-2, -5)
(0, 0)
(-3, 4)
4 , -1 34
14
2 , -2 12
12
31–33. y
x
21
345
21 3 4 5-5-4-3 -1-1-2-3-4-5
(-1.5, 2.5)
-2
2 , -2 12
12
4 , -1 34
14
3535 The length of the base AB is 4 units. The length
of the height AC is 3 units. Use the formula to fi nd the area of the triangle.
37. Quadrants II and IV; Sample answer: In both Quadrants II and IV, the coordinates have different signs. 39. Sample answer: The fi rst coordinate tells the location of the point to the left or right of the y-axis and the second point tells the location of the point above or below the x-axis. The coordinates of a point defi ne its unique location. Any given point is defi ned by only one ordered pair. 41. G 43. -3
Pages 428–433 Chapter Study Guide and Review
1. true 3. true 5. false; x > 7
6–8. y
xO
2
4
6
8
1 3 5 7 9 102 4 6 8
10
1
3
5
7
9
X (5, 0)
Y (4.75, 6)
Z(2, 8 )12
9. (11, 5), (12, 5.5), (11.5, 5.25), (12.5, 5.75); They appear to form a line.
y
xO
1
2
3
4
6
7
10 12 142 4 6 8
5(11, 5) (11.5, 5.25)
(12.5, 5.75)(12, 5.5)
11. Input (x) 3x + 1 Output
1 3(1) + 1 4
3 3(3) + 1 10
7 3(7) + 1 22
13. Input (x) 2x + 4 Output
5 2(5) + 4 14
6 2(6) + 4 16
7 2(7) + 4 18
15. 2x 17. Multiply each term by 8; 12,288, 93,304
19. y = 7x + 1 21. y = x - 12
23. y = 16x Batches ofPretzels (x) Butter (y)
1 16
2 32
3 48
25. no 27. 27 small cars 29. p ≤ 45
31. 108 9 11 12 13 14
33. x > 3
10 119876543210
35. 4g ≤ 12; g ≤ 3
37. x ≥ 8
10 119876543210
39. 65 7-7 -6 -5 -4 3 421-3 -2 -1 0
41. 6 43. 16 45. 21 47. 5 49. (-4, 3)50–53.
x
y
(-2, 4)
(-3, -2)
(4, 1)
(2, -1)
Chapter 8 Properties of Triangles and Quadrilaterals
Page 440 Are You Ready?
1. 46 3. 58 5. 19 7. 58 9. 181 11. yes
Pages 443–445 Lesson 8-1A
1. plane; plane JKL p
33 no; Line segment TV measures 8 millimeters and line segment RS measures 13 millimeters so the line segments are not congruent. 5. intersecting 7. intersecting 9. plane; plane RST
1111 line; � EF or � FE ; The fi gure shown is a line that continues in both directions so it must be a line. It can be labeled as either � EF or � FE . 13. line segment;
−−− LM or
−−− ML
15. no 17. yes 19. intersecting 21. parallel
2323 Sample answer: � AC is parallel to � DF because
the lines are the same distance apart and do not intersect. � AC and � BE are perpendicular because the lines intersect to make a right angle. 25. Intersecting; since they are lines, they extend forever. These lines eventually intersect. 27. Sample answer: Line segment
nsline � �� AB continues in both directions without ending. 29. F 31. Sample answer: Both are similar in that they meet or cross at a point. The difference between the two is that perpendicular lines make a right angle where they meet or cross.
Pages 448–450 Lesson 8-1B
11 Using a protractor, the angle measures 137°.
Since this angle is between 90° and 180° it is an obtuse angle. 3. 180°; straight 5. 20°; acute 7. 163°; obtuse 9. 115°; obtuse
1111 Using a protractor, the angle of the roof
measures 120°. Since this angle is between 90° and 180° it is an obtuse angle.
1313 Using a protractor, the angle of the exit sign
measures 90°. Since this angle is exactly 90° it is a right angle. 15. 115° 17. 60° 21. ∠X and ∠Y have the same measure, but ∠X looks bigger because the rays are longer. 23. Sample answer: First, align the center of the protractor with the vertex of the angle. Next, make sure one side of the angle passes through zero on the protractor. Last, use the scale where the fi rst side of the angle crosses 0°. 25. obtuse 27. Sample answer: You can estimate using fraction circles to compare the angle to the fraction circles. If the angle is the same
as the 1 _ 4 fraction circle, it is a right angle. If it is less
than this fraction circle, it is an acute angle. Anything greater is an obtuse angle.29.
31.
33.
35.
Pages 453–456 Lesson 8-1C
1. supplementary 3. complementary
55 30° + x° = 180° - 30 = - 30
x° = 150°
So the value of x is 150. 7. 70 9. supplementary 11. complementary pp
1313 85° + 95° = 180°
Since the sum of their measures is 180°, the angles are supplementary. 15. 88 17. 155 19. 3521. Sample answer: If the measure of ∠1 is 50°,
what is the measure of ∠2? 23. 115° 25. vertical angles 27. vertical angles 29. Always; Sample answer: Vertical angles are congruent. 31. Never; Sample answer: Since an obtuse angle is greater than 90°, the sum of two obtuse angles must be greater than, not equal to, 180°. g
3333 a. 25; Since x° and 65° are complementary, their
sum will equal 90°. So, 90° - 65° = 25°. The value of x is 25. 33b. 60; Since y°, x°, 65°, and 30° are supplementary, their sum will equal 180°. y° + 25° + 65° + 30° = 180° y° + 120° = 180° - 120 = -120 y° = 60°The value of y is 60.33c. Two; Sample answer: The 65° angle and the angle labeled x° are complementary and the 30° angle and the angle labeled y° are complementary. 35a. Sample answer: an obtuse angle 35b. a right angle 35c. no, two acute angles will never add up to 180° because each acute angle, by defi nition, has a measure that is less than 90°. Two angles that are both less than 90° will never add up to 180°. 37. The measures of the two angles must be equal. If two angles are supplementary to the same angle, say x°, then each angle has a measure of (180 - x)° and thus have the same measure themselves. 39. 95 41. adjacent 43. neither 45. adjacent47. Sample answer:
21
Pages 461–463 Lesson 8-2B
1. obtuse 3. scalene
55 60 + 73 + x = 180 133 + x = 180 - 133 = - 133 x = 47So the value of x is 47. 7. 120 9. obtuse 11. acute
2323 29 + 62 + x = 180 91 + x = 180 - 91 = - 91 x = 89 So the measure of the third angle is 89°.25a. right triangle 25b. by the fl agpole 27. Sample answer: If you know the length of the sides of a triangle, you can determine if any lengths
R01_R39_EM_SelAns_895129.indd R22R01_R39_EM_SelAns_895129.indd R22 1/19/10 8:47 AM1/19/10 8:47 AM
Selected Answers and Solutions R23
Selected Answers and Solutions
For Homework Help, go to Hotmath.com
are congruent to classify the triangle. If you know the angles of the triangle, since two angles are acute, you can use the third angle to classify the triangle. 29. F 31. B 33. Sample answer: The set of measures cannot form a triangle because 12 + 13 is less than 26 and the theorem states that the sum must be greater than the sum of both sides. 35. Sample answer: The set of measures cannot
form a triangle because 3 1 _ 2 + 4 1 _
4 is less than 8 3 _
4 and
the theorem states that the sum must be greater than the sum of both sides.
Pages 464–465 Lesson 8-2C
1. Sample answer: He drew a diagram to solve the problem because the diagram allowed him to visualize the garden and understand the information. 3. 5 ways 5. 450 ft2, 388 ft2, 388 ft2 7. 12 ways 9. 4.6 cm
4.6 cm4.6 cm
11. $76.95 1313 For each table, there would be a
balloon on each corner and one on each side. The table is square so there would be 4 balloons on the corners and 4 on the sides. Each table would have 8 balloons. If there are 4 tables with 8 balloons on each table, she would need 32 balloons.
Pages 470–473 Lesson 8-3B
1. quadrilateral 3. square 5. 97 q
77 The railing of the steps has opposite sides that
are parallel and congruent. The opposite angles are congruent so it must be a parallelogram. 9. square 11. trapezoid 13. trapezoid 15. 133 17. 117
25. Sample answer: A book is shaped like a rectangle. It has four right angles. 27. Sample Answer: A trapezoid has bottom or base angles that are congruent. An isosceles trapezoid is an isosceles triangle whose top has been cut off parallel to its base.
29. Sample answer: The kite has two pairs of adjacent congruent sides. It also has one pair of opposite angles that are congruent. 31. sometimes 33. never 35. yes; sample answer:
37. C 39. G 41.
in.1 34in.1 3
4
in.1 34
43. 60 45. complementary 47. supplementary 49. 90°; right
Pages 476–479 Lesson 8-3C
11 The fi gure is a polygon because no sides cross,
it is a closed fi gure, and it has no curved sides. Since there are 8 sides connecting, it is called an octagon. 3. 1,620° 5. 135° 7. yes; pentagon 9. yes; pentagon 11. No; the fi gure is not closed.
1313 Draw all of the diagonals from one vertex as
shown and count the number of triangles formed.
Find the sum of the angle measures in the nonagon.7 × 180 = 1,260°So, the sum of the angle measures of a nonagon is 1,260°.
15. 3,600° 17. 140° 19. triangles and pentagons
2121 A decagon has 10 sides. Since it is a regular
decagon, each side is equal. To fi nd the perimeter, we can multiply 10 times the length of each side,
ns3.2 centimeters. So the perimeter is 32 centimeters. 23. 1,080° 25a. octagon 25b. 1,080°
25c.
27. Sample answer:
29. Sample answer: A regular polygon has all sides and angles congruent. A polygon that is not regular has different side lengths, different angle measures, or both. To fi nd the interior angle measure of a regular polygon, subtract 2 from the number of sides, multiply the result by 180, then divide that number by the number of angles. 31. D 33. 2160 35. Sample answer: ∠4 = 124°; ∠5 = 108°; ∠6 = 128° 37. Sample answer: The sum of the exterior angles of all the triangles is 360°
Pages 483-485 Lesson 8-3D
1. congruent
33 The fi gures do not have the same size or shape
so they are neither congruent nor similar. 5. −−
ST 7. similar 9. similar 11. neither 13. similar
1515 Corresponding sides represent the same side of
similar fi gures. So, −−
DE corresponds to −−
KL .17. −−
LN 19. similar 21. not similar 23. not similar25. 132 ft; 112 ft
2727 Use equivalent ratios to solve this problem.
12 _
8 = 21
_ x
× 1.75
× 1.75 So the value of x is 14.29. Sample answer: Triangle JKL is similar to
triangle TUV.
Parallelogram DEFG is congruent to parallelogram QRST.
31. Sample answer: The fi gure will have exactly the
same size and shape. Corresponding angles will have the same measure and corresponding sides will have the same length. 33. H 35. 80 37. 47°
Pages 492–495 Lesson 8-4B
1. y
x
′ ′
′′
33 The fi gures do not have the same shape and
size. They are not congruent. W and Z were moved 4 units down and 5 units to the right, and X and Y were moved 3 units down and 5 units to the right.
5. y
x
′′
′
′
7. y
x
′
′
′
′
99 The fi gures do not have the same shape and
size. They are not congruent. A was moved 2 units down and 3 units to the right, but B was moved 2 units down and 4 units to the right. 11. (-1, 1), (-1, -6), (6, 1), (6, -6) 13. E(5, 4), F(7, 4), G(7, 0), H(5, 0) 15. M(-6, -2), N(-4, -2), O(-4, -4), P(-6, -4) 17. Sample answer: There are two main images, stars and triangles. Both are translated over different parts of the egg. These translations allow for the tessellations of both the stars and the triangles on the egg.
23. 6 possibilities; (1, -4), (2, -4), (3, -4), (-1, -4), (-2, -4), (-3, -4) 25. The triangle was translated 6 units left and 3 units down.; (-6, -3) 27. The triangle was translated 5 units left and 1 unit up.; (-5, 1) 29. Sample answer: First fi nd the new coordinates of rectangle Q′R′S′T′ by adding 7 to each x-coordinate and subtracting 4 from each y-coordinate. Then graph rectangle QRST and rectangle Q′R′S′T′ on the same coordinate plane.31. I 33. A′(-5, -2), B′(-4, 2), C′(0, 2), and D′(1, -2)
Pages 498–501 Lesson 8-4C
11 y
x
′
′
′
′
Q′(-2, -4), R′(4, -1), S′(-1, 0), T′(-3, -2)
3.
5. y
x′
′
′
R′(-3, -1), S′(-2, -3), T′(2, -3)
7. y
x′
′
′
′
W′(-4, -2), X′(1, -4), Y′(2, -2), Z′(-3, 0)
9. y
x′
′
′
X′(1, 0), Y′(2, -4), Z′(3, -1)
1111 y
x
′
′
′
′
P′(-3, -2), Q′(-3, 4), R′(-5, 6), S′(-5, 0)
13.
15.
17.
19. The fi gures do not have the same shape and size. They are not congruent. S was refl ected over the y-axis and the distance from the y-axis did not change, but the refl ection of T was 1 unit up from the original fi gure.
27. neither 29. Sample answer: E, H, I31. Sample answer: When an image is refl ected over the x-axis, the y-coordinates of the vertices are opposites. When an image is refl ected over the y-axis, the x-coordinates of the vertices are opposites. 33. F 35. y
x
′
′
′
′
37. neither
Pages 504-506 Lesson 8-4D
1.
x
y
′′
′
A′(0, 0), B′(0, -3), C′(-3, 0)
3.
x
y
′ ′
′
A′(0, 0), B′(3, 0), C′(0, -3)
55 The sun can be rotated and still look like it
does in its original position so it has rotational symmetry. The sun matches itself at 45°, 90°, 135°, 180°, 225°, 270°, and 360°.
A = 8 · 9 Replace b with 8 and h with 9. A = 72 cm2 Multiply.11. 180 in2 13. 8 ft 15. 166 1 _
2 ft2 17. 227 ft2
1919 No;
A = bh Area of parallelogram20,000 = 250 · 70 Replace b with 250 and h with 70.20,000 ≠ 17,500 Multiply.Since 17,500 square feet is less than 20,000 square feet, the height cannot be 70 feet. It must be greater than 70 feet.
21. Sample answer:
10 in.
5 in. 50 in2
23. Sample answer:
28 ft
7 ft196 ft2
25. 5 in. 27. 17.5 in2 29. The rectangle; the area of the rectangle is 5y units2. The area of the parallelogram cannot be greater than 5y units2 since
A = 747 Multiply.The area of the triangle is 747 square feet. 13. 19 cm 15. 4,853.52 ft2
1717 a. A = 1 _ 2 bh Area of triangle
A = 1 _ 2 (5)(n) Replace b with 5 and h with n.
A = 5n _ 2 Multiply.
The expression is 5n _ 2 .
17b. y
xO
63
91215182124
3027
1 3 5 7 92 4 6 8 10
(2, 5)
(4, 10)
(6, 15)
(8, 20)
17c. The points appear to form a line.
19. The formula is 1 _ 2 bh, not bh.
100 = b · 20 _
2
b = 10 m21. Sample answer:
12 cm
4 cm
12 cm
8 cm
Area of fi rst triangle is 24 cm2; Area of second triangle is 48 cm2; 1:2
or 1 _ 2 .
23. 40 25. B 27. 20 m2 29. 38.76 cm2
Pages 537–539 Lesson 9-1D
1. 90.4 ft2 3. 112 m2 5. 161.5 ft2
77 A = 1 _ 2 h(b1 + b2) Area of trapezoid
A = 1 _ 2 (12)(5 + 23)
Replace h with 12, b1 with 5, and b2 with 23.
A = 1 _ 2 (12)(28) Add 5 and 23.
A = 168 Multiply.The area is 168 square yards.
9. 121 ft2 11. 470 1 _ 4 ft2 13. 81 tiles
15. 1,904 in2
17. 50 in2 8 in.
12 in.
5 in.
1919 a. You need to calculate the area of the
trapezoid and subtract the area of the building to fi nd the area of the lawn; 7,000 ft2.19b. 7,000 ÷ 2,000 = 3.5; So, they would need at least 4 bags of seed.
21. 100 cm2 23. Since 9 = 1 _ 2 (1)(b1 + b2), the
possible lengths have a sum of 18. 25. 11,000 cm2
27. G 29. 988 ft2 31. 21 m 33. 8 7 _ 12
ft 35. 13 yd
Pages 543–546 Chapter 9-2B
1. 1.5 m 3. 10 in. 5. 22 _
7 × 21 = 66 ft
77 C = πd Circumference of a circleC ≈ 3.14 · 13 Replace π with 3.14 and d with 13.C ≈ 40.8 Multiply.
The circumference of the circle is 40.8 centimeters rounded to the nearest tenth.
9. 22 _
7 × 14
_ 15
= 2 14 _
15 in. 11. 2.5 mm 13. 34 cm
15. 3.14 × 8 = 25.1 ft 17. 22 _
7 × 7 = 22 mi
19. 22 _
7 × 35 = 110 ft 21. 22
_ 7 × 42 = 132 mm
23. 37.7 cm
2525 First calculate the approximate circumference
of the tree, then divide that number by 6 feet to fi nd the number of people needed to reach around the base of the tree.
C = πd Circumference of a circleC ≈ 3.14 · 36 Replace π with 3.14 and d with 36.C ≈ 113.04 Multiply.Now divide the circumference, 113.04, by 6 feet, the distance each person can reach: 113.04 ÷ 6 = 18.84. Therefore, it would take 19 people to reach around the base of the tree.27a. 30 mm 27b. 31.4 mm 27c. 31.4159 mm 27d. Sample answer: The more decimal places of the estimate of π, the more precise the circumference.29. Greater than; Sample answer: Since the radius is 4 feet, the diameter is 8 feet. Since π is a little more than 3, the circumference will be a little more than 3 times 8, or 24 feet.
3131 no; Sample answer: The circumference of each
candle is about 12.6 inches. So, 12.6 × 8 or 100.8 inches of ribbon are needed to make all of the candles. Since 2 yards is equal to 72 inches, and 72 < 100.8, she does not have enough ribbon for all of the candles.33. 18 in. 35. 257 cm37. Sample answer:
estimated circumference: 21 in.; using calculator: 22.0; The estimate is close to the more accurate value found on the calculator. 39. Sample answer: The circumference is about 3 times the measure of the diameter. 41. I 43. D 45. 12.74 in2 47. 375 in2
radius is 5.5 feet.A = πr2 Area of a circleA = 3.14 · 5.52 Replace π with 3.14 and r with 5.5.A = 94.985 Multiply.The area is 95.0 square feet rounded to the nearest tenth.11. 3.14 × 6.3 × 6.3 = 124.6 cm2 13. 1.2 in2 15. 207.6 ft2
1717 circle; You need to calculate the area of the
triangle and the area of the circle and compare them.
A = 1 _ 2 bh Area of triangle
A = 1 _ 2 (100)(100) Replace b with 100 and h with 100.
A = 5,000 Multiply.The area of the triangle is 5,000 square feet.A = πr2 Area of a circleA = 3.14 · 502 Replace π with 3.14 and r with 50.A = 7,850 Multiply.The area of the circle is 7,850 square feet. Since 5,000 is less than 7,850, the area of the circle is greater.19a. 1,962.5 ft2 19b. 5,024 ft2 21. 62.8 m2 23. 103.4 cm2 25. D 27. A 29. 210 in2 31. 39.5 cm2
Pages 556–558 Lesson 9-3A
11 P = 2b + 2h Perimeter of a rectangle P = 2(18) + 2(5) Replace b with 18 and h with 5. P = 36 + 10 Multiply. P = 46 Add.The perimeter is 46 yards.3. 88 m
55 Add all of the distances around the composite
fi gure. P = 40 + 21 + 21 + 40 + 21 + 21 Sum of all sidesP = 164 yd Add. The perimeter is 164 yards.
7. 62.27 cm 9. 64 ft 11. 106 yd
1313 Adding ten meters to each end of the court
makes the new length 46 meters. Adding ten meters to each side of the court makes the new width 34 meters. The perimeter is then 46 + 34 + 46 + 34, or 160 meters.15. Sample answer: 111.4 cm
20 cm 20 cm
30 cm
17. Sample answer: Perimeter is the distance around the outside of a fi gure while area is the measure of the amount of space enclosed by the perimeter. 19. D
21. 22 _
7 × 7 _
11 × 7 _
11 = 1 3 _
11 in2 23. 22
_ 7 × 7 = 22 ft
25. 56 ft2
Pages 563–565 Lesson 9-3C
1. 112 m2 3. 145 m2 5. 189 ft2
77 The fi gure can be separated into a rectangle
and a trapezoid. Find the area of each and then add them together.
A = bh Area of parallelogramA = 8 · 4 Replace b with 8 and h with 4.A = 32 Multiply.The area of the rectangle is 32 square inches.
A = 1 _ 2 h(b1 + b2) Area of trapezoid
A = 1 _ 2 (4)(5.3 + 8)
Replace h with 4, b1 with 5.3, and b2 with 8.
A = 1 _ 2 (4)(13.3) Add 5.5 and 8.
A = 26.6 Multiply.The area of the trapezoid is 26.6 square inches. The area of the whole figure is 32 + 26.6, or 58.6 square inches. 9. 257 mm2 11. 66.2 yd2 13. about 592.8 ft2
1515 a. Find the area of the triangle.
A = 1 _ 2 bh Area of triangle
A = 1 _ 2 (22.8)(12) Replace b with 22.8 and h with 12.
A = 136.8 Multiply.The area of the triangle is 136.8 square feet.Find the area of the rectangle.
A = bh Area of rectangleA = 22.8 · 14.5 Replace b with 22.8 and h with 14.5.A = 330.6 Multiply.Add both areas. 136.8 + 330.6 = 467.4 ft2
15b. 467.4 ÷ 350 ≈ 1.34; Since only whole gallons of paint can be purchased, you will need 2 gallons of paint. At $20 each, the cost will be 2 × $20, or $40. 17. Sample answer: Area of rectangle: 5 × 5 = 25. So, an approximate area is 25 × 2,400 or 60,000 mi2. 19. A 21a. 3,150 ft2 21b. $9,418.50 23. 30 ft 25. 69.4 cm2 27. 176.6 in2
Pages 566–567 Lesson 9-3D PSI
1. Sample answer: By making a model, D.J. could fi rst see if he had enough chairs before setting them all up. 3. 3 or 4 blocks 5. 16 students 7. 3 hours
99 The price for adults is $40 per ticket and the price
for children is $30 per ticket. 2($40) + 3($30) = $170 11. 5 boys
V = bwh Volume of a rectangular prismV = (6)(6) (4 3 _
4 ) Replace b with 6, w with 6, and h with 4 3 _ 4 .
V = 171 Multiply.The volume is 171 cubic inches.9. 84 cm3 11. 6,664.77 m3 13. 2,702.5 in3 15. 17 m 17. 6 in. 19. 360 mi3 21. >
2323 a.
V = bwh Volume of a rectangular prism
V = (5)(4.5)(2.25) Replace b with 5, w with 4.5, and h with 2.25.
V = 50.625 Multiply.Currently, there are 50.625 cubic inches of sand in the container.23b. The volume of the container is 5 × 4.5 × 3, or 67.5 cubic inches. Therefore, 67.5 - 50.625, or 16.875, cubic inches of sand could be added before the container overfl ows.
23c. 50.625 of the total 67.5 cubic inches are fi lled
with sand. So, 50.625 _
67.5 = 0.75. After changing 0.75
to a percent, you know that 75% of the container is now fi lled with sand. 25a. 577.5 ft3 25b. 3-bedroom moving truck 25c. 641.25 ft3 27. She added the base, width, and height instead of multiplying them. V = bwh; V = 13.7 × 6.8 × 21.4 = 1,993.624 cm3 29. Each of the three dimensions being multiplied is expressed in a unit of measure. Just like the product 5 × 5 × 5 can be expressed using exponents as 53, feet × feet ×
feet can be expressed with exponents as feet3. 31. F 33. 1,500 mm2
After replacing b with 35.7, h with 15.1, and w with 25.5, the surface area is 3,668.94 square meters. 11. 390 in2 13. Yes; the approximate surface area of the rectangular prism is (2 × 13 × 6) + (2 × 13 × 8) + (2 × 6 × 8) or 460 ft2. 15. area; Sample answer: The length and width of the house will determine the land area needed to build the house; m2 or ft2
17. length; Sample answer: The height of a tree is also its length
1919 Package A
In the formula, use 14 for b, 12 for h, and 3 for w.
The surface area of Package A is 492 square inches, which is larger than the surface area of Package B, 404 square inches. Package A has a greater surface area.
Package A
V = bwh Volume of a rectangular prism= (14)(3)(12) Replace b with 14, w with 3, and h with 12.= (42)(12) Multiply.= 504 Multiply.
The volume of Package A is 504 cubic inches.
Package B
V = bwh Volume of a rectangular prism= (11)(8)(6) Replace b with 11, w with 8, and h with 6.= (88)(6) Multiply.= 528 Multiply.
The volume of Package B is 528 cubic inches. Package A has the greater surface area, but Package B has the greater volume. 21a. 48 in2; 144 in2 21b. 336 in2 23. B 25. 4:9, 4 to 9, or 4 _
9 27. 231 in3 29. 301.4 ft2
Pages 584–589 Chapter Study Guide and Review
1. volume 3. perimeter 5. volume 7. 24 units2 9. 18.125 m2 11. 6 ft 13. 4.5 m2 15. 99 in2 17. 195 m2 19. 66.5 ft2 21. r = 29 cm 23. d = 18 ft 25. 53.4 cm 27. 125.6 ft 29. 3.14 × 12 × 12 ≈ 452.2 in2
108 = ( 1 _ 2 · 3 · 8) · h Replace V with 108, b with 3, and
h with 8. 108 = 12h Multiply.108
_ 12
= 12 · h _ 12
Divide both sides by 12.
9 = h Simplify.The height of the prism is 9 inches.15. Sample answer: rectangular prism: length, 7; width, 5; height, 6; triangular prism: area of base, 35 sq. meters; height, 6 meters 17. Sample answer: Both three-dimensional shapes use the same formula to fi nd the volume. The difference is when you fi nd the B in the formula for triangular prisms,
you will use 1 _ 2 bh instead of base times height.
19. H 21. Cabinet A: 3,888 in3; Cabinet B: 4,760 in3; Tia should purchase cabinet B.
Pages 605–606 Lesson 10-1D
1. 196 ft3 3. 70 ft3
55 V = 1 _ 3 Bh Volume of a pyramid
V = 1 _ 3 (8 · 5)h Replace B with 8 · 5 since the
base is a rectangle. V = 1 _
3 (8 · 5)(10) Replace h with 10.
V = 133.3 Multiply.The volume is 133.3 cubic yards.7. 560 ft3 9. 284.7 cm3 11. 85,730,400 ft3 13. 1,805 m3
1515 To fi nd the height, substitute the given values
into the formula and then solve for h.
V = 1 _ 3 Bh Volume of a pyramid
504 = 1 _ 3 (14 · 12)h Replace V with 504 and B with 14 · 12.
504 = 56h Multiply.504
_ 56
= 56h _ 56
Divide both sides by 56.
9 = h Simplify.The height is 9 inches.17. Sample answer: The base of the pyramid is a
triangle. He should have found V = 1 _ 3 ( 1 _
2 × 6 ×
7)10; 70 ft3
19. Sample answer: The formula for the volume of
a pyramid multiplies by 1 _ 3 . A prism is 3 times larger
than a pyramid. 21. F 23. F
Pages 609–611 Lesson 10-2B
1. 6,612.8 in3
33 V = πr2h Volume of a cylinder
V ≈ 3.14(2.5)2(6.2) Replace π with 3.14, r with 2.5, and h with 6.2.
V ≈ 121.675 Multiply.The volume is about 121.7 cubic yards rounded to the nearest tenth.5. 117.8 ft3 7. 1,921.7 m3
99 V = πr2h Volume of a cylinder
V ≈ 3.14 (6)2(5) Replace r with 6 and h with 5. V ≈ 565.2 Multiply.
1919 The formula calls for the radius, and since the
diameter is 6 cm, the radius is 3 cm.
V = πr2h Volume of a cylinder
226.2 ≈ 3.14(3)2h Replace V with 226.2, π with 3.14, and r with 3.
226.2 ≈ 28.26h Multiply.226.2
_ 28.26
≈ 28.26h _ 28.26
Divide both sides by 28.26.
8 ≈ h Simplify.21. Sample answer: radius, 4 ft; height, 4 ft
4 ft
4 ft
23. Sample answer: The formula V = πr2h uses πr2 to fi nd the area of the fi rst “layer” of the volume. By multiplying the area of the circle by the height of the cylinder, the volume of all of the “layers” is found. 25. G 27. 80 cm3 29. 208 yd3
Pages 614–616 Lesson 10-2D
1. 307.7 yd3
33 V = 1 _ 3 πr2h Volume of a cone
≈ 1 _ 3 · 3.14 · 72
· 13 Replace π with 3.14, r with 7, and h with 13.
≈ 666.726 Multiply.The volume of the cone is about 666.7 cubic inches rounded to the nearest tenth.5. 47.1 m3 7. 13.6 in3 9. 267.5 ft3 11. 77.3 yd3
1313 Since the diameter is 250 meters, use 125 meters
for the radius.V = 1 _
3 πr2h Volume of a cone
V ≈ 1 _ 3 · 3.14 · 1252 · 1,500 Replace r with 125 and
h with 1,500.V ≈ 24,531,250 Multiply.
The volume of the volcano is about 24,531,250 cubic meters. 15. 11.0 in.
17d. Sample answer: Changing the radius impacts the volume more than changing the height. The volume increases more when you change the radius, because when you calculate the volume, you square the radius and not the height.19. Sample answer:
2 m
8 m
4 m
8 m
21. A 23. 3,014.4 mm3 25. 7,385.3 m3
Pages 618–619 Lesson 10-3A PSI
1. Sample answer: A three-dimensional object allows you to see all of the combined areas that make up the total surface area of the object.
33 You will make a diagram showing the wall
with the table against it. You will show the position of the balloons using a *. Counting the stars will tell you how many balloons are needed. Remember, there will only be one balloon on each corner.
wall
3 ft3 ft
8 ft
15 balloons are needed.5. mean 7. 11 9. Sample answer: 2 in. by 2 in. by 5 in.; 1 in. by 4 in. by 5 in.11a. 120 ft2 11b. 2 qt
Pages 623–624 Lesson 10-3C
1. 3,014.4 yd2 3. 301.4 in2
55 S.A. = 2πrh + 2πr2 Surface area of a cylinder
= 2(3.14)(6.4)(3) + Replace π with 3.14, 2(3.14)(6.4)2 r with 6.4, and h with 3.
= 120.576 + 257.2288 Multiply.= 377.8048 Add.
The surface area is 377.8 square yards.
77 The surface area formula uses radius, and
since the diameter is given as 1 inch, the radius is 1 _ 2
or 0.5 inch. Also, since the question only asks for the outside of the pipe, you do not need to calculate the ends. You only need the lateral surface area of the cylinder, so the formula is S.A. = 2πrh. S.A. = 2πrh Surface area of the outside of a cylinder
≈ 2(3.14)(0.5)(180) Replace π with 3.14, r with 0.5, and h with 180.
≈ 565.2 Multiply.The surface area of the outside of the pipe is 565.2 square inches; 565.2 in2.9a. rectangular prism: 328 in2; cylinder: 301.44 in2
9b. rectangular prism 11. Surface area describes the area of all the surfaces of a solid. Volume describes the capacity, or amount of space contained inside a solid. 13. D 15. 2 blocks by 2 blocks by 2 blocks; 4 blocks by 2 blocks by 1 block 17. 527.5 m3 19. 62.8 ft3
Pages 628–629 Lesson 10-4B
1. 450 in3 3. 326 m2
55 The top of the fi gure is a rectangular pyramid
and the bottom is a rectangular prism. To fi nd the volume of the whole fi gure, you will fi nd the volume of each piece and add them together.
V = 1 _ 3 Bh Volume of a pyramid
= 1 _ 3 (8 · 8)h
Replace B with 8 · 8 since the base is a rectangle.
= 1 _ 3 (8 · 8)(6) Replace h with 6.
= 128 Multiply.The volume of the top section is 128 cubic millimeters.V = Bh Volume of a rectangular prism
= 8 · 8 · 9 Replace B with 8 · 8 and h with 9.= 576 Multiply.
The volume of the bottom section is 576 cubic millimeters, so the volume of the whole figure is 704 cubic millimeters.7. 100 in3 9. 292 yd2
1111 You need to fi nd the surface area of the
television and the surface area of the sides of the
cylinder. The surface area of the bottom of the cylinder will be included in the surface area of the bottom of the television since both ends of the cylinder are the same. That eliminates the need for subtracting the overlapping part of the cylinder.
TelevisionIn the formula, use 35 for b, 20 for h, and 5 for w.S.A. = 2bh + 2bw + 2hw
The surface area of the television is 1,950 cubic inches.
CylinderIn the formula, use 3.14 for π, 7.5 for r, and 3 for h.S.A. = 2πrh
≈ 2(3.14)(7.5)(3) ≈ 141.3 Multiply.
The surface area of the outside of the base is 141.3 square inches.Therefore, the total surface area is 2,091.3 square inches.15. C 17. 175.8 yd2 19. 376.8 m2 21. 527.5 m3
= 216, 216 ÷ 9 = 24; The mean amount she earned is $24. 9b. $80 9c. 9c. Sample answer: This value that is considerably higher than all the other values causes the mean to be greater than all the values, except $25 and $80. Without the value, the mean would better represent the average of the data. 11a. 40; 40 11b. No; both means are equal. 13. Sample answer: pages read: 27, 38, 26, 39, 40 15. If the precipitation for the month of July is 3 inches, then the mean would decrease since this amount is smaller than the mean. If the precipitation for the month of July is 4 inches, then the mean would probably not be affected since the
original mean is about 4 inches. If the precipitation for the month of July is 5 inches, then the mean would increase since this amount is greater than the mean. 17. C 19. 80
Louisville is 70° and the mode for Lexington′s temperatures is 76°. Since 76° - 70° = 6°, the mode was used to make this claim.15a. Cranes: median: 40, mode: 31, range: 19; Panthers: median: 40, mode: 40, range: 615b. Sample answer: The Panthers had the better record. Even though the mean and median are the same, the Panthers’ mode is higher. 17a. True; the mode of the data set is 1. 17b. False; the median of the data is 2. 19a. 1 19b. Sample answer: The data have a small range and are all relatively close.21. $4.61 23. 46 min
Pages 659–660 Lesson 11-1F
11 The mean or mode best represent the data. The
mode is 45 and 60. The mean is 56.4. There are no extreme values. 3. Since there are repeated numbers, the mode, 47, best represents the data.
55 outlier: 2.43; without the outlier: mean: 7.2,
median: 7.3, mode: none; with the outlier: mean: 6.3, median: 6.19, mode: none; The mean best describes the data without the outlier. The median best describes the data with the outlier. 7a. 1,1487b. With the outlier, the mean is 303.75, the median is 28.5, there is no mode, and the range is 1,138. Without the outlier, the mean is 22.3, the median is 14, there is no mode, and the range is 33. 7c. With the outlier, the best measure is the median; without the outlier, the best measure is the median.9. Sample answer: 125, 32, and 19 11. C 13. I15. median: $17; mode: $18; range: $12
1. The mode is Republican. It means that more U.S. presidents have been Republican than any other political party.
3a. Number of Letters Tally Frequency
3–4 35–6 97–8 39–10 2
3b. 4 _ 17
55 a. Sample answer:
Temperatures Tally Frequency
40–41 | 1
42–43 |||| ||| 8
44–45 |||| 4
46–47 |||| || 7
5b. Most of the temperatures were either between 42 and 43 or 46 and 47.
77 a. T-Shirts SoldT-Shirt Size Tally Frequency
S 9M 11L 6
XL 4
7b. The mode is medium. More T-shirts were soldin medium than any other size. 7c. 9 _
30 or 3 _
10
9a. Speed (miles per hour) Tally Frequency
20–29 230–39 740–49 450–59 3
9b. Most of the speeds are between 30 and 39 miles per hour. The mode is 30 miles per hour, although it cannot be determined from the frequency table. The range is 30 miles per hour, which also cannot be determined from the frequency table.
9c. The smaller the intervals, the less the frequencies. If the intervals were broader, the frequencies would decrease. The mode and range do not change because the individual data values do not change. 11. The mode of a set of data is determined by looking at individual data values. The mode cannot be determined from a frequency table. 13. D 15. There are no outliers, so the mean, 5, or median, 5.5, would be the measure of central tendency that best represents the data. 17. median: $5; mode: $5; range: $3
Pages 670–672 Lesson 11-2C
1. 36 3. $60.00 - $69.99
55 The bar that shows the greatest number of
cyclists is the interval from 60–64 with a frequency of 9.7. 16
9.
10–1
45–
90–
4
15–1
9
Number of States
Freq
uenc
y
4
6
2
8
0
10
Number of States Visited by Students in Marty’s Class
20–2
4
25–2
9
1111 6th grade; The 6th grade had around 18
students with sales of $400 - 599. The 7th grade had around 16 students with sales of $400 - 599. So the 6th grade had more students with sales in this interval. 13. 24 students15.
50–9
9
0–49
Num
ber o
f Bar
s
Calories
150–
199
100–
149
200–
249
250–
299
300–
349
350–
399
46
20
810
Calories of Various Types of Frozen Bars
17. Sample answer: Ages of students at summer camp: 3, 4, 5, 7, 7, 8, 8, 10, 10, 11, 13, 15, 15, 16 19. 40–45; all the other intervals represent 5 whole numbers 21. A 23. I 25. The median and mode best represent the data. The median and the mode are both 45. There are no extreme values. 27. median: 47 airplanes; mode: 55 airplanes
have between 500–999 songs and 31% of students who said they have over 1,000 songs. So there are 11% + 31% or 42% of students who have 500 or more songs.5. Class President Ballots
Lacey25%
Troy25%
Melissa31%
Omar19%
77 oxygen; Oxygen makes up 64% of the elements
in the human body which is the greatest percent of all the elements. 9. Oxygen and carbon make up about 82% of the entire body.11. 18%
1313 135 students; Since 54% of the students that
were surveyed said they preferred apples as their favorite fruit, fi nd 54% of 250 students. 250 × 0.54 = 135 studentsSo, there would be 135 students who would prefer apples if there were 250 students surveyed.15. Sample answer: Mei did not represent 5% as a decimal correctly. It should be 0.05 × 40 = 2.; 2 people 17. A19.
80–89
70–79
60–69
50–59
4
6
2
0
8
Num
ber o
f Stu
dent
s
10
12
90–99
Percentage on Test
Test Scores
Pages 683–685 Lesson 11-4A
1. line plot; The line plot shows the greatest value as a numerical value rather than a bar. 3. line graph; A line graph shows the trend over time. g p
55 bar graph; The bar graph shows the maximum
speeds, not just the interval in which the data occurs in. 7. line graph; A line graph shows the trend over time. 9. bar graph; A bar graph allows for the prices to be compared.
11. Sample answer: bar graph;
18221826
1818
18101814
1830
Year
of
Inde
pend
ence
CountryArge
ntinaBolivi
aChile
Colombia
Equad
or
Mexico Peru
Venezu
ela
Independence of Latin AmericanCountries
1313 Sample answer:
7 8 9 10 11 15141312
Number of Neighbors
× ×
×
×
The line plot allows you to easily see how many countries have a given number of neighbors. The bar graph however allows you to see the number of neighbors each given country has.
15. False; counterexample: to compare the price of fi ve different cell phones, a line graph would not be appropriate because these data do not show change over a period of time 17. Sample answer: Circle graphs are best used for data showing a relationship of the parts to the whole. 19. F 21. 18%23.
411–460
361–410
311–360
240–310
2
3
1
0
4
Num
ber o
f Brid
ges
5
6
Length (ft)
Bridges
Pages 691–693 Lesson 11-4C
11 Graph B; From the length of the bars, it
appears that Cy Young had about 3 times as many wins as Jim Galvin. However, Jim Galvin had 365 wins and Cy Young had 511 wins. So, the conclusion is not valid. 3. Sample answer: The mean is 8,638 and the median is 8,941. Since the median is greater than the mean, use the median to emphasize the average length. 5. Sample answer: There are not equal intervals on the x-axis. 7. The median or the mode
nsbecause they are much closer in value to most of the pieces of data. 9. Sample answer: The scale of the graph is not divided into equal intervals, so differences in heights appear less than they actually are.
1111 A line graph would allow you to see the
dramatic increase from year to year.
475
01 2 3 4 5
500
525
550
Rent
($) 575
600
625
Year
Monthly Cost to Rent an Apartment
13. Sample answer: Outliers may distort measures of central tendency; data shown in graphs may be exaggerated or minimized by manipulating scales and intervals. 15a. 225 min 15b. Sample answer: The ratio of the area of the cell phones are not proportional to the number of minutes. 17. line graph; Sample answer: A line graph shows change over a period of time.
Pages 694–695 Lesson 11-4D PSI
1. Add the number of students in math and the number of students in Spanish, then subtract the number of students who are in both. 3. 26 students 5. 6 owners 7. $235
99 6; 10; In order to fi nd the amount of students
that like just softball and just basketball, subtract the amount of students that liked both from the total amount of students that liked each sports. softball: 14 - 8 = 6; basketball: 18 - 8 = 10. So 6 students liked softball only and 10 students liked basketball only.11. 27 runs
Pages 698–703 Chapter Study Guide and Review
1. false; mean 3. false; median 5. true 7. false; scale 9. 27 days 11. $55 13. 24; 23; 9 15. 42; 36; 46 17. 84; 82; 7 19. Sample answer: Since the set of data has no extreme values or numbers that are identical, the mean, 7.1, would best represent the data.21. mean: 9.6 in.; median: 10; mode: 9; range: 9; outlier: 3
Heights (in.) Tally Frequency
3 | 1
9 ||||⁄ | 6
10 |||| 4
11 | 1
12 ||| 3
23. 14 students
25. Favorite Movie Type
Action25%
Romance10%
Comedy40%Drama
25%
27. The section representing comedy is 4 times the size of the section representing westerns. 29. line graph 31. line plot 33. circle graph 35. Sample answer: The average used by Timea was the mean. This measure is greater than the price of most of the shoes because of the outlier, $105. So, it is misleading to use this measure for the price of shoes. 37. 5%
Chapter 12 ProbabilityPage 710 Are You Ready?
1. certain 3. impossible 5. 1 _ 2 7. 1 _
8 9. 1 11. 7 _
10
Pages 714–716 Lesson 12-1A
1. 1 _ 9 3. 2 _
9 5. 5 _
9 7. The complement of selecting a
“Go Back 1 Space” card is selecting any card other
than that card. Its probability is 3 _ 4 , 0.75, or 75%.
9. 0 or 0 _ 1 11. 3 _
4 13. 5 _
8
1515 There are 2 chances out of 10 to draw a 7 or 9.
So, the probability of selecting either of those
numbers is 2 _ 10
or 1 _ 5 .
17. 7 _ 10
19. 1 _ 2 21. 3 _
5
23. Picking a black jelly bean is impossible since the probability of picking a black jelly bean is 0%.25. Picking a purple, red, or yellow jelly bean is very likely to happen since the probability of picking a purple, red, or yellow jelly bean is 90%.p
2727 The complement of selecting a girl is selecting
probability of an event occurring or its complement occurring is certain to happen. Therefore, the sum of these probabilities is 1. For example, if there is a 30% chance of rain, then the complement is a 70% chance of no rain. It is certain that one of these two events will occur. 33. G 35. D 37. 2 : 4 or 1 : 2 39. 1 : 5
Pages 721–723 Lesson 12-1C
1. Let R = Ramiro, G = Garth, and L = Lakita. The different ways are RGL, RLG, GRL, GLR, LRG, and LGR. So, there are 6 ways the three students can line up.
33 1 _ 16
; Sample answer: There is a 1 _ 4 chance she will
choose the waves screen saver and a 1 _ 4 chance she
will choose the family background photo. So, the
probability of selecting both of those is 1 _ 4 × 1 _
4 = 1 _
16 .
5. Let 1 = CD 1, 2 = CD 2, 3 = CD 3, and 4 = CD 4. The different ways are 1234; 1243; 1324; 1342; 1423; 1432; 2134; 2143; 2314; 2341; 2413; 2431; 3124; 3142; 3214; 3241; 3412; 3421; 4123; 4132; 4213; 4231; 4312; and 4321. So, Kame can listen to four CDs 24 ways.7. 8 possible combinations Book Gift Bag
The Poky Little Puppy yellow
The Poky Little Puppy green
The Tale of Peter Rabbit yellow
The Tale of Peter Rabbit green
Tootle yellow
Tootle green
Green Eggs and Ham yellow
Green Eggs and Ham green
9.
11.
13. 1 _ 8 ;
R01_R39_EM_SelAns_895129.indd R37R01_R39_EM_SelAns_895129.indd R37 1/19/10 9:51 AM1/19/10 9:51 AM
R38 Selected Answers and Solutions
Sele
cted
Ans
wer
s an
d So
lutio
ns 1515 1 _ 12
; Sample answer: There are 12 possible
outcomes and there is only 1 correct answer for each question. There is only one chance of getting each question correct.17. 30 ways; Sample answer: By just choosing a three-student group, the order in which the names are drawn does not matter. When the order matters, the sample space is increased. A three-person group of Kayla, Jeremy, and Chi-Wei is the same as a three-person group of Jeremy, Chi-Wei, and Kayla. However, these two groupings would refl ect different orderings of captain, co-captain, and secretary. 19. Sample answer: The results when a number cube is rolled and a coin is tossed. 21. I 23. Sample answer: The tree diagram is showing all the possible outcomes of seeing 2 different movies at 3 different times.
Pages 728–730 Lesson 12-1E
1. 42 3. 12 5. 1 _ 64
7. 48 9. 20
1111 There are 3 possible outcomes to be captain
and 3 possible outcomes to be co-captain. So, 3 × 3 = 9 possible outcomes.
13. 50 15. 1 _ 9
1717 a.
17b. Sample answer: You can use the
Fundamental Counting Principle to fi nd the total number of outcomes by multiplying the number of bread choices (two) by the number of meat choices (fi ve). So, there are a total of 10 possible sandwiches.
17c. 1 _ 10
, 0.1, 10%; Sample answer: There are 2 × 5
or 10 different possible outcomes of sandwich choices. There is 1 possible outcome for a sandwich that includes white bread and ham. The probability
of randomly selecting this sandwich is 1 _ 10
.
19. Sample answer: William has 4 shirts that he can wear with a choice of 3 different pants. He has 12 different possible outfi ts. 21. Sample answer: You can use the Fundamental Counting Principle to calculate the total possibilities of a situation quicker
than having to draw a tree diagram to determine the probability. 23. G 25. 1227. Coin Spinner
Heads A
Heads B
Heads C
Heads D
Tails A
Tails B
Tails C
Tails D
29. 3 _ 7 31. 9 _
14 33. 4 _
7
Pages 734–736 Lesson 12-2B
1. 1 _ 10
33 1 _ 20
; There is only 1 orange color out of 8
possible colors and 2 As out of 5 possible letters. So, the probability of spinning an orange and
getting an A is 1 _ 8 × 2 _
5 = 2 _
40 or 1 _
20 .
5. 9 _ 10
, 0.09, 9% 7. 1 _ 4 9. 1 _
8
1111 3 _
100 ; There are 3 green tiles out of 10 so the
probability of selecting a green tile is 3 _ 10
. There is
1 blue tile out of 10 so the probability of selecting a
blue tile is 1 _ 10
. So, the probability of green and blue
is 1 _ 10
× 3 _ 10
= 3 _
100 .
13. 1 _ 25
1515 a. 1 _ 4 ; The probability of the DVD being comedy
is 12 _
24 or 1 _
2 and the probability of the DVD not being
comedy is 12 _
24 or 1 _
2 . So, 1 _
2 × 1 _
2 = 1 _
4 .
15b. 1 _ 18
; The probability of the DVD being drama
is 8 _ 24
or 1 _ 3 and the probability of the DVD being
action is 4 _ 24
or 1 _ 6 . So, 1 _
3 × 1 _
6 = 1 _
18 .
15c. 5 _ 36
; The probability of the DVD being comedy
or drama is 20 _
24 or 5 _
6 and the probability of the DVD
being action is 4 _ 24
or 1 _ 6 . So, 5 _
6 × 1 _
6 = 5 _
36 .
17. 2 _ 5 19. 1 _
20 21. 72 23. 1 _
12
Pages 740–742 Lesson 12-2D
1. 1 _ 6 3. 1 _
12 5. 1 _
45
77 independent; Sample answer: Spinning the
spinner will not affect the results of rolling a number cube.
15. independent; Sample answer: The fi rst roll will not affect the results of the second roll.
1717 dependent; Sample answer: The fi rst student
already picked a partner, which will affect the pick for the second student because there will be less students to choose from.
1919 3 _ 10
, 0.3, 30%; The probability of selecting a
girl is 3 _ 5 and then selecting a boy would be 1 _
2 . So,
the probability of selecting a girl then a boy is
3 _ 5 × 1 _
2 = 3 _
10 .
21a. 1 _ 6 21b. 1 _
12 23. 3 _
8 25. B 27. 5/68 29a. 1 _
5 ; 1 _
3
29b. 1 _ 15
29c.
31. 30 33. 120
Pages 745–747 Lesson 12-3A
1. 3 _ 25
, 0.12, or 12% 3. 3 _ 10
, 0.3, or 30% 5. 3 _ 5 , 0.6, or
60% 7. 180
99 40; There are 2 out of 25 students who
participate in gymnastics as shown in the table. If 500 students participated in sports, there would be 2 out of every 25 students who would participate
in gymnastics. So, 2 _ 25
× 500 = 40 students who
would participate in gymnastics.11a. about 60,000 11b. about 72,500 11c. about 7,200
1313 about 6 free throws; Jaden makes free throws
15% of the time, or 3 out of every 20 free throws. If he shot 40 free throws, you would expect him to
make about 3 _ 20
× 40 = 6 free throws.
15. about 100 times 17. Yes; Mitch can predict that
one out of four sixth-graders will attend the dance.
Since 1 _ 4 = 25
_ 100
, about 25 of the sixth-graders will
attend the dance. 19. 35 21. 15 _
77
23. 6 ways
Video 1, Video 2, Video 3Video 1, Video 3, Video 2Video 2, Video 1, Video 3Video 2, Video 3, Video 1Video 3, Video 1, Video 2Video 3, Video 2, Video 1
25. 7 _ 15
27. 1 _ 5
Pages 750–751 Lesson 12-3C PSI
1. Sample answer: You are able to actually see the results of an activity rather than predict the results or use the theoretical results. The results may be different than the theoretical probability.3. 20 5. 6 ways 7. 2, 9, 9; 3, 8, 9; 4, 7, 9; 4, 8, 8; 5, 6, 9; 5, 7, 8; 6, 6, 8; 6, 7, 7
99 Sample answer: 2,000 pieces/day × 6 days/
week × 50 wk/yr × 5 yr, or about 3,000,000 pieces 11. 30