Math 106 Finite Mathematics, Final Exam(SPRING 2016)

MATH 106 Finite Mathematics 2162-OL4-7980-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. 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, and upload it into the Final Exam folder in “Assignments”. DO NOT UPLOAD THIS EXAM! 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. A high school football team of 40 players includes 16 players who played on offense last year, 17 who played defense, and 12 who weren’t on last year’s team. How many players from last year played both offense and defense? 1. _____ A. 7 B. 4 C. 11 D. 5 2. The McKinleys buy a $230,000 home by putting 20% down and financing the balance with a 30-year fixed-rate 4.2% mortgage, compounded monthly. What is the amount of their monthly loan payment to amortize the loan? 2. _____ A. $1124.74 B. $899.56 C. $1155.11 D. $899.79 3. During her four years at college, Niki received A's in 30% of her courses, B's in 50% of her courses, and C's in the remaining 20%. If A = 4, B = 3, and C = 2, find her grade point average. 3. ______ A. 3.3 B. 3.1 C. 3.2 D. 3.0 4. A normal distribution of raw scores has a mean of 50 and a standard deviation of 7. Approximately 95% of the distribution can be found between what two raw scores? 4. ______ A. 36 and 50 B. 50 and 64 C. 36 and 64 D. 43 and 57 MATH 106 Finite Mathematics 2162-OL4-7980-V1 Page 2 of 10 5. Determine which region corresponds to the feasible region of the system of linear inequalities: 3𝑥 + 7𝑦 ≥ 1 4𝑥 + 3𝑦 ≥ −5 A. Region I C. Region III B. Region II D. Region IV 5. _______ 6. Find the equation of the line passing through (– 2, 1) and (5, – 2): 6. _______ A. 3x – 7y = – 13 B. 7x + 3y = – 11 C. x – 3y = – 5 D. 3x + 7y = 1 II III IV I MATH 106 Finite Mathematics 2162-OL4-7980-V1 Page 3 of 10 7. Which of the corner points for the system of linear inequalities graphed below minimizes the objective function C = 7x + 6y ? 7. _______ A. (0, 26) C. (4, 2) B. (2, 6) D. (8, 0) 8. Identify the single row operation that transforms the matrix as shown: 8. ________ [ 1 2 0 1 | 15 7 ] → [ 1 0 0 1 | 1 7 ] A. 2𝑅2 + 𝑅1 → 𝑅1 C. 7𝑅1 + 𝑅2 → 𝑅2 B. −2𝑅2 + 𝑅1 → 𝑅1 D. 2𝑅1 + 𝑅2 → 𝑅2 9. – 10. A home healthcare agency employs registered nurses (RNs) and certified nurse’s assistants (CNAs). An individual RN performs 100 medical care procedures and 40 patient welfare tasks per month, and an individual CNA performs 15 medical care procedures and 280 patient welfare tasks per month. Enough RNs and CNAs are needed per month to perform at least 500 medical procedures and at least 1500 patient welfare tasks. Monthly labor costs are $16000 per RN and $3000 per CNA. The agency wants to minimize labor costs. Let x represent number of RNs employed per month and y represent number of CNAs employed per month. 9. Identify constraint on monthly number of patient welfare tasks performed: 9. _______ A. 40𝑥 + 280𝑦 ≥ 500 C. 100𝑥 + 15𝑦 ≥ 500 B. 40𝑥 + 280𝑦 ≥ 1500 D. 100𝑥 + 15𝑦 ≥ 1500 10. State the objective function. 10. _______ A. 𝐶 = 16000𝑥 + 3000𝑦 C. 𝐶 = 500𝑥 + 1500𝑦 B. 𝐶 = 3000𝑥 + 16000𝑦 D. 𝐶 = 1500𝑥 + 500𝑦 MATH 106 Finite Mathematics 2162-OL4-7980-V1 Page 4 of 10 11. The amount of money you should have in a retirement account paying 8% interest compounded quarterly in order to be able to withdraw $10,000 a quarter for 15 years once you retire can be determined using formula for: 11. _______ A. Periodic payments: present value of an annuity / installment payment on loan B. Periodic payments: future value of an ordinary annuity C. Single payment: compound interest D. Single payment: simple annual interest 12. The following histogram correctly corresponds to which of the following frequency tables? 12. ______ A B C D Value Frequency Value Frequency Value Frequency Value Frequency 1 X 1 X 1 X 1 X 2 XXX 2 XX 2 XX 2 XX 3 XXXX 3 XXX 3 XXX 3 XXX 4 XXXXX 4 XXXX 4 XXXXX 4 XXXXX 5 XXXX 5 XXX 5 XXX 5 XX 6 X 6 X 6 X 6 X 0 1 2 3 4 5 6 1 2 3 4 5 6 MATH 106 Finite Mathematics 2162-OL4-7980-V1 Page 5 of 10 SHORT ANSWER (work NOT required to be shown) 13. For the line graphed at left: a. Determine the slope: _______________________ b. Determine y – intercept if it exists: _______________________ c. Express equation in slope-intercept form : _______________________ d. Express equation in general (standard) form: _______________________ 14. The May 2016 makeup of the US House of Representatives by party affiliation and gender follows: Male (M) Female (F) Total Democrat (D) 127 66 193 Republican (R) 225 22 247 Total 352 88 440 (Report your answers as fractions or as decimal values rounded to the nearest hundredth.) Find probability that a single randomly-selected member of the US House of Representatives is: (a) Female and Democrat: Answer: ______________ (b) Female or Democrat: Answer: ______________ (c) Female given that the selected Representative is Democrat: Answer: ______________ MATH 106 Finite Mathematics 2162-OL4-7980-V1 Page 6 of 10 15. Given the following Venn diagram: List the members of the following sets: a. (𝐴 ∪ 𝐶) Answer: ______________ b. (𝐴 ∩ 𝐵) ∩ 𝐶 Answer: ______________ c. 𝐴′ ∩ 𝐵′ ∩ 𝐶′ Answer: ______________ MATH 106 Finite Mathematics 2162-OL4-7980-V1 Page 7 of 10 SHORT ANSWER, with work required to be shown, as indicated. 16. You’re at the library to do research for your statistics project. You need 5 sources. There are 5 finite mathematics sources and 11 statistics sources to choose from. Order doesn’t matter. (a) How many ways can 5 sources be randomly selected out of the 16 sources? Show work. (b) How many ways can 5 sources be chosen, if 2 must be finite math and 3 must be statistics? Show work. (c) Using your answers to parts (a) and (b), if 5 sources are randomly selected from the 16 sources, what is the probability that 2 are finite math and 3 are statistics? 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. 4𝑥 + 3𝑦 = 14 3𝑥 + 7𝑦 = 1 18. Lakesha needs $3,700 in two years for her college tuition. How much money should she deposit lump sum in an account paying 8.4% compounded monthly to achieve that goal? Round answer to nearest cent. Show work. MATH 106 Finite Mathematics 2162-OL4-7980-V1 Page 8 of 10 ______________________________________________________________________________ 19. The 2015 US Department of Justice, Bureau of Justice Statistics publication Probation and Parole in the United States, 2014 (www.bjs.gov) states that 826 thousand US adult residents were on parole in 2007, a figure which increased to 857 thousand in 2014. a. Multiple choice: The linear regression model most closely fitting this data (where p represents number [in thousands] of US adult residents on parole and t represents years since 2007) is: A. p = 0.23t + 2007 C. p = 4.43t + 2007 B. p = 4.43t + 826 D. p = 0.23t + 826 b. Use the model to predict the number US adult residents (in thousands) on parole in 2024 (round answer to one place after decimal) Show work! c. Fill in the blanks to interpret the slope of the equation: The rate of change of US adult residents (in thousands) on parole with respect to time is ____________________ per ______________. (Include units of measurement.) 20. A donut shop has a fixed operating cost of $124 per day and a variable operating cost of $0.12 (12 cents) per donut produced. How many donuts can be made for a total daily cost of $310? Show work ______________________________________________________________________________ 21. There is a 0.73 probability that MATH 106 students will correctly follow all instructions on the Final Exam. What is the probability that exactly 73 of the 100 students taking MATH 106 in a particular term correctly follow all Final Exam instructions? Round answer to the nearest ten thousandth (four places after decimal). Show work. MATH 106 Finite Mathematics 2162-OL4-7980-V1 Page 9 of 10 ______________________________________________________________________________ 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 56, 80, 108, 76, 56, and 62. (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 19.91, what percentage of the data set falls within one standard deviation of the mean? Show work/explanation. (d) _______ A. 83.3% C. 66.7% B. 68.3% D. 34.2% MATH 106 Finite Mathematics 2162-OL4-7980-V1 Page 10 of 10 24. A local bicycle rental agency charted daily demand as shown in the following table: Number of customers per day 14 16 18 20 22 Probability 0.3 0.2 0.3 0.1 0.1 Find the expected number of customers. 25. A survey of 200 consumers revealed the following movie rental preferences: 130 rented from NetflixTM, 93 rented from RedboxTM, and 48 reported renting from both. (a) What is the probability that a randomly selected consumer rented from either NetflixTM or RedboxTM ? Show work. (b) Let N = {consumers who rent from NetflixTM} and R = {consumers who rent from RedboxTM}. Determine the number of consumers belonging to each of the regions I, II, III, IV. Region I: ________ Region II: __________ Region III: _________ Region IV: __________ ______________________________________________________________________________ U N R II IV I III