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MATH 106 Final Exam Finite Mathematics (UMUC)-Which of the corner points for the system of linear inequalities ..

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

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 02461 2 3 4 5 602461 2 3 4 5 6024681 2 3 4 5 6024681 2 3 4 5 6
Page 3 of 9 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

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 IIIIIIIV

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 TVViewer Age 18 – 39Viewer Age 40 +TotalComedy 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 ??(??n??) :
___________________________________ c. Determine ??(??’ n??’):
___________________________________ Page
6 of 9 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

19. According to the US Census Bureau,
“United States Census 2010 – Essay Writing Service: Write My Essay by Top-Notch Writer”, 33 million Americans were age 65 or
older in 1995; an amount which climbed to 40 million in 2010 – Essay Writing Service: Write My Essay by Top-Notch Writer. (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. ______________________________________________________________________________

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%

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

Order | Check Discount