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2. Shonda buys an Amalgamated dining room furniture set for $11,000, makes a down payment of 20%, and finances the rest with 60-month store financing at an annual interest rate of 5.1% compounded monthly. What is the amount of her monthly loan payment to amortize the loan?
A. $166.47
B. $165.26
C. $184.07
D. $181.87
3. Which of the following statements is TRUE?
A. If x ∈ (is a member of) ???? ???????????? ????∈???? then ????∈(????∪????)
B. If ????∈???? ???????? ????∈???? then ????∈(????∩????)
C. If ????∈???? ???????????? ????∈???? then ????∈(????∩????)
D. None of the above statements are true.
4. Two balls are drawn in succession, without replacement, out of a box containing 2 red and 5 white balls. What is the probability that the first ball drawn is red and the second ball drawn is also red?
A. 1/3
B. 5/21
C. 10/21
D. 1/21
10. The mean time from check-in to completion for a customer service task at the Townsburg branch of the DMV is 112 minutes, with a standard deviation of 18 minutes. Assuming a normal distribution, what is the probability that a randomly chosen customer experiences service done in less than 94 minutes?
A. 0.3413
B. 0.4772
C. 0.1587
D. 0.6826
11. Dwayne’s Digital Doctors is a small business specializing in personal information technology (IT) device repair. The company has fixed costs of $618 a day and variable costs of $8.50 per IT device repaired. The company charges $60 per IT device repaired. How many IT devices must be brought in for repair each day for this company to break even? Round answer to the nearest whole device.
A. 73
B. 12
C. 11
D. 7
12. Which of the following statements is TRUE?
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 of the variance.
C. The variance can be a negative number.
D. The variance is a measure of central tendency of a data distribution.
16. Seventeen people are summoned to jury duty. 11 are women and 6 are men.
(a) In how many ways can 12 jurists be randomly selected out of the 17 people? Show work.
(b) In how many ways can 12 jurists be chosen, if 7 must be women and 5 must be men? Show work.
(c) If 12 jurists are randomly selected from the 17 people, what is the probability that 5 are men and 7 are women? Round answer to nearest ten-thousandth (4 places after decimal). Show work.
17. Solve the system of equations using substitution, elimination by addition, or augmented matrix methods (your choice). Show work.
7????+5????= 4
5????−2????= 14
18. Vijay wants to start a retirement account that will have $460,000 in it when he retires in 15 years. How much should he invest every six months in his account to do this if interest is 15% compounded semiannually? Show work.
A. $4,448.77
B. $4,435.77
C. $4,790.74
D. $17,612.13
19. According to Pricewaterhouse Coopers, "Global State of Information System Security 2015", there were 3.4 million “detected and reported information security incidents” (cyberattacks, etc.) against computer networks in the USA in 2009. In 2014, that number had risen to 42.8 million.
(a) Which of the following linear equations could be used to predict annual number (in millions) of detected and reported information security incidents “y” in a given year “x”, where x = 0 represents the year 2009? Explain/show work.
????. ????=7.88????+2009 ????. ????= 0.13????+2009 ????. ????=7.88????+3.4 ????. ????= 0.13????+3.4
(b) Use the equation from part (a) to predict the number (in millions) of detected and reported information security incidents in the year 2027. Round answer to nearest tenth of a million. Show work.
(c) Fill in the blanks to interpret the slope of the equation: The rate of change of detected and reported information security incidents against computer networks in the US with respect to time is __________ per ___________. (Include units of measurement.)
20. Amanda is selling an antique dining room furniture set through a broker. She wants to get $1300 for herself, but the broker gets 15% of the selling price as commission. What should the selling price be? Show work.
A. $1380.00
B. $1495.00
C. $1529.41
D. $1411.76
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 65, 71, 88, 100, 73, and 71.
(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 13.24, what percentage of the data set falls within one standard deviation of the mean? Show work/explanation.
(d) _______
A. 34.2% C. 68.3%
B. 66.7% D. 83.3%
25. A marketing survey of 2000 randomly-selected convenience store customers found that 1415 of them bought a glazed donut yesterday. 1605 said they bought a frosted crème-filled donut yesterday. 180 customers said they bought neither yesterday.
(a) What is the probability that a single randomly-selected customer bought a glazed donut or a frosted crème-filled donut yesterday? Show work.
MATH 106 Finite Mathematics 2165-OL2-6980-V1 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 graphing calculator/spreadsheet software. 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. Amalgamated Furniture Company makes dining room tables and chairs. A table requires 8
labor-hours for assembling and 2 labor-hours for finishing. A chair requires 2 labor-hours for
assembly and 1 labor-hour for finishing. The maximum labor-hours available per day for
assembling and finishing are 400 and 120, respectively. Production costs are $600 per table and
$150 per chair. Let x represent number of tables and y represent number of chairs made per day.
Identify the daily production constraint for assembly:
1. _______
A. 8 + 2 ≥ 400 C. 8 + 2 ≤ 400 B. 2 + ≥ 120 D. 2 + ≤ 120 2. Shonda buys an Amalgamated dining room furniture set for $11,000, makes a down payment
of 20%, and finances the rest with 60-month store financing at an annual interest rate of 5.1%
compounded monthly. What is the amount of her monthly loan payment to amortize the loan?
2. _______
A. $166.47 C. $184.07 B. $165.26 D. $181.87 3. Which of the following statements is TRUE:
A.
B.
C.
D. If ∈ (is a member of) ∈ then ∈ ( ∪ )
If ∈ ∈ then ∈ ( ∩ )
If ∈ ∈ then ∈ ( ∩ )
None of the above statements are true. 3. ________ Page 1 of 10 MATH 106 Finite Mathematics 2165-OL2-6980-V1 4. Two balls are drawn in succession, without replacement, out of a box containing 2 red and 5
white balls. What is the probability that the first ball drawn is red and the second ball drawn is
also red?
4. _______
1
5
10
1
A.
B.
C.
D.
3
21
21
21 5. Which histogram below accurately reflects 15 survey responses presented in the following
frequency table?
Value
1
2
3
4
5
6 Frequency
X
XXXXX
X
X
XXXXXX
X
5. ______ HISTOGRAM A 6 6 4 4 2 2 0 HISTOGRAM C 1 4 5 HISTOGRAM D 0
1 2 3 4 HISTOGRAM 5 6 B 8 8 6 6 4 4 2 2 0 2 3 6 0
1 2 3 4 5 6 1 2 3 4 5 6 Page 2 of 10 MATH 106 Finite Mathematics 2165-OL2-6980-V1 6. Determine which graph shows the correct solution region of the system of linear inequalities:
+ ≥2 + 3 ≥ 3 ≥0
≥0
6. _______ GRAPH A. GRAPH B. GRAPH C. GRAPH D. 7. Find the equation of the line passing through (5, 2) and (– 2, 1):
a. x – y = 3 b. 3x – 7y = 1 c. x – 7y = – 9 7. _______
d. x + y = 7 Page 3 of 10 MATH 106 Finite Mathematics 2165-OL2-6980-V1 8. The total 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:
8. _______
A. Sequence of payments: present value of an annuity / amortization
B. Sequence of payments: future value of an ordinary annuity
C. Single-payment, compound interest
D. Single-payment, simple interest 9. Which of the corner points for the system of linear inequalities graphed below minimizes the
objective function P = 7x + 6y ? 9. _______
A. (3, 0) C. (2, 0) B. (0, 4) D. (1, 2) 10. The mean time from check-in to completion for a customer service task at the Townsburg
branch of the DMV is 112 minutes, with a standard deviation of 18 minutes. Assuming a normal
distribution, what is the probability that a randomly chosen customer experiences service done in
less than 94 minutes?
10. ______
A. 0.3413
C. 0.1587
B. 0.4772 D. 0.6826 Page 4 of 10 MATH 106 Finite Mathematics 2165-OL2-6980-V1 11. Dwayne’s Digital Doctors is a small business specializing in personal information
technology (IT) device repair. The company has fixed costs of $618 a day and variable costs of
$8.50 per IT device repaired. The company charges $60 per IT device repaired. How many IT
devices must be brought in for repair each day for this company to break even? Round answer to
the nearest whole device.
11. _________
A. 73 C. 11 B. 12 D. 7 12. Which of the following statements is TRUE?
A.
B.
C.
D.
* 12. ______ If all of the data values in a data set are identical, then the standard deviation is 0.
The standard deviation is the square of the variance.
The variance can be a negative number.
The variance is a measure of central tendency of a data distribution.
* * * * * * * * * * * * Page 5 of 10 MATH 106 Finite Mathematics 2165-OL2-6980-V1 SHORT ANSWER (work NOT required to be shown)
13. For the linear equation −7 + 4 = 56:
a. Determine the slope: _______________________ b. Determine y – intercept if it exists: _______________________ c. Express equation in slope-intercept form: _______________________ 14. Let () = 92, () = 107, ( ∩ ) = 67, and () = 140.
a. Determine ( ′ ) : ___________________________________ b. Determine ( ∪ ) : ___________________________________ c. Determine (′ ∩ ′ ): ___________________________________ 15. The Gallup Organization recently conducted a “straw poll” of 1500 randomly-selected
American voters to determine their current Presidential candidate preferences. Voters were also
asked their age in years (18 to 39 or 40+). Following table was obtained.
Presidential Candidate Preferred
Democrat
Independent
Libertarian
Republican
Total Voter Age 18 - 39
327
163
65
71
626 Voter Age 40 +
273
176
84
341
874 Total
600
339
149
412
1500 (Report your answers as fractions or as decimal values rounded to the nearest hundredth.)
Find the probability that a randomly-selected American voter preferred:
(a) the Libertarian candidate and is age 40+ Answer: ______________ (b) the Libertarian candidate or is age 40+ Answer: ______________ (c) the Libertarian candidate given that voter is age 40+ Answer: ______________ Page 6 of 10 MATH 106 Finite Mathematics 2165-OL2-6980-V1 SHORT ANSWER, with work required to be shown, as indicated.
16. Seventeen people are summoned to jury duty. 11 are women and 6 are men.
(a) In how many ways can 12 jurists be randomly selected out of the 17 people? Show work. (b) In how many ways can 12 jurists be chosen, if 7 must be women and 5 must be men? Show
work. (c) If 12 jurists are randomly selected from the 17 people, what is the probability that 5 are men
and 7 are women? Round answer to nearest ten-thousandth (4 places after decimal). Show
work. ______________________________________________________________________________
17. Solve the system of equations using substitution, elimination by addition, or augmented
matrix methods (your choice). Show work.
7 + 5 = 4
5 − 2 = 14 18. Vijay wants to start a retirement account that will have $460,000 in it when he retires in 15
years. How much should he invest every six months in his account to do this if interest is 15%
compounded semiannually? Show work.
A. $4,448.77 C. $4,790.74 B. $4,435.77 D. $17,612.13 ______________________________________________________________________________
Page 7 of 10 MATH 106 Finite Mathematics 2165-OL2-6980-V1 19. According to Pricewaterhouse Coopers, "Global State of Information System Security
2015", there were 3.4 million “detected and reported information security incidents”
(cyberattacks, etc.) against computer networks in the USA in 2009. In 2014, that number had
risen to 42.8 million.
(a) Which of the following linear equations could be used to predict annual number (in
millions) of detected and reported information security incidents “y” in a given year “x”,
where x = 0 represents the year 2009? Explain/show work.
. = 7.88 + 2009 . = 0.13 + 2009 . = 7.88 + 3.4 . = 0.13 + 3.4 (b) Use the equation from part (a) to predict the number (in millions) of detected and
reported information security incidents in the year 2027. Round answer to nearest tenth
of a million. Show work. (c) Fill in the blanks to interpret the slope of the equation: The rate of change of detected
and reported information security incidents against computer networks in the US with
respect to time is __________ per ___________. (Include units of measurement.) 20. Amanda is selling an antique dining room furniture set through a broker. She wants to get
$1300 for herself, but the broker gets 15% of the selling price as commission. What should the
selling price be? Show work.
A. $1380.00 C. $1529.41 B. $1495.00 D. $1411.76 ______________________________________________________________________________
21. There is a 0.89 probability that MATH 106 students will correctly follow all instructions on
the Final Exam. What is the probability that exactly 89 of the 100 students taking MATH 106 in
a particular term correctly follow all Final Exam instructions? Round answer to the nearest ten
thousandth (four places after decimal). Show work. ______________________________________________________________________________ Page 8 of 10 MATH 106 Finite Mathematics 2165-OL2-6980-V1 22. The feasible region shown below is bounded by lines – x + 2y = 4, 3x + y = 4, 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 65, 71, 88, 100, 73, and 71.
(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 13.24, what percentage of the data set falls within one standard deviation of
the mean? Show work/explanation.
(d) _______
A. 34.2%
C. 68.3%
B. 66.7% D. 83.3% Page 9 of 10 MATH 106 Finite Mathematics 2165-OL2-6980-V1 24. A local car rental agency charted daily demand as shown in the following table:
Number of customers
Probability 6
0.15 Find the expected number of customers. 8
0.20 10
0.25 12
0.30 14
0.10 Show work. 25. A marketing survey of 2000 randomly-selected convenience store customers found that 1415
of them bought a glazed donut yesterday. 1605 said they bought a frosted crème-filled donut
yesterday. 180 customers said they bought neither yesterday.
(a) What is the probability that a single randomly-selected customer bought a glazed donut
or a frosted crème-filled donut yesterday? Show work. (b) Let G = {customers who bought a glazed donut yesterday} and C = {customers who
bought a frosted crème-filled donut yesterday}. Determine the number of attendees belonging
to each of the regions I, II, III, IV. U G C
II
I III IV Region I: ________ Region II: __________ Region III: _________ Region IV: __________
______________________________________________________________________________ Page 10 of 10