MATH 106 Finite Mathematics 2168-OL1-6383-V1 MATH 106 FINAL EXAMINATION

MATH 106 Finite Mathematics 2168-OL1-6383-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 calculator. You must complete the exam individually.
Collaboration or consultation with others is NOT allowed. Use of instructors’ solutions
manuals and/or online problem solving services is 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. The Polk family purchases a home for $225,000, make a down payment of 25%, and finances
the rest with a 30-year fixed-rate mortgage at an annual interest rate of 3.9% compounded
monthly. What is the amount of their monthly mortgage payment?
1. _______
A. $1085.00
C. $848.97
B. $1061.25 D. $849.00 2. Customers shopping at a particular supermarket spend a mean time shopping of 33 minutes,
with a standard deviation of 9 minutes. Assuming a normal distribution, what is the probability
that a randomly chosen customer will spend between 15 and 51 minutes shopping in the
supermarket?
2. ______
A. 0.3413 C. 0.6826 B. 0.9544 D. 0.7580 3. The Tralfaz appliance company manufactures small electric grills. The company has
production costs defined as () = 9.15 + 27200 where x is the number of grills made each
month. Revenue is defined as () = 21.95 where x is the number of grills sold each month.
How many grills must be sold each month for this manufacturing process to break even?
3. ________
A. 875 B. 1240 C. 2125 D. 2973 Page 1 of 9 MATH 106 Finite Mathematics 2168-OL1-6383-V1 4. Find the values of x and y that maximize the objective function P = 9x + 5y for the feasible
region shown below.
A. ( 3 , 0 ) 4. _______ B. ( 1 , 2 )
C. ( 2 , 0 )
D. ( 0 , 3 ) 5. 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?
5. ________
A. 5⁄36 (0.138889)
C.
1⁄1296 (0.000772)
B. 1⁄30 (0.033333) D. 1⁄7776 (0.000129) 6. Which of the following statements is NOT true?
A.
B.
C.
D. 6. ______ If all of the data values in a data set are identical, then the standard deviation is 0.
The standard deviation is the square root of the variance.
The variance can be a negative number
The variance is a measure of the dispersion or spread of a distribution about its mean. 7. If K = {3, 7, 11, 15} and M = {7, 12, 15, 18}, list {| ∈ ∈ }
7. ______
A. { 3, 7, 11, 12, 15, 18 } C. {∅} B. D. { 7, 15 } { 3, 7, 7, 11, 12, 15, 15, 18 } Page 2 of 9 MATH 106 Finite Mathematics 2168-OL1-6383-V1 8. Determine which shaded region corresponds to the solution region of the system of linear
inequalities + 2 ≤ 4
≥0
4 + ≤ 4
≥0
5. _______
GRAPH A. GRAPH B. GRAPH C. GRAPH D. Page 3 of 9 MATH 106 Finite Mathematics 2168-OL1-6383-V1 9 – 10. At Burger Heaven a “double” contains 2 meat patties and 6 pickles, whereas a “triple”
contains (wait for it!) 3 meat patties and 3 pickles. Near closing time one day, only 24 meat
patties and 48 pickles are available. If a “double” sells for $1.50 and a “triple” sells for $2.00,
then how many of each should be made in order to maximize profit? Let x represent number of
“double” burgers and y represent number of “triple” burgers.
9. Identify the production constraint for meat patties:
9. _______
A. 2 + 3 ≤ 48 C. 6 + 3 ≥ 48 B. 2 + 3 ≤ 24 D. 6 + 3 ≥ 24 10. State the objective function.
10. _______
A. = 1.5 + 2 C. = 24 + 48 B. = 48 + 24 D. = 2 + 1.5 11. You can win Transylkota’s “Deep-6” lottery jackpot if you correctly choose 6 non-repeating
integer numbers between 1 and 36 (in any order) and those numbers are drawn. You buy one
ticket. What is the probability that it’s the jackpot winner?
11. ______
A. () = 6⁄366
C.
() = 1⁄36,6
B. () = 1/36,6 D. () = 1⁄366 12. Find the equation of the line passing through (9, 3) and ( – 3 , 1):
A. 2x – 3y = 9 B. 2x – 3y = – 9 C. x + 6y = 3 12. ______
D. x – 6y = – 9 Page 4 of 9 MATH 106 Finite Mathematics 2168-OL1-6383-V1 ______________________________________________________________________________
SHORT ANSWER (Work not required to be shown)
13. Consider the following graph of a line.
(a) Determine the slope.
______________ (b) State the y-intercept.
______________ (c) Find the slope-intercept form of
the equation of the line:
______________________
14. “Guilt and focusing on decision making” (Gangemi & Mancini, Journal of Behavioral
Decision Making, Vol 20, Jan 2007) reported on 171 volunteer students participating in an
experiment where each was randomly assigned to one of three groups. One group was made to
feel guilty, one group was made to feel angry, and the third group was not influenced.
Immediately after reaching these emotional states, the students were asked to decide whether or
not to spend lots of money to repair a very old car (not a “historic”/antique). The “stated” option
was “spend the money to repair the car”. The following raw data was recorded:
Emotional State
Guilt
Anger
Neutral
Totals Choose stated option C
45
8
7
60 Don’t choose stated option C’
12
50
49
111 Totals
57
58
56
171 (Report your answers as fractions or as decimal values rounded to the nearest hundredth.) Find the probability that a randomly-selected student:
(a) is in the “guilt” emotional state, or chooses the stated
option:
(b) chooses the stated option, given that the student is in the
“guilt” state:
(c) chooses the stated option and is in the “guilt” state? Answer: ______________ Answer: ______________
Answer: ______________ Page 5 of 9 MATH 106 Finite Mathematics 2168-OL1-6383-V1 15. Let () = 55, () = 65, ( ∪ ) = 85, and () = 100.
a. Determine (′ ) : ___________________________________ b. Determine [( ∪ ) − ( ∩ )] : ___________________________________ c. Determine (′ ∩ ′ ): ___________________________________ SHORT ANSWER, with work required to be shown, as directed.
16. There is a collection of 13 books. 8 of the books are fiction and 5 of the books are nonfiction. As an assignment, a student must read 6 of the books over the summer.
(a) In how many ways can 6 of the 13 books be chosen? Show work. (b) In how many ways can the 6 books be chosen, if 3 of the books must be fiction and 3 of the
books must be non-fiction? Show work. (c) If 6 books are selected at random from the collection of 13 books, what is the probability that
3 are fiction and 3 are non-fiction? Give answer as a fraction or as a decimal rounded to nearest
ten-thousandth (4 places after decimal) Show work.
______________________________________________________________________________
17. Solve the system of equations using elimination by addition, substitution, or augmented
matrix methods (your choice). Show work.
4 + 3 = −7
3 − 2 = −18
______________________________________________________________________________
18. 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. $129.49 C. $134.01 B. $204.55 D. $125.19 Page 6 of 9 MATH 106 Finite Mathematics 2168-OL1-6383-V1 19. According to Symantec Corporation, "2016 Internet Security Threat Report"
(https://www.symantec.com/security-center/threat-report), “spear-phishing” cyberattacks against
American small businesses are steadily increasing. 18% of all “spear-phishing” cyberattacks
against American businesses in 2011 targeted businesses with less than 250 employees. In 2015,
43% of all “spear-phishing” cyberattacks against American businesses targeted businesses with
less than 250 employees.
(a) Which of the following linear equations could be used to predict annual percentage of
all “spear-phishing” cyberattacks against US businesses that target “small” businesses
(“y”) in a given year “x” since 2011, where x = 0 represents the year 2011?
Explain/show work.
. = 0.16 + 18 . = 0.16 + 2011 . = 6.25 + 18 . = 6.25 + 2011 (b) Use the equation from part (a) to predict the percentage of all “spear-phishing”
cyberattacks against US businesses that will target “small” businesses in the year 2018.
Round answer to nearest tenth of a percent. Show work.
(c) Fill in the blanks to interpret the slope of the equation: The rate of change of percent
of all “spear-phishing” cyberattacks against US businesses that target “small” businesses
with respect to time is __________ per ___________. (Include units of measurement.)
______________________________________________________________________________
20. The feasible region shown below is bounded by lines x + 2y = 2, x + y = 2, and y = 0.
Find the coordinates of corner point A. Show work. Page 7 of 9 MATH 106 Finite Mathematics 2168-OL1-6383-V1 21. A local car rental agency charted daily demand as shown in the following table:
Number of customers
Probability
Find the expected number of customers. 8
0.3 10
0.2 12
0.3 14
0.1 16
0.1 Show work ______________________________________________________________________________
22.
There is a 0.86 probability that MATH 106 students will correctly follow all instructions
on the Final Exam. What is the probability that exactly 86 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. 23. A psychologist studied the number of words spoken by a sample of 8 four-year-olds. The
numbers of words recorded per each 3-year-old were 43, 50, 46, 54, 67, 46, 80, and 62.
(a) State the mode (if one exists. If not, indicate “none”). (b) Find the median. Show work/explanation. (c) State the mean. Show work/explanation. (d) The sample standard deviation is 12.77. What percentage of the data fall within one
standard deviation of the mean? Show work/explanation.
(d) _______
A. 34%
B. 68%
C. 75%
D. 88% Page 8 of 9 MATH 106 Finite Mathematics 2168-OL1-6383-V1 24. Amanda is selling an antique dining room furniture set through a broker. She wants to get
$1200 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. $1560.00 B. $1623.53 D. $1411.76 25. A mall developer surveyed 500 customers yesterday to learn what they go shopping for at
the mall. 320 customers said they shopped for clothes. 295 customers said they went shopping
for electronics. 175 customers said they shopped for both clothes and electronics.
(a) What is the probability that a single randomly-selected shopped for either clothing or
electronics yesterday, but not both? Show work. (b) Let C = {customers shopping for clothes} and E = {customers shopping for electronics}.
Determine the number of customers belonging to each of the regions I, II, III, IV.
U C E
II
I III IV Region I: ________ Region II: __________ Region III: _________ Region IV: __________
______________________________________________________________________________ Page 9 of 9