MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Provide an appropriate response. 1) Find the line passing through the two points. Write the equation in standard form. (10, 9) and (10, 1) A) + = 11 B) + = 19 C) = 10 D) = 9 Solve the problem. 2) The cost of manufacturing a computer part is related to the quantit produced,, during a production run. When 100 parts are produced, the cost is $300. When 600 parts are produced, the cost is $4800. Find an equation of the line relating quanit produced to cost. Write the final answer in the form C = m + b. A) C = 600 + 9 B) C = 9 + 600 C) C = 9-600 D) C = 9 Provide an appropriate response. 3) Solve the quadratic inequalit. Epress our answer in interval notation. ( - 1)( + 5) < 0 A) (-, 1) B) (-1, 5) C) (-5, - ) D) (-5, 1) Find the degree of the polnomial. 4) h() = 14 4 + 0.18 2-6 - 9 A) 7 B) 8 C) 4 D) -9 1) 2) 3) 4) Graph the function. 5) f() = 2 - - 1 5) 5 4 3 2 1-5 -4-3 -2-1 -1 1 2 3 4 5-2 -3-4 -5 1
A) 5 4 3 2 1 B) 5 4 3 2 1-5 -4-3 -2-1 -1 1 2 3 4 5-2 -3-4 -5-5 -4-3 -2-1 -1 1 2 3 4 5-2 -3-4 -5 C) D) 5 4 3 2 1 5 4 3 2 1-5 -4-3 -2-1 -1 1 2 3 4 5-2 -3-4 -5-5 -4-3 -2-1 -1 1 2 3 4 5-2 -3-4 -5 Provide an appropriate response. 6) Solve for : 2 4 = 8 + 5 A) -5 B) 5 C) -15 D) 15 Solve the equation. 7) Solve for t: e -0.07t = 0.05 Round our answer to four decimal places. A) 44.321 B) 42.7962 C) -66.4815 D) -70.1312 6) 7) Solve the problem. 8) Since life epectenc has increased in the last centur, the number of Alzheimer's patients has increased dramaticall. The number of patients in the United States reached 4 million in 2000. Using data collected since 2000, it has been found that the data can be modeled b the eponential function = 4.19549 (1.02531), where is the ears since 2000. Estimate the Alzheimer's patients in 2025. Round to the nearest tenth. A) 7.8 million B) 3.9 million C) 4.8 million D) 8.0 million 9) Suppose that $2200 is invested at 3% interest, compounded semiannuall. Find the function for the amount of mone after t ears. A) A = 2200 (1.015) 2t B) A = 2200 (1.0125) 2t C) A = 2200 (1.015) t D) A = 2200 (1.03) 2t 8) 9) 2
Use the properties of logarithms to solve. 10) log b ( + 3) + log b = log b 54 A) -6 B) 3 C) -6, -3 D) 6 Solve the problem. 11) A countr has a population growth rate of 2.4% compounded continuousl. At this rate, how long will it take for the population of the countr to double? Round our answer to the nearest tenth. A) 2.9 ears B) 30 ears C).29 ears D) 28.9 ears Make the indicated conversion. Assume a 360-da ear as needed. 12) 0.05 to percent A) 50% B) 0.0005% C) 0.05% D) 5% Find the compound interest earned. Round to the nearest cent. 13) $14,000 at 5% compounded annuall for 3 ears A) $701.50 B) $2206.75 C) $2100.00 D) $1435.00 Solve the problem. Round to the nearest cent as needed. 14) An actuar for a pension fund need to have $14.6 million grow to $22 million in 6 ears. What interest rate compounded annuall does he need for this investment to growth as specified. Round our answer to the nearest hundredth of a percent. A) 7.07% B) 7% C) 0.07% D) 7.7% 10) 11) 12) 13) 14) Find the effective rate APY corresponding to the given nominal rate. Round results to the nearest 0.01 percentage points. 15) 18% compounded continuousl. A) 20% B) 19.7% C) 18.01% D) 19.72% 15) Evaluate the s-angle-n at i. Round to three decimal places. 16) s 13 0.04 A) 15.026 B) 41.627 C) 18.292 D) 16.627 16) SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Use an amortization table to solve the problem. Round to the nearest cent. 17) You have purchased a new house and have a mortgage for $90,000 at 6% compounded monthl. The loan is amortized over 20 ears in equal monthl paments of $644.79. Find the total amount paid in interest when the mortgage is paid off. 17) 3
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Perform the operation, if possible. 18) Let A = -1 5 1 and B = A) -13-41 -22 B) -6-2 9-5 -7-3. Find AB. 6-8 2 6-10 9 5-35 -3-6 -40 2 C) 13 41 22 D) -13-41 -22 18) Find the identit matri. 19) 1 2 3 4 5 6 7 8 9 A) 0 0 1 0 1 0 1 0 0 B) 1 C) 1 0 0 0 1 0 0 0 1 D) 1 1 1 1 1 1 1 1 1 19) Answer the question. 20) Which of the following matrices has an inverse? A) -2 3 4 1 B) 3-2 1 4 0 7 C) 0 4 0-2 D) 0-1 3 5-1 3 20) Graph the solution set of the sstem of linear inequalities. 21) -4 > 2 3 + < 6 21) 25-25 25-25 4
A) B) 25 25-25 25-25 25-25 -25 C) D) 25 25-25 25-25 25-25 -25 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Solve the problem. 22) Formulate the following problem as a linear programming problem (DO NOT SOLVE):A small accounting firm prepares ta returns for two tpes of customers: individuals and small businesses. Data is collected during an interview. A computer sstem is used to produce the ta return. It takes 2.5 hours to enter data into the computer for an individual ta return and 3 hours to enter data for a small business ta return. There is a maimum of 40 hours per week for data entr. It takes 20 minutes for the computer to process an individual ta return and 30 minutes to process a small business ta return. The computer is available for a maimum of 900 minutes per week. The accounting firm makes a profit of $125 on each individual ta return processed and a profit of $210 on each small business ta return processed. How man of each tpe of ta return should the firm schedule each week in order to maimize its profit? (Let 1 equal the number of individual ta returns and 2 the number of small business ta returns.) 22) 5
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Use graphical methods to solve the linear programming problem. 23) Suppose an horse feed to be mied from sobean meal and oats must contain at least 100 lb of protein, 20 lb of fat, and 9 lb of mineral ash. Each 100-lb sack of sobean meal costs $20 and contains 50 lb of protein, 10 lb of fat, and 8 lb of mineral ash. Each 100-lb sack of oats costs $10 and contains 20 lb of protein, 5 lb of fat, and 1 lb of mineral ash. How man sacks of each should be used to satisf the minimum requirements at minimum cost? 23) A) 0 sacks of sobeans and 2 sacks of oats B) 2 sacks of sobeans and 0 sacks of oats C) 7 3 sacks of sobeans and 5 6 sacks of oats D) 1 3 11 sacks of sobeans and 1 9 sacks of oats 11 Use slack variables to convert the constraints into linear equations. 24) Maimize z = 31 + 52 subject to: 61 + 72 30 1 + 62 40 with: 1 0, 2 0 24) A) 61 + 72 = s1 + 30 1 + 62 = s2 + 40 C) 61 + 72 + s1 = 30 1 + 62 + s1 = 40 B) 61 + 72 + s1 30 1 + 62 + s2 40 D) 61 + 72 + s1 = 30 1 + 62 + s2 = 40 Provide an appropriate response. 25) Convert the inequalit to a linear equation b adding a slack variable. 91 + 2 + 43 240 25) A) 91 + 2 + 43 + s1 + 240 = 0 B) 91 + 2 + 43 + s1 = 240 C) 91 + 2 + 43 + s1 240 D) 91 + 2 + 43 + s1 240 6
26) The following chart depicts basic solutions to a sstem of linear inequalities. Which of the solutions is NOT feasible? 26) 1 2 s1 s2 (A) 0 0 11 6 (B) 0 11 3 0-4 3 (C) 0 3 2 0 (D) 11 1 0 0 2 2 (E) 6 0-1 0 (F) 4 1 0 0 A) (B) and (E) B) (A), (D), (E), (F) C) (A), (B), (C) D) (B) 27) Write the basic solution for the following simple tableau: 27) 1 2 3 s1 s2 s3 P 0 10 7 0 1 1 0 12 1-7 6 0 0 1 0 28 0 0 10 1 0 0 0 30 0-5 -8 0 0 4 1 50 A) 1 = 28, 2 = 10, 3 = 0, s1 = 30, s2 = 12, s3 = 0, P = 50 B) 1 = 28, 2 = 0, 3 = 0, s1 = 30, s2 = 12, s3 = 0, P = - 50 C) 1 = 28, 2 = 10, 3 = 7, s1 = 30, s2 = 12, s3 = 0, P = 50 D) 1 = 28, 2 = 0, 3 = 0, s1 = 30, s2 = 12, s3 = 0, P = 50 Pivot once about the circled element in the simple tableau, and read the solution from the result. 28) 28) A) 3 = 10, 2 = 10, z = 7; 1, s1, s2 = 0 B) 3 = 5, 2 = -7, z = 10; 1, s1, s2 = 0 C) 3 = 5, 2 = -7, z = -10; 1, s1, s2 = 0 D) 3 = 10, 2 = 7, z = 10; 1, s1, s2 = 0 Find the transpose of the matri. 29) 2 7 6 3 1 7 8 6 A) 1 2 7 7 8 6 6 3 B) 1 7 8 6 2 7 6 3 C) 2 1 7 7 6 8 3 6 D) 3 7 7 1 3 6 6 8 29) 7
Provide an appropriate response. 30) Write the modified problem for the following linear programming problem (DO NOT SOLVE): 30) Maimize subject to P = 91-42 + 3 41-2 + 23 3-1 - 72 + 93-4 1-2 + 23 = 8 1, 2, 3 0 A) Maimize P = 91-42 + 3 + Ma1+ Ma2 subject to 41-2 + 23 + s1 = -3 1 + 72-93 - s2 + a1 = -4 1-2 + 23 + a2 = - 8 1, 2, 3, s1, s2, a1, a2 0 B) Maimize P = 91-42 + 3 - Ma1 - Ma2 subject to 41-2 + 23 + s1 = 3 1 + 72-93 - s2 + a1 = 4 1-2 + 23 + a2 = 8 1, 2, 3, s1, s2, a1, a2 0 C) Maimize P = 91-42 + 3 + Ma1 + Ma2 subject to 41-2 + 23 + s1 = 3 1 + 72-93 - s2 + a1 = 4 1-2 + 23 + a2 = 8 1, 2, 3, s1, s2, a1, a2 0 D) Maimize P = 91-42 + 3 - Ma1 - Ma2 subject to 41-2 + 23 + s1 = -3 1 + 72-93 - s2 + a1 = -4 1-2 + 23 + a2 = - 8 1, 2, 3, s1, s2, a1, a2 0 31) Use the big M method to find the optimal solution to the problem. Maimize P = 61 + 22 subject to 1 + 22 20 21 + 2 16 1 + 2 9 1, 2 0 A) ma P = 46 at 1, 2 = 2 B) ma P = 46 at 1 = 7, 2 = 2 C) ma P = 46 at 1 = 2, 2 = 7 D) ma P = - 46 at 1 = 2, 2 = 7 31) 8
Use a truth table to decide if the two statements are equivalent. 32) ~(~q); q A) True B) False 32) Use the Venn diagram below to find the number of elements in the region. 33) n(a B C) A) 16 B) 18 C) 44 D) 8 Solve the problem. 34) In a Power Ball lotter, 5 numbers between 1 and 12 inclusive are drawn. These are the winning numbers. How man different selections are possible? Assume that the order in which the numbers are drawn is not important. A) 120 B) 792 C) 95,040 D) 248,832 List the outcomes of the sample space. 35) A bo contains 10 blue cards numbered 1 through 10. List the sample space of picking one card from the bo. A) {8} B) {100} C) {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} D) {10} 33) 34) 35) Find the probabilit. 36) A packet of sour worms contains four strawberr, four lime, two black currant, two orange sour, and three green apples worms. What is the probabilit that Dustin will choose a green apple sour worm, P(green apple)? 36) A) P(green apple) = 1 5 B) P(green apple) = 0 C) P(green apple) = 3 5 D) P(green apple) = 1 15 Find the indicated probabilit. 37) Find the probabilit of correctl answering the first 3 questions on a multiple choice test if random guesses are made and each question has 4 possible answers. 37) A) 3 4 B) 1 81 C) 1 64 D) 4 3 Find the probabilit. 38) A single fair die is rolled. The number on the die is a 3 or a 5. 38) A) 1 3 B) 2 C) 1 6 D) 1 36 9
39) Samantha is taking courses in math and English. The probabilit of passing math is estimated at 0.4 and English at 0.6. She also estimates that the probabilit of passing at least one of them is 0.8. What is her probabilit of passing both courses? A) 0 B) 0.8 C) 0.12 D) 0.2 Use a tree diagram to find the indicated probabilit. 40) 3.9% of a secluded island tribe are infected with a certain disease. There is a test for the disease, however the test is not completel accurate. 92% of those who have the disease will test positive. However 4.4% of those who do not have the disease will also test positive (false positives). What is the probabilit that an given person will test positive? Round our answer to three decimal places if necessar. A) 0.036 B) 0.482 C) 0.078 D) 0.042 Use Baes' rule to find the indicated probabilit. 41) Two shipments of components were received b a factor and stored in two separate bins. Shipment I has 2% of its contents defective, while shipment II has 5% of its contents defective. If it is equall likel an emploee will go to either bin and select a component randoml, what is the probabilit that a defective component came from shipment II? A) 0.286 B) 0.714 C) 0.5 D) 0.2 39) 40) 41) Prepare a probabilit distribution for the eperiment. Let represent the random variable, and let P represent the probabilit. 42) Two marbles are drawn from a bag in which there are 4 red marble and 2 blue marble. The 42) number of blue marbles is counted. A) P 0 0.719 1 0.280 2 0.001 B) P 0 0.333 1 0.333 2 0.333 C) P 0 0.07 1 0.53 2 0.4 D) P 0 0.4 1 0.53 2 0.07 Find the epected value. 43) Suppose that 1,000 tickets are sold for a raffle that has the following prizes: one $300 prize, two $100 prizes, and one hundred $1 prizes. What is epected value of a ticket? A) $1 B) $100 C) $0.60 D) $300 44) A fair coin is tossed three times, and a plaer wins $3 if 3 tails occur, wins $2 if 2 tails occur and loses $3 if no tails occur. If one tail occurs, no one wins. What is the epected value of the games? A) $3.00 B) $2.00 C) $0.75 D) -$3.00 43) 44) Provide an appropriate response. 45) The number of loaves of whole wheat bread left on the shelf of a local quik stop at closing (denoted b the random variable X) varies from da to da. Past records show that the probabilit distribution of X is as shown in the following table. Find the probabilit that there will be at least three loaves left over at the end of an given da. 45) i 0 1 2 3 4 5 6 pi 0.20 0.25 0.20 0.15 0.10 0.08 0.02 A) 0.20 B) 0.65 C) 0.15 D) 0.35 10
Answer Ke Testname: REVIEW_1324_FINAL_REVIEW 1) C 2) C 3) D 4) C 5) A 6) D 7) B 8) A 9) A 10) D 11) D 12) D 13) B 14) A 15) D 16) D 17) $64,749.60 18) A 19) C 20) A 21) C 22) Maimize P = 1251 + 2102 subject to 2.51 + 32 40 23) B 24) D 25) B 26) A 27) D 28) C 29) C 30) B 31) B 32) A 33) D 34) B 35) C 36) A 37) C 38) A 39) D 201 + 302 900 1, 2 0 11
Answer Ke Testname: REVIEW_1324_FINAL_REVIEW 40) C 41) B 42) D 43) C 44) C 45) D 12