MATH 106 Finite Mathematics 2152-US1-4010-V1 fall 2015

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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. Use of instructors’ solutions

manuals or online problem solving services in 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. (Work not required to be shown)

Problems #16–25 are Short Answer with work required to be shown.

MULTIPLE CHOICE

1. Which of the corner points for the system of linear inequalities graphed below maximizes the

objective function P = 5x + 4y ?

1. _______

A. (0, 4) C. (1, 2)

B. (3, 0) D. (2, 0)

2. Find the equation of the line passing through (1, – 7) and (4, 1): 2. _______

A. 8x + 3y = – 13 B. 2x + y = – 5 C. 2x – y = 9 D. 8x – 3y = 29

MATH 106 Finite Mathematics 2152-US1-4010-V1

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3. A survey of 15 randomly selected students responded to the question “How many hours a day

do you work on MATH 106?” as follows: 3, 2, 2, 4, 6, 5, 2, 5, 1, 4, 2, 3, 2, 3, 4 . Which

histogram below accurately reflects the frequency distribution of the 15 students’ responses?

3. ______

HISTOGRAM A HISTOGRAM C

HISTOGRAM B HISTOGRAM D

4. Identify the single row operation that transforms the matrix as shown: 4. ________

[

10 ?4

?5 2

|

9

?4.5

] ? [

?5 2

?5 2

|

?4.5

?4.5

]

A. 0.5????1 ? ????1 C. ????2 + ????1 ? ????1

B. ????2 ? ????1 D. 3????2 + ????1 ? ????1

5. The amount of money you should deposit in an account paying 8% compounded quarterly in

order to receive quarterly payments of $1000 for the next 4 years can be determined using

formula for:

5. _______

A. Single-payment, simple interest

B. Single-payment, compound interest

C. Sequence of payments: present value of an ordinary annuity

D. Sequence of payments: future value of an ordinary annuity

0

2

4

6

1 2 3 4 5 6

0

2

4

6

1 2 3 4 5 6

0

2

4

6

8

1 2 3 4 5 6

0

2

4

6

8

1 2 3 4 5 6

MATH 106 Finite Mathematics 2152-US1-4010-V1

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6. – 7. The Black Entertainment Television Company (BET) employs copy coordinators and

programming analysts. According to company data, a copy coordinator reviews 5 scripts and 3

show schedules per day, whereas a programming analyst reviews 2 scripts and 7 show schedules

per day. The company needs enough staff on hand to review at least 12 scripts per day and at

least 17 show schedules per day. A copy coordinator makes $230 per day and a programming

analyst makes $190 per day. The company wants to minimize daily labor costs. Let x represent

number of copy coordinators and y represent number of programming analysts.

6. Identify the daily production constraint for scripts:

6. _______

A. 5???? + 2???? ? 12 C. 5???? + 2???? ? 12

B. 5???? + 2???? ? 17 D. 5???? + 2???? ? 17

7. State the objective function.

7. _______

A. ???? = 190???? + 230???? C. ???? = 12???? + 17????

B. ???? = 230???? + 190???? D. ???? = 17???? + 12????

8. In the dice game “Yahtzee”, five-of-a-kind gives the maximum score for a single turn. What

is the probability of getting 5 “5”s in a single roll of 5 six-sided dice?

8. ________

A. 1?7776 (0.000129) C. 1?1296 (0.000772)

B. 1?30 (0.033333) D. 5?36 (0.138889)

9. Maria purchases a new home for $320,000. She makes a down payment of 20%, and

finances the rest with a 30-year fixed loan at an annual interest rate of 3.75% compounded

monthly. What is the amount of her monthly loan payment to amortize the loan?

9. _______

A. $1481.97 C. $1511.11

B. $1888.89 D. $1185.58

10. The mean time from prescription drop-off to medicine pickup for a customer served at

Heisenberg’s Pharmacy is 51 minutes, with a standard deviation of 17 minutes. Assuming a

normal distribution, what is the probability that a randomly chosen customer experiences service

done between 34 and 68 minutes?

10. ______

A. 0.6826 C. 0.3413

B. 0.4772 D. 0.5000

MATH 106 Finite Mathematics 2152-US1-4010-V1

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

11. _________

A. {Ø} C. { 7, 15 }

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

12. Determine which region defines the solution region of the following system of linear

inequalities graphed below:

12. ________

2???? ? 5???? ? ?3

?3???? + ???? ? ?2

A. Region I C. Region III

B. Region II D. Region IV

I

III

II

IV

MATH 106 Finite Mathematics 2152-US1-4010-V1

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SHORT ANSWER (work NOT required to be shown)

13. For the linear equation 8???? + 3???? = 72:

a. Determine the slope: _______________________

b. Determine x – intercept if it exists: _______________________

c. Determine y – intercept if it exists: _______________________

d. Express equation in slope-intercept form: _______________________

14. 1000 randomly-selected respondents to a TV marketing survey were asked their age in years

(18 to 39 or 40+) and the kind of TV show most often watched. Following table was obtained.

Show Most

Watched on TV

Viewer Age

18 - 39

Viewer Age

40 +

Total

Comedy 208 88 296

Drama 150 74 224

News 32 140 172

Sports 228 80 308

Total 618 382 1000

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

Find the probability that a randomly-selected respondent most often watches:

(a) drama shows and is age 18 – 39. Answer: ______________

(b) drama shows or is age 18 – 39. Answer: ______________

(c) drama shows given that viewer is age 18 – 39. Answer: ______________

15. Let ????(????) = 60, ????(????) = 75, ????(???? ? ????) = 113, and ????(????) = 150.

a. Determine ????(????

?

) : ___________________________________

b. Determine ????(???? ? ????) : ___________________________________

c. Determine ????(????

? ? ????

?

): ___________________________________

MATH 106 Finite Mathematics 2152-US1-4010-V1

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

16. Eighteen people are summoned to jury duty. 10 are women and 8 are men.

(a) In how many ways can 12 jurists be randomly selected out of the 18 people? Show work.

(b) In how many ways can 12 jurists be chosen, if 8 must be women and 4 must be men? Show

work.

(c) If 12 jurists are randomly selected from the 18 people, what is the probability that 4 are men

and 8 are women? Round answer to nearest ten-thousandth (4 places after decimal). Show

work.

______________________________________________________________________________

17. Cara needs $9,000 in 11 years. What amount can she deposit at the end of each quarter at

8% annual interest compounded quarterly so she will have her $9,000? Show work.

A. $125.19 C. $134.01

B. $129.49 D. $540.69

18. Solve the system of equations using substitution, elimination by addition, or augmented

matrix methods (your choice). Show work.

3???? ? 2???? = ?2

?4???? + 3???? = 1

______________________________________________________________________________

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19. According to the US Census Bureau, "United States Census 2010", 33 million Americans

were age 65 or older in 1995; an amount which climbed to 40 million in 2010.

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

Americans age 65 or older (in millions) “y” in a given year “x”, where x = 0 represents

the year 1995? Explain/show work.

????. ???? =

7

15 ???? + 33 ????. ???? =

15

7

???? + 33

????. ???? =

7

15 ???? + 1995 ????. ???? =

15

7

???? + 1995

(b) Use the equation from part (a) to predict the number of Americans age 65 or older (in

millions) in the year 2040. Round answer to nearest tenth of a million people. Show

work.

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

of Americans age 65 or older with respect to time is

______________________ per ________________. (Include units of measurement.)

20. A local car rental agency charted daily demand as shown in the following table:

Number of customers 8 10 12 14 16

Probability 0.3 0.2 0.3 0.1 0.1

Find the expected number of customers. Show work

______________________________________________________________________________

21. According to a recent report, 0.10 is the probability that a randomly-selected American

citizen knows that Janet Yellen is the Chair of the Federal Reserve Board of the US Government.

Nine Americans are randomly selected. Find the probability that exactly 3 of the 9 Americans

selected identifies Ms Yellen as the Chair of the Federal Reserve Board. Round answer to the

nearest thousandth (three places after decimal). Show work.

MATH 106 Finite Mathematics 2152-US1-4010-V1

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______________________________________________________________________________

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 network security specialist records the number of incoming e-mails containing links that

six randomly-selected network users receive in a day. Numbers are 27, 23, 19, 38, 27, and 22.

(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 of

the data set above is 6.6, what percentage of the data set falls within one standard deviation of

the mean? Show work/explanation.

(d) _______

A. 34.2% C. 66.7%

B. 83.3% D. 68.3%

MATH 106 Finite Mathematics 2152-US1-4010-V1

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24. You have $5000 to invest in a single payment. Which is the better investment: 8.7%

compounded annually or 8.4% compounded monthly? Show work

25. A dietitian surveyed her group of 100 patients and found that most of them ate fast food

yesterday. 45 patients said they ate at “Greasies” yesterday. 55 patients said they ate at

“Pluckies” yesterday. 15 patients said they ate at both “Greasies” and “Pluckies” yesterday.

(a) What is the probability that a single randomly-selected patient either ate at “Greasies” or

at “Pluckies” (but not both) yesterday? Show work.

(b) Let G = {patients who ate at “Greasies”} and P = {patients who ate at “Pluckies”}.

Determine the number of attendees belonging to each of the regions I, II, III, IV.

Region I: ________ Region II: __________ Region III: _________ Region IV: __________

______________________________________________________________________________

U

G P

II

IV

I III