Math 101 Final Exam
Spring 2015 / Blue
page 1
Make sure that your scantron color matches the color of this page. Be sure to read ALL directions
before beginning this exam.
On your scantron, encode your name as specified on the scantron, encode your Dawgtag as your
“Identification Number,” and encode your section number in the column “OP” under the area labeled
“Special Codes”. The sections are listed below and are listed by when your lab section meets.
The last page of this exam is the formula sheet and the z-score table. When you are finished be sure to
turn in your scantron and be sure all information is correct.
01
9 a.m. Tuesday
11
12 noon Tuesday
02
9 a.m. Wednesday
12
12 noon Wednesday
03
9 a.m. Thursday (Foster)
13
12 noon Thursday
04
9 a.m. Thursday (Hao)
14
1 p.m.
Tuesday
05
8 a.m. Tuesday
15
1 p.m.
Wednesday
06
8 a.m. Wednesday
16
1 p.m.
Thursday (Gunawardana)
07
8 a.m. Thursday
17
1 p.m.
Thursday (Tram)
1. What is the effective annual yield of an investment which pays 6.2% compounded quarterly?
Round to the nearest hundredth of a percent.
a) 6.32%
b) 6.33%
c) 6.34%
d) 6.35%
e) 6.36%
Page 2
2. How many check digits are in a (5,9)-block code?
a) 5
b) 4
c) 9
d) 45
e) 14
d) 43
e) None of these
3. How many vertices on a tree with 44 edges?
a) 43!
b) 44!
c) 45
4. Suppose the check matrix for a block code is given below. Decode the word 110011 and determine
if it is a codeword or if it differs from a codeword by a single digit. The decoded message is:
1

0
1

1
0

0

a) 100
b) 110
0
1
1
0
1
0
1

0
0

0
0 
1 
c) 101
d) 011
e) None of these
5. Compute 7 + 11 + 14 in  ₆
a) 1
b) 2
c) 3
d) 32
e) none of these
Page 3
The following table is to be used for questions 6 and 7. The table represents a recent survey of fans
of the history channel at a given high school.
class
Freshman
Sophomore
Junior
Senior
Swamp People
24
29
32
21
Ancient Aliens
43
21
11
25
Pawn Stars
53
50
24
44
6. If it is known that the student is a freshman what is the probability they prefer Swamp People?
a) 0.22
b) 0.20
c) 0.24
d) 0.23
e) None of these
7. If a student prefers Ancient Aliens what is the probability they are a Senior?
a) 0.25
b) 0.28
c) 0.26
d) 0.18
e) None of these
8. Given the sets A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10 } and B = { multiples of 3 } , what is the probability
you choose a number from set B given you chose a number in set A ? (This is P(B│A).
a) 0.4
b) 0.3
c) 0.2
d) 0.1
e) 0
9. The ages of individuals at a concert are a normal distribution with a mean of 23 and a standard of
deviation of 1.54. What percent of those in attendance were above the age of 25?
a) 1.30%
b) 90.32%
c) –1.3%
d) 9.68%
e) None of these
Page 4
10. Given a graph with edge set {AB, AC, AD, AE, AF, BC, DE , EF, DF}. Which vertices are adjacent to
vertex C ?
a) {A, B}
b) {A, B, C}
c) {A, C}
d) {D, E, F}
e) None of these
Use the following data set to answer questions 11, 12 and 13.
7
15
9
11
21
3
5
9
19
29
4
11. What is the range?
a)
12.
b) 26
c) 11
d)
9
e) None of these
What is the value of the first quartile?
a)
13.
25
3
b) 5
c)
9
b) 10
c)
11
d) 19
e) None of these
What is the mean?
a)
9
d) 12
e) None of these
14. Suppose a linear code has codewords {00000, 01011, 10101, 11111}. What is the maximum number
of errors which can be detected?
a) 0
b) 1
c) 2
d) 3
e) None of these
Page 5
15. In a connected graph the degrees of all of the vertices are added together. Which of the following
could not be the sum of those degrees?
a) 247
b) 202
c) 266
d) All of the preceding could be
e) None of the preceding could be.
16. Fifty dollars is deposited into an account each month which pays 2% interest compounded
monthly. What is the total value of the account after seven years? Round to the nearest cent.
a) $4504.20
b) $4500.00
c) $4504.19
d) 57.51
e) None of these
17. A dart is thrown and lands somewhere not on a line, inside the large square. If all of the inside
squares are the same size what are the odds the dart lands in a square with an even number in it?
a) 3 : 5
b) 5 : 3
6
144
11
19
50
99
21
85
12
53
18
36
1331
101
c) 8 : 3
53
d) 3 : 8
77
e) None of these
page 6
18. What is the weight of the minimal spanning tree for the graph given?
A
12
B
9
16
26
30
E
20
19
18
33
C
a) 55
b) 56
25
D
c) 88
d) 218
e) None of these
19. In order for a connected graph to have an Euler circuit the graph must have
a)
No more than two vertices of odd degree
d) Exactly two vertices of odd degree
b)
No vertices of odd degree
e) An even number of vertices of odd degree
c) At least one vertex of odd degree
20. Two standard six-sided dice are rolled and the sum of the top two numbers is computed. What
is the probability this sum is smaller than six?
a) 5/12
b) 7/12
c) 5/18
d) 13/18
e) None of these
Page 7
21. In a poll of precinct committeemen the following table represents their preferences for a
replacement for commissioner.
# of votes
First
Second
Third
7
A
C
B
5
B
C
A
4
C
B
A
d) D
e) there is a tie
3
B
A
C
Who is the winner using the Borda Count?
a)
A
b)
B
c) C
22. The table below represents the probability distribution of the number of dogs owned per
household in a given community where x represents the number of dogs owned. Find the mean number
of dogs owned per household in this community.
a) 0.8
b) 1.0
X
P(X)
0
0 .22
1
0.62
2
0.10
3
0.06
c) 0.92
d) 1.012
e) None of these
23. In a recent poll of 2500 pet owners it was found 57% preferred dogs to cats. A 95% confidence
interval lies between which two values?
a) 53% and 61%
b) 55% and 59%
c) 52% and 60%
d) 56% and 58% e) None of these
page 8
24. Given the following preference table who is the winner using plurality?
Number of
votes
First
9
A
7
B
10
D
8
B
12
C
5
D
4
C
Second
B
C
C
A
B
A
A
Third
D
A
D
D
A
B
D
Fourth
C
D
A
C
D
C
B
a) A
b) B
c) C
d) D
e) There is no winner
.
25. What is a Hamiltonian circuit using the nearest-neighbor algorithm starting at A for the graph
below?
A
14
19
21
25
12
B
E
33
17
D
26
20
29
C
a) AEBCDA
b) ACBEDA
c) ACBDEA
d) ABCDEA
e) None of these
26. What is the value of the fraction 5/16 when it is converted to a percent?
a) 80%
b) 3.2%
c) .3125%
d) 312.5%
e) 31.25%
page 9
Use the following data for problems 27 through 30.
A box contains 3 red marbles, 4 blue marbles, 2 yellow marbles and 5 green marbles.
27. Which event is most likely to occur if a single marble is drawn?
a) The marble is red or blue.
b) The marble is blue or green.
c) The marble is not green.
d) The marble is not blue.
e) The marble is not yellow.
28. What are the odds against drawing a red marble?
a) 3 : 14
b) 3 : 11
c) 14 : 3
d) 11 : 3
e) None of these
29. What is the probability of drawing a red marble then a blue marble without replacement?
a)
6 / 91
b) 3 / 49
c) 7 / 196
d) 1 / 2
e) None of these
30. What is the probability of drawing a marble which is not blue?
a) 5 / 7
b) 2 / 7
c) 3 / 7
d) 4 / 7
e) None of these
31. A sum of $6000 is invested at 3.5% simple interest for six years. The total interest earned is
a) $7260.00
b) $210.00
c) $21.00
d) $365.00
e) $1260.00
Page 10
32. The first 9 digits of an ISBN-10 are 1-212-38415. What is the correct check digit?
a)
4
b)
5
c)
6
d)
7
e) None of these
33. A bank will not loan more than 70% of the appraised value on farmland. If some farmland appraises
for $ 850,000 how much cash must a buyer have in order to get the loan approved?
a) $ 250,000
b) $ 255,000
c) $ 600,000
d) $ 595,000
e) No answer listed
34. What is the sample standard deviation for the following data set? Round to the nearest
hundredth.
5
a) 10
7
7
b) 9.80
11
c) 4.00
14
16
d) 4.38
e) None of these
35. Given the following preference table who is the winner using plurality with elimination?
# of votes
17
12
11
8
7
First
A
C
D
B
B
Second
C
B
B
D
D
Third
B
A
C
A
C
Fourth
D
D
A
C
A
a) A
b) B
c) C
d) D
e) there is no winner
page 11
36. Given the following generator matrix, find the codeword for 0111
1
0

0

0
a) 11110101
b) 01110011
0
1
0
0
0
0
1
0
c) 01100111
0
0
0
1
0
1
0
1
1
0
0
0
1
0
0
1
0
1
1

1
d) 01110111
e) none of these
37. What is the Hamming distance between u and v if u =1100110 and v = 0110101 ?
a) 1
b) 2
c) 3
d) 4
e) None of these
38. A new pair of tennis shoes costs $65.75. In addition to the purchase price there is an additional
7.25% sales tax. What is the total cost with tax? Round appropriately.
a) $ 73.00
b) $70.52
c) $70.51
d) $4.77
e) None of these
39. Which algorithm guarantees the minimal cost Hamiltonian circuit?
a) Nearest
Neighbor
b) Cheapest
Link
c) Kruskal’s
Algorithm
d) Brute
Force
e) Lowndes’
Algorithm
page 12
40. Bubba takes out a loan for his new four wheel drive truck. Bubba borrows $43,000.00 at 3.5%
interest. How much are his monthly payments if he finances the truck for six years? Round to the
nearest cent.
a) $ 662.99
b) $ 782.24
c) $ 663.00
d) $ 741.75
e) None of these