Chapter 5: Automobile Ownership

Transcription

1 Chapter 5: Automobile Ownership Answer Guide Although consumers consider gas mileage, condition, options, status, and other things when purchasing a new or used car, the look of the car is a major determinant of what car people will buy. 3. $ g + d(x m) 7. $17, a) c(x) = { 46 when x 200; (x 200) when x > 200 c) (200, 46) 11. $ $ Let x = number of lines in the ad Let c(x) = cost of the ad c(x) = { 29 when x 5; (x 5) when x > a) $22 b) $43 c) c(x) = { 11x when x 3; (x 3) when x > With the tremendous crunching and availability of data due to the prevalence of technology, we are bombarded by statistics on a daily basis. Understanding how to interpret this information is becoming increasingly important. 3. b and e 5. a) $189 b) $ South-Western/Cengage Learning 1

2 c) Stephanie s d) median e) Because there is an outlier, the median is better representative than the mean. 11. a) $275 b) $ c) $200, $210, and $300 d) Q 1 = 210, Q 2 = , Q 3 = 320, Q 4 = 700 e) 110 f) $45; yes, there is one lower outlier, $10. g) $485; yes, there is one upper outlier, $ (x/8) 0.2(x/8) or 0.8(x/8) 15. answers vary 17. answers vary 19. You need the least number, which is not one of the quartiles You need facts data to back up any theory you have. Using convenient anecdotal evidence to create a theory is not wise. 3. $ Martina did not take into account the frequency of each price. 7. a) b) If the data has an outlier, then a modified boxplot would more appropriately represent the data. c) 0 9. a) y = 0.16x + 24, b) r = c) Yes; r is close to 1. d) When 60,000 miles is substituted into the regression equation, the predicted price is approximately $15,122. That is almost $4,000 lower than the asking price for the car. That is sufficient reason to ask for the price to be lowered South-Western/Cengage Learning 2

3 11. a) 18 b) 0 c) $226 d) $ Driving a car is a tremendous responsibility, and often the source of parent-teenager conflicts. Teenage drivers have the highest frequency of accidents. 3. a) $1,467 b) $ c) $ a) $ b) $ $73, a) property damage b) $1,400 c) collision d) $ a) p/12 b) 0.15(p/12) 13. ((x 0.35x)/12) or (0.65x/12) 15. a) x x d or 1.15x d b) (1.15x/2) This somewhat cynical quote compares the monetary value of computers to that of automobiles. As computer technology has become more sophisticated, the price of computers has drastically dropped. But, that is not the case for the automobile South-Western/Cengage Learning 3

4 3. a) (0, 11,200) and (7, 0) b) 1,600 c) y = 1,600x + 11,200 d) 5. a) $85,000 b) $3,400 c) 25 years 7. a) $8,250 b) $0 c) 2,750A + 22, a) $12,800 b) $9,600 c) 4 years 11. a) =A1/B1 b) = (A1/B1)*C1+A1 13. a) depreciation: y = 450x + 54,000; expense: y = 1,056.74x + 8,000 b) 2014 South-Western/Cengage Learning 4

5 c) Using a graphing tool the coordinates of the intersection point, rounded to the nearest hundredth, are (30.53, 40,261.73). This means that after a little more than 30.5 months, both your expenses-to-date and the car s value are the same. In the region before the intersection point, the expenses are lower than the value of the car. But, the region after the intersection point indicates a period of time that the value of the car is less than what you have invested in it To some people, the value of a car is more than monetary. It is emotional as well. While a car may depreciate monetarily, some people find that it has increased in personal value. 3. y = 28,000( ) x 5. $9, %; $4,902.82; $4,343.91; 20, w b) y = 17,895.97*(0.89) x c) approximately 11% d) $11, $18, D/(1 E/100) % years years; $35, South-Western/Cengage Learning 5

6 Answers will vary. Although this analyst is probably using a car as a metaphor, she does infer that it isn t enough to just know how to drive a car but to know all of the important information about the car as well h and 15 h 34 min a) miles b) $ a) 109 liters b) $ $ , a) D = 56T b) c) about 800 miles d) approximately 9 hours 17. a) 4.07 b) 2.62 c) 4.41 d) e) f) g) h) i) j) k) l) South-Western/Cengage Learning 6

7 m) n) p) q) 5, r) 3, s) 6, a) approx. $1.62 USD/L b) approx. $6.16/gal 21. a) (h/0.69) USD/L b) (3.8h/0.69) per gal The total braking distance is substantial for a normal, non-impaired driver. People driving under the influence of alcohol or drugs significantly increase their reaction time which increases the total stopping distance. 3. a) 42 b) 221,760 c) 3,696 d) 62 e) x f) 5,280x g) (5,280x/60) h) (5,280x/3,600) 5. a) 55 b) 55,000 c) 917 d) feet 9. a) 52 feet b) feet c) feet 11. David s total stopping distance is 315 feet. He does not have enough road ahead of him to bring the car to a safe stop before the accident South-Western/Cengage Learning 7

8 13. a) b) about 185 feet c) about 28 mi/h 15. a) =A1* b) =A1^2/20 + A1 c) =A2^2/170 + A2/ Clearly the quote is said in jest, but there is a great deal of truth in it. It highlights the fact that it is very easy to have an accident and drivers should always be alert and aware ft 5. The police were correct since according to the formula, Rona s minimum skid speed was approximately 39.7 miles per hour mi/h ft 11. a) 1.08 b) 52 ft and 48 ft ft 15. a) 72.6 ft b) 35.1 mi/h 17. a) =(B2^2/(8*B3)+B3/2) b) =sqrt(15*b1*b4) c) approximately 29 mi/h 2014 South-Western/Cengage Learning 8

9 Assessment d + 3a 5. a) y = 3,625x + 43,500 b) 9 years c) 6.5 years 7. a) depreciation: y = 225x + 37,800; expense: y = 710x + 7,000 b) c) Using a graphing tool, the coordinates of the intersection point, rounded to the nearest hundredth, are (31.87, ). This means that after a little less than 31 months, both your expenses-to-date and the car s value are the same. In the region before the intersection point, the expenses are lower than the value of the car. But, the region after the intersection point indicates a period of time that the value of the car is less than what you have invested in it. 9. a) property damage b) $7,000 c) $20,000 d) collision e) $3, South-Western/Cengage Learning 9

10 11. a) property damage under $11,700 b) $250,000 under BI c) $50,000 under PIP. d) $19,000 under PIP 13. a) 18.5% b) $8,252 c) $14,500 d) 28,158.50(0.815 y ) liters; $ a) 64 ft b) ft c) ft 19. The police were correct since according to the formula, Richie s minimum skid speed was approximately miles per hour ft; 25.9 mi/h 2014 South-Western/Cengage Learning 10