Core Connections, Course 3, Study notes of Analytical Geometry and Calculus

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Core Connections, Course 3

Selected Answers 1 8 - 7. a: P = $500 , I = $37.50 , r = 2.5% (0.025) , t = 3 years b: I = 200 (0.04)( 5 ) = $ 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 23 mm, y = 81 mm, z = 22.5 mm

Selected Answers 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. 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 8 - 47. a: 42! 53 b: 35! y^2 c: 64 x^4 = ( 6 x )^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. 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: 278 c: 625 d: 321 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 = 3 x – 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

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. 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: (^) ( 12 , –4) Power of 10 Decimal Form Fraction Form 1

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: x 2 10 =^10 ! (^1) x (^2) c: 1 4 d:^ x 2 8 - 96. a: – 7275 or – 2425 b: 2345 c: 28024 or 353 d: – 2770 e: –4 185 f: 10510 or (^10 ) 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 + 43 x b: After 23rd^ day.

Lesson 8.2.

8 - 109. a: 6! 105 b: 6.875! 106 c: 2! 105 8 - 110. a: x^7 b: y^3 c: x^7 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