MATH 106 Finite Mathematics 2168-OL1-6384-1A 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. Neither collaboration nor consultation with others is allowed. Use of instructors' solutions manuals or online problem solving services in NOT allowed. Record your answers and work on the separate answer sheet provided. There are 25 problems. Problems #1-12 are Multiple Choice. Problems #13-15 are Short Answer. (Work not required to be shown) Problems #16-25 are Short Answer with work required to be shown. MULTIPLE CHOICE 1. Which of the following statements is NOT true: A. B. C. D. 1. ________ If an event cannot possibly occur, then the probability of the event is 0. If events E and F are mutually exclusive events, then ( ) = . If only two outcomes are possible for an experiment, then the sum of the probabilities of the outcomes is equal to 1 Conditional probability is defined as ( ) (|) = () 2. - 3. A small company manufactures two types of radios - regular and short-wave. The manufacturing of each radio requires two operations: Assembly and Finishing. The regular radios require 1 hour of Assembly and 3 hours of Finishing. The short-wave radios require 3 hours of Assembly and 1 hour of Finishing. The total work-hours available per week in the Assembly division is 60, and in the Finishing division, 60. A profit of $50 is realized for every regular radio, and $75 for every short-wave radio. Let x represent number of regular radios and y represent number of short-wave radios made per week. 2. Identify the weekly production constraint for finishing: 2. _______ A. + 3 60 C. 3 + 60 B. + 3 60 D. 3 + 60 3. State the objective function. 3. _______ A. = 60 + 60 C. = 75 + 50 B. = 240 + 240 D. = 50 + 75 Page 1 of 9 MATH 106 Finite Mathematics 2168-OL1-6384-1A 4. Which histogram below accurately reflects 15 survey responses presented in the following frequency table? 4. _______ Value Frequency 1 X 2 XX 3 XXX 4 XXXXX 5 XXX 6 X HISTOGRAM A 6 6 4 4 2 2 0 HISTOGRAM C 1 4 5 HISTOGRAM D 0 1 2 3 4 HISTOGRAM 5 6 B 8 8 6 6 4 4 2 2 0 2 3 6 0 1 2 3 4 5 6 1 2 3 4 5 6 5. Two balls are drawn in succession, without replacement, out of a box containing 2 red and 5 white balls. What is the probability that the first ball drawn is white and the second ball drawn is red? 5. _______ 1 5 10 2 A. B. C. D. 3 21 21 3 6. Find the equation of the line passing through (4, 3) and (- 2 , - 7): A. 3x + 5y = 27 B. 3x - 5y = - 3 C. 5x - 3y = 11 6. _______ D. 2x - y = 5 Page 2 of 9 MATH 106 Finite Mathematics 2168-OL1-6384-1A 7. The Rodriguez family buys a $450,000 home by putting a 20% down payment and financing the balance with a 30-year fixed mortgage at 3.9%. What is the amount of their monthly loan payment to amortize the loan? 7. _______ A. $1698.01 B. $1701.82 C. $1697.98 D. $1697.03 8. A rental company buys a truck for $54,000. The cost to maintain the truck averages $8.00 per day. As a result, the total cost function is defined as () = 8 + 54000. The truck rents for $98.00 per day; as a result the total revenue function is defined as () = 98. Let x = number of days truck is rented. If the truck is rented every day, how many days will it take the company to break-even on the cost of buying & maintaining it? 8. _______ A. 600 B. 551 C. 6750 D. 6760 9. The shaded \"feasible region\" graphed below satisfies which system of linear inequalities? 9. ________ 12 10 (0,9) 8 6 (0,5) 4 (4,3) 2 0 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 -4 -6 -8 -10 A. B. C. D. 3 + 2 18 3 + 2 18 3 + 2 18 3 + 2 18 + 2 10 + 2 10 + 2 10 + 2 10 0 0 0 0 0 0 0 0 Page 3 of 9 MATH 106 Finite Mathematics 2168-OL1-6384-1A 10. Which of the corner points for the system of linear inequalities graphed below minimizes the objective function P = 3x + 4y ? 10. _______ A. (3, 0) C. (0, 4) B. (1, 2) D. (2, 0) 11. The mean time from check-in to completion for a customer served at the Otisburg branch of the Department of Motor Vehicles is 109 minutes, with a standard deviation of 17 minutes. Assuming a normal distribution, what is the probability that a randomly chosen customer experiences service done in greater than 126 minutes? 11. ______ A. 0.6826 C. 0.3413 B. 0.0228 D. 0.1587 12. The amount of money you should deposit in an account paying 8% compounded quarterly in order to receive quarterly payments of $1200 for the next 6 years can be determined using formula for: 12. _______ A. Sequence of payments: future value of an ordinary annuity B. Sequence of payments: present value of an annuity / amortization C. Single-payment, simple interest D. Single-payment, compound interest Page 4 of 9 MATH 106 Finite Mathematics 2168-OL1-6384-1A SHORT ANSWER (work NOT required to be shown) 13. For the linear equation 3 + 7 = 42: a. Determine the slope: _______________________ b. Determine y - intercept if it exists: _______________________ c. Express equation in slope-intercept form: _______________________ 14. Let () = 83, () = 50, ( ) = 105, and () = 140. a. Determine ( ) : ___________________________________ b. Determine ( ) : ___________________________________ c. Determine ( ): ___________________________________ 15. \"Guilt and focusing on decision making\" (Gangemi & Mancini, Journal of Behavioral Decision Making, Vol 20, Jan 2007) reported on 171 volunteer students participating in an experiment where each was randomly assigned to one of three groups. One group was made to feel guilty, one group was made to feel angry, and the third group was not influenced. Immediately after reaching these emotional states, the students were asked to decide whether or not to spend lots of money to repair a very old car (not a \"historic\"/antique). The \"stated\" option was \"spend the money to repair the car\". The following raw data was recorded: Emotional State Guilt Anger Neutral Totals Choose stated option C 45 8 7 60 Don't choose stated option C' 12 50 49 111 Totals 57 58 56 171 (Report your answers as fractions or as decimal values rounded to the nearest hundredth.) Find the probability that a randomly-selected student: (a) does NOT choose the stated option or is in the \"guilt\" emotional state: (b) does NOT choose the stated option, given that the student is in the \"guilt\" state: (c) does NOT choose the stated option and is in the \"guilt\" state? Answer: ________ Answer: ________ Answer: ________ Page 5 of 9 MATH 106 Finite Mathematics 2168-OL1-6384-1A SHORT ANSWER, with work required to be shown, as indicated. 16. Seventeen candidates have filed for the upcoming county council election. 7 are women and 10 are men. (a) In how many ways can 10 county council members be randomly elected out of the 17 candidates? Show work. (b) In how many ways can 10 county council members be randomly elected from 17 candidates if 5 must be women and 5 must be men? Show work. (c) If 10 county council members are randomly elected from 17 candidates, what is the probability that 5 are women and 5 are men? Round answer to nearest ten-thousandth (4 places after decimal). Show work. ______________________________________________________________________________ 17. Solve the system of equations using substitution, elimination by addition, or augmented matrix methods (your choice). Show work. 5 3 = 11 7 + 4 = 1 18. Vijay wants to start a retirement account that will have $460,000 in it when he retires in 15 years. How much should he invest every six months in his account to do this if interest is 15% compounded semiannually? Show work. A. $4,435.77 C. $4,790.74 B. $4,448.77 D. $17,612.13 ______________________________________________________________________________ Page 6 of 9 MATH 106 Finite Mathematics 2168-OL1-6384-1A 19. In the United States, fossil fuel use in 1985 represented 85% of total energy production. By 2005 that percentage was 79%. (a) The linear regression model most closely fitting this data (where y represents percentage of total energy production and x represents years since 1985) is: Explain/show work. A. y = - 3.3x + 1985 C. y = - 3.3x + 85 B. y = - 0.3x + 1985 D. y = - 0.3x + 85 (b) Use the equation from part (a) to predict fossil fuel use as a percentage of total American energy production in the year 2018. Round answer to nearest tenth of a percent. Show work. (c) Fill in blanks to interpret the slope of the equation: The rate of change of fossil fuel production as a percentage of total American energy production with respect to time is ______________________ per ________________. (Include units of measurement.) 20. You have $5000 to invest in a single payment. Which is the better investment: 9.6% compounded annually or 9.24% compounded monthly? Show work ______________________________________________________________________________ 21. According to a recent report, 0.10 is the probability that an American can identify Janet Yellen as the Chair of the Federal Reserve Board of the US Government. Twenty Americans are randomly selected. Find the probability that exactly 2 of the 20 Americans selected can identify Ms Yellen as the Chair of the Federal Reserve Board. Round answer to the nearest thousandth (three places after decimal). Show work. ______________________________________________________________________________ Page 7 of 9 MATH 106 Finite Mathematics 2168-OL1-6384-1A 22. The feasible region shown below is bounded by lines 2x - y = 4, x + 3y = 4, and y = 0. Find the 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 51, 66, 58, 43, 51, and 55. (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 7.75, what percentage of the data set falls within one standard deviation of the mean? Show work/explanation. (d) _______ A. 34.2% C. 50.0% B. 66.7% D. 68.3% Page 8 of 9 MATH 106 Finite Mathematics 2168-OL1-6384-1A 24. Air Weegotcha overbooks as many as five passengers per flight because some passengers with reservations do not show up for the flight. The airline's records indicate the following probabilities that it will be overbooked at flight time. Number overbooked at flight time Probability of number overbooked 0 0.70 1 0.17 2 0.06 3 0.04 4 0.02 5 0.01 Find the expected number of overbooked passengers per flight. 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 crme-filled donut yesterday. 180 customers said they bought neither yesterday. (a) What is the probability that a single randomly-selected customer bought a glazed donut or a frosted crme-filled donut yesterday, but not both? Show work. (b) Let G = {customers who bought a glazed donut yesterday} and C = {customers who bought a frosted crme-filled donut yesterday}. Determine the number of attendees belonging to each of the regions I, II, III, IV. U G C II I III IV Region I: ________ Region II: __________ Region III: _________ Region IV: __________ ______________________________________________________________________________ Page 9 of 9