Description

Formulas:

F = (1 + i)

n P

reff = (1 + i)

m − 1

Bnew = (1 + i) Bprevious + R

F = (1+i)

n−1

i

R

P = 1−(1+i)

−n

i

R

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Pace University

Spring 2020

MAT104 CRN 22008

Final Exam

Y. Shvartsberg

May 13, 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 22008

Final Exam

Y. Shvartsberg

May 13, 2020

Exam:

1. (6 points) Solve the system of equations by using the inverse of the coefficient matrix.

𝑥 − 3𝑦 = 5

{ 3𝑦 + 𝑧 = 0

2𝑥 − 𝑦 + 2𝑧 = 2

2. (6 points) Suppose that 𝑈 = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} and if 𝐴 = {0, 1, 5, 7}, 𝐵 = {2, 3, 5, 8},

𝐶 = {5, 6, 9}. List the elements of the indicated set.

a. 𝐶′

b. 𝐴′ ∪ 𝐵′

c. 𝐴′ ∩ 𝐵′

3. (8 points) A survey of 155 residents of Lake Placid were asked what kind of activities they participated

in on a daily basis during the summer months. The following information was determined.

107 swam

90 fished

76 walked

57 swam and fished

54 swam and walked

52 fished and walked

35 swam, fished, and walked

Determine the number of residents who participated in

a. exactly two of these activities

b. none of the activities

c. at least one of these activities

4. (6 points) On a math test there are 10 multiple-choice questions with 4 possible answers and 15 truefalse questions. In how many possible ways can the 25 questions be answered?

5. (8 points) There are 5 rotten plums in a crate of 25 plums. How many samples of 4 of the 25 plums

contain

a. Only good plums?

b. Three good plums and 1 rotten plum?

c. One or more rotten plums?

6. (6 points) How many different ways are there to arrange the 6 letters in the word SUNDAY if the letter

S must come first and the letter Y must be last?

7. (6 points) Suppose a red die and a green die are thrown. Let event E be “throw a 5 with the red die”, and

let event F be “throw a 6 with a green die”. Show that E and F are independent events.

Page 2 of 3

Pace University

Spring 2020

MAT104 CRN 22008

Final Exam

Y. Shvartsberg

May 13, 2020

8. (6 points) At a local college 45% of the students are female and 55% are male. Also 40% of the female

students are education majors, and 15% of the males are education majors. What is the probability a

student is female given the person is an education major?

9. (6 points) A true or false test has 10 questions. What is the probability of getting at least one question

correct by guessing?

10. (6 points) Find the five-number summary for the sample data: 13, 33, 36, 29, 25, 38, 52, 46, 49, 56.

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 shorter that 59 inches

or taller that 69 inches.

12. (6 points) Consider the probability distribution below. Find mean, variance, and standard deviation.

k

Pr(X=k)

1

-10

0

5

10

12

1

3

5

12

1

6

13. (6 points) Let X be the number of red balls drawn in 20 draws (with replacement) from an urn with six

red and four white balls. Approximate the probability that one draws at least 12 reds.

14. (6 points) A newborn child receives a $3000 gift toward a college education. How much will the $3000

be worth in 17 years if it is invested at 9% compounded quarterly?

15. (6 points) Calculate the rent of a decreasing annuity at 6% compounded monthly if payments are made

every month for 10 years and the present value is $350,000. Round to the nearest cent.

16. (6 points) Mr. and Mrs. Adams have purchased a $300,000 house and have made a down payment of

$60,000. They amortize the balance at 4% for 30 years. Calculate the monthly payments.

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