Solve the matrix equation for X. 1) A = 6 0, B = , AX = B A) D) -2 2 B) -12 0

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1 MATH 1324 FINAL EXAM. ANSWER ALL QUESTIONS. TIME 1.5HRS. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the matrix equation for X. 1) A = , B = , AX = B A) B) D) ) Find the compound interest earned by the deposit. Round to the nearest cent. 2) $8000 at 11% compounded annually for 20 years A) $16, B) $50, $17, D) $56, ) 3) $13,000 at 5% compounded semiannually for 6 years A) $ B) $ $ D) $ ) 4) $28,490 at 12% compounded continuously for 5 years A) $51, B) $18, $19, D) $51, ) Solve the problem using Bayesʹ Theorem. Round the answer to the nearest hundredth, if necessary. 5) For two events M and N, P(M) =.3, P(N M) =.5, and P(N Mʹ) =.2. Find P(M N). A) 0 B) D) 1.0 5) Convert the constraints into linear equations by using slack variables. 6) Maximize z = 1.1x x2 Subject to: 1.9x x x x2 32 x1 0, x2 0 A) 1.9x x2 = x x x2 = x x x2 + x x x2 + x4 32 B) 1.9x x2 + x3 = x x2 + x4 = 32 D) 1.9x x2 + x3 = x x2 + x3 = 32 6) Find the pivot in the tableau. 7) 7) A) 3 in row 2, column 3 B) 1 in row 2, column 5 4 in row 3, column 1 D) 2 in row 1, column 2 Find the expected value for the random variable. 8) z P(z) A) B) D) ) 1

2 Determine whether the two matrices are inverses of each other by computing their product. 9) , ) A) No B) Yes Solve the problem. 10) Anne purchased a bond for a museum valued at $25,000 for $13,450. If the bond pays 7% annual interest compounded monthly, how long must she hold it until it reaches its full face value? A) 8.89 years B) years 7.89 years D) 6.89 years 10) 11) A basketball fieldhouse seats 15,000. Courtside seats sell for $10, endzone for $6, and balcony for $4. Total revenue for a sell-out is $82,000. If half the courtside and balcony and all endzone seats are sold, the total revenue is $47,000. How many of each type are there? A) 3000 courtside 2000 endzone 10,000 balcony B) 3200 courtside 1800 endzone 10,000 balcony 4000 courtside 3000 endzone 8000 balcony 12) You have money in an account at 8% interest, compounded monthly. To the nearest year, how long will it take for your money to triple? A) 19 years B) 8 years 11 years D) 14 years 11) 12) 13) A male decreases his life expectancy by 1 year on average, for every point that his blood pressure is above 120. The average life expectancy is 76 years. Find the life expectancy for a male whose blood pressure is 125. A) 72 B) D) 76 13) 14) Tuition of $1900 is due when the spring term begins, in 6 months. What amount should a student deposit today, at 11%, to have enough to pay tuition? A) $ B) $99.05 $ D) $ ) Find the indicated term of the geometric sequence. 15) a = 2, r = 4; Find the 6th term. A) 2048 B) 32, D) ) Assume that, at a certain college, 33% of all physics majors belong to ethnic minorities. Given a random sample of 10 physics majors, find the probability of the indicated event. Round your answer as appropriate. 16) Only the first 2 belong to an ethnic minority. 16) A).1111 B) D)

3 The lists below show five agricultural crops in Alabama, Arkansas, and Louisiana. Alabama Arkansas Louisiana soybeans (s) soybeans (s) soybeans (s) peanuts (p) rice (r) sugarcane (n) corn (c) cotton (t) rice (r) hay (h) hay (h) corn (c) wheat (w) wheat (w) cotton (t) Let U be the smallest possible universal set that includes all of the crops listed; and let A, K, and L be the sets of five crops in Alabama, Arkansas, and Louisiana, respectively. Find the indicated set. 17) A K L 17) A) {s} B) {n, p, s} {n, p} D) {c, h, n, p, r, s, t, w} Use the given table to find the indicated probability. 18) People were given three choices of soft drinks and asked to choose one favorite. The following table shows the results. 18) cola root beer lemon-lime under 21 years of age between 21 and over 40 years of age P(person is over 40 person drinks cola)? A) B) 4 51 D) None of the above Find the requested probability. 19) A family has five children. The probability of having a girl is 1. What is the probability of having 2 19) no more than 3 boys? A).9688 B) D).5000 Use the simplex method to solve the linear programming problem. 20) Maximize z = 4x1 + 2x2 subject to: x1 + 5x2 14 2x1 + 3x2 12 with x1 0, x2 0 A) Maximum is 56 when x1 = 14, x2 = 0 B) Maximum is 24 when x1 = 6, x2 = 0 Maximum is 12 when x1 = 6, x2 = 0 D) Maximum is 14.6 when x1 = 2.5, x2 = ) Suppose P( =.048, P(M =.044, and P(M =.524. Find the indicated probability. 21) P(M) A).520 B) D) ) 3

4 Find the probability of the event. 22) A battery company has found that the defective rate of its batteries is.03. Each day, 22 batteries are randomly tested. On Tuesday, 1 is found to be defective. A).110 B) D) ) Find the sum of the first five terms of the geometric sequence. 23) a = -16, r = -4 A) -10,280 B) D) ) Perform the indicated operation. 24) Let A = Find 4A. 02 A) B) D) ) Find the future value of the annuity due. 25) Payments of $500 made at the beginning of each year for 15 years at 9% compounded annually A) $16, B) $19, $14, D) $12, ) Find the monthly house payment necessary to amortize the following loan. 26) In order to purchase a home, a family borrows $65,000 at 13% for 15 yr. What is their monthly payment? A) $ B) $46.94 $ D) $ ) Find the actual interest rate paid, to the nearest tenth, on the simple discount note. 27) $17,000; discount rate 8%; length of loan 9 mo A) 9.5% B) 8.5% 10.5% D) 7.5% 27) Find the value(s) of the function, subject to the system of inequalities. 28) Find the maximum and minimum of Z = 13x - 13y subject to: 0 x 5, 0 y 8, 4x + 5y 30, and 4x + 3y 20. A) 65, -78 B) -78, , -78 D) 65, 0 28) Find the odds in favor of the indicated event. 29) Rolling an odd number with a fair die. A) 3 to 2 B) 1 to 2 2 to 1 D) 1 to 1 29) Find the value. a 30) A) B) D) ) Use duality to solve the problem. 31) Minimize w = 4y1 + 4y2 subject to: 5y1 + 10y y1 + 20y2 150 y1 0, y2 0 A) 60 B) D) 20 31) 4

5 Given the matrices A and B, find the matrix product AB. 32) A = -1 3, B = Find AB A) B) AB is not defined. 32) D) Find the amount that should be invested now to accumulate the following amount, if the money is compounded as indicated. 33) $5900 at 7% compounded annually for 5 yr 33) A) $ B) $ $ D) $

6 Answer Key Testname: M1324FINAL 1) B 2) D 3) B 4) D 5) C 6) B 7) A 8) A 9) A 10) A 11) A 12) D 13) B 14) C 15) A 16) D 17) A 18) B 19) C 20) B 21) A 22) D 23) D 24) B 25) A 26) C 27) B 28) A 29) D 30) A 31) B 32) A 33) B 6