## Transcribed Text

Formulas:
F = (1 + i)n P
reff = (1 + i)m β 1
Bnew = (1 + i) Bprevious + R F = (1+i)nβ1 R
i
P = 1β(1+i)βn R
i
Homework:
1. Solve the system of equations by using the inverse of the coefficient matrix.
π₯ + π¦ + 2π§ = 1
{ 2π₯ + π¦ = 2
π₯ + 2π¦ + 2 π§ = 3
2. Suppose that A = {a, c, e, g, i}, B = {a, d, f}, and U = {a, b, c, d, e, f, g, h, i}. List the elements of the indicated set.
a. π΄β²
b. π΄ β© π΅β²
c. π΄β² βͺ π΅
3. In how many ways can 16 children be placed on 3 teams of 3, 5, and 4 members, with no member serving on more than one team?
4. The letters of the word βPROBLEMβ are arranged in a random order.
a. How many different arrangements are possible?
b. How many arrangements will start with βOEβ or βEOβ?
c. How many start with "M" and end with "P"?
5. An exam consists of six multiple-choice questions; each question has four choices. Assuming all the questions are answered, in how many ways can the test be completed?
6. Cars are being produced by two factories, but factory I produces twice as many cars as factory II in a given time. Factory I is known to produce 2% defectives and factory II produces 1% defectives. A car is examined and found to be not defective. What is the probability that it came from factory I?
7. Two cards are drawn (without replacement) from an ordinary deck of 52 cards. Find the probability that the second card is an ace of hearts if the first card is a red card (not an ace of hearts).
8. A box has 10 marbles in it, 6 red and 4 white. Suppose we draw a marble from the box, replace it, and then draw another. Find the probability that
a. Both marbles are white
b. Just one of the two marbles is white
9. Real estate ads suggest that 64% of homes for sale have garages, 21% have swimming pools, and 17% have both features. Are having a garage and a pool independent events? Explain.
10. Find the five-number summary for the sample data: 9, 21, 12, 24, 16, 28, 19, 31, 18, 29.
11. Scores on the aptitude test are normally distributed with a mean of 980 and a standard deviation of 110. What is the probability that a randomly selected student scores above 700?
12. Consider the probability distribution below. Find mean, variance and standard deviation.
k Pr(X=k)
-1 2
9
0 2
6
1 2
9
3 2
9
13. Suppose that 60% of the voters intend to vote for a conservative candidate. What is the probability a survey polling 8 people reveals that 2 or more intend to vote for a conservative candidate?
14. Find the amount that should be invested now to accumulate $ 110,000 at 4% compounded monthly in 10 years.
15. 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 $30,000. Round to the nearest cent.
16. In order to purchase a home, a family borrows $369,000 at 4.3% for 15 years. What is their monthly payment? Round the answer to the nearest cent.

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