MATH 106 Finite Mathematics Spring, 2017 2172-OL1-6382-V1 MATH 106 FINAL EXAMINATION This is an open-book exam. You may refer to your text and other...

MATH 106 Finite Mathematics Spring , 201 7 21 72 -OL1 -638 2-V1 Page 1 of 10 MATH 106 FINAL EXAMINATION This is an open -book exam. You may refer to your text and other course materials as you work on the exam, and you may use a calculator. You must complete the exam individually. Collaboration or consultation with others is NOT allowed. Use of instructors’ solutions manuals and/or online problem solving services is NOT allowed. Record your answers and work on the separate answer sheet provided. There are 25 problems. Problems #1 –12 are Mult iple Choice. Problems #1 3–15 are Short Answer. (Work not required to be shown) Problems # 16–25 are Short Answer with work required to be shown. MULTIPLE CHOICE 1. Jack purchases a car for $2 4,000, makes a down payment of 25 %, and finances the rest with a 5-year car loan at an annual interest rate of 2. 1% compounded monthly. What is the amount of his monthly loan payment? 1. _______ A. $ 316.29 C. $421.72 B. $ 331.50 D. $442.00 2. The Tralfaz appliance company manufactures small electric grills. The company has fixed costs of $27,200 per month and variable costs of $9.15 per unit produced. The electric grills are sold for $21.95 each. How many units must be sold each day for this manufactur ing process to break even? Round answer to the nearest whole uni t. 2. _______ A. 1240 C. 904 B. 2973 D. 2125 3. Customers shopping at a particular supermarket have normally shopping times with a mean of 44 minutes and a standard deviati on of 12 minutes . What is the probability that a randomly chosen customer will spend between 32 and 56 minutes shopping in the supermarket? 4. ______ A. 0.9544 C. 0.6826 B. 0.7580 D. 0.5000 MATH 106 Finite Mathematics Spring , 201 7 21 72 -OL1 -638 2-V1 Page 2 of 10 4. Find the va lues of x and y that maximize the objective function 6x + 5y for the feasible region (“feasible set”) shown below. 4. _______ A. (x, y) = (0, 20) B. (x, y) = (5, 15) C. (x, y) = (8, 10) D. (x, y) = (10, 0) 5. A jar contains 15 red jelly beans, 12 yellow jelly beans, and 1 8 orange jelly beans. Suppose that each jelly bean has an equal chance of being picked from the jar. If a jelly bean is selected at random from the jar, what is the probability that it is not yellow ? 5. ______ A. B. C. D. 6. Which of the following statements is NOT true ? 6. ______ A. If all of the data values in a data set are identical, then the standard deviation is 0. B. The standard deviation is the square root of the variance . C. The vari ance can be a negative number. D. The variance is a measure of the dispersion or spread of a distribution about its mean. 15 4 11 4 11 7 15 11 MATH 106 Finite Mathematics Spring , 201 7 21 72 -OL1 -638 2-V1 Page 3 of 10 7. Determine which s haded region corresponds to the solution region of the system of linear inequalities + ≥ 2 ≥ 0 + 3 ≥ 3 ≥ 0 7. _______ GRAPH A. GRAPH B . GRAPH C . GRAPH D . MATH 106 Finite Mathematics Spring , 201 7 21 72 -OL1 -638 2-V1 Page 4 of 10 8. – 9. A merchant makes two raisin nut mixtures. Each box of mixture A contains 8 ounces of peanuts and 2 ounces of raisins, and sells for $3.00. Each box of mixture B contains 10 ounces of peanuts and 4 ounces of raisins, and sells for $5.00. The company has available 5,600 ounces of peanuts and 1,100 ounces of raisins. The merchant will try to sell the am ount of each mixture that maximizes income R. Let x be the number of boxes of mixture A and let y be the number of boxes of mixture B. 8. Since the merchant has 1,100 ounces of raisins available, one inequality that must be satisfied is: 8. _______ A. 2x + 4 y  1,100 C. 3x + 5 y  1,100 B. 2x + 4 y  1,100 D. 2x + 3 y  1,100 9. State the objective function. 9. _______ A. R = 2x + 4 y C. R = 8 x + 10 y B. R = 3x + 5 y D. R = 5,600 x + 1,100 y 10 . In a certain manufacturing process, the probability of a type I defect is 0.10, the probability of a type II defect is 0.07, and the probability of having both types of defects is 0.05. Find the probability that neither defect occurs. 10 . ______ A. 0.83 C. 0.78 B. 0.88 D. 0.95 11 . Which of the following is NOT true? 11 . ______ A. If events E and F are independent events, then P(E ∩ F) = 0. B. If an event can not possibly occur, then the probability of the event is 0. C. A probability must be less than or equal to 1. D. If only two outcomes are possible for an experiment, then the sum of the probabilities of the outcomes is equal to 1. 12. Find the equation of the line passing through (4, – 1) and (3, 1) 12. _______ A. 5 x – 4y = 11 B. 3 x + 4 y = 8 C. 2 x + y = 7 D. 2 x + 5y = 3 MATH 106 Finite Mathematics Spring , 201 7 21 72 -OL1 -638 2-V1 Page 5 of 10 SHORT ANSWER (Work not req uired to be shown) 13. Let the universal set U = {1, 2, 3, 4, 5, 6, 7}. Let A = {1, 4, 5} and B = {4, 5, 7}. Determine the members of the set {′∪ } . Answer: ______________ 14. Consider the following graph of a line. (a) Determine the slope . __________________ (b) State the y – intercept (or “none” if none exists) __________________ Answer: ______________ (c) Find the slope -intercept form of the equation of the line. An swer: ____________________ ___________ (d) Write the equation of the line in general (standard) form Ax + By = C where A, B, and C are integers. Answer: ____________________ ___________ MATH 106 Finite Mathematics Spring , 201 7 21 72 -OL1 -638 2-V1 Page 6 of 10 15. 400 employees at a particular company were asked their status (full -time or part -time) and their primary means of transportation to and from work. The follow ing table was obtained. Primary Transportation Full -time Part -time Total Car 188 60 248 Bus 32 44 76 Subway 30 27 57 On Foot 10 9 19 Total 260 140 400 (Report your answers as fractions or as decimal values rounded to the nearest hundredth.) Find the probability that a randomly selected employee: (a) travels by car and is part -time. Answer: ______________ (b) travels by car or is part -time. Answer: ______________ (c) travels by car, given that the employee is part -time. Answer: ______________ MATH 106 Finite Mathematics Spring , 201 7 21 72 -OL1 -638 2-V1 Page 7 of 10 SHORT ANSWER, with work required to be shown, as direc ted . 16. For a six year period, Elliott deposited $ 800 each quarter into an account paying 3.6 % annual interest compounded quarterly. (Round your answers to the nearest cent.) (a) How much money was in the account at the end of 6 years? Show work. (b) How much interest was earned during the 6 year period? Show work. Elliott then made no more deposits or withdrawals, and the money in the account continued t o earn 3.6 % annual interest compounded quarterly, for 3 more years. (c) How much money was in the account after the 3 year period? Show work. (d) How much interest was earned during the 3 year period? Show work. 17. A contest has 15 fina lists. One finalist is awarded first prize, another finalist is awarded second prize, and another is awarded third prize. How many different ways could the prizes be awarded? Show work. 18. There is a collection of 13 books. 7 of the books are fiction and 6 of the books are non - fiction. As an assignment, a student must read 5 of the books over the summer. (a) In how many ways can 5 of the 13 books be chosen? Show work. (b) In how many ways can the 5 books be chosen, if 3 of the books must be fict ion and 2 of the books must be non -fiction? Show work. (c) If 5 books are selected at random from the collection of 13 books , what is the probability that 3 are fiction and 2 are non -fiction ? Show work. MATH 106 Finite Mathematics Spring , 201 7 21 72 -OL1 -638 2-V1 Page 8 of 10 19. The average temperature in Metropoli s in 1 980 was 54.2 degrees. In 2005, the average temperature in Metropolis was 56.7 degrees. Let y be the average temperature in Metropolis in year x, where x = 0 represents the year 1980. (a) Which of the following linear equations could be used to predict the average Metropolis temperature y in a given year x, where x = 0 represents the year 1980? Explain/show work. A. y = 0.10 x + 54.2 C. y = 2.5 x + 54.2 B. y = 0.10 x  143.8 D. y = 2.5 x  4895.8 (b) Use the equation from part (a) to predict the average temperature in Metropolis in the year 2020. Show work. (c) Fill in the blanks to interpret the slope of the equation: The rate of change of temperature with respect to time is ____________________ __ per ________________. (Include units of measurement.) 20. Solve the system of equations using substitution, elimination by addition , or by augmented matrix methods (your choice). Show work. 3+ 2 = 11 2− 5 = 1 ______________________________________________________________________________ 21. According to a recent report, 0.20 is the probability that an American can identify nitrogen as the gas that makes up most of the earth's atmosphere. Six Americans are randomly selected.

Find the probability that exactly 3 of the 6 Americans can identify n itrogen as the gas that makes up most of the earth's atmosphere. Show work. MATH 106 Finite Mathematics Spring , 201 7 21 72 -OL1 -638 2-V1 Page 9 of 10 ______________________________________________________________________________ 22. The feasible region shown below is bounded by lines x + 5y = 8, x + y = 2, and y = 0. Find t he coordinates of corner point A. Show work. 23. A network security specialist records the number of incoming e -mails containing links that six randomly -selected network users receive in a day. Numbers are 119, 124, 84, 99, 109, and 119 . (a) State the mode (if one exists). (b) Find the median. Show work /explanation . (c) Determine the sample mean. Show work (d) Using the sample mean found in part (c), and given that the sample standard deviation of the data set above is 15.2, what percentage of the data set falls within one standard deviation of the mean? Show work/explanation. (d) _______ A. 34.2 % C. 66.7% B. 83.3% D. 68.3% MATH 106 Finite Mathematics Spring , 201 7 21 72 -OL1 -638 2-V1 Page 10 of 10 24. If the probability distribution for the random variable X is given in the table, what is the expected value of X? Show work. xi – 30 10 20 60 pi 0.40 0.30 0.20 0.10 25. A marketing survey of 2000 randomly -selected convenience store customers found that 1415 of them bought a glazed donut yesterday . 1605 said they bought a frosted crème -filled donut yesterday. 180 customers said they bought neither yesterday. (a) What is the probability th at a single randomly -selected customer bought either a glazed donut or a frosted crème -filled donut yesterday? Show work. (b) Let G = {customers who bought a glazed donut yesterday } and C = {customers who bought a frosted crème -filled donut yesterday }. Determine the number of attendees belonging to each of the regions I, II, III, IV. Region I : ________ Region II: __________ Region III: _________ Region IV: __________ ______________________________________________________________________________ U C G II IV III I