```Selected Answers
for
Core Connections, Course 2
Lesson 1.1.1
1-3.
All responses vary.
1-4.
All responses vary. They all have at least one obtuse angle or they are all polygons.
1.5.
a: 17 mm
b: sort segment: 17 mm, long segment: 30 mm
1-6.
All responses vary.
Lesson 1.1.2
1-11. a: P = 20.5 in., A = 15 in.2
b: P = 61.4 cm., A = 210 cm2
c: P = 22 yds, A = 21 yds2
1-12. a: All responses vary.
b: All responses vary.
1-13. a: Event 2: All responses vary.
b: Event 2: All responses vary.
1-14.
1-15. a: 3
b: Explanations vary. Possible explanations: Guess and check or worked backwards by
subtracting and dividing.
2
Core Connections, Course 2
Lesson 1.1.3
1-18. 7
1-19. a: 79
b: 1.5
c: 23
1-20. a: 30 feet. 150 feet. 450 feet.
b: 50 stories
1-21.
3
4
is equivalent to
12
16
, so it is greater than
11
16 .
1-22. a: P = 18 un., A = 9 un.2
b: P = 24 ft., A = 28 ft2
c: P = 46 cm, A = 120 cm2
Lesson 1.1.4
1-35. Median is 82.
1-36. a: 84 inches
b: 36 inches
1-37. a:
b:
2
c:
–14
7
4
14
–5 0
6
28
d:
–4000 –
5 10 15
2000 4000
1-38. \$10.50
1-39. No. She needs \$1.00 more.
3
Lesson 1.1.5
1-45. 12345 ! 9 + 6 = 111111 , 123456 ! 9 + 7 = 1111111 , 1234567 ! 9 + 8 = 11111111 ,
12345678 ! 9 + 9 = 111111111 , 123456789 ! 9 + 10 = 1111111111
a: Patterns include: added number increases by 1, first factor in the multiplication adds
another digit, the next consecutive number, answers constantly add a digit of one as
they increase.
1-46. a:
1
4
or 25%
b: 1 12 or 150% OR
c:
2
3
3
4
or 75% depending on how you see the “whole”
or ! 66.7%
1-47. a: two-thirds
b: one whole and one-eighth
c: six-ninths
1-48. \$3.15
1-49. a: P = 34.5 in., A = 47 in2
b: P = 26.5 mm., A = 24 mm2
Lesson 1.2.1
1-57. a: Strawberry
1-58.
b:
0.01
1
5
0.8
25%
0
1-59. a: T
1
b: E
c: E
1-60. a: i: 80%, ii: 12.5%, iii: 10%
d: T
b: i:
8
10
or
e: T
80
100
or 45 , ii:
f: E
12.5
100
or 18 , iii:
10
100
1
or 10
1-61. Mean = 14 cm, Median = 14 cm
1-62. a: Only that it is between 70 and 75 mph
b: Possible answers: 50-55 mph OR 50-65 mph
c:
4
2
16
=
1
8
Core Connections, Course 2
Lesson 1.2.2
1-70. Most credible prediction: 2 purple, 3 orange, 1 yellow, 4 green
1-71. a:
=
3
6
1
2
b:
4
6
=
2
3
1-72. Estimate: \$8 per week for 10 weeks is \$80, \$40 more is \$120, so about 15
weeks; \$125 ÷ \$7.75 = 16.13 weeks, so 17 weeks
1-73. 3 feet, 6 feet, 12 feet
1-74. a: 20, 40, 80
b: 15, 30, 45, 75
c: 25, 50, 75, 125
d: 50, 150, 200, 250
Lesson 1.2.3
1-80. a:
=
4
12
1
3
b: 28
1-81. a: Make sure that half of the stuffed animals are teddy bears.
b: Possible response: Add 8 teddy bears or remove 8 of the other animals.
1-82. All responses vary.
1-83. a: 1100 yards
b: 1819 times
1-84. a: P = 44.85 m, A = 117 m2
b: P = 30 m, A = 18 m2
Lesson 1.2.4
1-90. a: 40%
1-91. a:
b:
1
4
1
5
b:
45
100
or
9
20
20 = 120
c: 1 100
100
d: 52.5%
, 0.25, 25%
, 0.2, 20%
c: Before the other coins are added.
1-92. a: 8
b: 12
c: 4
1-93. \$2.20, \$11.00, \$0.55
1-94. a:
5
24
b:
7
5
or 1 25
c:
16
45
5
Lesson 1.2.5
40
2
1-103. a: Yes, 10
of 5 squares,
25 = 100 = 5 . The shape can be rearranged and divided into groups 10
each with 2 shaded; both the numerator and denominator of the fraction 25 can be
multiplied by 15 .
b:
4
10
1-104. 12. 12 ÷ 2 = 6,!6 ! 4 = 2
1-105. a:
1
4
1-106. a:
4
8
, 25%
or
1
2
1-107. a: 25
b:
18
50
b:
31
20
, 36%
c: 1 12 , 150%
or 1 11
20
c:
b: 45
16
35
c: 30
Lesson 1.2.6
1-114. a:
c:
1-115. a:
5!3
6 3
1!8
2 8
2
8
= 15
18
b:
8
= 16
d:
+ 58 =
2!2
3 2
1!6
4 6
=
=
4
6
6
24
7
8
b: 4 is a factor of 8, so 8 can be a common denominator.
1-116. a: 30
1-117. –2, 0, 0.4,
1-118. a:
6
14
15
b: 24
1
2
,
5
8
, 1.1,
5
3
, 2
b:
17
14
= 1 143
c:
20
48
=
10
24
5
=12
Core Connections, Course 2
Lesson 1.2.7
1-124. 50%
1-125.
3
4
, Explanations vary.
1-126. a: x = 13
b: x = 87
c: x = 18
1-28. a:
b:
c:
d:
e:
f:
d: x = 50
1-27. (2,1) (4,7) (6,1)
1-29. a: P = 196 in., A = 2052 in.2
b: P = 221 cm, A = 2044 cm2
Lesson 1.2.8
a:
c:
2 ,
3
6
16 ,
12 , etc.
18
12 , etc.
32
b:
d:
22
24
20
14
,
,
55 , etc.
60
1 73 , etc.
1-138. 1 58
1-139. a: 1.5 muffins
b: Each person gets half a muffin.
1-140. C
1-141. a: A = 96 cm2, P = 40 cm
c: A = 144 cm2, P = 52 cm
b: A = 22 in.2, P = 25.05 in.
d: A = 696.67 m2, P = 114.67 m
7
Lesson 2.1.1
2-8.
10 tenths, 100 hundredths
2-9.
a: 0.4
b: 0.375
b: 1 ! ( 13 + 18 )
2-10. a:
2-11. a:
2-12
c: 1.5
5
50
b: 1
a: 7
c:
38
50
c:
24
24
d:
9
50
8 ! 3 =
! 24
24
13
24
" 50%
b: 18
2-13. a: terminates
b: repeats
c: repeats
d: terminates
2-14. a: mean = 38.9 inches, median = 40 inches
2-15. a:
4
16
or
1
4
, 0.25, 25%
b:
7
16
4 = 11 , 0.69, 69%
+ 16
16
c: 0 , 0%
2-16. a:
b:
12
3
4
2
7
2-17. a:
8
12
11
c:
6
6
3
b:
17
5
2
8
5
c:
d:
12
28
4
7
11
34
15
Core Connections, Course 2
Lesson 2.1.2
2-26. a: repeating
b: terminating
2-27. a: five-eighths
3 or
b: 3 10
2-28. a:
c:
3
8
2
8
c: terminating
33
10
, 0.375, 37.5%
b: 1! 18 =
=
d: 25
1
4
, 0.25, 25%
d: repeating
7
8
, 0.875, 87.5%
2-29. a:
10
8
6
4
2
c:
32 40 48 56 64 72 80 88 96 104 112
–9 –6 –3
–2
–4
–6
–8
b:
–7 –6 –5 –4 –3 –2 –1
2-30. a: California
0
1
2
3
b: New York
3 6 9 12
Lesson 2.2.1
2-36. a: 1728
b: 7098
2-37. a: Possible solutions: 4 + 1+ 1 , 3 + 3 , 3 + 1+ 1+ 1
b: Possible solutions: 5 + 5 + (!2) , 7 + 5 + (!2) + (!2)
2-38. a: 15 feet
b: 16 feet
c: 8 feet
d: 11 feet
2-39. Missing values from least to greatest:
a: 10, 30, 40
b: 8.1, 16.2, 24.3, 40.5
c: 2.2, 4.4, 6.6, 11.0
d: 3 13 , 6 23 , 13 13 , 16 23
2-40. a: Strategies will vary.
b: B = (–5, –5), C = (4, –2)
c: (3, –4)
2-41. a: mean = 28.3, median = 15
b: The median because the data is not symmetric, so the mean is more greatly impacted
by the outlier of 120.
9
Lesson 2.2.2
2-51. a: 5 + (!3) = 2
b: 4 + (!6) = !2
c: !4 + 4 = 0
d: !4 + 7 = 3
2-52. Answers will vary: 5 + 6 + 7 = 18, 5! 6 + 7 = 37, 6 ! 7 " 5 = 37
2-53. a: –1.75
b: –3.82
2-54. a: terminating, 0.875
b: repeating, 0.2
c: repeating, 0.571428
5
2
3
2-55. a: 1! 12 ! 15 = 10
10 ! 10 ! 10 = 10
d: terminating, 0.5
b:
4
30
2
= 15
Lesson 2.2.3
2-62. a: 5
b: 0
c: 13
d: 14
2-63. He will return to his starting place. Each foot to the right is “undone” by each foot to the
left.
2-64. a: P(not red) =
37
49
b: P(purple) = 0, there are not any purple marbles in the bag.
2-65. a: 10 units
2-66.
10
5
12
b: 30 units
of her time, or 50 minutes
Core Connections, Course 2
Lesson 2.2.4
2-79. a: 12
d: 6
b: 11
c: 6.4
e: 15
f: –51
2-80. a: 9(400 + 10) = 3600 + 90 = 3690
b: 6(500 + 90 + 2) = 3000 + 540 + 12 = 3552 or 6(600 + (!8)) = 3600 + (!48) = 3552
2-81. a:
b:
63
9
7
7
16
2-82. a:
45
100
c:
56
7
8
d:
49
7
1
1
2
14
15
, 45%
2
2 12
b: one and twenty-seven hundredths, 1.27
2-83. Diagrams will vary; They should show that 83 + 48 + 18 is
equivalent to 3 hours. The “present” portion should show
22.5 minutes or 0.375 hours.
2-84.
a: Mean = 65, Median = 61
b: See histogram at right.
Lesson 2.2.5
2-90. a:
b:
1
2
of
3
4
of all the cars are white sedans, or
1!3
2 4
=
3
8
c: 0.375, 37.5%
2-91. Yes. They are the same because the rectangles are both cut into 15 pieces, 2 of which
2-92. a: –20
b: –38 12
c: 0.88
2-93. a: No, adding first gives 33, multiplying first gives 15.
b: Yes, either way is 56.
2-94. A; probabilities cannot be negative as there is no probability less than 0, which represents
impossibility.
11
Lesson 2.2.6
2-101. a: 2
b: 8 13
c: 6 14
2-102. a: 4
b: 5 · 4 = 20
c: 20
2-103. a: 3! 14 ! 24 = 18
b: 3! 32
8 = 12
c: 4 ! 35
7 = 20
2-104.
2 ! 54
3
d: 3 18
y
b
a
= 36
2-105. See graph at right.
d
c
x
Lesson 2.3.1
2-115. a: 32, 40, 48, 56, 64, 72, 80
b: 0, 0.25. 0.5, 0.75, 1, 1.25, 1.5
c: x: 3, 6, 9
y: 0.5, 1, 1.5
2-116. a:
b:
0
25
d: x: 4, 8, 12, 16, 20
y: 4, 8, 12
0
6
2-118. a:
13
52
or
11
–5
d:
154
14
25
1
25
3
2-117. a: 10 16
c:
–30
1
b: 9 24
234
13
18
31
c: 1 53
1
4
b:
39
52
or
3
4
2-119. Mean = 12.08, Median = 12, Range = 4
43 = 0.43
2-120. a: 43% = 100
39 = 0.39
c: 39% = 100
12
9 == 0.9
b: 90% = 10
d: 64% = 16
25 = 0.64
Core Connections, Course 2
Lesson 2.3.2
y
Home Runs
2-124.
Season
x
2-125. a: Rescale the vertical axis evenly. (See graph at right above.)
b: Rescale both axes so that zero is at the origin and the end
points are on the axes. (See graph at right below.)
y
2-126. Scaling by any whole number from 7 to 10.
2-127. a:
c:
2-128. a:
8
15
! 10
21
b:
d:
33
80
b: 0
4
7
16
15
x
or
1
1 15
c: 60% or
18
30
2-129. a: It makes it 4 times larger because dividing “undoes” multiplication.
b: It also does not change the value of a number because a number over itself = 1.
c: Less than, because 80% is less than 100%. Greater than, because 120% is
greater than 100%.
Lesson 3.1.1
3-7.
a: 21
7
4
4
4
2
b: 7 + 3(4 + 2) = 25 , (7 + 3)4 + 2 = 42 , (7 + 3)(4 + 2) = 60
3-8.
a: !27.1! 53.2 = 53.2 ! (!27.1) = 80.3
b: 71.54 ! (!28.3) = !28.3 ! 71.54 = 99.84
c: !38.9 ! (!7.3) = !7.3 ! (!38.9) = 31.6
3-9.
a: 110 songs
3-10. a:
7
12
b: 84 pairs
c: 5 miles
b: 2 whole pizzas, 1 extra piece
c:
25
12
3-11. Reading the numbers from left to right: top 10, 5, middle 20, 200, 100, bottom 7, 70, 35;
(15)!(27) = 405
13
Lesson 3.1.2
3-19. a: –8
– –––
– –––
b: 0
– ++
– ++
3-20. a: –18
b: 33.1
c: 27
d: 50
3-21. a: 0
b: –3
c: 3
d: –6
3-22. a:
7
35
=
1
5
b:
20
35
=
c: –3
++ –––
++ –––
+ ––
–
–
4
7
3-23. a: seven-eighths, 87.5%
c:
25
35
=
b:
27
10
, 2.70
5
7
Lesson 3.2.1
3-34. a: remove 7 positive tiles. –1
b: remove 2 negative tiles. 8
c: remove 3 positive tiles. 3
3-35. a: 7 ! 4 = 4 ! 7 = 3
b: 5 ! (!2) = !2 ! 5 = 7
c: !1! (!3) = !3 ! (!1) = 2
3-36. a: + + + + +
–––
–––
++++
+++
––––
++++
–
3-37. a: Yes
14
17
12
5
or 1 12
c: 10. Removing –5 made the sum 5 larger.
b: j + j + k + k + k or 2j + 2k
c: 23 feet
3-38. a:
b: 5
d: 12 feet
b:
5
8
c:
3
15
or
1
5
d:
8
21
Core Connections, Course 2
Lesson 3.2.2
3-46. a: –2
_____
+++++ ++
c: 2
3-47. a: -13
_____
_____
__
b: –12
+++++
_____ __
d: 2
_ _ _ _ _ _ _
++
b: –2.31
c: –5
d: –200
3-48. a: The acrobat does a trick 3 times and then walks 10 ft to get to the end. The trick is 6 ft.
b: The acrobat does a trick two times to get to the end. The trick is 3.5 ft.
3-49. a:
4
12
b:
11
8
or 1 83
c:
7
12
3-50. a: P = 16 un., A = 15 sq. un.
b: P = 24 un., A = 27 sq. un.
c: P = 15.2 un., A = 13.8 sq. un.
Lesson 3.2.3
3-59. a: –12
b: !12 12
c: –18
3-60. a: –18
b: –18
c: 24
e: –4
f: 4
b: –14
c: 12
d: 0
3-61. a: !2 16
3-62. a:
13
12
1
or 1 12
b:
11
60
c:
6
24
d: 9.7
d: 0
or
1
4
d:
28
40
or
7
10
3-63. 21
15
Lesson 3.2.4
3 ! 5 6 ,
3-73. a: 2 10
100
3-74. a: 0.004
3-75.
1
1
10 ! 100
1
= 1000
b:
b: –0.0006
4
1000
42 ,
! 3 100
c: 0.28
1
1
1000 ! 100
1
= 100,000
d: She is correct
20335 ! (!282) = 20617 feet
3-76. mean = 3.9, range = 14, median = 3
3-75. a:
10
24
or
5
12
b:
6
20
or
3
10
Lesson 3.2.5
3-82.
!4 "
!3 "
= !8
!6
2
3-83. a: –9
3-84. a:
13
7
b: –13.7
b:
5
1
= 18
a:2 !
= "24
" 12
c: –28
c:
1
2
!1b:
" = 17
! 17
d: 6
d:
8
21
3-85. Possible answers include: 3! 8 + 6 " 2 = 28 , 6 ! 8 ÷ 3 + 2 = 18 , 3! 6 + 2 ! 8 = 34
3-86. a: 1
b: 13
c: 27
8
31
e: Each problem is a pair of fractions whose product is 1.
16
d: 2 and 5
Core Connections, Course 2
c:
Lesson 3.3.1
3-93. a: !
3
4
3-94. a: 4
1
2
b: !
or –0.75
3
4
or –0.75
b: !2 12
3-95. a:
b:
1!2
3 5
c: 0
d: not possible
c: !1 13
d: 5 13
c:
3-96. a: –8 – – – – – –
––
b: –4
2
15
of the playground.
––––––
3-97. 50
Lesson 3.3.2
3-107. a: 63
b: 63
3-108. a: (0.3)(0.04) = 0.012
b: 5.13 + 12.6 = 17.73
c: 47.7 ! 23.19 = 24.51
d: 47.7 ! 23.19 = 24.51
e: 1.4 + 0.14 = 1.54
3-109. a: Decimal in wrong place, 5.0
b: Decimal not aligned, 469.213
c: Did not add 0s, 37.163
d: Decimal in wrong place, 0.003702
e: Did not add 0 to top number, 3971.32
f: Decimals not aligned, 78.473
3-110. a:
9
20
d:
3-111. a: !
36
5
b:
= 7 15
4
5
1
5
c:
e: 12.308
b:
35
12
11
= 2 12
c: not possible
38
9
=4
2
9
f: 0.000208
d:
8
15
17
Lesson 3.3.3
3-120. a: Commutative Property of multiplication, Associative Property of multiplication,
multiplied terms together, then simplified.
indicated by grouping symbols, added each term.
3-121. a:11
b: 35
c: 14
3-122. a: Adding one positive piece and one negative piece will result in a value of –2.
b: Removing four negative tiles will result in a value of 2.
3-123. a:
b:
–10
2
3.4
–5
–3
3-124. a:
1
3
b:
3-125. a: 5
b: 8
3-126. a: –7
b: 70
16
c:
34
3
10
13.4
d:
5
15
–3
–5
–8
71%
c: 5 out of 9
c: 0
3-127. \$10.59
3-128. a: !
3
4
= !0.75
3-129. a: 3 12 ! 1+ 6 12
46 =
b: 0.46 = 100
23
50
c: 22.724 =
22724
1000
=
5681
250
b: 9 feet
c: 9 feet. The answers are the same. The distances are the same, they are just in a
different order; the Commutative Property supports this result.
18
Core Connections, Course 2
Lesson 4.1.1
4-6.
a: –1
b: 9
c: –24
4-7.
a: 7.13
b: 4.564
c: 2.88
4-8.
a: 210 sq ft
b: 30 sq yds
4-9.
a: 14
b: 40
c: 16
b: –30
c: –12
4-10. a: –14
d: 48
Lesson 4.1.2
4-16. a: 11
4-17. b: 54 sq yds
4-18. a:
4-19. a:
1
6
b: 8
c: \$131.22
b:
–3.6
–3
1.2
–1.8
4-20. a: 59.5
d: 0.34
d: 120 ft., \$30
1
2
c:
b:
–2
6
4
2
3
c:
–12
e: \$161.22
24
–8
–3
–11
b: 69.28
c: 35.38
e: 134.12
f: 37.431
d:
–56
7
–8
–1
19
Lesson 4.2.1
4-29. Missing prices from table: 1.80, 5.40, 7.20, 9.00, 10.80, 12.60, 14.40
4-30. Yes, it is proportional because each tune is the same cost, \$6.25.
4-31. a: 4
d: –11
4-32. a:
c: –15
e: 14
f: 24
b:
6
–6
b: –1
3
–1
c:
–24
–8
–5
–7
4-33. a: 18.5 min
d:
12
1.2
24
4
10
6
10
11.2
b: 17.6 min
Lesson 4.2.2
4-41. Yes. The graph is a line that contains (0, 0), or all y-values are 3.15 times their
corresponding x-values.
4-42.
4 =
P(Brown) = 10
2 =
P(Red) = 10
1
5
2
5
3 = 30% = 0.3 ,
= 40% = 0.4 , P(Green) = 10
1 = 10% = 0.1
= 20% = 0.2 , P (Purple) = 10
4-43. a: The acrobat repeats a trick 4 times to cross a 12-foot tightrope; x = 3
b: The acrobat crosses twice, once by repeating a trick 4 times and then walking 3 feet,
the other time by doing the trick once and then walking 21 feet; r = 6.
4-44. a: Distributive Property, Commutative Property of Addition, Commutative Property of
Multiplication; –2
b: Multiplies terms, Commutative Property of Addition, 22
subtracted terms; 20
d: Associative Property of Addition, 8
4-45. Possible answers: \$27 is one third of \$81; \$81 is \$54 more than \$27; \$27 is \$54 less than
\$81; \$81 is three times \$27.
20
Core Connections, Course 2
Lesson 4.2.3
4-50. a: Pounds of Nails
Cost (\$)
3
5
6
8
10
20
x
0.86 1.26 2.15 2.58 3.44 4.30 8.60 0.43x
c: Nails cost \$0.43 per pound.
Bus Cost per
Student
(dollars)
b: \$0.45
2
\$24.13, \$17.50, \$10. No, it can never pass through (0,0).
4-52. 176.6º C
4-53. a:
7
30
1
b: ! 14
1
c: ! 24
Students on Trip
4-54. 185
Lesson 4.2.4
4-60. Yes. See diagram at right.
2.2 yards of dirt
are excavated
each hour.
4-61. 0.13 cm/sec
4-62.
2.2
4-63. a: 0
c: –96
4-64. a: 54 feet
D = 2.2H
2.2
A = 59.5 square feet, P = 31.6 feet
1
b: –20
H 0 1 D 0 2.2 d: –166
b: 2(15) + 2(12) or 12 + 15 + 12 + 15
4-65. a: Not proportional, the equation should only contain multiplication.
b: Proportional
c: Not proportional, the equation should only contain multiplication.
4-66. a: 60 bricks
b: Between 6 and 7 ft or 6 ft, 8 in.
4-67. a: The new shape will be larger because the scale factor is greater than one.
b: Answers vary, but should be greater than 0 but less than 1.
c: Answers vary, but should be greater than 1.
4-68. Maude’s probability is 5 out of 8 while Claude’s is 7 out of 12. Reasoning may vary, but
the grandmother has a greater probability.
4-69. a: \$21
b: \$32
c: \$52.50
21
Lesson 4.3.1
2
2
4-75. a: 2x + 3x un , 6x + 6 un.
4-76. a: 25
b: The area would not change.
b: 45
c: 30
4-77. No. It does not contain the point (0, 0).
4-78. A = 130 ft2, cost = \$650
4-79.
6 = 6.54 miles per hour
6 11
b: 5x2 + 7x + 5
4-81.
21
100
, twenty-one hundredths
4-82. a: right or scalene triangle
c: trapezoid
4-83. a:
–6
–14
4-84. a: 17.5 ft.
22
b:
48
–8
b: obtuse or scalene triangle
d: rhombus or parallelogram
c:
–96
12
–8
4
b: 175 sq. ft.
0.06
0.2
0.3
0.5
d:
–20
4
–5
–1
c: 2
Core Connections, Course 2
Lesson 4.3.2
4-93. a: 4x + 4 units
b: 4x + 4 units
4-94. Scale factor: divide by 5 or multiply by
4-95. a:
1
6
b:
1
4
1
5
; new sides: 4,
c:
18
5
1
2
or 3 53 ,
12
5
d:
or 2 25
1
3
4-96. \$7.68/pound
b: !\$23.75 = \$23.75
4-97. a: 250 ft =250 ft
d: \$198.32 = \$198.32
c: !5 yds = 5 yds
e: !86 m = 86 m
4-98.
A = x 2 + x , P = 6x
a: P = 42 un., A = 56 sq. un.
b: P = 15 un., A = 8.75 sq. un.
c: P = 90 un. , A = 240 sq. un.
4-99. 24 in.
4-100.
4
15
4-101. a: 3
d: 1
b: –24
c: 7
e: 7
f: 0
4-102. See diagram at right. decimal = 0.45, percent = 45%
23
Lesson 4.3.3
4-112. a: 4x + 4 un.
x2 + x + 1 un2
b: 2x + 4 un.
x + 1 un2
c: 4x + 6 un.
x2 + 2x + 1 un2
4-113. a: –4x + 4
b: 10
c: 3(x + 2)
e: 2x3 – 3
4-114. a:
b:
or
seventeenhundredths
fifty-fivehundredths
0.17
4-115. a:
7
10
4-116. a:
20
100
17%
b:
2 =
= 10
1
5
9
50
5
c: 1 32
b: 40%
c:
4-117. a: –x – 1
b: x2 + x
4-118. a:\$2.67
b: \$1.33
4-119. a: –1
b: 2
4-120. a: 24 units
55%
0.55
75
100
=
3
4
d: 66.6%
c: 1
b: 18 units
d: 8
c: 10 units
4-121. a: 88 units
b: Kris is wrong, the player who is 88 inches is 7 feet 4 inches tall.
24
Core Connections, Course 2
Lesson 5.1.1
5-9.
a = 72, b = 50%, c = 40%
5-10. a:
x gal
0 gal
0%
55%
80 gal
b: 44 gal now. 36 gal needed to fill tank.
100%
5-11. a: 15
b: 44 , 36
24
e: Possible response: Divide the product
by the given factor to find the missing
value in the Giant One.
c:
5.5
5.5
, 38.5
b:
c:
, 26.4
\$11.34 is earned
per hour.
11.34
1
22
15
8
15
22
15
0.6
0.6
11.34
5-12. See Proportions Web at right.
5-13. a:
d:
7
or 1 15
t 0 1 A = 11.34t
A 0 11.34 7
or 1 15
Lesson 5.1.2
5-18. a: 25%
b:
3
1
or 3:1
5-19. 70 points
5-20. a: 10 ft x 15 ft
b: bathroom: 63 ft2
living room: 150 ft2
kitchen: 105 ft2
5 or ! 1
5-21. a: ! 10
2
7
b: 1 24
5-22. a:
30
50
or
3
5
c: 318 ft2
b: x = 9 meters, y = 30 meters
25
Lesson 5.2.1
5-29. a:
13
52
5-30. a:
11
44
or 25%
b:
4
6
b:
22
44
or ≈ 66.67%
d: P(face card) with normal deck is 12
52 . It is more
likely to draw a heart in the modified deck because
there are fewer non-face cards.
5-31.
c:
3
18
c:
12
44
e:
33
44
or ≈ 16.67%
mean = 3.75 miles, median = 3.5 miles
5-32. a: 459 in.2
b: 93.38 m2
5-33. a: 23
b: 2
c: 9
d: –5
Lesson 5.2.2
5-38. a:
8
20
>
4
20
; Game I
b:
4
20
=
8
40
; Equal Chance
c:
5
40
<
4
25
or 12.5% < 16% ; Game II
5-39. a:
8
20
b: 1
c:
9
20
5-40. 80%
5-41. a: 27
c: 6
b: 12
d: 61
5-42. a: See graph at right.
b: parallelogram. 30 un2
26
Core Connections, Course 2
Lesson 5.2.3
5-49. a: independent
b: dependent
c: independent
d: independent
5-50. a: WA, WC, WB, SA, SB, SC
d:
1+1
3 6
=
b:
1
2
1
3
c:
1
2
e: 0
5-51. A= 3x + 3, P = 2x + 10
a: P = 28 cm, A = 30 cm2
b: P = 11 cm, A = 4.5 cm2
c: P = 40 cm, A = 48 cm2
5-52. 72.5%; Possible reasoning:
5-53. a: 8x +5
29 ! 2.5
40 2.5
=
72.5
100
c: 14x2 + 6x +8
b: 7x + 1
d: x2 + 6x + 5
Lesson 5.2.4
5-60. 8 possible sundaes
See table at right.
5-61. a:
5
40
or
1
8
2 cups
5-62.
43
46
c:
750
50000
or
b:
2!cups
6 cups
=
c: She did not;
2
36
5-64. a:
or
3
200
4 cups
6 cups
0%
33.3%
5-63.
b:
100%
Ch V M Co H C ChH ChC VH VC MH MC CoH CoC 1
3
66.6%
3
10
!
2
6
because the two ratios cannot be related by a Giant One.
1
18
0.32
0.4
0.8
1.2
b:
c:
154
11
14
25
d:
63
–9
–7
–16
234
18
13
31
27
Lesson 5.2.5
5-71. a: See probability tree at right. 9 possibilities
b: P(match) =
3
9
Y
Y (YY)
G (YG)
W (YW)
G
Y (GY)
G (GG)
W (GW)
W
Y (WY)
G (WG)
W (WW)
. The game is not fair.
5-72. 12 possible outfits.
5-73. a: \$31 billion or \$31,000,000,000
b: \$217 billion or \$217,000,000,000
c: 3%
5-74. a: 4
c: 1
b: –50
d: 1
5-75. P = 6x + 2, A = x2 + 2x +1
Lesson 5.2.6
5 = 1
5 =
5-83. a: 1! 14 ! 12
b: 1! 14 = 43 or 13 + 12
3
c: Lose a turn. It is a greater fraction.
5-84. a: 13.75 cm2
3
4
b: 7.75 cm2
5-85. \$350
5-86. a: 66 blue blocks
b: 11 green blocks
5-87. a: 3 58
b:
3
10
c: 3 45
b:
3
5
c:
5-88. a:
5-89.
3
5
9
25
21
225
5
5-90. a: See graph at right.
b: Rectangle. A = 24 un2; P = 20 un
-5
5
-5
c: Answers vary; change (2, 3) and (–2, 3) to (2, 5) and (–2, 5).
5-91. \$0.85/pound
5-92. a: 58
28
b: 96
c: 50
d: –16
Core Connections, Course 2
Lesson 5.3.1
x feet
x feet
7 feet
x feet
x feet
7 feet
x feet
x feet
5-99. See diagram at right. P = 6x + 14 ft
5-100. a:
–18
–12
–6
0
6
12
18
–36 –27 –18
–9
0
9
18
b:
27
36
c:
–700
d:
–350
–44 –33
0
350
–22 –11
0
700
11
1050
22
33
1400
1750
44
5-101. \$53.33
5-102. a: 8
b: –6
5-103.
c: –9
d: 117
86.8 pieces of candy
wrapped per minute
86.8
86.8
1
t 0 1 P = 86.8t
P 0 86.8 Lesson 5.3.2
5-110. a:
1
9
b:
1
9
5-111. a: \$1.50
b: \$9
5-112. a: 106
b: 50
5-113. a: x – 2x + 2 – 3 = –x – 1
c: 41
b: –x + 2x + x2 – 1 = x + x2
5-114. a: P = x + x + x + x + 1 + (x – 1) + 1 + 1 + (x – 2) or 6x units
b: A = x2 + x + 1 un2
29
Lesson 5.3.3
5-123. a: The longer side has two more than the shorter side.
b: The x + 2 side.
c: 12 units and 14 units
5-124. a: –11
b: –11
c: 54
5-125. a: 6x – 1
b: 3x – 12
5-126. a: ≈ 11.4%
b: ≈ 9.38%
5-127. a: Yes. Justifications vary.
c: Middle School
b: Distributive Property
Lesson 5.3.4
5-138. a: 60
b: 8
c: 120
d: Subtract known from total.
5-139. 468 miles. 234 miles.
5-140. a: 4x + 8
b: –45 – 5x
c: 7x – 21
5-141. a: –13
b: 12
c: –1
d: –42
c: –9
f: 24
5-142. x = 26 23 mm, y = 81 mm, z = 22.5 mm. Scale factor =
3
2
Lesson 5.3.5
5-144. 50 boys and 106 girls
5-145. a:
b:
0
0
c:
–16
6
8
6
–2
6
d:
–16
4
–4
0
52
5.2
10
15.2
5-146. C
5-147. a:
1
10
5-148. a: 20
30
b:
4
10
=
2
5
c: 20 people
b: –4
Core Connections, Course 2
Lesson 6.1.1
b: 2x2 + 4x – x + 2 – 3 = 2x2 + 3x – 1
6-6.
x – x + 1 – 3 = –2
6-7.
Parts a, c, and d match the perimeter.
6-8.
23 or !1 3
a: ! 20
20
d:
6-9.
19
15
b:
4
or 1 15
e:
c: ! 63 or ! 12
5
24
53
56
25 or !1 7
f: ! 18
18
a: About 12. There are 6 possible outcomes and 72 divided by 6 is 12.
b: About 36. Half of the possible outcomes are even.
c: 30 times
6-10.
a: One possible answer: \$13 is one third of \$39.
b: One possible answer: 17 feet is 8 less than 25 feet.
c: One possible answer: 38 lbs. is twice as much as 19 lbs.
6-11. a: –5 < –2
b: 8 > –1
c: –5 < 0
d: –15 < –14
Lesson 6.1.2
6-17. a: Mat A = 4x + 2 ! 2x ! 1 , Mat B = 4x ! 2x + 6 ! 4 , 1 < 2; Mat B is larger
b: Mat A = 5x + 23 – 2x – 1, Mat B = 5x – 2x _ 4 + 6, 2 = 2, Equal
6-18. a: It should have one pair of opposite sides labeled x and the other pair labeled 4x.
b: One is four times the length of the other.
c: One is 6 feet, the other 24 feet.
6-19. a: –92
d: 2
b: –42
c: –5
e: 53
d: ! 12 or –0.5
y
6-20. a: 2(x – 3) = 2x – 6
b: 5(x + 7) = 5x + 35
c: 10x + 20 = 10(x + 2)
x
6-21. Quadrilateral (or parallelogram); See graph at right.
6-22. 15% is \$4.11
31
Lesson 6.1.3
6-29. a:
b:
3
5
c:
–4
6-30. a: n + 7
b: 2x
6-31. a: 7 is the constant term when the expression is not simplified (5 is the constant term
when the expression is written in simplified form).
b: 2 and 4x +1. 4 and x
c: Possible answer: –3m + 17
d: 4 and 11 are coefficients; –37 is a constant term; 4x2, 11y, and 37 are the three terms;
4x 2 + 11y ! 37 is an expression (but so are 4x2, 11y, and 37); x and y are variables.
e: 8 and m + n are factors of 8(m + n), which is a product.
The entire expression is a sum.
6-32. a: \$123
b: 75%; \$615
5!m
m
is a quotient;
c: \$902
6-33. 16 or 17 times
6-34. a: P = 4x + 6, A = 4x + 4
b: P = 4x + 12, A = 2x + 5
Lesson 6.1.4
6-42. a: x < 1
x
b: x ! 10
6-43. a: No
b: Yes
c: Yes
6-44. a: 30
b: –21
b: 0
6-45. P = 4x + 4
a: 32 cm
b: 26 cm
x
d: Yes
6-46. a: One possible answer: A triangle has a long side that is twice as long as the short side;
the medium side is two more than the short side; the total perimeter is 74 units; how
long is the short side?; other scenarios could involve ages, distances, etc.
b: Possible answer: short side length, long side length, and medium side length
6-47. a: 1.5 gallons
32
b: 20 minutes
Core Connections, Course 2
Lesson 6.2.1
6-54. 3(x + 1) = 12 or 3x+3 = 12
b: x = 3
6-55. She is correct.
b: x + 1 = 4
c: 3 + 1 = 4
6-56. a: 25(3x – 2)
b: 16x(2x + 3)
c: –10(4m + 3)
6-57. a: x = –4
b: x = 4
c: x = 14
d: 9m(7m – 6)
6-58. A and D are equivalent because they both equal positive 4;
B, C, and E are equivalent because they all equal –4.
6-59. a: 58.8x – 29.7
b:
3
5
23
x ! 36
Lesson 6.2.2
6-65. a: Correct
b: Incorrect
6-66. a: x – 4
b: 2x + 12
6-67. a: –2 < 4
b: –20 = –20
c: 13 < 24
d: –8 < –4
6-68. a: 9
b: 6
6-69. a: P = 40.3 yds, A = 77 sq yds
b: P = 60 ft, A= 150 sq ft
6-70. x is number of yards gained by Alston, x + 3x + 3x + 10 = 430; 180 yds.
33
Lesson 6.2.3
6-81. a: x = 7
b: x = 15
6-82. a: 224 students
b: 50%
6-83. a: 91%
b: 88.5%
6-84. a: 4(5y – 21)
b: 24b (b + 4)
6-85. a:
b:
13
1
13
c: 10%
c:
16
–2
–8
14
–5.04
1.2
–10
d:
–4.2
–3
0
15
0
15
6-86. 51 acres
6-87. a: x = –6
6-88. a: ! 146
700 or !
b: x = –4
73
350
23
d: 13 45
7
c: ! 80
b: 0.12
e: !
35
34
1
or !1 34
6-89. P = 17 un, P = 8.5 un
6-90. a: 6
f: –1.8 or !1 45
b: A= 12 sq un, A= 3 sq un
b: 9
c: 14
6-91. a: See graph at right. Trapezoid
b: 24 sq un
6-92.
34
p + 30 ! 35 , 0 ! p ! 10 less than or equal to
10 sections but greater than or equal to
0 sections, since there cannot be a negative
number of trim pieces.
1
2
Core Connections, Course 2
Lesson 6.2.4
6-97. Let p represent the number of pepperoni pizzas,
p = ( p ! 8) + 3p = 112 16 veggie, 24 pepperoni, 72 combo pizzas
6-98. a: Both work but adding 5 to both sides will isolate the x term.
b: x = 4
6-99. a: 2.5
b: s = 14 t = 40
c: Answers will vary, but the scale factor should be between 0 and 1.
6-100. a: A = 79.05 sq ft, P = 35.9 ft
b: A = 151.29 sq mi, P = 49.2 mi
c: A = 15.75 sq cm, P = 17 cm
d: A = 2653.2 sq cm, P = 278.89 cm
6-101. a: 30(3k ! 2)
b: 6d(5d ! 3)
6-102. a: Cannot be determined
b: Yes, Mat B greater
c: Yes, Mat A greater
6-104. a: x = 4
b: x = 19
c: x = 5
6-105. a: n – 3
b: 3x + 9
c: 5x – 2
Lesson 6.2.5
6-106. height = x = 18cm, base = 3x = 54 cm
6-107. a:
1
7
b:
1
13
c: 0
b: Yes, 4 23 .
c: No, has subtraction.
6-109. a: m = 3 feet
b: m + 7 = 2m + 4; 3 feet
c: 10 feet
6-110. a: x = 5
b: x = 8
c: x = 16
6-111. Lower = 320 feet = x – 355, Middle = 675 feet = x, Upper = 1430 feet = 80 + 2x
6-112. a: 71
b: –102
6-113. a: 3(4) + 7 , 2(7) + 5
c: 72
b: 6(3) + 7, 4(7) ! 3
d: 49
c: 5(5) ! 2, 2(9) + 5
6-114. 26.57 blocks/hour
6-115. \$49.50 + \$12.99s ! \$100 , s ! 3.89 ; She can buy 3 shirts.
35
Lesson 6.2.6
6-122. a: x = 0
b: No solution
6-123. a: Incorrect
b: Correct
c: All numbers
6-124. a: No, fractional coefficients are more complex.
b: Yes, all constants are together on one side of the mat.
c: Most simple because x is isolated.
d: Part C is most efficient.
\$16 · 4 = \$64
\$16
6-125. a: \$80; See diagram at right.
\$80
b: \$8
0%
20%
c: \$12
100%
20% · 4 = 80%
6-126. a: 4(4x ! 1)
b: 5x(!2 + x)
c: 6(5y ! 4x)
6-127. a: 2x + 7 = 13, x = 3
b: 3 j + 15 = 27, j = 4
c: 2n + 4(6) = 44, n = 10
Lesson 6.2.7
b: x = 12
6-135. a: x = 1
b: x = 1.5
c: x = 8.36
d: x = 3
6-136. Reasoning will vary.
a: 57 lb
6-137. a: 0.4
b: 8.5 lb
c: 76 lb
b: –2
c: !
a: 13 , 33.3% , 0.3
c:
45
50
90%, 0.9
6-139. a: x + 6
36
b: y ! 5
13
44
d:
b:
14
40
, 35%, 0.35
d:
12
75
, 16%, 0.16
c: 2x + 3
4
15
d: 5y
e: 4.8
f: ! 10
13
e: 11; 3; 13; 40
Core Connections, Course 2
Lesson 7.1.1
Lunches:
75
Distance (miles)
7-10. 55 mph
7-11. See graph at right.
7-12. See diagram at far right.
No Lunches:
225
300
0%
25%
100%
75%
Time (hours)
7-13. a: 8x ! 1
b: !8x ! 1
c: 14x 2 + 6x + 8
d: 5x ! 20
7-14. Yes
7-15. Side lengths: 12.5 ft, 10 ft, and 7.5 ft,
P(original) = 20 ft, P(new) = 50 ft,
A(original) = 22 ft2, A(new) = 137.5 ft2
Lesson 7.1.2
7-21. a: No, she will only go a little over 23 miles.
b: 0.77 hours or 46.3 minutes
7-22. a:
5
6
7-23. a:
11
10
b:
c: They are scale factors or reciprocals.
b: !1.8 + 1.1x
1
x ! 12
7-24. 0%
6
5
42 students
28 students
60%
40%
0%
70
100%
D
7-25. a: 6 possible bouquets. See diagram at right.
F
7-26. a: 1.5 degrees F
S
D
b: Q1 = –2, Q3 = 5
c: IQR = 5 – (–2) = 7
C
L
C
S
37
Lesson 7.1.3
7-33.
(0.2)(25.7) = 5.14 kwh , 25.7 ! 5.14 = 20.56 kwh ,
OR 100% ! 20% = 80% , (0.8)(25.7) = 20.56 kwh
7-34. a: 7x + 1
b: 2x + 1
7-35. a: 24
b: 32
c: x 2 + 3x
d: 6x ! 4
7-36. Australia: 60, 66, Africa: 60, 72, Britain: 58, 67, Turkey: 54, 54
7-37. a: 24
e: –2.81
f:
11
d: ! 164
120 or !1 30
c: 2 57
b: 42
3
8
stem
7-38. a: See sample plot at right.
leaf
4
Frequency
b: See histogram at far right.
c: The data is symmetric, single-peaked,
and relatively closely packed.
3
2
1
d: No apparent outliers, either the mean
or median would be appropriate.
100
e: median: 122 lbs, mean: 124.82 lbs
110 120 130 140 150
Weight of a Player (pounds)
f: Data spreads from 106 to 147, or a range of 41.
Lesson 7.1.4
7-45. Method 1: (0.15)(2800) = 420 , 2800 ! 420 = 2380 calories per day,
Method 2: 100% ! 15% = 85% 2800(0.85) = 2380 calories per day
7-46. x = growth of semi-dwarf; x + 0.5x + 3x = 27 ;
The dwarf grew 3 in., the semi-dwarf grew 6 in., and the full-size tree grew 18 in.
7-47. \$75
7-48. a: 24
7-49. a: P(5 or 3) =
7-50. a: 2x 2 + x ! 10
38
b: ≈ 29%
2
6
=
1
3
b: P(5 and 3) =
c:
1!1
6 6
=
1
36
7
24
c: P(12) =
1
36
b: x 2 ! 9x + 11
Core Connections, Course 2
Lesson 7.1.5
7-57. a: Q1 = 9.5, median = 11.5, Q3 = 14.5
b:
c: 14.5 ! 9.5 = 5
9
8
10 11 12 13 14 15 16 17
7-58. 48
7-59. 420 minutes
7-60. a: x < 3
b: x < !1
c: x ! "2
7-61. a: \$13.50
7-62. a: 3.3x + 13.2
b:
1
2
c: 5.2x + 6.82
x+6
Lesson 7.1.6
7-70. a: x = –2
b: x = ! 52 or –2.5
7-71. a: x = –2
b: x = !
7-72.
1
c: x = 15
4
3
x + 2x + 2x + 8 = 43 ; # of zucchini plants = x. 7 zucchini, 14 cucumbers, 22 tomatoes
7-73. a: 80, 40, 20
b: 75, 45, 30, 15
c: 125, 75, 50, 25
d: 450, 300, 150, 50
7-74. a: 18
b: median = 70, first quartile = 58.5,
third quartile = 83; See graph at right.
2
3
4
5
6
7
589
023445578
023334455678
017
03
4
c: The data slightly non-symmetric; has a
large single peak, 74 is possible outlier.
d: Median, 43, is better choice the mean
age is 42.4 years old.
b:
12
10
8
Frequency
7-75. a:
6
4
2
0
10
20 30
40 50
60 70 80
Age
39
Lesson 7.1.7
7-80. 87.5%, 0.875,
7
8
7-81. a: x = 235.29
7-82. a: 77
b: x = 120
b: Q1 = 62, Q3 = 83
c: 21
d: 73.36
7-83. a: W = 40 ft, L = 85 ft
b: A = 3400 sq ft
7-84. a: F
c: T
b: T
d: T
7-85. 12 slices = 20 minutes, 30 minutes = 18 slices
Lesson 7.1.8
7-90. a: \$3700
b: \$3800 (The first is better by \$100.)
7-91. \$19,040
7-92. a: \$30 is the discount
b: Yes
c: Yes
7-93. a: x = 2
b: x = 0
c: x = 17.56
7-94. No, his savings increase by adding money each week, not multiplying.
7-95. a: 25%
b: 50%
c: No, single points not given.
d: 5, it splits the data in half.
40
Core Connections, Course 2
Lesson 7.2.1
7-100. a: x = 4
b: x = 6
6 or
7-101. P(blue or pink) = 16
c: m = 475
3
8
7-102. 30%
7-103. a:
e:
5
24
120
800
b:
or
40
12
or 3 13
c:
3
f: ! 27
8 or !3 8
3
20
77
16
d: ! 60
7 or !8
13
or 4 16
1
g: ! 21
4
7
42 or ! 21
h: ! 100
50
7-104. She will have \$1556.88 in 5 months.
Number of Guesses
7-105. a: See histogram at right.
b: See box plot at far right.
Q1 = 68, Med = 77.5, Q3 = 93.5
c: Median, outlier of 152.
d: The box plot.
60 100 140
Amount of Jelly
Beans Guessed
Lesson 7.2.2
7-112. a: x = 50
7-113. a:
15
3
b: m = 4
c: x = 2.4
b: x = 7.7
c: y = 40
d: x = 84
7-114. x = number of customers week 1 , x + (x + 18) + 2(x + 18) ! 4 + 92 = 382 , x = 60 , so
60 + 18 = 78 customers in week 2.
7-115. a: x = 2
7-116. The blue section is
is 83 .
b: x = 5.75
1
6
, the red section is
c: x = 5.2
1,
3
the green section is
d: x = 6
1
8
and the purple section
7-117. Answers in back of book: Checkpoint 7B.
41
Lesson 8.1.1
8-8.
Note: 2 1 means 21
a: See diagram at right.
b: Median = 89, Q1 = 63.5, Q3 = 99
8-9.
a: ! 13
60
b:
c: !
11
36
8-10. a: x = 1
11
38
d: !
4
3
or !1 13
b: x = –2
8-11. x = 2 short sides; x + x + (x + 12) + (3x ! 9) = 117 .
Sides are 19 cm, 19 cm, 31 cm and 48 cm.
3
4
5
6
7
8
9
10
3
5
07
7
49
678
000
8-12. \$0.25, \$1, \$0.50, \$5, \$1.50, \$2, \$2.50
8-13. a: See histogram at right.
Frequency
10
b: The data is nearly symmetric with no outliers so either
mean or median are appropriate. Mean = 16.69 books,
median = 13.5 books
c:
5
0
0
10
20
30
10
20
30
40
40
d: The typical student reads about 13.5 books; the distribution is nearly symmetrical and
single-peaked; some students may say there is a slight right skew, apparent in the box
plot; the IQR is 12.5 so there is a lot of variability in the number of books read; there
are no apparent outliers.
8-14. a:
b:
c:
8-15. a: x = –8
b: x = 3
c: x = –15
b: 29.75%
c: 10.5%
d:
8-16. 1.6%
8-17. \$8.40
8-18. a: 9%
42
d:7.9%
Core Connections, Course 2
Lesson 8.1.2
Right Hand
8-23. a: Possible solution plot at right.
b: With his left hand, Lue’s median shot is 5 or 6 inches
closer to the bull’s eye; with his right hand, the
distribution of Lue’s shots is symmetric and single peaked;
with his left hand, the distribution is skewed with a peak at
the bull’s-eye; Lue has more tosses closer to the bull’s-eye
with his left hand; IQR for left hand is about 4.5; neither
hand threw any outliers, but students may feel that 14 is an
outlier for the left hand.
Left Hand
0
6
12
18
c: Lue throws more consistently with his left hand because the IQR is smaller on the box
plots.
8-24. a = 0.3, b = 40%, c = 40%, d = 15%
8-25. a: \$50.40
8-26. She will swim 1034.48 meters.
8-27. Mrs. Chen is 51 years old.
8-28. a: x = 3 43
b: x = 4
c: x = 22.62
43
Lesson 8.2.1
8-35. a: Not representative; neighborhoods in towns tend to have different characteristics from
each other like wealth, ethnic makeup, proximity to services, traffic, etc.
b: Fairly representative; but this will also survey non-voters; it would be better to survey
only voters.
c: Not representative; this samples the population of people who attend church and who
favor the particular pancake restaurant and have the time and money for a leisurely
brunch.
d: Possibly; it might be pretty representative because you will get active citizens who are
also more likely to vote; but if a “hot topic” is on the agenda, you might get mostly
those who are passionate about the one agenda item.
e: This sample is just about the best you are going to get for a representative sample of
voters.
8-36. a: The price increased by 40%.
b: 28.6%
c: Sample response: Each percentage was related to a different whole or original price.
8-37. a:
120
35
or
24
7
3
b: ! 27
4 or !6 4
c:
18
5
or 3 53
8-38. a: A = 420 sq un, P= 112 un
b: A = 744 sq un, P = 186 un
8-39. a: Answers between 25-45 mph
b:
8-40. a: x = 7
c: x = 2
44
b: x = –2
d: x = 4
Core Connections, Course 2
Lesson 8.2.2
8-45. See box plot at right. True % of grocery store shoppers
8-46. a: No, she needs 5 more tiles.
b: Yes, she will have 50 left over tiles.
See diagram below.
8-47. 12 cm
7
8-48. a: ! 24
b: !
c:
35
60
27
12
10
13 feet
1 ft.
1 ft.
20
30
40
50
7 feet
7
or ! 12
or 2 14
d: ! 56
99
e: 1
f:
36
12
or 3
8-49. a: 11.5
b: 6
c:
45
16
13
or 2 16
8-50. \$10.80
Lesson 8.3.1
8-60. a: 40º
b: 100ø
8-61. a: x + x + 10 = 24, x = 7
8-62. a:
27
60
or
9
20
1
e: ! 16
8-63. a:
c: 90º
d: 35º
b: k + 55 = 90, k = 35
3
b: ! 20
c:
252 or ! 14
f: ! 1350
75
7
g: !11 40
40
18
or 2 29
d:
49
16
1
or 3 16
h: –24
b: mean = 25.35, median = 19.5, double-peaked,
measures of center fall between peaks.
Typical times center around 10 minutes and 45 minutes.
0 10 20 30 40 50 60
8-64. Probabilities the same at 60%.
8-65. 0.75x = 61.5, x = 82 miles
45
Lesson 8.3.2
8-74. x = 30º
8-75. a: vertical
b: complementary
c: supplementary
D
8-76. See graph at right.
a: trapezoid
A
b. ∠A = acute, ∠B = obtuse, ∠C and ∠D = right
C
B
pre-emergent
8-77. a: See parallel box plot at right.
b: Yes. Both are fairly symmetric with no outliers.
c: Post-emergent thrushes.
post-emergent
20 30 40 50 60 70 80 90100
8-78. a: \$0.40, \$1, \$2.40, \$3
Price (\$)
b: See sample graph at far right.
c: Yes, because the data makes a straight line through (0,0).
8-79. x = shortest side x + 3x + (10 + 2x) = 142 sides: 22 cm, 54 cm,
and 66 cm
Amount of taffy
(ounces)
Lesson 8.3.3
8-85. a:
b:
c:
d:
8-87. a: r = 3 cm, d = 6 cm
b: r = 1.5 in., d = 3 in.
c: r = 1 mm, d = 2 mm
8-88. Commission = \$80.7, Total pay = \$206.70
8-89. 325 students
8-90. a: 53º
e: 75º
46
b: 95º
c: 47º
d: 43º
f: f = 153º, i = 27º
g: 65º
h: 85º
Core Connections, Course 2
Lesson 8.3.4
8-98. a: 45º
b: 135º
c: 30º
8-99. \$11.25
8-100. (0.35) (60) = 21, 60 – 21 = 39 mpg, 100% – 35% = 65%, (0.65) (60) = 39 mpg
8-101. Mat A has –3 and Mat B has –2, so Mat B is greater.
8-102. a:
8
8
, 96
b:
16
16
, 128
c:
1.5
1.5
, 30
d:
2.5
2.5
, 105
8-103. P (black) = 20%
8-104. No, she can make several quadrilaterals.
3 cm
60°
8-105. Sample diagram at right.
3 cm
8-106. a: 40º and 50º = acute, 130º and 92º = obtuse, 90º = right
b: 40º and 50º
c: 130º and 50º
8-107. a: 4
b: 4
c: 3 58
3
d: 3 20
f: !
e: –1
3
4
8-108. Any can be moved. Move B to (0, 3) or farther, or move A to (–2, 1) or farther up.
8-109. a: x = 7
b: x = –2
c: x = 0
d: x =
2
3
47
Lesson 9.1.1
9-10. a: π cm
b: ≈ 22 m
c: ≈
1
3
mile
d: ≈ 4 in.
9-11. a: Yes
b: Mean = 40.25, median = 42.5; either mean or median is acceptable since the
distribution is fairly symmetrical.
9-12. 2%
9-13. a: x = –12, –8, -4, 0, 4, 8, 12; y = –12, –8, –4, 0, 4, 8, 12
b: x = –30, –20, –10, 0, 10, 20, 30; y = –15, –10, –5, 0, 5, 10, 15
9-14. a: 0.3, 0.075, 0.9, 0.75, 1.2, 7.5
b: Yes, equivalent ratios of \$/eraser
c: \$10.80
9-15. 48 classical, 40 jazz, 32 rock
9-16. a: 6π ≈ 18.84 inches
Method of Sampling
b: 27π ≈ 84.78 cm.
9-17. See table at right.
9-18.
Call every hundredth name in the People with phones who have their
phone book.
number listed.
\$28.14
9-19. Both teams seem to
be very even in total
points; team 1 is
more consistent and
has fewer very low
scores, so it may be
the better choice,
even though Team 2
has a slightly higher
median at this time.
Description of
Actual Population
Call people at home at 10 a.m.
People who do not work outside the
home.
leaves the mall.
People who shop at the mall.
at the bank.
Mail questionnaires to people.
topic to return the questionnaire.
Ask everyone on the school bus.
Students who ride the bus.
9-20. a: 35.6
b: 68.93
c: 15.01
d: 14.39
e: 27
f: 27.5
9-21. a: 25º
48
b: 55º
c: 63º
Core Connections, Course 2
Lesson 9.1.2
b: ≈ 314 cm2
9-32. a: 176.7 m2, 47.1 m
b: a: 254.5 in.2, 56.5 in.
c: 7854 cm2, 50 cm
9-33. See sample diagrams at right.
5.2 cm
9-34. a: Complementary, 22
45°
b: Supplementary, 144
c: Vertical, supplementary, d: 114º, c: 114º, e: 66º
45°
d: Complementary, 30º
4 cm
Objects drawn to scale
9-35. 26 lbs more per tree
9-36.
7
12
5.2 cm
4 cm
cup
9-37. 10 feet by 17 feet
9-38. 1 18 inches
9-39. 9
9-40. a = b = d, c = e
9-41. a:
1
4
b:
11
16
c: 0
Lesson 9.1.3
9-45. a: ≈ 46.27 m
b: ≈ 146.5 sq m
9-46. 21 sq cm
9-47. a: ≈ 50.24 sq ft
b: ≈ 0.2826 sq cm
9-48. Increase it by \$0.90, the new price will be \$3.15.
9-49. a: 2x + 7
b: 2.5x + 16
c: x – 8.8
9-50. a: 25 feet of fence per day per employee
b:
25
1
= 150
x
c: 6 employees
49
Lesson 9.2.1
9-55. a: No
b: Yes
c: No
9-56. a: V= 1 in.3
SA= 6 in.2
b: V= 3 in.3
SA= 14 in.2
c: V= 3 in.3
SA= 14 in.2
9-57. a: 1.20x + 1.50y
9-58. a: 1464 in.
d: Yes
b: \$6.60
b: 146.4 cm
c: 93.6 cm
d: 57.64 in.
9-59. a: A ≈ 153. 9 cm2, C ≈ 44 cm
9-60. a: A = 59 sq. units, P = 40 units
b: A = 130 sq. units, P = 58 units
Lesson 9.2.2
9-65. a: triangles, trapezoids, pentagons
b: hexagon
9-66. a: 192 cm2
b: Two dimensions multiplied
c: 144 cm3
d: Three dimensions multiplied
9-67. 175 miles
9-68. Drawings will vary but must be to scale.
9-69. a:
28
5
= 5 53
7
e: ! 12
9-70. a: False
50
c: 10
d: !4
29
50
7
g: ! 100
h: !56 12
b: False
c: False
d: True
b: –100
f:
1
2
Core Connections, Course 2
Lesson 9.2.3
9-77. Surface area = 46 sq. un., volume = 15 cubic un.
9-78. a: ≈ 201.06 cm2
9-79. a:
5
1250
=
1
250
9-80. a: 113
f: 0
b: ≈ 2827.43 cm2
b: 500 inches or 41 feet, 8 inches
25
36
b: 2401
c:
g: 3
h: 3x
d: 100
c: 102
e: –38
i: –2
9-81.
29 = 8.75 + 2.25x x = 9
9.82.
a: See plot at right; center, shape, and spread are nearly
identical for both groups; median of boys may be about
30 pages higher, but that difference is very small when
compared to variability; both distributions are symmetric;
IQR is about 160-180 pages; neither group has outliers.
Girls
Boys
0
50 100 150 200 250 300
b: It cannot be concluded that girls read more. The difference
of 30 pages is less than 14 of an IQR.
Lesson 9.2.4
9-87. a: Yes, triangle base.
b: No, it is two-dimensional.
c: No, not a polygon.
d: Yes, “L” shaped base.
9-88. a: 500 m3, V = 5000 m3, SA = 2200 m2
b: 40.5 cm3, V = 324 cm3, SA = 326.6 cm2
9-89. a: Sketch should be rectangle.
b: Sketch should be pentagon.
9-90. A ≈ 226.98 mm2, C ≈ 53.4 mm
9-91. a:
2
3
9-92. a: 24 mpg