Mat142 Final Exam

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MAT142 Final Exam


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  • 1. 
    Five runners (Andy, Beth, Dale, Ella and Tri) are in a one mile race.  Beth finished 3 seconds before Dale.  Dale finished 7 seconds after Andy.  Andy finished 5 seconds after Tri.  Tri finished 3 seconds before Ella.  Who finished in second place?
    • A. 

      Andy

    • B. 

      Beth

    • C. 

      Dale

    • D. 

      Ella

    • E. 

      Tri

  • 2. 
    Write a description of the set:  {15, 16, 17, 18, ... }
    • A. 

      All natural numbers greater than 14

    • B. 

      All natural numbers greater than 15

    • C. 

      All rational numbers greater than 14

    • D. 

      The numbers fifteen, sixteen, seventeen, and eighteen

    • E. 

      None of the above

  • 3. 
    Determine if the set is the empty set:  {x such that x < 7 and x > 10}.
    • A. 

      The set is the empty set.

    • B. 

      The set is not the empty set.

  • 4. 
    Determine whether the given statement is true or false:  20 is an element of {14, 16, 18, 20}
    • A. 

      True

    • B. 

      False

  • 5. 
    Determine whether the given statement is true or false:  19 is not an element of {1, 2, 3, ..., 34}
    • A. 

      True

    • B. 

      False

  • 6. 
    Find the cardinal number of the given set:The set of all numbers x such that x is a natural number and 6 < x < 12.
    • A. 

      4

    • B. 

      5

    • C. 

      6

    • D. 

      7

    • E. 

      8

  • 7. 
    Find the cardinal number for the given set:  {2, 6, 10, .. , 42}.
  • 8. 
    Consider the following sets:A = {2, 3, 4, 5, 6}B = {1, 2, 3, 4, 5}Choose the statement below that is true.
    • A. 

      The sets are equal and equivalent.

    • B. 

      The sets are equal but not equivalent.

    • C. 

      The sets are not equal but are equivalent.

    • D. 

      The sets are not equal and not equivalent.

    • E. 

      None of the above.

  • 9. 
    Determine whether the set is finite or infinite:  x such that x is a natural number and x > 119.
    • A. 

      Finite set

    • B. 

      Infinite set

  • 10. 
    Consider the following sets:U = {1, 2, 3, 4, 5, 6, 7}A = {4, 5, 6, 7}B = {3, 4, 7}Find the intersection of the complement of A and the complement of B.
  • 11. 
    Consider the following sets: U = {1, 2, 3, 4, 5, 6, 7} A = {3, 4, 5, 6} B = {3, 4, 7} Find the complement of the union of A and B.
  • 12. 
    Set A contains 4 letters and 7 numbers.  Set B contains 11 letters and 2 numbers.  0 letters and 0 numbers are common to both sets A and B.  Find the number of elements in set A or Set B.
  • 13. 
    Consider the following sets: U = {a, b, c, d, e, f, g, h} A = {a, d, g} B = {b, d, g}C = {b, c, e, f, h} Find the union of the following two intersections:1) the intersection of A and the complement of C2) the intersection of the complement of B and the complement of C
  • 14. 
    A television sells for $700.  Instead of paying the total amount at the time of the purchase, the same television can be bought by paying $200 down and $50 a month for 14 months.  How much is saved by paying the total amount at the time of purchase?
  • 15. 
    Each day a small business owner sells 200 pizza slices at $2.00 per slice and 85 sandwiches at $4.00 each.  Business expenses come to $110 per day.  What is the owner's profit for a ten-day period?
  • 16. 
    A vending machine accepts nickels, dimes, and quarters only.  Exact change is needed to make a purchase.  How many ways can a person with four nickels, three dimes, and two quarters make a 35-cent purchase from the machine?
  • 17. 
    Consider the following sets:Set X = {4,6,9}Set Y = {4,6,9,12}Choose the statement(s) that are true.
    • A. 

      Set X is a subset of Set Y.

    • B. 

      Set X is a proper subset of Set Y.

    • C. 

      Both A and B are true.

    • D. 

      None of the statements are true.

  • 18. 
    Consider the following sets: Set X = {4,7,10,13,16} Set Y = {7,4,10,13,16} Choose the statement(s) that are true.
    • A. 

      Set X is a subset of Set Y.

    • B. 

      Set X is a proper subset of Set Y.

    • C. 

      Both A and B.

    • D. 

      None of the statments are true.

  • 19. 
    A pizza parlor offers mushrooms, onions, and sausage as toppings for the plain cheese base.  How many different types of pizzas can be made?  Assume that you can order a plain cheese pizza, a 1-topping pizza, a 2-topping pizza, or a 3-topping pizza.
  • 20. 
    How many different groups of students can show up for a seminar with an enrollment of 15?
  • 21. 
    A politician has run for office two times.  In the first election 11,240 people voted for him.  In the second election 13,134 people voted for him.  9,349 people voted for him in both elections.  How many people voted for this politician in the first or the second election?
  • 22. 
    A survey of 76 college students was taken to determine where they got the news about what's going on in the world.  Of those surveyed, 38 got the news from newspapers, 31 from television, and 17 from both newspapers and television.  How many got the news from only newspapers?
  • 23. 
    A survey of 76 college students was taken to determine where they got the news about what's going on in the world.  Of those surveyed, 38 got the news from newspapers, 31 from television, and 17 from both newspapers and television.  How many got the news from only television?
  • 24. 
    A survey of 76 college students was taken to determine where they got the news about what's going on in the world.  Of those surveyed, 38 got the news from newspapers, 31 from television, and 17 from both newspapers and television.  How many got the news from newspapers or from television?
  • 25. 
    A survey of 76 college students was taken to determine where they got the news about what's going on in the world.  Of those surveyed, 38 got the news from newspapers, 31 from television, and 17 from both newspapers and television.  How many got the news from neither newspapers nor television?
  • 26. 
    A survey of 118 college students was taken to determine the musical styles they liked.  Of those, 35 students listened to rock, 33 to classical, and 35 to jazz.  Also, 24 students listened to rock and jazz, 15 to rock and classical, and 15 to classical and jazz.  Finally, 12 students listened to all three musical styles.  How many listened to only rock music?
  • 27. 
    A survey of 118 college students was taken to determine the musical styles they liked.  Of those, 35 students listened to rock, 33 to classical, and 35 to jazz.  Also, 24 students listened to rock and jazz, 15 to rock and classical, and 15 to classical and jazz.  Finally, 12 students listened to all three musical styles.  How many listened to classical and jazz but not to rock?
  • 28. 
    A survey of 118 college students was taken to determine the musical styles they liked.  Of those, 35 students listened to rock, 33 to classical, and 35 to jazz.  Also, 24 students listened to rock and jazz, 15 to rock and classical, and 15 to classical and jazz.  Finally, 12 students listened to all three musical styles.  How many listened to classical and to jazz but not to rock?
  • 29. 
    A survey of 118 college students was taken to determine the musical styles they liked.  Of those, 35 students listened to rock, 33 to classical, and 35 to jazz.  Also, 24 students listened to rock and jazz, 15 to rock and classical, and 15 to classical and jazz.  Finally, 12 students listened to all three musical styles.  How many listened to exactly one music style?
  • 30. 
    Suppose that the local sales tax rate is 4%, and you purchase a car for $24,200.  How much tax is paid?
  • 31. 
    Suppose that the local sales tax rate is 4%, and you purchase a car for $24,200.  What is the total cost of the car (including tax)?
  • 32. 
    An exercise machine with an original price of $730 is on sale at 21% off.  What is the exercise machine's sale price?
  • 33. 
    A sofa regularly sells for $850.  It is on sale for $646.  Find the percent decrease of the sale price from the regular price.
  • 34. 
    $12,000 is borrowed at a simple interest rate of 7% for 180 days.  How much interest will be owed at the end of the 180 days?  If necessary, round your answer to the nearest dollar.
  • 35. 
    $3,000 is borrowed, and at the end of 3 months, the balance due is $3045.  What was the simple interest rate?  If necessary, round to the nearest tenth of a percent.
  • 36. 
    If you would like to have $4,000 in 3 months, how much money should you invest today into an account that earns a simple interest rate of 9.0%?  If necessary, round your answer to the nearest dollar.
  • 37. 
    $5,000 is deposited into an account earning interest compounded daily with an interest rate of 8%.  How much money will be in the account after 4 years?  If necessary, round to the nearest dollar.
  • 38. 
    How much money should be deposited today in an account that earns 6% compounded semiannually so that it will accumulate to $13,000 in three years?  If necessary, round your answer to the nearest dollar.
  • 39. 
    At the time of her grandson's birth, a grandmother deposits $14,000 in an account that pays 7% compounded monthly.  What will be the value of the account at the child's twenty-first birthday, assuming that no other deposits or withdrawals are made during this period?  If necessary, round to the nearest dollar.
  • 40. 
    You deposit $10 at the end of each month into an annuity that earns 6% interest compounded monthly.  How much money will be in the account after 10 years?  If necessary, round to the nearest dollar.
  • 41. 
    In order to have $24,000 in 6 years, how much should you deposit each quarter into an annuity that earns 7.25% compounded quarterly?  If necessary, round to the nearest dollar.
  • 42. 
    The cost of a sports utility vehicle is $30,000.  This can be financed by paying $2,000 down and $436 per month for 72 months.  What is the amount financed?
  • 43. 
    The cost of a sports utility vehicle is $30,000.  This can be financed by paying $2,000 down and $436 per month for 72 months.  What is the total installment price?
  • 44. 
    The cost of a sports utility vehicle is $30,000.  This can be financed by paying $2,000 down and $436 per month for 72 months.  What is the finance charge?
  • 45. 
    The price of a home is $136,000.  The bank requires a 20% down payment and three points at the time of closing.  The cost of the home is financed with a 30-year fixed-rate mortgage at 8.5%.  Find the required down payment amount.
  • 46. 
    The price of a home is $136,000.  The bank requires a 20% down payment and three points at the time of closing.  The cost of the home is financed with a 30-year fixed-rate mortgage at 8.5%.  Find the amount of the mortgage.
  • 47. 
    The price of a home is $136,000.  The bank requires a 20% down payment and three points at the time of closing.  The cost of the home is financed with a 30-year fixed-rate mortgage at 8.5%.  How much must be paid for the three points at closing? Round to the nearest dollar.
  • 48. 
    The price of a home is $136,000.  The bank requires a 20% down payment and three points at the time of closing.  The cost of the home is financed with a 30-year fixed-rate mortgage at 8.5%.  Find the monthly mortgage payment.  Round to the nearest dollar.
  • 49. 
    Convert 13 meters to yards.  Round to the nearest hundredth.
  • 50. 
    Convert 6 feet to meters.  Round to the nearest tenth.
  • 51. 
    Convert 30 ounces to grams.  Round to the nearest whole number.
  • 52. 
    For each kilogram of a person's weight, 2.5 milligrams of a medicine is to be given.  What amount of medicine (in milligrams) should be given to a person who weighs 71 pounds?  Round your answer to the nearest whole number.
  • 53. 
    A person who is five feet tall is standing 182 feet from the base of a tree, and the tree casts a 195 foot shadow.  The person's shadow is 13 feet in length.  What is the height of the tree?
  • 54. 
    The doorway into a room is 3 feet wide and 11 feet high.  What is the length of the longest rectangular panel that can be taken through this doorway diagonally?  Round to the nearest tenth.
  • 55. 
    A rectangular field is two times as long as it is wide.  If the perimeter of the field is 330 yards, what is the length of the field?
  • 56. 
    A school playground is in the shape of a rectangle 700 feet long and 200 feet wide.  If fencing costs $13 per yard, what will it cost to place fencing around the playground?
  • 57. 
    One side of a square flower bed is 7 feet long.  How many plants are needed if they are to be spaced 7 inches apart around the outside of the bed?
  • 58. 
    What will it cost to carpet a rectangular floor measuring 18 feet by 30 feet if the carpet costs $28.10 per square yard.  Round to the nearest whole number.
  • 59. 
    A rectangular kitchen floor measures 10 feet by 15 feet.  A stove on the floor has a rectangular base measuring 3 feet by 4 feet, and a refrigerator covers a rectangular area of the floor measuring 4 feet by 5 feet.  How many square feet of tile will be needed to cover the kitchen floor (not counting the area used by the stove and refrigerator)?
  • 60. 
    How many flowers, spaced every 6 inches, are needed to surround a circular garden with a 50-foot radius?  Round to the nearest whole number.
  • 61. 
    A building contractor is to dig a foundation 48 feet long, 18 feet wide, and 9 feet deep.  The contractor pays $5 per load for trucks to remove the dirt. Each truck hold 9 cubic yards of dirt.  What is the cost to have all of the dirt hauled away?
  • 62. 
    A single six-sided die is rolled twice (the sides are numbered 1 through 6).  Find the probability of getting two numbers whose sum exceeds 20.
  • 63. 
    Six stand-up comics, A, B, C, D, E, and F are to perform on a single evening at a comedy club.  The order of performance is determined by random selection.  Find the probability that Comic B will perform fifth.  Round your answer to the nearest hundredth.
  • 64. 
    A box contains 27 transistors, 7 of which are defective.  If 7 are selected at random, find the probability that none of them are defective.  Round your answer to the nearest hundredth.
  • 65. 
    A city council consists of five Democrats and six Republicans.  If a committee of six people is selected at random, find the probability of selecting three Democrats and three Republicans.  Round your answer to the nearest hundredth.
  • 66. 
    You are dealt one card from a 52-card deck.  Find the probability that you are not dealt a six.  Round to the nearest hundredth.
  • 67. 
    You are dealt one card from a 52-card deck.  Find the probability that you are dealt a three or a red card.  Round to the nearest hundredth.
  • 68. 
    The mathematics department of a college has 5 male professors, 9 females professors, 13 male teaching assistants, and 5 female teaching assistants.  If a person is selected at random from the group, find the probability that the selected person is a professor or a male.  Round to the nearest hundredth.
  • 69. 
    A single six-sided die (with sides numbered 1 through 6) is rolled twice.  Find the probability of rolling an even number the first time and a number greater than 1 the second time.  Round to the nearest hundredth.
  • 70. 
    A coin is tossed and a die is rolled.  Find the probability of getting heads and a number greater than 5.  Round to the nearest hundredth.
  • 71. 
    The probability that a certain state will be hit by a major tornado in any single year is 1/13.  What is the probability that the state will be hit by a major tornado two years in a row?  Round to five decimal places.
  • 72. 
    The probability that a certain state will be hit by a major tornado in any single year is 1/13.  What is the probability that the state will be hit by a major tornado in three consecutive years?  Round to five decimal places.
  • 73. 
    The probability that a certain state will be hit by a major tornado in any single year is 1/13.  What is the probability that the state will not be hit by a major tornado in the next ten years?  Round to three decimal places.
  • 74. 
    The probability that a certain state will be hit by a major tornado in any single year is 1/13.  What is the probability that the state will be hit by a major tornado at least once in the next ten years?  Round to three decimal places.
  • 75. 
    Elizabeth brought in a box of donuts to share.  There are 24 donuts in the box.  2 are jelly-filled, 4 are lemon-filled, and 18 are custard-filled.  You randomly select one donut, eat it, and select another donut.  Find the probability of selecting a jelly-filled donut followed by a custard-filled donut.  Round to the nearest hundredth.
  • 76. 
    It is estimated that there are 15 deaths for every 10 millions people who use airplanes.  A company that sells flight insurance provides $100,000 in case of death in a plane crash.  A policy can be purchased for $1.  Determine how much the insurance company can make over the long run for each policy it sells.  Round to the nearest hundredth.
  • 77. 
    A 25-year old can purchase a one-year life insurance policy for $10,000 at a cost of $100.  Past history indicates that the probability of a person dying at age 25 is 0.03.  Determine the company's expected gain per policy.  Round to the nearest whole number.
  • 78. 
    Fourteen different blood pressure measurements are listed below:144130135143130130141138127118150118130141What is the mean blood pressure?  Round to the nearest tenth.
  • 79. 
    Fourteen different blood pressure measurements are listed below: 144 130 135 143 130 130 141 138 127 118 150 118 130 141 What is the median blood pressure?  Round to the nearest tenth.
  • 80. 
    Fourteen different blood pressure measurements are listed below: 144 130 135 143 130 130 141 138 127 118 150 118 130 141 What is the mode of the blood pressure data?
  • 81. 
    Fourteen different blood pressure measurements are listed below: 144 130 135 143 130 130 141 138 127 118 150 118 130 141 What is the midrange of the blood pressure data?
  • 82. 
    The mean price of a particular model of a new car is $22,000, and the standard deviation is $2,000.  What percentage of buyers pay more than $28,000 for this particular model of car?  Round to the nearest hundredth of a percent.
  • 83. 
    Scores on the GRE are normally distributed with a mean of 595 and a standard deviation of 73.  Find the percentage of people who score between 376 and 595.  Round to the nearest hundredth.
  • 84. 
    Scores on a test are normally distributed with a mean of 533and a standard deviation of 86.  Find the percentage of people who score above 705.  Round to the nearest tenth.