MATH 106 Finite Mathematics 2172-OL4-7981-V1 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. Which of the following statements is TRUE: A. B. C. D. 1. _____ If then x is a member of ( ) If then x is a member of ( ) If then x is a member of ( ) None of the above statements are true. 2. The Carters buy a $285,000 home by putting 20% down and financing the balance with a 30year fixed-rate 4.05% mortgage, compounded monthly. What is the total amount of interest paid to the lender over the entire 30-year loan? 2. _____ A. $1095.09 B. $166,232.17 C. $166,232,40 D. $228,000 3. A survey of athletes revealed that for minor aches and pains, 30 used aspirin, 50 used ibuprofen, and 15 used both. No athletes reported using neither. How many athletes were surveyed? 3. ______ A. 95 B. 80 C. 50 D. 65 4. A normal distribution of raw scores has a mean of 0 and a standard deviation of 1. 34% of the distribution can be found between what two raw scores? 4. ______ A. - 1 and 0 B. - 1 and 1 C. 0 and 2 D. - 2 and 2 Page 1 of 10 MATH 106 Finite Mathematics 2172-OL4-7981-V1 5. Determine which region corresponds to the feasible region of the system of linear inequalities: 3 + 7 1 4 + 3 5 II I III IV A. Region I C. Region III B. Region II D. Region IV 5. _______ 2 6. Find equation of the line passing through (4, 1) and parallel to = 3 + 1: A. 3x - 2y = 10 B. 3x + 2y = 14 C. 4x - 6y = 10 6. _______ D. 4x + 6y = 20 Page 2 of 10 MATH 106 Finite Mathematics 2172-OL4-7981-V1 7. Which of the corner points for the system of linear inequalities graphed below maximizes the objective function P = 6x + 5y ? 7. _______ A. (6, 4) C. (8, 0) B. (0, 6) D. (0, 15) 8. Acme Press produces technical manuals for operation of large earthmoving equipment. Producing the manuals costs the company $400,000 plus $10 for each manual published. Acme's revenue comes from sale of the manuals at $30 per manual. For what number of manuals is the cost equal to the revenue (the \"break-even\" point)? 8. ________ A. 10,000 B. 40,000 C. 20,000 D. 13,334 9. - 10. A company produces two types of shoes - casual, and athletic - at its two factories, Factory I and Factory II. Factory I daily production is 100 pairs of casual shoes and 300 pairs of athletic shoes. Factory II daily production is 200 pairs of casual shoes and 100 pairs of athletic shoes. The company must produce at least 8000 pairs of casual shoes, and 9000 pairs of athletic shoes. The cost of operating Factory I is $1500 per day and the cost of operating Factory II is $2000. The company wants to minimize production costs. Let x represent number of days Factory I operates and y represent number of days Factory II operates. 9. Identify constraint on daily number of pairs of athletic shoes produced: 9. _______ A. 300 + 100 9000 B. 300 + 100 8000 C. 100 + 300 9000 D. 100 + 300 8000 10. State the objective function. 10. _______ A. = 8000 + 9000 B. = 9000 + 8000 C. = 2000 + 1500 D. = 1500 + 2000 Page 3 of 10 MATH 106 Finite Mathematics 2172-OL4-7981-V1 11. Which chart below depicts a histogram of 15 survey responses presented in the following frequency table? Value 1 2 3 4 5 6 Frequency X XX XXXXXX XXX XX X 11. ______ CHART A CHART C 8 6 5 4 3 2 1 0 1 2 3 4 5 6 0 CHART B 5 CHART 8 8 6 6 4 4 2 2 10 D 0 0 1 2 3 4 5 6 1 2 3 4 5 6 12. The amount of money you should deposit quarterly in an account paying 9% compounded quarterly in order to have $175,000 after 30 years can be determined using formula for: A. B. C. D. 12. _______ Single payment: simple annual interest Single payment: compound interest Periodic payments: present value of an annuity / installment payment on loan Periodic payments: future value of an ordinary annuity Page 4 of 10 MATH 106 Finite Mathematics 2172-OL4-7981-V1 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 slopeintercept form : _______________________ d. Express equation in general (standard) form: _______________________ 14. The May 2017 makeup of the US House of Representatives by party affiliation and gender follows: Democrat (D) Republican (R) Total Male (M) 132 220 352 Female (F) 62 21 83 Total 194 241 435 (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) Male and Republican: Answer: ______________ (b) Male or Republican: Answer: ______________ (c) Male given that the selected Representative is Republican: Answer: ______________ Page 5 of 10 MATH 106 Finite Mathematics 2172-OL4-7981-V1 15. Given the following Venn diagram: List the members of the following sets: a. ( ) Answer: ______________ b. ( ) Answer: ______________ c. ( ) Answer: ______________ Page 6 of 10 MATH 106 Finite Mathematics 2172-OL4-7981-V1 SHORT ANSWER, with work required to be shown, as indicated. 16. Fifteen people work in an office. 8 are women and 7 are men. The flu virus is coming. (a) In how many ways can the flu virus randomly select 6 workers out of the 15 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 15 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 = 9 7 + 3 = 1 18. EZ Photo Company needs five copying machines in 2 1/2 years for a total cost of $15,000. How much money should be deposited now to pay for these machines, if the interest rate is 8% compounded semiannually? Round answer to nearest cent. Show work. Page 7 of 10 MATH 106 Finite Mathematics 2172-OL4-7981-V1 ______________________________________________________________________________ 19. According to Pricewaterhouse Coopers, "Global State of Information System Security 2015", there were 3.4 million \"detected and reported information security incidents\" (cyberattacks, etc.) against computer networks in the USA in 2009. In 2014, that number had risen to 42.8 million. (a) Which of the following linear equations could be used to predict annual number (in millions) of detected and reported information security incidents \"y\" in a given year \"x\