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 corner points for the system of linear inequalities graphed below maximizes the objective function P = 7x + 6y ? 1. A. (0, 0) C. (1, 2) B. (0, 3) D. (2, 0) Page 1 of 9 2. Which of the following statements is NOT true: 2. A. A probability must be less than or equal to 1. B. If an event cannot possibly occur, then the probability of the event is 0. C. If only two outcomes are possible for an experiment, then the sum of the probabilities of the outcomes = 1. D. If events G and H are independent events, then P (G H) = 0. 3. Find the equation of the line passing through (4, - 1) and (3, 1): 3. A. 5x - 4y = 11 B. 3x + 4y = 8 C. 2x + 5y = 3 D. 2x + y = 7 4. Sam purchases a new truck for $60,000, makes a down payment of 20%, and finances the rest with 60-month dealer financing at an annual interest rate of 3.6% compounded monthly. What is the amount of his monthly loan payment to amortize the loan? 4. A. $875.36 C. $1,094.19 B. $944.00 D. $1,180.00 5. The mean time to get an oil change done at Leaky's Garage is 61 minutes, with a standard deviation of 15 minutes. Assuming normal distribution, what is the probability that a randomly chosen customer experiences an oil change done between 46 and 76 minutes? 5. A. 0.3413 C. 0.5000 B. 0.6826 D. 0.4772 6. One six-sided die is rolled once. What is the probability of rolling a number less than 3? 1 1 A. 6 C. 2 1 B. 2 3 3 D. 6. 7. Which of the following statements is FALSE? A. B. C. D. 7. If all of the data values in a data set are identical, then the standard deviation is 0. The variance is one of the measures of data dispersal relative to the mean. The standard deviation is the square of the variance. The variance can never be a negative number. 8. - 9. Leaky's Garage employs supervisors and technicians. According to the union contract, a supervisor does 3 brake jobs and 4 mufflers per day, whereas a technician does 7 brake jobs and 4 mufflers per day. The home office requires enough staff on hand for at least 24 brake jobs per day and at least 18 mufflers per day. A supervisor makes $90 per day and a technician makes $100 per day. The home office is looking to minimize daily labor costs. Let x represent number of supervisors and y represent number of technicians. 8. Identify the daily production constraint for mufflers: A. 3 + 7 24 18 C. 4 + 4 B. 4 + 4 24 18 D. 3 + 7 8. 9. 9. State the objective function. A. = 90 + 100 18 C. = 24 + B. = 100 + 90 24 D. = 18 + 10. 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 manufacturing process to break even? Round answer to the nearest whole unit. A. 2973 C. 1240 B. 2125 D. 904 10. 11. Determine which region defines the solution region of the following system of linear inequalities: 11. 2 5 3 3 + 2 I II III IV A. Region I C. Region III B. Region II D. Region IV 12. A Social Security number consists of 9 single digits. Repetition of digits (which means: sampling WITH replacement) is allowed. The total of possible Social Security numbers that could exist is found by evaluating: A. 10 9 C. C10,9 B. D. P10,9 109 12. SHORT ANSWER (work NOT required to be shown) 13. For the linear equation 7 6 = 42: a. Determine the slope: b. Determine y - intercept if it exists: c. Express equation in slope-intercept form: 14. Let A = {1, 3, 5, 7, 9, 11, 13, 15}, let B = {- 1, - 3, 7, - 5, - 11, 9, - 13}, and let U = . a. List the elements of B' : b. List the elements of : c. How many elements comprise U ? 15. 1000 students at a particular college were asked their status (full-time or part-time) and their chosen undergraduate degree field of study. The following table was obtained. Undergraduate Major Engineering Education Health Sciences Social Sciences Total Full-time 192 32 210 178 612 Part-time 14 104 116 154 388 Total 206 136 326 332 1000 (Report your answers as fractions or as decimal values rounded to the nearest thousandth.) Find the probability that a randomly selected student: (a) majors in engineering and is part-time. Answer: (b) majors in engineering or is part-time. Answer: (c) majors in engineering, given that the student is part-time. Answer: SHORT ANSWER, with work required to be shown, as indicated. 16. Thirteen people work in an office. 8 are women and 5 are men. The flu virus is coming. (a) In how many ways can the flu virus randomly select 6 workers out of the 13 to get sick? Show work. (b) In how many ways can the flu choose 6 workers, if 3 must be women and 3 must be men? Show work. (c) If the flu virus randomly selects 6 workers from the 13 in the office, what is the probability that 3 are men and 3 are women? 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 + 2 = 13 2 7 = 1 18. If $300,000 is to be saved over 25 years, how much should be deposited monthly if the investment earns 8% compounded monthly? Show work. A. $315.45 C. $216.62 B. $260.87 D. $180.48 19. According to the US Department of Justice's Bureau of Justice Statistics, 2.4% of US firearms purchase/transfer applications submitted in 1999 were rejected due to background check information. In 2009, the rejection rate of applications submitted due to background check information was 1.4%. (a) ) Which of the following linear equations could be used to predict application rejection rate y in a given year x, where x = 0 represents the year 1999? Explain/show work. A. y = - 10x + 1999 C. y = - 10x + 2.4 B. y = - 0.1x + 1999 D. y = - 0.1x + 2.4 (b) Use the equation from part (a) to predict the firearms application rejection rate (%) in the year 2019. Round answer to nearest hundredth of a percent. Show work. (c) Fill in the blanks to interpret the slope of the equation: The rate of change of application rejection rate with respect to time is per . (Include units of measurement.) 20. Tamika's savings account has a balance of $4069. If she makes no deposits or withdrawals for 4 years, and the account accrues interest at 5% compounded quarterly, what will be the total amount of money in her savings account at the end of the 4-year period? Show work 21. According to a recent Pew Research Center report, 0.8 is the probability that a randomly selected American adult knows what Twitter is. Eight American adults are randomly selected. Find the probability that exactly 6 of the 8 American adults randomly selected knows what Twitter is. Round answer to nearest ten-thousandth (4 places after decimal). Show work 22. The feasible region shown below is bounded by lines - x + 3y = 3, x + y = 4, and y = 0. Find the coordinates of corner point A. Show work. 23. A developmental psychologist studies the number of words that six children have learned at a particular age. The numbers are 8, 3, 6, 11, 14, and 6. (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 3.9, what percentage of the data set falls within one standard deviation of the mean? Show work/explanation. (d) A. 66.7% C. 50.0% B. 68.3% D. 34.2% Page 8 of 9 24. The probability distribution for the random variable x is displayed in the following table: xi pi 13 0.20 8 0.25 -5 0.30 9 0.10 10 0.15 Find the expected value E(X) . Show work. 25. An instructor surveyed her class of 45 students and found that most of them watched TV and/or got on the Internet last night. 10 students said they watched TV but did not get on the Internet. 16 students said they got on the Web but did not watch TV last night. 43 of the students watched TV or got on the Internet (or both) last night. (a) What is the probability that a single randomly-selected student got on the Internet last night? Show work. (b) Let T = {students who watched TV} and W = {students who got on the Internet}. Determine the number of attendees belonging to each of the regions I, II, III, IV. U T W I II III IV Region I: Region II: Region III: Region IV