Project #3031 - Finite Math Final Exam

 

MATH 106 FINAL EXAMINATION

This is an open-book exam. You may refer to your text and other course materials as you work

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. Bob purchases a car for $26,000, makes a down payment of 25%, and finances the rest with a

3-year car loan at an annual interest rate of 3.0% compounded monthly. What is the amount of

his monthly loan payment?

1. _______

A. $787.22

B. $756.11

C. $590.42

D. $567.08

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

_4 −3

9 2__ 5

_7

__

A. _4 −3

1 8__ 5

−3

__ B. _−8 6

___9 2__−10

_7

__

C. _4 −3

1 2__ 5

_7

__ D. _ 4 −3

−14 −7__ 5

−9

__

MATH 106 Finite Mathematics Spring, 2013, 1.4

Page 2 of 10

3. Find the values of x and y that maximize the objective function 5x + 4y for the feasible

region shown below. 3. _______

A. (x, y) = (0, 20)

B. (x, y) = (5, 15)

C. (x, y) = (8, 10)

D. (x, y) = (10, 0)

4. Customers shopping at a particular supermarket have normally shopping times with a mean of

44 minutes and a standard deviation of 12 minutes. What is the probability that a randomly

chosen customer will spend between 32 and 56 minutes shopping in the supermarket?

4. ______

A. 0.9544

B. 0.7580

C. 0.6826

D. 0.5000

MATH 106 Finite Mathematics Spring, 2013, 1.4

Page 3 of 10

5. Determine which shaded region corresponds to the feasible region, the solution region of the

system of linear inequalities

2x + y £ 4

x + y £ 4

x ³ 0

y ³ 0

5. _______

GRAPH A. GRAPH B.

GRAPH C. GRAPH D.

MATH 106 Finite Mathematics Spring, 2013, 1.4

Page 4 of 10

For #6 and #7:

A merchant makes two raisin nut mixtures.

Each box of mixture A contains 8 ounces of peanuts and 2 ounces of raisins, and sells for $2.60.

Each box of mixture B contains 12 ounces of peanuts and 4 ounces of raisins, and sells for $3.20.

The company has available 4,500 ounces of peanuts and 2,000 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 2,000 ounces of raisins available, one inequality that must be satisfied

is: 6. _______

A. 2.6x + 3.2y ³ 2,000

B. 2x + 4y £ 2,000

C. 6x + 5.8y £ 2,000

D. 2x + 4y ³ 2,000

7. State the objective function. 7. _______

A. 3.2x + 2.6y

B. 2.6x + 3.2y

C. 8x + 12y

D. 20x + 6y

8. A jar contains 12 red jelly beans, 8 yellow jelly beans, and 16 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 red?

8. _______

A.

10

3

B.

3

1

C.

3

2

D.

10

7

MATH 106 Finite Mathematics Spring, 2013, 1.4

Page 5 of 10

9. When solving a system of linear equations with the unknowns x1 and x2

the following reduced augmented matrix was obtained. 9. _______

__1 −9

_0 0__ 5

_1

__

What can be concluded about the solution of the system?

A. The unique solution to the system is x1 = −9 and x2 = 5.

B. There are infinitely many solutions. The solution is x1 = − 9t + 5 and x2 = t, for any real

number t.

C. There are infinitely many solutions. The solution is x1 = 9t + 5 and x2 = t, for any real

number t.

D. There is no solution.

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

A. If all of the data values in a data set are identical, then the standard deviation is 0.

B. The standard deviation is the square root of the variance.

C. The variance is a measure of the dispersion or spread of a distribution about its mean.

D. The variance can be a negative number.

11. In a certain manufacturing process, the probability of a type I defect is 0.10, the probability

of a type II defect is 0.08, and the probability of having both types of defects is 0.03.

Find the probability that neither defect occurs. 11. ______

A. 0.79

B. 0.82

C. 0.85

D. 0.97

12. Which of the following is NOT true? 12. ______

A. If events E and F are independent events, then P(E Ç F) = 0.

B. If an event cannot possibly occur, then the probability of the event is 0.

C. A probability must be less than or equal to 1.

D. If only two outcomes are possible for an experiment, then the sum of the probabilities of

the outcomes is equal to 1.

MATH 106 Finite Mathematics Spring, 2013, 1.4

Page 6 of 10

SHORT ANSWER:

13. Let the universal set U = {1, 2, 3, 4, 5, 6}. Let A = {1, 3, 6} and B = {2, 3}.

Determine the set A¢ Ç B . Answer: ______________

(Be sure to notice the complement symbol applied to A.)

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: ____________________

MATH 106 Finite Mathematics Spring, 2013, 1.4

Page 7 of 10

15. A residential college compiled information about dining hall preferences, surveying 350

students, asking them if they are vegetarians. The results are shown below.

Vegetarian Not a

vegetarian

Totals

Male 30 110 140

Female 70 140 210

Totals 100 250 350

(Report your answers as fractions or as decimal values rounded to the nearest hundredth.)

Find the probability that a randomly selected survey respondent is:

(a) a male or a vegetarian Answer: ______________

(b) a male vegetarian. Answer: ______________

(c) vegetarian, given that the respondent is male. Answer: ______________

SHORT ANSWER, with work required to be shown, as indicated.

16. For a five year period, Gail deposited $600 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.

Gail 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. A contest has 40 finalists. One finalist is awarded first prize, another finalist is awarded

second prize, and another is awarded third prize. How many different ways could the prizes be

awarded? Show work.

MATH 106 Finite Mathematics Spring, 2013, 1.4

Page 8 of 10

18. A bookstore customer is looking over a collection of 13 best-selling books. 6 of the books

are fiction and 7 of the books are non-fiction.

(a) In how many ways can the customer choose 4 of these books to purchase? Show work.

(b) In how many ways can the customer choose 4 of these books to purchase, if 2 books must be

fiction and 2 books must be non-fiction? Show work.

(c) If the 4 books are selected at random by the customer, what is the probability that the

purchase consists of 2 fiction books and 2 non-fiction books? Show work.

19. In 1999, a typical American consumed 63 liters of bottled water, and in 2003, a typical

American consumed 85 liters of bottled water. Let y be the number of liters of bottled water

consumed by a typical American in the year x, where x = 0 represents the year 1999.

(a) Which of the following linear equations could be used to predict the number of liters of

bottled water consumed in a given year x, where x = 0 represents the year 1999? Explain/show

work.

A. y = −5.5x + 85

B. y = 5.5x + 63

C. y = 11x + 63

D. y = 11x + 41

(b) Use the equation from part (a) to estimate the number of liters of bottled water consumed by

a typical American in 2015. Show work.

(c) Fill in the blanks to interpret the slope of the equation: The average rate of change of bottled

water consumed 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.

2x + y = −7

x − 2y = −11

MATH 106 Finite Mathematics Spring, 2013, 1.4

Page 9 of 10

21. The feasible region shown below is bounded by lines −x + 2y = 1, x + y = 1, and y = 0.

Find the coordinates of corner point A. Show work.

22. 120 moviegoers were observed during a movie screening at a theatre. 52 of the

moviegoers ate popcorn. 34 of the moviegoers ate candy. 72 of the moviegoers ate popcorn

or candy (or both).

(a) How many of the moviegoers ate both popcorn and candy? Show work.

(b) Let P = {moviegoers eating popcorn}, and C = {moviegoers eating candy},

corresponding to the circles below. Determine the number of moviegoers belonging to each of

the regions I, II, III, IV.

U

P C

II

IV

I III

MATH 106 Finite Mathematics Spring, 2013, 1.4

Page 10 of 10

23. Use the sample data 62, 60, 90, 71, 60, 45, 67.

(a) State the mode.

(b) Find the median. Show work/explanation.

(c) State the mean.

(d) The sample standard deviation is 13.7. What percentage of the data falls within one

standard deviation of the mean? Show work/explanation.

(d) _______

A. 71%

B. 68%

C. 57%

D. 43%

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 – 20 10 30 50

pi 0.50 0.15 0.25 0.10

25. The probability is 0.4 that a marriage will end in divorce within 10 years.

Five newly married couples are randomly selected. Find the probability that exactly 3 of the 5

couples will be divorced within 10 years. Show work.

Subject Mathematics
Due By (Pacific Time) 03/10/2013 10:00 am
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