Math 300 Semester Review Name. Let U = {1, 2, 4, 5, a, b, c, d, e}. Find the complement of the set. 1) N = {a}

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1 Math 300 Semester Review Name Let U = {1, 2, 4, 5, a, b, c, d, e}. Find the complement of the set. 1) N = {a} 1) Objective: (2.2) Find Complement of Set Find the indicated cardinal number. 2) Find n(g), given that n(d G) = 20 and D = {7, 8, 9, 10}. 2) Objective: (2.3) Find Cardinal Number: Cartesian Products For the given sets, construct a Venn diagram and place the elements in the proper region. 3) Let U = {1, 2, 3, 4, 5, 6, 7, 8} 3) A = {3, 6, 8} B = {4, 6} C = {1, 6, 7, 8} Objective: (2.3) Place Elements in Venn Diagram Write a description of the shaded region using the symbols A, B, C,,, -, and as needed. 4) 4) Objective: (2.3) Describe Shaded Area of Venn Diagram Draw an appropriate Venn diagram and use the given information to fill in the number of elements in each region. 5) n(a) = 30, n(b) = 28, n(c) = 35, n(a B) = 12, n(a C) = 15, n(b C) = 14, n(u) = 67 5) Objective: (2.4) Draw Venn Diagram, Label Size of Each Region Given a group of students: G = {Allen, Brenda, Chad, Dorothy, Eric} or G = {A, B, C, D, E}, list and count the different ways of choosing the following officers or representatives for student congress. Assume that no one can hold more than one office. 6) Four representatives 6) Objective: (10.1) List and Count Different Ways to Choose a Committee

2 7) A president, a secretary, and a treasurer, if the president must be a woman and the other 7) two must be men Objective: (10.1) List and Count Different Ways to Choose a Committee 8) A computer printer allows for optional settings with a panel of four on-off switches in a 8) row. How many different settings can be selected if no three adjacent switches can all be off? Objective: (10.1) Solve Apps: Counting 9) Four married couples have reserved eight seats in a row at the theater, starting at an aisle 9) seat. In how many ways can they arrange themselves if the four men occupy the four seats closest to the aisle? Objective: (10.2) Solve Apps: Use Counting Principle (Seating Arrangements) 10) Three noncollinear points determine a triangle. How many different triangles are 10) determined by 7 points in a plane, no three of which are collinear? Objective: (10.3) Solve Apps: Combinations 11) License plates are made using 3 letters followed by 3 digits. How many plates can be 11) made if repetition of letters and digits is allowed? Objective: (10.3) Solve Apps: Mixed Counting Problems If two fair dice, one red and one white, are rolled, in how many ways can the result be obtained? 12) The product of the numbers on the two dice is a perfect square. 12) Objective: (10.5) Solve Apps: Additive Counting Principle (Two Dice) 13) The chorus has six sopranos and eight baritones. In how many ways can the director 13) choose a quartet that contains at least one soprano? Objective: (10.5) Solve Apps: Complements Principle of Counting 14) It has been observed in one country, that 59 out of every 100 births is a baby with brown 14) eyes. In 640 births how many brown eyed babies would you expect? Objective: (11.1) Solve Apps: Empirical Probability 15) Mr. Larsen's third grade class has 22 students, 12 girls and 10 boys. Two students must be 15) selected at random to be in the spring play. What is the probability that one boy and one girl will be chosen? Order is not important. Objective: (11.1) ^Solve Apps: Probability

3 Find the indicated probability. 16) The age distribution of students at a community college is given below. 16) Age (years) Number of students (f) Under Over A student from the community college is selected at random. Find the probability that the student is at least 31. Round approximations to three decimal places. Objective: (11.2) Solve Apps: Find Probability of (A or B) Given Table Find the probability. 17) In one town, 70% of adults have health insurance. What is the probability that 8 adults 17) selected at random from the town all have health insurance? Objective: (11.3) Solve Apps: Use Special Multiplication Rule 18) Find the probability that when a 10 question multiple choice test has 4 possible answers 18) for each question, a student will select at least 6 correct answers from the 10 possible. Objective: (11.4) Solve Apps: Binomial: Find Prob of At Least/At Most x Successes 19) Computer Specialists is planning a group vacation to one of the following locations: Alaska (A), Florida (F), San Antonio (S), or Hawaii (H). The employees rank the four possible sites according to the following voter profile. Number of Votes Ranking 5 A > H > F > S 7 H > S > A > F 4 F > S > H > A 7 A > F > S > H 5 A > H > S > F 6 H > F > S > A 8 F > S > A > H (a) Determine the winner using the plurality method. (b) Determine the winner using the pairwise comparison method. (c) Determine the winner using the Borda method. (d) Determine the winner using the Hare method. Objective: (16.1) Determine Outcome by Plurality Method MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the future value of the deposit if the account pays simple interest. 20) $630 at 5% for 6 months 20) A) $ B) $ C) $ D) $ Objective: (13.1) Find Future Value: Simple Interest

4 Use the compound interest formula to compute the future value of the investment. 21) $3000 at 7.5% compounded monthly for 4 years 21) A) $20, B) $ C) $ D) $ Objective: (13.1) Find Future Value: Compound Interest Find the effective annual interest rate for the given nominal annual interest rate. Round your answers to the nearest 0.01%. 22) 4.1% compounded daily (assume 365 days per year) 22) A) 0.01% B) 0.04% C) % D) 4.18% Objective: (13.1) Find Effective Annual Yield 23) Jolene is buying some furniture for her new apartment. The total cost is $1400 and she places a 23) down payment of $140. There is add-on interest of 5%. What is the total amount she will be financing? A) $ B) $ C) $ D) None of the above is correct. Objective: (13.2) Solve Apps: Financing with Add-on Interest 24) On the January 25 billing date, Vivian had a balance due of $ on her credit card. The 24) transactions during the following month were: January 26 Charge : curtains $386 January 27 Payment $ February 16 Charge: tires $ The interest rate on the card is 1.3% per month. Using the average daily balance method, find the finance charge on February 25 (January has 31 days). A) $2.59 B) $9.08 C) $8.96 D) $9.02 Objective: (13.2) Solve Apps: Average Daily Balance Method Use the Rule of 78 to find the payoff amount for the loan paid in full before the date of maturity. 25) Finance charge: $ ) Total number of payments: 107 Amount per payment: $310 Remaining number of payments, when paid in full: 10 A) $ B) $ C) $ D) $ Objective: (13.3) Find Payoff Amount by Rule of 78

5 If necessary, use the table of monthly payments below. Round your answer to the nearest cent. Monthly Payments to Repay Principal and Interest on a $1000 Mortgage Term of Mortgage (Years) Annual Rate (r) % $ $ $ $ $ $ $ % % % % % % % % % % % % ) Find the monthly payment needed to amortize principal and interest for the following fixed-rate 26) mortgage. Mortgage amount: $75,000 Term of mortgage: 15 years Interest rate: 5.5% A) $ B) $ C) $ D) $ Objective: (13.4) Find Monthly Payment on Fixed-Rate Mortgage The following problem involves adjustable-rate mortgage. You will need a table of monthly payments. 27) Harry has a 1-year ARM for $85,000 over a 30-year term. The margin is 2%, and the index rate 27) starts out at 8.5% and increases to 10% at the first adjustment. The balance of principal at the end of the first year is $74, Find the amount of monthly payment for the first month of the first year. A) $ B) $ C) $ D) None of the above is correct. Objective: (13.4) Solve Apps: Adjustable-Rate Mortgages

6 28) The following information on Company X appears in a stock table. 28) YTD 52-WEEK YLD VOL NET %CHG HI LO STOCK (SYM) DIV % PE 100s CLOSE CHG Company X CMX Find the cost to purchase 160 shares of Company X at the day's closing price. Assume that the transaction is broker-assisted and includes typical discount broker's commissions as follows, using Firm B: Automated (Online) Automated (Phone) Broker- Assisted Brokerage Firm A $8.95 $13.95 $33.95 Brokerage Firm B $9.99 $34.99 $44.99 Brokerage Firm C $7.95 $12.95 $32.95 A) $ B) $ C) $ D) $ Objective: (13.5) Find Cost of Stock Purchase 29) For the given stock investment, find the percentage return: 29) Number Purchase Price Dividend of Shares Per Share Per Share Sale Price Per Share 500 $9.30 $1.88 $13.30 A) 63.2% B) 43.0% C) 163.2% D) 44.2% Objective: (13.5) Find Percentage Return of Stock Investment 30) Suppose you like to listen to your MP3 player while you jog. Your playlist contains ) songs, 8 of which are Journey songs. Your 3-mile jog allows time for listening to 6 songs. If your MP3 player is set to "shuffle" mode (so it plays randomly selected songs, with no repetitions until all 100 songs have been played), what is the probability that you will hear exactly 2 Journey songs on your run? Objective:

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

MATH 1324 Review for Test 4 November 2016 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Prepare a probability distribution for the experiment. Let x