[Solution]MATH 106 Finite Mathematics-Which of the following statements is TRUE

MATH 106 Finite MathematicsThere 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…

MATH 106 Finite MathematicsThere 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 CHOICE1. 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 Van Burens buy a $245,000 home by putting 20% down and financing the balance with a30-year fixed-rate 3.75% mortgage, compounded monthly. What is the amount of their monthlyloan payment to amortize the loan?2. _____A. $1134.63B. $907.71C. $835.13D. $908.393. A survey of athletes revealed that for minor aches and pains, 30 used aspirin, 50 usedibuprofen, and 15 used both. No athletes reported using neither. How many athletes weresurveyed?3. ______A. 95B. 80C. 50D.654. A normal distribution of raw scores has a mean of 0 and a standard deviation of 1. 68% of thedistribution can be found between what two raw scores?4. ______A. – 1 and 1B. 0 and 1C. 0 and 2D. – 2 and 2Page 1 of 10MATH 106 Finite Mathematics5. Determine which region corresponds to the feasible region of the system of linearinequalities:3 + 7 ≤ 14 + 3 ≥ −5IIIIIIIVA. Region IC. Region IIIB. Region IID. Region IV6. Find the equation of the line passing through (3, 2) and (1, – 8):A. 3x – y = 7B. 5x – y = 13C. 2x – y = 45. _______6. _______D. 5x – 2y = 11Page 2 of 10MATH 106 Finite Mathematics7. Which of the corner points for the system of linear inequalities graphed below maximizes theobjective function P = 2x + 3y ?7. _______A. (0, 15)C. (6, 4)B. (0, 6)D. (8, 0)8. Identify the single row operation that transforms the matrix as shown:[127 −2|37A.−21 + 2 → 2C.21 + 2 → 2B.−21 + 2 → 1D.02 → 2→[108. ________7−2|−11119. – 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 ofathletic shoes. Factory II daily production is 200 pairs of casual shoes and 100 pairs of athleticshoes. The company must produce at least 8000 pairs of casual shoes, and 9000 pairs of athleticshoes. 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 daysFactory 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 ≥ 9000B. 300 + 100 ≥ 8000C. 100 + 300 ≥ 9000D. 100 + 300 ≥ 800010. State the objective function.10. _______A. = 8000 + 9000B. = 9000 + 8000C. = 2000 + 1500D. = 1500 + 2000Page 3 of 10MATH 106 Finite Mathematics11. The amount of money you should deposit quarterly in an account paying 9% compoundedquarterly in order to have $175,000 after 30 years can be determined using formula for:11. _______Periodic payments: present value of an annuity / installment payment on loanPeriodic payments: future value of an ordinary annuitySingle payment: compound interestSingle payment: simple annual interestA.B.C.D.12. Which chart below depicts a histogram of 15 survey responses presented in the followingfrequency table?Value123456FrequencyXXXXXXXXXXXXXXX12. ______CHARTACHARTC865432101234560CHART B5CHART8866442210D00123456123456Page 4 of 10MATH 106 Finite MathematicsSHORT ANSWER (work NOT required to be shown)13. For the line graphed at left:a. Determine the slope:_______________________b. Determine y – intercept ifit exists:_______________________c. Express equation in slopeintercept form :_______________________d. Express equation ingeneral (standard) form:_______________________14. The May 2016 makeup of the US House of Representatives by party affiliation and genderfollows:Democrat (D)Republican (R)TotalMale (M)127225352Female (F)662288Total193247440(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 10MATH 106 Finite Mathematics15. Given the following Venn diagram:List the members of the following sets:a. ( ∩ )Answer: ______________b. ( ∪ ) ∪Answer: ______________c. ( ∩ ) ∪Answer: ______________Page 6 of 10MATH 106 Finite MathematicsSHORT 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 5 workers out of the 15 to get sick?Show work.(b) In how many ways can the flu choose 5 workers, if 3 must be women and 2 must be men?Show work.(c) If the flu virus randomly selects 5 workers from the 15 in the office, what is the probabilitythat 2 are men and 3 are women? Round answer to nearest ten-thousandth (4 places afterdecimal). Show work.______________________________________________________________________________17. Solve the system of equations using substitution, elimination by addition, or augmentedmatrix methods (your choice). Show work.5 − = 137 + 3 = 518. 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 10MATH 106 Finite Mathematics______________________________________________________________________________19. According to Pricewaterhouse Coopers, "Global State of Information System Security2015", 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 hadrisen to 42.8 million.(a) Which of the following linear equations could be used to predict annual number (inmillions) of detected and reported information security incidents “y” in a given year “x”,where x = 0 represents the year 2009? Explain/show work.A. = 7.88 + 2009C. = 0.13 + 2009B. = 7.88 + 3.4D. = 0.13 + 3.4(b) Use the equation from part (a) to predict the number (in millions) of detected andreported information security incidents in the year 2022. Round answer to nearest tenthof a million. Show work.(c) Fill in the blanks to interpret the slope of the equation: The rate of change of detectedand reported information security incidents against computer networks in the US (inmillions) with respect to time is __________ per ___________. (Include units ofmeasurement.)20. Cara needs $9,500 in 11 years. What amount can she deposit at the end of each quarter at8% annual interest compounded quarterly so she will have her $9,500? Show work.A. $136.69C. $134.01B. $129.49D. $361.35______________________________________________________________________________21. There is a 0.81 probability that MATH 106 students will correctly follow all instructions onthe Final Exam. What is the probability that exactly 81 of the 100 students taking MATH 106 ina particular term correctly follow all Final Exam instructions? Round answer to the nearest tenthousandth (four places after decimal). Show work.Page 8 of 10MATH 106 Finite Mathematics______________________________________________________________________________22. The feasible region shown below is bounded by lines x + y = 2, 5x – y = 3, 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 ata particular age. The numbers are 25, 41, 49, 33, 43, and 49.(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 ofthe data set above is 9.4, what percentage of the data set falls within one standard deviation ofthe mean? Show work/explanation.(d) _______A. 34.2%C. 68.3%B. 66.7%D. 83.3%Page 9 of 10MATH 106 Finite Mathematics24. The probability distribution for the random variable x is displayed in the following table:130.20xipi80.25–50.3090.10100.15Find the expected value E(X) . Show work.______________________________________________________________________________25. A survey of 500 consumers revealed the following preferences for getting rides to citydestinations: 290 reported using UberTM, 220 reported using a taxicab service, and 110 reportedusing both.(a) What is the probability that a randomly selected consumer reported using neitherUberTM nor a taxicab service to get around in the city? Show work.(b) Let U = {consumers who reported using UberTM} and T = {consumers who reportedusing a taxicab service}. Determine the number of consumers belonging to each of the regions I,II, III, IV.500UTIIIIIIIVRegion I: ________ Region II: __________ Region III: _________ Region IV: ________________________________________________________________________________________Page 10 of 10

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