MAT 104 Pace University Algebra Mathematics Exam Practice

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Pace University
Spring 2020
MAT104 CRN 21594
Final Exam
P. Orgas
May 14, 2020
Exam Instructions:
1. You may use a scientific calculator.
2. This exam is “closed book,” which means you are NOT permitted to use any additional resources or
materials handed out in class, your own notes from the course, the text book, and anything posted by
your instructor on the Blackboard shell of the course.
3. The exam must be taken completely alone. Showing it or discussing it with anyone is forbidden.
4. You may not consult any external resources. This means no internet searches, materials from other
classes or books or any notes you have taken in other classes etc. You may not use Google or any other
search engines for any reason. You may not use any shared Google documents.
5. You may not consult with any other person regarding the exam. You may not check your exam answers
with any person.
6. Completed exam must be uploaded as PDF file via Blackboard Assignment page within 24 hours from
the time the exam was made available by the instructor.
7. SHOW ALL YOUR WORK. NO CREDIT will be given for the correct answer without work to back it
up.
Formulas:
F = (1 + i)n P
reff = (1 + i)m − 1
Bnew = (1 + i) Bprevious + R
F=
P=
(1+i)n −1
i
1−(1+i)−n
i
R
R
Page 1 of 3
Pace University
Spring 2020
MAT104 CRN 21594
Final Exam
P. Orgas
May 14, 2020
Exam:
1. (6 points) Solve the system of equations by using the inverse of the coefficient matrix.
𝑥 − 𝑦 + 4𝑧 = 17
+𝑧=5
{ 5𝑥
𝑥 + 2𝑦 + 𝑧 = 11
2. (6 points) Let U = {1, 3, 5, 7, 9, 11}, A = {1, 5, 9, 11}, B = {3, 5, 7}, and C = {1, 3, 11}. List the
elements of the indicated set.
a. 𝐴 ∩ 𝐵
b. 𝐴 ∩ (𝐵 ∪ 𝐶)′
c. 𝐴′ ∪ 𝐵 ∪ 𝐶
3. (8 points) A survey of 100 families showed that
10 had a dog and a cat;
0 had a dog and a parakeet;
0 had a cat and a parakeet;
42 had neither a cat nor a dog, and in addition did not have a parakeet;
0 had a cat, a dog, and a parakeet.
a. How many had a parakeet only?
b. How many had only one pet?
c. How many did not have a dog?
4. (6 points) A coin is tossed five times and the sequence of heads and tails is observed. What is the
number of different outcomes having more heads than tails?
5. (6 points) How many advisory committees can be formed with four professors and two students from a
department with 10 professors and 50 students?
6. (6 points) There are 12 horses in a race. In how many ways can the first three positions of the order of
the finish occur? (Assume there are no ties.)
7. (8 points) In the current first-year class of a community college, all the students come from three local
high schools. Schools I, II, and III supply respectively 40%, 50%, and 10% of the students. The failure
rate of students is 4%, 2%, and 6%, respectively.
a. What is the probability that a randomly selected student will fail?
b. Given that a student fails, what is the probability that he or she came from school I?
8. (6 points) The probabilities that stock A will rise in price is 0.7 and that stock B will rise in price is 0.6.
Further, if stock B rises in price, the probability that stock A will also rise in price is 0.8. What is the
probability that only one of the stocks A or B will rise in price?
Page 2 of 3
Pace University
Spring 2020
MAT104 CRN 21594
Final Exam
P. Orgas
May 14, 2020
9. (6 points) A true or false test has 6 questions. What is the probability of getting at most one question
correct by guessing?
10. (6 points) Find the five-number summary for the sample data: 20, 21, 23, 24, 26, 27, 29, 30, 31, 33, 34.
11. (6 points) The average height of women is 64 inches. The standard deviation is 2 inches. The heights
have a normal distribution. Find the probability that a randomly selected woman is taller than 59 inches.
12. (6 points) Consider the probability distribution below. Find mean, variance, and standard deviation.
k Pr(X=k)
-1
0.1
0
0.3
1
0.3
2
0.3
13. (6 points) A true-false exam consists of 75 questions. What is the probability that someone guessing will
get no more than 30 correct answers?
14. (6 points) A savings account has a balance of \$2,300. Assuming an interest rate of 6% compounded
quarterly, how much will the account be worth in 6 years?
15. (6 points) Calculate the future value of an annuity of \$300 per month for 10 years at 6% interest
compounded monthly. Round to the nearest cent.
16. (6 points) A loan of \$100,000 is to be repaid with monthly payments for six years at 6% interest
compounded monthly. Calculate the monthly payment. Round to the nearest cent.
Page 3 of 3

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algebra

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system of equations

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