PRINTABLE VERSION Practice Final Exam Question 1 Give the slope of the line passing through the points ( 2 , -5 ) and ( 2 , -3 ). a) b) c) d) e) f) None of the above. Question 2 Give the equation of the line that passes through the points ( -1 , 3 ) and ( 4 , -3 ). a) b) c) d) e) f) None of the above. Question 3 Suppose you buy a piece of office equipment for $13,000. After 6 years you sell it for a scrap value of $3,000. The equipment is depreciated linearly over 6 years. The value of the piece of equipment after 1 years is (rounded to the nearest whole dollar) a) $3,000 b) $11,571 c) $11,333 d) $12,444 e) $12,231 f) None of the above. Question 4 A manufacturer has a monthly fixed cost of $100,000 and a production cost of $17 for each unit produced. The product sells for $29 per unit. Find the break-even point. a) b) c) d) e) f) None of the above. Question 5 A company has fixed monthly costs of $130,000 and production costs on its product of $18 per unit. The company sells its product for $59 per unit. The cost function, revenue function and profit function for this situation are a) b) c) d) e) f) None of the above. Question 6 A manufacturer has a monthly fixed cost of $30,000.00 and a production cost of $9 for each unit produced. The product sells for $23 per unit. If the manufacturer produces and sells 11,000 units one month, then his profit is a) $124,000 b) $2,530,000 c) $990,000 d) $69,000 e) $223,000 f) None of the above. Question 7 Which of the following matrices are in row-reduced form? (Note: The dotted vertical line in each matrix should be a single vertical line.) I. II. III. a) None of them b) I and II only c) I and III only d) II and III only e) All of them f) None of the above. Question 8 Given that the augmented matrix in row-reduced form below is equivalent to the augmented matrix of a system of linear equations. Determine whether the system has a solution and find the solution(s) to the system, if they exist. (Note: The dotted vertical line in the matrix above should be a single vertical line.) a) x = 2, y = 5 b) x = 2, y = 5, z = -7 c) x = -2, y = -5 d) No solution e) x = -2, y = -5, z = 7 f) None of the above. Question 9 Use the Gauss-Jordan elimination process on the following system of linear equations to find the value of z. a) b) c) d) e) f) None of the above. Question 10 Use Gauss-Jordan elimination process to solve the following system of linear equations. a) x = 1, y = 6, z = -10 b) No Solution. c) x = 2, y = 3, z = -11 d) x = 4, y = 5, z = -12 e) Infinitely many solutions. f) None of the above. Question 11 Perform the indicated operation, if possible. -7 a) b) c) d) e) f) None of the above. Question 12 +2 Solve for x. + = a) b) c) d) e) f) None of the above. Question 13 Let E = a) b) and F = . Compute the product EF, if possible. c) d) e) f) None of the above. Question 14 Find the inverse of the given matrix, if it exists. a) b) c) d) e) f) None of the above. Question 15 A company produces two types of the jackets; windbreakers and rainbreakers. The company has at most 67 hours of finishing time per week and 64 hours of packaging time per week. Each windbreaker jacket takes 45 minutes of finishing time and 22 minutes of packaging time per week, whereas each rainbreaker jacket takes 68 minutes of finshing time and 35 minutes of packaging time per week. The company's profit for each windbreaker and rainbreaker jacket is 24 and 41, respectively. Let x denote the number of windbeaker jackets they should produce and y denote the number of rainbreaker jackets they should produce. The company wants to maximize profit. Set up the Linear Programming Problem for this situation. a) Max P = 24x + 41y s.t. 68x + 45y< 67 , 35x + 22y< 64 , x> 0 , y> 0 b) Max P = 41x + 24y s.t. 68x + 45y< 4020 , 35x + 22y< 3840 , x> 0 , y> 0 c) Max P = 41x + 24y s.t. 45 x + 68y> 4020 , 22x + 35y> 3840 , x> 0 , y> 0 d) Max P = 24x + 41y s.t. 45 x + 68y< 4020 , 22 x + 35 y< 3840 , x> 0 , y> 0 e) Max P = 24x + 41y s.t. 45 x + 68y< 67 , 22x + 35y< 64 , x> 0 , y> 0 f) None of the above. Question 16 Given the linear programming problem Minimize C = x + 6y subject to x< 7 y< 10 x + y> 10 x> 0, y> 0 Use the method of corners to determine the where the minimum occurs, and give the minimum value. a) ( 0 , 0 ) with C = 0 b) ( 7 , 0 ) with C = 7 c) ( 7 , 3 ) with C = 25 d) ( 7 , 10 ) with C = 67 e) ( 0 , 10 ) with C = 60 f) None of the above. Question 17 Mr. Smith wishes to retire in 8 years. When he retires he would like to have $500,000 in his bank account. Mr. Smith's bank pays 5% per year compounded annually. How much should he deposit now to attain his goal? a) $338,421.68 b) $338,415.68 c) $338,419.68 d) $338,422.68 e) $338,417.68 f) None of the above. Question 18 John got a part time weekend job at a local restaurant to save for a new car. He plans on depositing $200 per month for the next 2 years in a savings account with a rate of 3% per year compounded monthly. How much will he have saved toward his down payment at the end of the 2 year period? a) $4,920.56 b) $4,980.56 c) $4,910.56 d) $4,950.56 e) $4,940.56 f) None of the above. Question 19 You want to have $6,000 by the time you finish college in 4 years. How much money should you deposit each quarter for the next 4 years into an account paying 5% per year compounded quarterly so that you can have $6,000 when you finish college? a) $344.08 b) $339.08 c) $341.08 d) $342.08 e) $340.08 f) None of the above. Question 20 Esther pays $532 per month for 6 years for a car. She made a down payment of $2,500. If the loan costs 7.1% per year compounded monthly, what was the cash price of the car? a) $28,616.45 b) $45,083.28 c) $33,616.45 d) $50,083.28 e) $31,116.45 f) None of the above. Question 21 Given the following Venn diagram, find n[ A ( B C )c ]. a) 87 b) 91 c) 94 d) 88 e) 90 f) None of the above. Question 22 (Car Sales) Of the cars sold during the month of July, 95 had air conditioning, 102 had automatic transmission, and 73 had power steering. 7 cars had all three of these extras. 25 cars had none of these extras. 21 cars had only air conditioning, 55 cars had only automatic transmissions, and 35 cars had only power steering. 9 cars had both automatic transmission and power steering. How many cars had exactly two of the given options? a) 104 b) 76 c) 2 d) 69 e) 86 f) None of the above. Question 23 Suppose 7 people arrive at a bank at the same time. In how many ways can they line up to wait for the next available teller? a) 5,040 b) 49 c) 720 d) 7 e) 120 f) None of the above. Question 24 As part of a quality-control program, 3 batteries from a box of 16 is chosen at random for testing. In how many ways can this test batch be chosen? a) 3 b) 6 c) 3,360 d) 48 e) 560 f) None of the above. Question 25 An urn contains 3 blue balls and 6 orange balls. In how many ways can we select 2 blue balls and 4 orange balls from the urn? a) 18 b) 30 c) 366 d) 45 e) 2,158 f) None of the above. Question 26 A business organization needs to make up a 5 member fund-raising committee. The organization has 9 accounting majors and 7 finance majors. In how many ways can the fund-raising committee be formed if at most 1 accounting major is on the committee? a) 9 b) 21 c) 336 d) 315 e) 30 f) None of the above. Question 27 Given that P(E) = 0.36, P(F) = 0.36, and P(E F) = 0.14. Find P(E F). a) b) c) d) e) f) None of the above. Question 28 A classroom of children has 18 boys and 20 girls in which five students are chosen to do presentations. What is the probability that at least four boys are chosen? a) 0.4308 b) 0.1390 c) 0.1219 d) 0.0171 e) 0.3089 f) None of the above. Question 29 An experiment consists of choosing a colored urn with equally likely probability and then drawing a ball from that urn. In the brown urn, there are 24 brown balls and 11 white balls. In the yellow urn, there are 18 yellow balls and 8 white balls. In the white urn, there are 18 white balls and 16 blue balls. What is the probability of choosing the yellow urn and a white ball? a) b) c) d) e) f) None of the above. Question 30 A recording company obtains the blank CDs used to produce its labels from three compact disk manufacturers: I, II, and III. The quality control department of the company has determined that 7% of the compact disks produced by manufacturer I are defective, 1% of those produced by manufacturer II are defective, and 5% of those produced by manufacturer III are defective. Manufacturers I, II, and III supply 27%, 34%, and 39%, respectively, of the compact disks used by the company. What is the probability that a randomly selected label produced by the company will contain a defective compact disk? a) b) c) d) e) f) None of the above. Question 31 An arcade booth at a county fair has a person pick a coin from two possible coins available and then toss it. If the coin chosen lands on heads, the person gets a prize. One coin is a fair coin and one coin is a biased coin (unfair) with only a 37% chance of getting a head. Assuming equally likely probability of picking either coin, what is the probability that the fair coin was the one chosen, given that you got a head? a) b) c) d) e) f) None of the above. Question 32 The probability distribution of a random variable X is given below. x 2 3 5 9 10 P(X=x) 9/35 1/7 4/35 2/7 1/5 Given the mean Find the variance (Var(X)) and the standard deviation, respectively. a) Variance = 3410.3058, Standard Deviation = 58.3978 b) Variance = 91.6747, Standard Deviation = 9.5747 c) Variance = 51.2205, Standard Deviation = 7.1568 d) Variance = 1691.0000, Standard Deviation = 41.1218 e) Variance = 11.2784, Standard Deviation = 3.3583 f) None of the above. Question 33 Consider the following binomial experiment. The probability that a green jelly bean is chosen at random from a large package of jelly beans is 1/8. Sally chooses 10 jelly beans, what is the probability that at most 2 will be green jelly beans? a) 0.1195 b) 0.8805 c) 0.5000 d) 0.8695 e) 0.3600 f) None of the above. Question 34 Consider the following binomial experiment. At a certain university, the probability that an entering freshman will graduate within four years is 81/100. From an incoming class of 1,860 freshmen, find the variance of the number of students who will graduate in four years. a) b) c) d) e) f) None of the above. Question 35 Let Z be a standard normal variable. Find P(Z > 2.23). a) b) c) d) e) f) None of the above. Question 36 Let Z be a standard normal variable. Find the value of z if z satisfies P(Z > z) = 0.0020. a) b) c) d) e) f) None of the above. Question 37 Suppose X is a normal random variable with = 35 and = 10. Find P(55.5 < X < 69.7). a) b) c) d) e) f) None of the above. Question 38 Suppose X is a normal random variable with = 40 and = 20. Find P(X > 20.2). a) b) c) d) e) f) None of the above. Question 39 Use the appropriate normal distribution to approximate the resulting binomial distributions. A fair coin is tossed 130 times. What is the probability of obtaining between 61 and 77 tails, inclusive? a) b) c) d) e) f) None of the above. Question 40 Use the normal distribution to approximate the following binomial distribution. You claim that 73% of the voters in your district will vote for you. If the district has 350 voters, what is the probability that at least 273 will actually vote for you? a) b) c) d) e) f) None of the above. PRINTABLE VERSION Practice Final Exam Question 1 Give the slope of the line passing through the points ( 2 , -5 ) and ( 2 , -3 ). a) b) c) d) e) f) None of the above. Question 2 Give the equation of the line that passes through the points ( -1 , 3 ) and ( 4 , -3 ). a) b) c) d) e) f) None of the above. Question 3 Suppose you buy a piece of office equipment for $13,000. After 6 years you sell it for a scrap value of $3,000. The equipment is depreciated linearly over 6 years. The value of the piece of equipment after 1 years is (rounded to the nearest whole dollar) a) $3,000 b) $11,571 c) $11,333 d) $12,444 e) $12,231 f) None of the above. Question 4 A manufacturer has a monthly fixed cost of $100,000 and a production cost of $17 for each unit produced. The product sells for $29 per unit. Find the break-even point. a) b) c) d) e) f) None of the above. Question 5 A company has fixed monthly costs of $130,000 and production costs on its product of $18 per unit. The company sells its product for $59 per unit. The cost function, revenue function and profit function for this situation are a) b) c) d) e) f) None of the above. Question 6 A manufacturer has a monthly fixed cost of $30,000.00 and a production cost of $9 for each unit produced. The product sells for $23 per unit. If the manufacturer produces and sells 11,000 units one month, then his profit is a) $124,000 b) $2,530,000 c) $990,000 d) $69,000 e) $223,000 f) None of the above. Question 7 Which of the following matrices are in row-reduced form? (Note:The dotted vertical line in each matrix should be a single vertical line.) I. II. III. a) None of them b) I and II only c) I and III only d) II and III only e) All of them f) None of the above. Question 8 Given that the augmented matrix in row-reduced form below is equivalent to the augmented matrix of a system of linear equations. Determine whether the system has a solution and find the solution(s) to the system, if they exist. (Note:The dotted vertical line in the matrix above should be a single vertical line.) a) x = 2, y = 5 b) x = 2, y = 5, z = -7 c) x = -2, y = -5 d) No solution e) x = -2, y = -5, z = 7 f) None of the above. Question 9 Use the Gauss-Jordan elimination process on the following system of linear equations to find the value of z. a) b) c) d) e) f) None of the above. Question 10 Use Gauss-Jordan elimination process to solve the following system of linear equations. a) x = 1, y = 6, z = -10 b) No Solution. c) x = 2, y = 3, z = -11 d) x = 4, y = 5, z = -12 e) Infinitely many solutions. f) None of the above. Question 11 Perform the indicated operation, if possible. -7 a) b) c) d) e) f) None of the above. Question 12 +2 Solve for x. + = a) b) c) d) e) f) None of the above. Question 13 Let E = a) b) and F = . Compute the product EF, if possible. c) d) e) f) None of the above. Question 14 Find the inverse of the given matrix, if it exists. a) b) c) d) e) f) None of the above. Question 15 A company produces two types of the jackets; windbreakers and rainbreakers. The company has at most 67hours of finishing time per week and 64 hours of packaging time per week. Each windbreaker jacket takes 45 minutes of finishing time and 22 minutes of packaging time per week, whereas each rainbreaker jacket takes 68 minutes of finshing time and 35 minutes of packaging time per week. The company's profit for each windbreaker and rainbreaker jacket is 24 and 41,xrespectively. denote the number Let of windbeaker jackets they should produce y denote andthe number of rainbreaker jackets they should produce. The company wants to maximize profit. Set up the Linear Programming Problem for this situation. x + 22y< 64 ,x> 0 , y> 0 a) Max P = x24+ 41y s.t. 68x + 45y< 67 , 35 x + 22y< 3840 ,x> 0 , y> 0 b) Max P = x41+ 24y s.t. 68x + 45y< 4020 , 35 x + 35y> 3840 ,x> 0 , y> 0 c) Max P = x41+ 24y s.t. 45x + 68y> 4020 , 22 x + 35y< 3840 ,x> 0 , y> 0 d) Max P = x24+ 41y s.t. 45x + 68y< 4020 , 22 x + 35y< 64 ,x> 0 , y> 0 e) Max P = x24+ 41y s.t. 45x + 68y< 67 , 22 f) None of the above. Question 16 Given the linear programming problem Minimize Cx =+ 6y subject to x< 7 y< 10 x +y> 10 x> 0,y> 0 Use the method of corners to determine the where the minimum occurs, and give the minimum value. a) ( 0 , 0 ) with C0 = b) ( 7 , 0 ) with C7 = c) ( 7 , 3 ) with C25= 67= d) ( 7 , 10 ) with C 60= e) ( 0 , 10 ) with C f) None of the above. Question 17 Mr. Smith wishes to retire in 8 years. When he retires he would like to have $500,000 in his bank account. Mr. Smith's bank pays 5% per year compounded annually. How much should he deposit now to attain his goal? a) $338,421.68 b) $338,415.68 c) $338,419.68 d) $338,422.68 e) $338,417.68 f) None of the above. Question 18 John got a part time weekend job at a local restaurant to save for a new car. He plans on depositing $200 per month for the next 2 years in a savings account with a rate of 3% per year compounded monthly. How much will he have saved toward his down payment at the end of the 2 year period? a) $4,920.56 b) $4,980.56 c) $4,910.56 d) $4,950.56 e) $4,940.56 f) None of the above. Question 19 You want to have $6,000 by the time you finish college in 4 years. How much money should you deposit each quarter for the next 4 years into an account paying 5% per year compounded quarterly so that you can have $6,000 when you finish college? a) $344.08 b) $339.08 c) $341.08 d) $342.08 e) $340.08 f) None of the above. Question 20 Esther pays $532 per month for 6 years for a car. She made a down payment of $2,500. If the loan costs 7.1% per year compounded monthly, what was the cash price of the car? a) $28,616.45 b) $45,083.28 c) $33,616.45 d) $50,083.28 e) $31,116.45 f) None of the above. Question 21 Given the following Venn diagram, find ( B n[CA)c ]. a) 87 b) 91 c) 94 d) 88 e) 90 f) None of the above. Question 22 (Car Sales ) Of the cars sold during the month of July, 95 had air conditioning, 102 had automatic transmission, and 73 had power steering. 7 cars had all three of these extras. 25 cars had none of these extras. 21 cars had only air conditioning, 55 cars had only automatic transmissions, and 35 cars had only power steering. 9 cars had both automatic transmission and power steering. How many cars had exactly two of the given options? a) 104 b) 76 c) 2 d) 69 e) 86 f) None of the above. Question 23 Suppose 7 people arrive at a bank at the same time. In how many ways can they line up to wait for the next available teller? a) 5,040 b) 49 c) 720 d) 7 e) 120 f) None of the above. Question 24 As part of a quality-control program, 3 batteries from a box of 16 is chosen at random for testing. In how many ways can this test batch be chosen? a) 3 b) 6 c) 3,360 d) 48 e) 560 f) None of the above. Question 25 An urn contains 3 blue balls and 6 orange balls. In how many ways can we select 2 blue balls and 4 orange balls from the urn? a) 18 30 366 45 2,158 None of the above. Question 26 A business organization needs to make up a 5 member fund-raising committee. The organization has 9 accounting majors and 7 finance majors. In how many ways can the fund-raising committee be formed if at most 1 accounting major is on the committee? Acc Fin 1 4 c(9,1)c(7,4) = 315 2 3 c(9,2)c(7,3) = 1260 3 2 c(9,3)c(7,2) = 1764 4 1 c(9,4)c(7,1) = 882, Answer = 315+1260+1764+882 =4221 9 21 336 315 30 None of the above. Question 27 Given that P(E) = 0.36, P(F) = 0.36, and P(E F) = 0.14. Find P(E F). a) b) c) d) e) f) None of the above. Question 28 A classroom of children has 18 boys and 20 girls in which five students are chosen to do presentations. What is the probability that at least four boys are chosen? a) 0.4308 b) 0.1390 c) 0.1219 d) 0.0171 e) 0.3089 f) None of the above. Question 29 An experiment consists of choosing a colored urn with equally likely probability and then drawing a ball from that urn. In the brown urn, there are 24 brown balls and 11 white balls. In the yellow urn, there are 18 yellow balls and 8 white balls. In the white urn, there are 18 white balls and 16 blue balls. What is the probability of choosing the yellow urn and a white ball? a) b) c) d) e) f) None of the above. Question 30 A recording company obtains the blank CDs used to produce its labels from three compact disk manufacturers: I, II, and III. The quality control department of the company has determined that 7% of the compact disks produced by manufacturer I are defective, 1% of those produced by manufacturer II are defective, and 5% of those produced by manufacturer III are defective. Manufacturers I, II, and III supply 27%, 34%, and 39%, respectively, of the compact disks used by the company. What is the probability that a randomly selected label produced by the company will contain a defective compact disk? a) b) c) d) e) f) None of the above. Question 31 An arcade booth at a county fair has a person pick a coin from two possible coins available and then toss it. If the coin chosen lands on heads, the person gets a prize. One coin is a fair coin and one coin is a biased coin (unfair) with only a 37% chance of getting a head. Assuming equally likely probability of picking either coin, what is the probability that the fair coin was the one chosen, given that you got a head? a) b) c) d) e) f) None of the above. Question 32 The probability distribution of a random variable X is given below. x 2 3 5 9 10 P(X=x)9/351/7 4/352/7 1/5 Given the mean Find the variance (Var(X)) and the standard deviation, respectively. Standard Deviation = 58.3978 a) Variance = 3410.3058, Standard Deviation = 9.5747 b) Variance = 91.6747, Standard Deviation = 7.1568 c) Variance = 51.2205, Standard Deviation = 41.1218 d) Variance = 1691.0000, Standard Deviation = 3.3583 e) Variance = 11.2784, f) None of the above. Question 33 Consider the following binomial experiment. The probability that a green jelly bean is chosen at random from a large package of jelly beans is 1/8. Sally chooses 10 jelly beans, what is the probability that at most 2 will be green jelly beans? a) 0.1195 b) 0.8805 c) 0.5000 d) 0.8695 e) 0.3600 f) None of the above. Question 34 Consider the following binomial experiment. At a certain university, the probability that an entering freshman will graduate within four81years /100. isFrom an incoming class of 1,860 freshmen, find the variance of the number of students who will graduate in four years. a) b) c) d) e) f) None of the above. Question 35 Let Z be a standard normal variable. Find P(Z > 2.23). a) b) c) d) e) f) None of the above. Question 36 Let Z be a standard normal variable. Find the value of z if z satisfies P(Z > z) = 0.0020. a) b) c) d) e) f) None of the above. Question 37 Suppose X is a normal random variable with = 35 and = 10. Find P(55.5 < X < 69.7). a) d) e) f) None of the above. Question 40 Use the normal distribution to approximate the following binomial distribution. You claim that 73% of the voters in your district will vote for you. If the district has 350 voters, what is the probability that at least 273 will actually vote for you? a) b) c) d) e) f) None of the above