Math 1130 Exam 3 Review MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find a general term, (a k), that fits the displayed terms of the given sequence. 1) 1) 1 , 5 , 9 , 13 , 17 5 A) (4k + 3) k=1 5 B) (4k - 3) k=1 4 C) (4k + 3) k=0 4 D) (4k - 3) k=0 Write the first five terms of the arithmetic sequence with the given first term a and common difference d. 2) a = 21; d = -5 A) 0, 21, 16, 11, 6 B) -21, -16, -11, -6, -1 D) 25, 19, 13, 7, 1 C) 21, 16, 11, 6, 1 Write the first five terms of the geometric sequence with the given first term a and common ratio r. 1 3) a = 6; r = 3 2 2 2 2 A) 2, , , , 3 9 27 81 B) 6, C) 6, 18, 54, 162, 486 2 2 2 D) 6, 2, , , 3 9 27 2) 3) 19 20 22 , , 7, 3 3 3 Determine the first five terms of the geometric sequence. 4) a 1 = 6, r = -5 4) A) -5, -30, 150, -750, 3750 C) 6, -30, 150, -750, 3750 B) 6, 1, -4, -9, -14 D) 6, 30, 150, -750, 3750 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. 5) Suppose a person deposits $1000 in a savings account at the end of every six months. What is the value of the account at the end of five years if interest is at a rate of 10% compounded semiannually? 5) 6) A person establishes the following retirement plan: an immediate deposit of $10,000 and quarterly payments of $1,500 at the end of each quarter into a savings account that earns 5% compounded quarterly, what is the amount of the investment after 21 years? 6) 7) Suppose an annuity due consists of 6 yearly payments of $200 and the interest rate is 5% compounded annually. Determine (a) the present value and (b) the future value at the end of 6 years. 7) 8) Suppose a corporation pays $50,000 for a machine that has a useful life of eight years and a salvage value of $5000. A sinking fund is established to replace the machine at the end of 8 years. The replacement machine will cost $70,000. If equal payments are made into the fund at the end of every 6 months and the fund earns interest at the rate of 10% compounded semiannually, what should each payment be? 8) 9) Suppose Lena deposits $500 at the beginning of every month into a bank account that pays 5.4% compounded monthly. After five years, how much will she have? 9) 1 10) A 20-year loan for $100,000 is to be amortized by equal semiannual payments. If interest is at the nominal rate of 10% compounded semiannually, find (a) the semiannual payment; (b) the interest in the first payment; (c) the principal repaid in the first payment. 10) 11) A person purchased a television set for $850 and agreed to pay it off by monthly payments of $50. If the store charges an interest rate of 9% compounded monthly, how many months will it take to pay off the debt? 11) 12) Mary amortizes a loan of $80,000 for a new home by obtaining a 15 -year mortgage at the rate of 9.9% compounded monthly. Find (a) the monthly payment, (b) the total interest charges, and (c) the principal remaining after 8 years. 12) 13) 13) 2x - y + 3z = 12 Solve the following system algebraically: x + y - z = -3 x + 2y - 3z = -10 14) A manufacturer produces two products, A and B. For each unit of A sold the profit is $8. For each unit of B sold the profit is $11. From past experience it has been found that 25 percent more of A can be sold than of B. Next year the manufacturer desires a total profit of $42,000. How many units of each product must be sold? 14) 15) A nut shop packages mixtures of different nuts for sale. From peanuts, cashews and almonds, the owner wants to prepare a mixture which will sell for $4.45 for a 1 pound bag. The cost per pound of these nuts is $1.50, $6.00, and $4.00, respectively. The amount of peanuts is to be three times the amount of almonds. How much of each type of nut will be in the final blend? 15) 16) A manufacturer sells his product at $12.50 per unit, selling all he produces. His fixed cost is $5,000 and his variable cost per unit is $8.50. (a) At what level of production will he break even? (b) At what level of production will he have a profit of $10,000? 16) 17) Find the equilibrium point if the demand equation for a product is p = supply equation is p = q - 3 and the 20 17) 80 . q 18) Find the Break Even Point for a product whose Total Revenue, y TR, (in $) and Total Cost, 18) y TC , (in $) are as follows: y TR = (10q - 25)q y TC = 2000 + 75q 19) 19) 1 6 0 4 If A = 2 3 1 0 , determine (a) a32, and (b) the order of A. 4 7 2 8 20) Solve the matrix equation: x 5 y - 1 = 2y 2x 5 4 2x 20) 2 21) 21) 1 3 3 Find the transpose of the matrix: 4 5 6 7 8 9 22) 22) 3 -1 4 -1 Perform the indicated operations and simplify your answer: 4 2 + 2 0 5 6 -8 -4 3 23) If A = 1 2 3 ; B = 2 -1 -2 , then find (A + B)T. 3 4 5 1 -3 -2 23) 24) 24) 1 3 0 4 Solve the matrix equation: x 2 + 2 5 + y 3 = 3 3 1 0 x - y - 3 5 2 -8 3 25) If A = 2 1 and B = -2 9 , find 2A - 3B. 4 -3 1 -7 25) 5 2 7 -1 -8 3 26) If A = 2 1 , B = -2 9 , and C = 5 -2 , find 7A + 6B - 3C. 4 -3 1 -7 3 -3 26) 27) Perform the indicated operations and simplify your answer: 2 3 - 1 2 1 1 -3 0 0 27) 28) Let A = 1 1 ; B = 3 -5 ; C = -2 2 . Find A B + 2C 4 -1 2 -1 -9 2 28) 29) The prices (in dollars per case) for 3 types of pens are represented by the price vector: P = 99 79 109 . An office supply store orders cases of these pens in the quantities given by 5 the column vector: Q = 3 . Find the total cost (in dollars) of the purchase. 6 3 29) Answer Key Testname: MATH 1130 EXAM 3 REVIEW 1) B 2) C 3) D 4) C 5) $12,577.89 6) The amount of the investment is $294,084.69 after 21 yrs. 7) (a) $1065.90 (b) $1428.40 8) $2747.54 9) $34,506.95 10) (a) $5827.82 (b) $5000.00 (c) $827.82 11) 18.25 months, approximately 12) (a) $854.80 (b) $73,864 (c) $51,650.92 13) x = 1, y = -1, z = 3 14) 2500 units of A, 2000 units of B 15) 0.3 lb of peanuts; 0.6 lb of cashews; 0.1 lb of almonds 16) (a) 1,250 units (b) 3,750 17) p = 1; q = 80 18) Break Even Point is: (20 units, $3,500) 19) (a) 7 (b) 3 × 4 20) x = 10, y = 5 1 4 7 21) 3 5 8 3 6 9 11 -3 22) 4 12 -2 -2 3 4 23) 1 1 1 3 24) x = -2, y = -1 -31 0 25) 10 -25 -10 -5 -47 36 26) -13 67 22 -58 5 27) 5 28) -2 -1 -1 -2 5 29) PQ = 99 79 109 3 = 1386 6 4