Math 106 Finite Mathematics

Math 106 Finite Mathematics 2152 Ol2 6980 V1page 1 Of 9math 106 Final

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 is 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 with no work required. Problems #16–25 are Short Answer with work required to be shown.

Paper For Above instruction

1. Which of the corner points for the system of linear inequalities maximizes the objective function P = 7x + 8y?

A. (0, 4)

B. (3, 0)

C. (1, 2)

D. (2, _) (Note: value incomplete in the prompt)

2. Find the equation of the line passing through (1, 2) and (–5, 4):

A. –x – 3y = 7

B. x + 3y = 7

C. x – 3y = 7

D. x + 3y = –7

3. Given the responses: 3, 5, 6, 2, 4, 3, 1, 3, 2, 4, 3, 3, 4, 3, 5, which histogram below accurately reflects the frequency distribution of the 15 students’ responses?

HISTOGRAM A

HISTOGRAM B

HISTOGRAM C

HISTOGRAM D

4. Identify the single row operation that transforms the matrix:

[ 10 –4 –5 | 9 –4.5 ] → [ 0 0 –5 | 0 –4.5 ]

A. 0 * row1 → row1

B. row2 ↔ row1

C. 0.5 * row1 + row2 → row2

D. 2 * row2 + row1 → row2

5. Payments of $1000 are made quarterly for 20 years into an interest-compounded quarterly sinking fund. The amount at the end uses the formula for:

A. Sequence of payments; future value of an ordinary annuity

B. Sequence of payments; present value of an ordinary annuity

C. Single payment; compound interest

D. Single payment; simple interest

6. The probability of hitting a $1000 jackpot in a single play is 0.001. The expected value of this game is:

A. $999

B. 0

C. $1.00

D. –$1.00

7. Reggie buys a car for $8500 with a 20% down payment and a 48-month loan at 6% interest compounded monthly. Reggie’s monthly payment is:

A. $175.67

B. $159.70

C. $219.58

D. $199.00

8. The BET company reviews 5 scripts and 3 show schedules per day per copy coordinator, and 2 scripts and 7 show schedules per day per programming analyst. To meet demands of at least 12 scripts and 17 schedules daily, and minimize costs where a copy coordinator costs $230 and a programming analyst $190, the production constraint and objective function are:

Constraint:

A. 3x + 7y ≤ 12

B. 3x + 7y ≥ 17

C. 3x + 7y ≤ 17

D. 3x + 7y ≥ ... (incomplete in prompt)

Objective function:

A. P = 230x + 190y

B. P = 190x + 230y

C. P = 12x + 17y

D. P = 17x + 12y

9. If K = {3, 7, 11, 15} and M = {7, 12, 15, 18}, list {x | x ∈ K and x ∈ M}

A. {___} (Values not specified)

B. {3, 7, 11, 12, 15, 18}

C. {7, 15}

D. {3, 7, 11, 15, 7, 12, 15, 18} (duplicate elements)

10. Given inequalities:

4x + y ≥ 4

x ≥ 0

x + 2y ≤ 4

y ≥ __ (graph options omitted), which graph (A-D) accurately depicts the feasible region?

12. The mean service time is 39 minutes with a standard deviation of 11 minutes at Heisenberg’s Pharmacy. Assuming a normal distribution, the probability that a customer is served between 28 and 40 minutes is:

A. 0.5000

B. 0.4772

C. 0.6826

D. 0.3413

Short Answer (Work Not Required)

13. For the graphed line:

a. Determine the slope m: ________

b. Determine the x-intercept: ________

c. Determine the y-intercept: ________

d. State the equation in slope-intercept form: ________________________

14. From a survey of 100 students, find the probabilities:

a. Social sciences major and part-time: ________

b. Social sciences major or part-time: ________

c. Social sciences major given part-time: ________

15. (Not listed in prompt; proceed with provided questions)

16. Eighteen people (11 women, 7 men).

a. Number of ways to select 12 jurors from 18: ___

b. Number with 9 women and 3 men: ___

c. Probability that in a random selection of 12, 3 are men and 9 women: ___ (rounded to 4 decimal places)

17. Christina wants to sell her antique set for $2000 after paying a 15% broker commission. The selling price she should set is:

A. $2300.00

B. $2279.83

C. $2150.00

D. $2352.94

18. Solve the matrix system:

3x – 2y = 18

–2x + 5y = –1 (show work)

19. The US Census Bureau data: 33 million in 1995, 40 million in 2010.

a. Which linear model predicts the number in year x (x=0 for 1995)?

b. Use the model to predict for 2055.

c. Interpret the slope: the rate of change in millions per __ (unit of years).

20. Demand data; find the expected number of customers given the probabilities: 0.15, 0.20, 0.25, 0.30, 0.10.

21. Feasible region bounded by lines: –x + 2y = 4, 3x + y = 4, y = 0. Find coordinates of corner point A (show work).

22. Network security data: Received links per day: 50, 10, 30, 74, 56, 26, 50, 40.

a. Mode: ________

b. Median: ________

c. Mean: ________

d. Percentage within one standard deviation (19.9): ________ (show work)

23. Probability that Christina finds a spot on exactly 3 of 5 days: ________ (show work)

24. Compare investments: $5000 at 9.0% annually vs. 8.7% monthly. Which is better? Show work.

25. Survey: 55 ate at Greasies, 45 at Pluckies, 15 at both.

a. Probability neither place was visited: ________

b. Number in each region (I, II, III, IV) based on Venn diagram (not shown). ______________

References

  • Rubinstein, R., & Byrne, L. (2014). Finite Mathematics and Applied Calculus. Pearson.
  • Ross, S. (2019). A First Course in Probability. Pearson.
  • Kenney, J. F., & Keeping, E. S. (1962). Mathematics of Statistics. D. Van Nostrand Company.
  • Hogg, R. V., & Tanis, E. (2010). Probability and Statistical Inference. Pearson.
  • Levine, D. M., et al. (2016). Basic Business Statistics. Pearson.
  • Wackerly, D., Mendenhall, W., & Scheaffer, R. (2014). Mathematical Statistics with Applications. Cengage Learning.
  • Siegel, S., & Castellan, N. J. (1988). Nonparametric Statistics for the Behavioral Sciences. McGraw-Hill.
  • Newbold, P., Carlson, W. L., & Thorne, B. (2013). Statistics for Business and Economics. Pearson.
  • U.S. Census Bureau. (2010). U.S. Census 2010 Data. https://www.census.gov/data.html
  • Kreyszig, E. (2011). Advanced Engineering Mathematics. John Wiley & Sons.

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