MATH 106 Finite Mathematics Fall, 2012, 1.1 Page 1 of 10 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. 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. Julie purchases a car for $20,000, makes a down payment of 10%, and finances the rest with a 4-year car loan at an annual interest rate of 9% compounded monthly. What is the amount of her monthly loan payment? 1. _______ A. $447.93 B. $497.70 C. $510.00 D. $566.67 2. Find the result of performing the row operation (−5)R1 + R2 → R2 2. _______ �−1 −23 −4� 3 6 � A. �−1 −28 −4� 3 6 � B. �−1 −28 6� 3 −9 � C. �−1 −22 −14� 3 21 � D. �−16 183 −4� −27 6 � . MATH 106 Finite Mathematics Fall, 2012, 1.1 Page 2 of 10 3. Find the values of x and y that maximize the objective function 4x + 5y 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. Adult American have normally distributed heights with a mean of 5.8 feet and a standard deviation of 0.2 feet. What is the probability that a randomly chosen adult American male will have a height between 5.6 feet and 6.0 feet? 4. ______ A. 0.5000 B. 0.6826 C. 0.7580 D. 0.9544 MATH 106 Finite Mathematics Fall, 2012, 1.1 Page 3 of 10 5. Determine which shaded region corresponds to the solution region of the system of linear inequalities x + y ≥ 2 3x + y ≥ 3 x ≥ 0 y ≥ 0 5. _______ GRAPH A. GRAPH B. GRAPH C. GRAPH D. MATH 106 Finite Mathematics Fall, 2012, 1.1 Page 4 of 10 For #6 and #7: A merchant makes two raisin nut mixtures. Each box of mixture A contains 10 ounces of peanuts and 3 ounces of raisins, and sells for $4.20. Each box of mixture B contains 8 ounces of peanuts and 2 ounces of raisins, and sells for $3.60. The company has available 5,100 ounces of peanuts and 1,600 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 1,600 ounces of ...

1. MATH 106 Finite Mathematics Fall, 2012, 1.1
Page 1 of 10
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.
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. Julie purchases a car for $20,000, makes a down payment of
10%, and finances the rest with a
4-year car loan at an annual interest rate of 9% compounded
monthly. What is the amount of her

2. monthly loan payment?
1. _______
A. $447.93
B. $497.70
C. $510.00
D. $566.67
2. Find the result of performing the row operation (−5)R1 +
R2 → R2 2. _______
�−1 −23 −4�
3
6
�
A. �−1 −28 −4�
3
6
� B. �−1 −28 6�
3
−9
�

3. C. �−1 −22 −14�
3
21
� D. �−16 183 −4�
−27
6
�
.
MATH 106 Finite Mathematics Fall, 2012, 1.1
Page 2 of 10
3. Find the values of x and y that maximize the objective
function 4x + 5y for the feasible
region shown below. 3. _______
A. (x, y) = (0, 20)
B. (x, y) = (5, 15)
C. (x, y) = (8, 10)

4. D. (x, y) = (10, 0)
4. Adult American have normally distributed heights with a
mean of 5.8 feet and a standard
deviation of 0.2 feet. What is the probability that a randomly
chosen adult American male will
have a height between 5.6 feet and 6.0 feet? 4. ______
A. 0.5000
B. 0.6826
C. 0.7580
D. 0.9544
MATH 106 Finite Mathematics Fall, 2012, 1.1
Page 3 of 10
5. Determine which shaded region corresponds to the solution
region of the system of linear
inequalities
x + y ≥ 2

5. 3x + y ≥ 3
x ≥ 0
y ≥ 0
5. _______
GRAPH A. GRAPH B.
GRAPH C. GRAPH D.
MATH 106 Finite Mathematics Fall, 2012, 1.1
Page 4 of 10
For #6 and #7:
A merchant makes two raisin nut mixtures.
Each box of mixture A contains 10 ounces of peanuts and 3
ounces of raisins, and sells for $4.20.
Each box of mixture B contains 8 ounces of peanuts and 2
ounces of raisins, and sells for $3.60.
The company has available 5,100 ounces of peanuts and 1,600
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. 6. Since the merchant has 1,600 ounces of raisins available, one
inequality that must be satisfied
is:
6. _______
A. 4.2x + 3.6y ≤ 1,600
B. 10x + 3y ≥ 1,600
C. 3x + 2y ≥ 1,600
D. 3x + 2y ≤ 1,600
7. State the objective function.
7. _______
A. 5,100x + 1,600y
B. 4.2x + 3.6y
C. 10x + 3y
D. 10x + 8y
8. A jar contains 10 red jelly beans, 12 yellow jelly beans, and
18 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

7. probability that it is not red?
8. _______
A.
4
3
B.
3
2
C.
3
1
D.
4
1
MATH 106 Finite Mathematics Fall, 2012, 1.1
Page 5 of 10

8. 9. When solving a system of linear equations with the unknowns
x1 and x2
the following reduced augmented matrix was obtained. 9.
_______
�1 30 0�
7
1
�
What can be concluded about the solution of the system?
A. There is no solution.
B. The unique solution to the system is x1 = 3 and x2 = 7.
C. There are infinitely many solutions. The solution is x1 =
−3t + 7 and x2 = t, for any real
number t.
D. There are infinitely many solutions. The solution is x1 = 3t
+ 7 and x2 = t, for any real
number t.
10. Which of the following is NOT true? 10. ______

9. A. A probability must be less than or equal to 1.
B. If only two outcomes are possible for an experiment, then the
sum of the probabilities of
the outcomes is equal to 1.
C. If an event cannot possibly occur, then the probability of the
event is a negative number.
D. If events E and F are mutually exclusive events, then P(E ∩
F) = 0.
11. In a certain manufacturing process, the probability of a type
I defect is 0.18, the probability
of a type II defect is 0.16, and the probability of having both
types of defects is 0.06.
Find the probability that neither defect occurs. 11. ______
A. 0.60
B. 0.66
C. 0.72
D. 0.94
12. Which of the following statements is NOT true? 12.
______
A. The variance can be a negative number.
B. If all of the data values in a data set are identical, then the
standard deviation is 0.

10. C. The variance is a measure of the dispersion or spread of a
distribution about its mean.
D. The standard deviation is the square root of the variance.
MATH 106 Finite Mathematics Fall, 2012, 1.1
Page 6 of 10
SHORT ANSWER:
13. Let the universal set U = {1, 2, 3, 4, 5, 6, 7}. Let A = {1, 4,
5} and B = {4, 5, 7}.
Determine the set A′ ∪ 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: ______________

11. (c) Determine the slope. Answer: ______________
(d) Find the standard form of the line, Ax + By = C Answer:
____________________
(e) Find the slope-intercept form of the equation of the line.
Answer: ____________________
MATH 106 Finite Mathematics Fall, 2012, 1.1
Page 7 of 10
15. A student organization surveyed their members about their
enrollment status. 400 members
responded to the question “Are you a full-time student?” and
the following table was compiled.
Gender
Male Female Totals
Full-time? Yes 30 45 75
No 190 135 325
Totals 220 180 400

12. (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 female full-time student. Answer: ______________
(b) a female or a full-time student. Answer: ______________
(c) female, given that the respondent is a full-time student.
Answer: ______________
SHORT ANSWER, with work required to be shown, as
indicated.
16. For a six year period, George deposited $800 each quarter
into an account paying 6.4%
annual interest compounded quarterly. (Round your
answers to the nearest cent.)
(a) How much money was in the account at the end of 6
years? Show work.
(b) How much interest was earned during the 6 year period?
Show work.
George then made no more deposits or withdrawals, and the

13. money in the account continued to
earn 6.4% annual interest compounded quarterly, for 7 more
years.
(c) How much money was in the account after the 7 year
period? Show work.
(d) How much interest was earned during the 7 year period?
Show work.
17. Three flags are arranged vertically on a flagpole, with one
flag at the top, one flag in the
middle, and one flag at the bottom. To create the flagpole
arrangement, 18 flags are available,
each flag a different color. How many different flagpole
arrangements of 3 flags are possible?
MATH 106 Finite Mathematics Fall, 2012, 1.1
Page 8 of 10
18. There is a collection of 11 books. As an assignment, a
student must read any 4 of the books
over the summer.
(a) In how many ways can 4 of the 11 books be chosen? Show

14. work.
6 of the books are fiction and 5 of the books are non-fiction.
(b) In how many ways can the 4 books be chosen, if 2 of the
books must be fiction and 2 of the
books must be non-fiction? Show work.
(c) If 4 books are selected at random from the collection of 11
books, what is the probability that
2 are fiction and 2 are non-fiction? Show work.
19. In 1999, a typical American consumed 63 liters of bottled
water, and in 2001, a typical
American consumed 74 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 = 11x + 30
B. y = 11x + 63
C. y = 5.5x + 63

15. D. y = −5.5x + 74
(b) Use the equation from part (a) to estimate the number of
liters of bottled water consumed by
a typical American in 2007. 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.
4x + 3y = 2
8x − 4y = −16
MATH 106 Finite Mathematics Fall, 2012, 1.1
Page 9 of 10
21. 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.

16. 22. A survey of 80 adults found the following: 43 of the
adults like to jog. 57 like to swim.
75 like to jog or swim (or both).
(a) How many of the surveyed adults like both jogging and
swimming? Show work.
(b) Let J = {joggers} and S = {swimmers}. Determine
the number of surveyed adults
belonging to each of the regions I, II, III, IV.
U
S J
II
IV
III I

17. MATH 106 Finite Mathematics Fall, 2012, 1.1
Page 10 of 10
23. Use the sample data 65, 60, 51, 75, 51, 62, 84.
(a) State the mode.
(b) Find the median. Show work/explanation.
(c) State the mean.
(d) The sample standard deviation is 12.1. What percentage
of the data fall within one
standard deviation of the mean? Show work/explanation.
(d) _______
A. 57%
B. 68%
C. 71%
D. 86%
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 – 80 20 30 40
pi 0.25 0.15 0.40 0.20

18. 25. In 2010, the probability that a voting-age citizen voted in
the November, 2010 congressional
election was 0.46. Five voting-age citizens in 2010 were
randomly selected. Find the probability
that exactly 3 of the 5 citizens voted in the 2010 election. Show
work.
Answer Sheet
MULTIPLE CHOICE. Record your answer choices.
1.7.
2.8.
3.9.
4.10.
5.11.
6.12.
SHORT ANSWER. Record your answers below.
13.
14. (a)
(b)

19. (c)
(d)
(e)
15. (a)
(b)
(c)
SHORT ANSWER with Work Shown. Record your answers and
work.
Problem Number
Solution
16
Answers:

20. (a)
(b)
(c)
(d)
Work for (a), (b), (c), and (d):

21. 17
Answer:
Work:
18
Answers:
(a)
(b)
(c)
Work for (a), (b), and (c):

22. 19
Answers:
(a)
(b)
(c)

23. Work for (a) and (b):
20
Answer:
Work:

24. 21
Answer:
Work:

25. 22
Answers:
(a)
(b) Region I:
Region II:
Region III:
Region IV:

26. Work for (a):
23
Answers:
(a)
(b)
(c)
(d)
Work for (b) and (d):

27. 24
Answer:
Work:

28. 25
Answer:
Work: