DESTINY EXAM QUESTIONS

MATH 106 Finite Mathematics Spring, 2014 V1.5

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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. 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. (Work not required to be shown) Problems #16–25 are Short Answer with work required to be shown. MULTIPLE CHOICE 1. Leslie purchases a car for $23,000, makes a down payment of 10%, and finances the rest with a 4-year car loan at an annual interest rate of 3.3% compounded monthly. What is the amount of her monthly loan payment? 1. _______ A. $542.42 B. $460.93 C. $512.14 D. $488.18

2. Find the result of performing the row operation (−3)R1 + R2 → R2 2. _______

!3 4 1 12 ' −2 −7 *+

A. ! 3 4−9 −12 ' −2 6 *+ B. ! 3 4 −8 0 '

−2 −1 *+

C. !3 4 1 0 ' −2 −7 *+ D. !0 −32 1 12 '

19 −7 *+

MATH 106 Finite Mathematics Spring, 2014 V1.5

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3. Find the values of x and y that maximize the objective function 3x + 2y for the feasible

region shown below. 3. _______

A. (x, y) = (5, 15) B. (x, y) = (8, 10) C. (x, y) = (0, 20) D. (x, y) = (10, 0)

4. Kindergarten children have normally distributed heights with a mean of 39 inches and a standard deviation of 2 inches. What is the probability that a randomly chosen kindergarten child will have a height between 37 and 41 inches? 4. ______ A. 0.6826 B. 0.7580 C. 0.5000 D. 0.9544

MATH 106 Finite Mathematics Spring, 2014 V1.5

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5. Determine which shaded region corresponds to the solution region of the system of linear inequalities

x + y ≥ 2 x + 3y ≥ 3 x ≥ 0 y ≥ 0 5. _______ GRAPH A. GRAPH B.

GRAPH C. GRAPH D.

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For #6 and #7: A merchant makes two raisin nut mixtures. Each box of mixture A contains 14 ounces of peanuts and 4 ounces of raisins, and sells for $4.50. Each box of mixture B contains 6 ounces of peanuts and 2 ounces of raisins, and sells for $2.80. The company has available 4,800 ounces of peanuts and 2,100 ounces of raisins. The merchant will try to sell the amount of each mixture that maximizes income. Let x be the number of boxes of mixture A and let y be the number of boxes of mixture B. 6. Since the merchant has 4,800 ounces of peanuts available, one inequality that must be satisfied is: 6. _______ A. 14x + 4y ≤ 4,800 B. 14x + 6y ≥ 4,800 C. 14x + 6y ≤4,800 D. 4.5x + 2.8y ≥ 4,800 7. State the objective function. 7. _______ A. 2.8x + 4.5y B. 14x + 4y C. 20x + 6y D. 4.5x + 2.8y 8. A jar contains 10 red jelly beans, 12 yellow jelly beans, and 18 orange jelly beans. Suppose that each jelly bean has an equal chance of being picked from the jar. If a jelly bean is selected at random from the jar, what is the probability that it is not yellow? 8. _______

A. 7

3 B.

7

4 C.

10

7 D.

10

3

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9. When solving a system of linear equations with the unknowns x1 and x2 the following reduced augmented matrix was obtained. 9. _______

! 1 −3 0 0 ' 7 0 *+

What can be concluded about the solution of the system?

A. There are infinitely many solutions. The solution is x1 = − 3t + 7 and x2 = t, for any real number t.

B. There are infinitely many solutions. The solution is x1 = 3t + 7 and x2 = t, for any real number t.

C. There is no solution.

D. The unique solution to the system is x1 = −3 and x2 = 7.

10. Which of the following is NOT true? 10. ______

A. If events E and F are independent events, then P(E ∩ F) = 0. B. If only two outcomes are possible for an experiment, then the sum of the probabilities of

the outcomes is equal to 1. C. If an event cannot possibly occur, then the probability of the event is 0. D. A probability must be less than or equal to 1.

11. In a certain manufacturing process, the probability of a type I defect is 0.12, the probability of a type II defect is 0.07, and the probability of having both types of defects is 0.05. Find the probability that neither defect occurs. 11. ______

A. 0.81 B. 0.76 C. 0.95

D. 0.86 12. Which of the following statements is NOT true? 12. ______

A. The standard deviation is the square root of the variance. B. The variance can be a negative number.

C. The variance is a measure of the dispersion or spread of a distribution about its mean. D. If all of the data values in a data set are identical, then the standard deviation is 0.

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SHORT ANSWER: 13. Let the universal set U = {1, 2, 3, 4, 5, 6}. Let A = {2, 4, 6} and B = {3, 4}. Determine the set A' ∪ B . Answer: ______________

14. Consider the following graph of a line.

(a) State the x-intercept. Answer: ______________ (b) State the y-intercept. Answer: ______________ (c) Determine the slope. Answer: ______________ (d) Find the slope-intercept form of the equation of the line. Answer: ____________________ (e) Write the equation of the line in the form Ax + By = C where A, B, and C are integers. Answer: ____________________

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15. A company compiled information about the gender and working status of its 420 employees,

as shown below.

Full-time Part-time Totals

Male 210 40 250 Female 90 80 170 Totals 300 120 420

(Report your answers as fractions or as decimal values rounded to the nearest hundredth.) Find the probability that a randomly selected employee is:

(a) a male employee or a part-time employee. Answer: ______________ (b) a male part-time employee. Answer: ______________ (c) part-time, given that the employee is male. Answer: ______________

SHORT ANSWER, with work required to be shown, as indicated. 16. For a five year period, Paul deposited $900 each quarter into an account paying 5.6% annual interest compounded quarterly. (Round your answers to the nearest cent.) (a) How much money was in the account at the end of 5 years? Show work. (b) How much interest was earned during the 5 year period? Show work.

Paul then made no more deposits or withdrawals, and the money in the account continued to earn 5.6% annual interest compounded quarterly, for 4 more years. (c) How much money was in the account after the 4 year period? Show work. (d) How much interest was earned during the 4 year period? Show work.

17. Three flags are arranged vertically on a flagpole, with one flag at the top, one flag in the middle, and one flag at the bottom. To create the flagpole arrangement, 20 flags are available, each flag a different color. How many different flagpole arrangements of 3 flags are possible? Show work.

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18. There is a collection of 14 prepared lunches. 9 of the lunches are sandwiches and 5 of the lunches are wraps. (a) In how many ways can 6 of the 14 lunches be chosen for a group of co-workers? Show work. (b) In how many ways can the 6 lunches be chosen from the collection of 14 lunches, if 3 of the lunches must be sandwiches and 3 of the lunches must be wraps? Show work. (c) If the 6 lunches are selected at random from the collection of 14 lunches, what is the probability that the lunches consist of 3 sandwiches and 3 wraps? Show work.

19. In 1968, there were 3.1 trillion cigarettes purchased worldwide, and in 1984, there were 4.3

trillion cigarettes purchased worldwide. Let y be the number of cigarettes purchased worldwide

(in trillions) in the year x, where x = 0 represents the year 1968.

(a) Which of the following linear equations could be used to predict the number of trillions of cigarettes y purchased worldwide in a given year x, where x = 0 represents the year 1968? Explain/show work. A. y = 1.2x − 14.9 B. y = 1.2x + 3.1 C. y = 0.075x + 3.1 D. y = 3.1x + 4.3 (b) Use the equation from part (a) to estimate the number of cigarettes purchased worldwide in the year 1996. Show work. (c) Fill in the blanks to interpret the slope of the equation: The rate of change of cigarettes purchased worldwide with respect to time is ______________________ per ______________. (Include units of measurement.)

20. Solve the system of equations using elimination by addition or by augmented matrix methods

(your choice). Show work.

3x − y = 8

6x − 5y = 13

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21. 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.

22. A survey of 80 adults found the following: 43 of the adults like to jog. 57 like to swim.

75 like to jog or swim (or both).

(a) How many of the surveyed adults like both jogging and swimming? Show work. (b) Let circle J = {joggers} and circle S = {swimmers}. Determine the number of surveyed adults belonging to each of the regions I, II, III, IV.

U

S J II

IV

III I

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23. Consider the sample data 77, 38, 62, 43, 77, 45, 64. (a) State the mode. (b) Find the median. Show work/explanation. (c) State the mean. (d) The sample standard deviation is 16.2. What percentage of the data fall within one standard deviation of the mean? Show work/explanation. (d) _______ A. 50% B. 57% C. 68% D. 71%

24. If the probability distribution for the random variable X is given in the table, what is the expected value of X? Show work.

xi – 40 10 20 30 pi 0.15 0.50 0.25 0.10

25. According to a recent report, 0.56 is the probability that an American adult owns a smartphone. Six American adults are randomly selected. Find the probability that exactly 2 of the 6 American adults owns a smartphone. Show work.