
Concept explainers
Making Decision. Consider the following situations, which each involve two options. Determine which option is less expensive. Are there unstated factors that might affect your decision?
41. You currently drive 250 miles per week in a car that gets 21 miles per gallon of gas. You are considering buying a new fuel-efficient car for $16,000 (after trade-in on your current car) that gets 45 miles per gallon. Insurance premiums for the new and old car are $800 and $400 per year, respectively, you anticipate spending $1500 per year on repairs for the old car and having no repairs on the new car. Assume gas costs $3.50 per gallon. Over a five-year period, is it less expensive to keep your old car or buy the new car?
42. You currently drive 300 miles per week in a car that gets 15 miles per gallon of gas. You are considering buying a new fuel-efficient car for $12,000 (after trade-in on your current car) that gets 50 miles per gallon. Insurance premiums for the new and old car are $800 and $ 600 per year, respectively. You anticipate spending $1200 per year on repairs for the old car and having no repairs on the new car. Assume gas costs $3.50 per gallon. Over a five-year period, is it less expensive to keep your old car or buy the new car?
43. You must decide whether to buy a new car for $22,000 or lease the same car over a three-year period. Under the terms of the lease, you make a down payment of $1000 and have monthly payments of $250. At the end of three years, the leased car has a residual value (the amount you pay if you choose to buy the car at the end of the lease period) of $10,000. Assume you can sell the new car at the end of three years at the same residual value. Is it less expensive to buy or to lease?
44. You must decide whether to buy a new car for $22,000 or lease the same car over a four-year period. Under the terms of the lease, you make a down payment of $1000 and have monthly payments of $300. At the end of four years, the leased car has a residual value (the amount you pay if you choose to buy the car at the end of the lease period) of $8000. Assume you can sell the new car at the end of four years at the same residual value. Is it less expensive to buy or to lease?
45. You have a choice between going to an in-state college where you would pay $4000 per year for tuition and an out-of-state college where the tuition is $6500 per year. The cost of living is much higher at the in-state college, where you can expect to pay $700 per month in rent, compared to $450 per month at the other college. Assuming all other factors are equal, which is the less expensive choice on an annual (12 month) basis?

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Chapter 4 Solutions
Using & Understanding Mathematics: A Quantitative Reasoning Approach (7th Edition)
- x³ In(e²) dx x³ ln(x4) dxarrow_forwardQUESTION 7: In(re) d /(x)5 Ꮖ dx dxarrow_forwardA restaurant serves three fixed-price dinners costing $12, $15, and $20. For a randomly selected couple dining at this restaurant, let X = the cost of the man's dinner and Y = the cost of the woman's dinner. The joint pmf of X and Y is given in the following table. p(x, y) 15 y 12 20 12 0.05 0.10 0.35 x 15 0.00 0.20 0.10 20 0.05 0.05 0.10 (a) Compute the marginal pmf of X. x 12 Px(x) Compute the marginal pmf of Y. y Pyly) 12 15 20 15 20 (b) What is the probability that the man's and the woman's dinner cost at most $15 each? (c) Are X and Y independent? Justify your answer. X and Y are independent because P(x, y) = Px(x) · Py(y). X and Y are not independent because P(x, y) =Px(x) · Pyly). X and Y are not independent because P(x, y) * Px(x) · Py(y). X and Y are independent because P(x, y) * Px(x) · Py(y). (d) What is the expected total cost, in dollars, of the dinner for the two people? $ (e) Suppose that when a couple opens fortune cookies at the conclusion of the meal, they find the…arrow_forward
- Let X = the time between two successive arrivals at the drive-up window of a local bank. If X has an exponential distribution with λ = 1, (which is identical to a standard gamma distribution with α = 1), compute the following. (If necessary, round your answer to three decimal places.) (a) the expected time between two successive arrivals (b) the standard deviation of the time between successive arrivals (c) P(X ≤ 1) (d) P(2 ≤ X ≤ 4) You may need to use the appropriate table in the Appendix of Tablesarrow_forwardIn each case, determine the value of the constant c that makes the probability statement correct. (Round your answers to two decimal places.) USE SALT (a) (c) 0.9842 (b) P(0 ≤ Z ≤ c) = 0.3051 (c) P(CZ) = 0.1335 You may need to use the appropriate table in the Appendix of Tables to answer this question.arrow_forwardSarrow_forward
- QUESTION 6: Politics. Public awareness of a mayoral candidate before and after a successful campaign was approximated by P(t) 5.4t t² +36 +0.2 0arrow_forward(d) In(t-5) dt t-5 QUESTION 3: Sketch the area, and then find the area bounded by the given curves y = x² = 1; - y=x-2; -2≤ x ≤1arrow_forwardQUESTION 4: A college language class was chosen for a learning experiment. Using a list of 50 words, the experiment measured the rate of vocabulary memorization at different times during a continuous 5-hour study session. The average rate of learning for the entire class was inversely proportional to the time spent studying and was given approximately by V'(t) = 15 t 1≤t≤5 Average cost. The total cost (in dollars) of printing x dictionaries is C'(x) = 20,000+ 10x. (A) Find the average cost per unit if 1,000 dictionaries are produced. (B) Find the average value of the cost function over the interval [0, 1,000].arrow_forward
- Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill
