Selected Answers for

Core Connections, Course 3

Selected Answers 1

Lesson 8.1.1 8-7. a: P = $500 , I = $37.50 , r = 2.5% (0.025) , t = 3 years

b: I = 200(0.04)(5) = $40 8-8. If she takes the loan, she will need to pay back $372; she saves $22 by waiting. 8-9. 5% 8-10. a: 4 x + 2( ) b: –5 9 + x( ) c: 7 x – 3( ) 8-11. a:

#  OF  STUDENTS   Hours  Spent  Studying  Per  Week  Hours  of  After-­‐School  Activities  Per  Week   Less  Than  8  Hours   Eight  or  More  Hours  

Less  Than  5  Hours   2948 = 60%   40%  

Five  or  More  Hours   1650 = 32%   72%  

b: There is an association, but it is opposite what we might expect. 8-12. x = 26 2

3 mm, y = 81 mm, z = 22.5 mm

2 Core Connections, Course 3

Lesson 8.1.2 8-18. Rachel will have $1480, so she will still be $20 short. 8-19. a: 7 zeros. 23 zeros b: Answers will vary. 8-20. a: Answers will vary. b: $3954.16 c: $1031.52 8-21. a: No, it can never pass through (0, 0). b: Yes, there is an association because for every extra student who goes on the trip, the

cost decreases for all the students. Non-linear negative association; the association is very strong; there is no scatter at all in this relationship.

8-22. a: – 1360 b: 1136 c: – 1128 d: – 43 or –1 13 8-23. See graph at right. New vertices: 0, 2( ) , 6, 4( ) , and 4, 8( ) .

All pairs of corresponding sides are parallel.

Number of Students on

the Trip

Bus Cost per Student ($)

10 $35

15 $23.33

20 $17.50

35 $10

Students on Trip

Bus C

ost p

er

Stud

ent

(dol

lars

)

Selected Answers 3

Lesson 8.1.3 8-30. a: 1 represents 100%, or the full amount in the account, and r represents the interest

rate. They are added so that you calculate the percent based on the previous balance, not just the principal.

b: $3813.77 8-31. a: 16 b: 729 c: 15625 d: 16 e: 729 f: 15625 g: Answers will vary. 8-32. Exponent Form: 43, 53, 83

Factored Form: 3!3!3 ; 5 !5 !5 ; 6 !6 !6 ; 7 !7 !7 ; 9 !9 !9 Standard Form: 27; 48; 216; 343; 512; 729 8-33. Let x represent Carrie’s number, x + (x + 9)+ (x + 6) = 207 , x = 64 , x + 6 = 70 , Fran’s

number is 70. 8-34. See graph at right. (2, 5), (2, 1), (5, 0) 8-35. $1813.28, non-linear growth

x

y

A B

C

4 Core Connections, Course 3

Lesson 8.2.1 8-47. a: 42 !53 b: 35 ! y2 c: 64 x4 = (6x)4 8-48. Products: 659.01; 6,893,000; 58,600; 92 8-49. See graph at right. (4 ,4), (7, 4), (6, 7). 8-50. Yes, there is a strong association. If the kelp rate is low, there are

a greater percentage of small crabs. If the kelp rate is high, larger crabs grow. 8-51. ≈ 450. 250. 50 8-52. $46.54 8-53. 1.9 !106 is greater because the power of 10 is larger. 8-54. a: 3.7 !108 b: 7.6 !103 8-55. a: 7776 b: 827 c: 625 d: 132 8-56. a: Both strategies will work eventually, but adding five to both sides will isolate the

x term. b: x = 4 8-57. a: y = 3x – 2 b: Answers will vary. 8-58. This parabola should point downward and pass through (0, 0) and (–2, 0); the vertex is at

(–1, 2). The graph is non-linear.

0

Selected Answers 5

Lesson 8.2.2 8-66. a: 3 b: 34 x4 = 81x4 c: 38 !(13)

2 = 729 d: 7291

8-67. a: Negative b: 6 hours 8-68. a: Solution is incorrect. b: Solution is correct. 8-69. See graph at right. a: (1, !2) , (4,1) , (1, 2) b: (!4, !2) , (2, 4) , (!4, 6)

c: (2, !1) , (!1, 2) , (2, 3) 8-70. a: y = ! 1

2 x +32 b: x = !2y

8-71. a: > b: > c: = d: < e: < f: <

x

6 Core Connections, Course 3

Lesson 8.2.3 (Day 1) 8-88. a: 9.25 !10"1 b: Correct c: Correct d: 8.3!103 8-89. a: The one moves one decimal place to the

right, and the denominator of the fraction is multiplied by 10.

b: They should write 11 zeros after the decimal point followed by a 1.

8-90. a: $6964.42 b: Yes, $8812.22 c: The graph would be a curve that begins at $6439 and curves upwards. 8-91. a: 6 b: 17 c: –4.5 d: 3 e: 13 f: –4 8-92. a: x = 2 b: x = 5.75 c: x = 5.2 d: x = 6 8-93. a: –2, –7( ) b: 1

2 , –4( )

Power of 10

Decimal Form

Fraction Form

1

0.1

0.01

0.001

0.0001

0.00001

Selected Answers 7

Lesson 8.2.3 (Day 2) 8-94. a: 5.4678 !103 b: 3.2 !10"3 c: 8.00702 !106 8-95. a: 1

35= 3!5 b: x210 = 10!1x2 c: 14 d: x2

8-96. a: – 7275 or – 2425 b: 2345 c: 24280 or 335

d: – 2770 e: –4 518 f: 10510 or 10 12

8-97. a: Receiving nutrition advice. b: See table below. c: There does not appear to be an association. Only about 35% of athletes eat a balanced

breakfast, regardless of whether they received the nutritional advice or not. 8-98. a: (1, 4) b: (1, –3) c: The new shape is the same size as the original. It is rotated 180° or reflected over the

x-axis and the y-axis. 8-99. a: y = 27 + 43x b: After 23rd day.

Lesson 8.2.4 8-109. a: 6 !105 b: 6.875 !106 c: 2 !105 8-110. a: x7 b: y3 c: x7 8-111. a: Positive b: None c: Positive d: Negative 8-112. a: The picture would be 32 inches tall. b: The picture would be 2.25 inches wide. 8-113. a: ≈ $40 b: ≈ $55, draw a trend line and read the point from the y-axis. c: ≈ $75, extend the trend line. 8-114. a: 4.5 pounds b: 40 dozen

# OF ATHLETES Received Nutrition Advice

Did Not Receive Nutrition Advice

Regularly Ate a Balanced Breakfast

Often Did Not Eat a Balanced Breakfast 66% 65%

8 Core Connections, Course 3

Lesson 8.3.1 8-124. a: 8 b: 1 c: –2 d: –9 8-125. a: 2.4 !108 b: 1.4 !10"9 c: 2.25 !10"2 8-126. a: x = 7 b: x = 1

2 y –1 c: x = 2 d: x = 38 y + 3

8-127. See table at right. a: y = 2

3 x + 2

b: 23

c: Linear growth, it has a constant growth rate or slope. 8-128. a: 208 = 2.5 b: s = 14, t = 40 c: Answers will vary. 8-129. Answers will vary. 8-130. a: 100 ° b: 43 ° c: 47° d: d = 148 ° ; f = 32 ° e: 69° 8-131. Let b = bank balance, m = # months, b = 3m + 210, b = 4.5m +187 . The girls will have

the same amount of money in 15 13 months. 8-132. a: Prices: $0.40; $1; $2.40; $3 b: See graph at right. c: Yes, because the data makes a straight line through (0, 0) .

d: The slope is 210 or 0.2. The slope is the same as the price per ounce ($0.20 per ounce). e: y = 0.2x 8-133. a: x = 9 b: x = 14

3 c: x = 135 or 2.6 d: x = 7

8-134. a: 6.4 !10–3 b: 1!100 c: 5 !10–4 8-135. a: (–2, 2), (–2, 0), (1, 2) b: (4, –1), (4, –3), (1, –1) c: (–1, 4), (–3, 4), (–1, 1) d: (–8, –2), (–8, –6), (–2, –2)

Amount of Taffy (oz)

Pric

e ($

)

x –6 3 6 0 –9 1 y –2 4 6 2 –4