Math 235 Final Exam Practice test. Name

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1 Math 235 Final Exam Practice test Name Use the Gauss-Jordan method to solve the system of equations. 1) x + y + z = -1 x - y + 3z = -7 4x + y + z = -7 A) (-1, -2, 2) B) (-2, 2, -1) C)(-1, 2, -2) D) No solution 2) x - y + 4z = -22 3x + z = -5 x + 5y + z = 5 A) (-5, 0, 2) B) (-5, 2, 0) C)(0, 2, -5) D) No solution Solve the problem. 3) An airline with two types of airplanes, P1 and P2, has contracted with a tour group to provide transportation for a minimum of 400 first class, 900 tourist class, and 1500 economy class passengers. For a certain trip, airplane P1 costs $10,000 to operate and can accommodate 20 first class, 50 tourist class, and 110 economy class passengers. Airplane P2 costs $8500 to operate and can accommodate 18 first class, 30 tourist class, and 44 economy class passengers. How many of each type of airplane should be used in order to minimize the operating cost? A) 14 P1 planes and 7 P2 planes B) 5 P1 planes and 22 P2 planes C)13 P1 planes and 9 P2 planes D) 9 P1 planes and 13 P2 planes 1

2 Find the simple interest. Assume a 360-day year. Round results to the nearest cent. 4) $5995 at 3% for 11 months A) $ B) $ C) $ D) $ Find the amount of compound interest earned. 5) $6000 at 7% compounded annually for 3 years A) $13, B) $3,066, C) $ D) $

3 Shade the Venn diagram to represent the set. 6) (A B C')' A) B) C) D) 3

4 Use a Venn diagram to answer the question. 7) A local television station sends out questionnaires to determine if viewers would rather see a documentary, an interview show, or reruns of a game show. There were 200 responses with the following results: 60 were interested in an interview show and a documentary, but not reruns; 8 were interested in an interview show and reruns, but not a documentary; 28 were interested in reruns but not an interview show; 48 were interested in an interview show but not a documentary; 20 were interested in a documentary and reruns; 12 were interested in an interview show and reruns; 16 were interested in none of the three. How many are interested in exactly one kind of show? A) 76 B) 86 C)96 D) 106 Find the probability of the given event. 8) A single fair die is rolled. The number on the die is less than 6. A) 1 6 B) 1 C) 5 7 D) 5 6 9) Two fair dice are rolled. The sum of the numbers on the dice is 6 or 9. A) 5 12 B) 3 2 C) 1 54 D) 1 4 4

5 Find the probability. 10) A spinner has equal regions numbered 1 through 15. What is the probability that the spinner will stop on an even number or a multiple of 3? A) 1 3 B) 12 C) 7 9 D) ) Each digit from the number 9,878,558 is written on a different card. If one of these cards is selected at random, what is the probability of drawing a card that shows 9, 8, or 7? A) 3 7 B) 5 7 C) 9 7 D) 1 Find the indicated probability. 12) The distribution of B.A. degrees conferred by a local college is listed below, by major. Major Frequency English 2073 Mathematics 2164 Chemistry 318 Physics 856 Liberal Arts 1358 Business 1676 Engineering What is the probability that a randomly selected degree is in Chemistry or Physics? A) B) 1174 C) D)

6 13) The following contingency table shows age at retirement (broken down by career) for a group of retired people. Retirement Age Career Over 65 Attorney College Professor Administrative Assistant Store Clerk Totals Suppose one of these people is selected at random from the age group. Find the probability that the person selected was an attorney. A) B) C) D) ) Find the probability that the sum is no more than 6 when two fair dice are rolled. A) 7 5 B) C) D) ) When a single card is drawn from an ordinary 52-card deck, find the probability of getting a black 10 or a black 2. A) 1 1 B) C) 1 D) ) When two balanced dice are rolled, there are 36 possible outcomes. Find the probability that the first die is 3 or that doubles are rolled. A) 1 B) 11 C) 1 D) ) If you pick a card at random from a well shuffled deck, what is the probability that you get a face card or a spade? A) 9 26 B) C) D)

7 Use a Venn diagram to find the indicated probability. 18) If P(A B) = 0.63, P(A) = 0.32, and P(B) = 0.46, find P(A B). A) 0.11 B) 0.27 C) 0.56 D) ) Suppose P(R) = 0.57, P(S) = 0.45, and P(R S) = Find P(R' S). A) 0.09 B) 0.79 C) 0.88 D) 0.64 Solve the problem. 20) A survey revealed that 38% of people are entertained by reading books, 27% are entertained by watching TV, and 35% are entertained by both books and TV. What is the probability that a person will be entertained by either books or TV? Express the answer as a percentage. A) 65% B) 35% C) 30% D) 100% 7

8 21) 100 employees of a company are asked how they get to work and whether they work full time or part time. The figure below shows the results. If one of the 100 employees is randomly selected, find the probability of getting someone who carpools or someone who works full time. 1. Public transportation: 8 full time, 9 part time 2. Bicycle: 5 full time, 5 part time 3. Drive alone: 34 full time, 26 part time 4. Carpool: 7 full time, 6 part time A) 0.58 B) 0.6 C) 0.67 D) 0.23 Use the given table to find the indicated probability. 22) The following table contains data from a study of two airlines which fly to Smalltown, USA. Number of flights Number of flights Totals arrived on time arrived late Podunk Airlines Upstate Airlines If a flight is selected at random, what is the probability that it was on Upstate Airlines and that it arrived on time? A) B) C) D)

9 Find the indicated probability. 23) The following contingency table provides a joint frequency distribution for a group of retired people by career and age at retirement. Age at Retirement Over 65 Total Attorney College Professor Administrative Assistant Store Clerk Total Suppose one of these people is selected at random. Compute the probability that the person selected was a store clerk. A) B) C) D) Solve the problem. 24) Suppose 6 people sit at a circular table. Find the probability that 2 particular people are sitting next to each other. A) 0.2 B) 0.33 C) 0.4 D) ) A roulette wheel contains 84 slots numbered 1 through 84. The slots 1,4,7,... are red, the slots 2,5,8,... are green, and the slots 3, 6, 9,... are brown. When the wheel is spun, a ball rolls around the rim and falls into a slot. What is the probability that the ball falls into a green slot? A) 1 4 B) 1 3 C) 2 5 D) 2 3 9

10 Find the requested probability. 26) A coin is biased to show 40% heads and 60% tails. The coin is tossed twice. What is the probability that the coin turns up heads once and tails once? A) 48% B) 60% C)40% D) 24% Find the probability of the event. 27) A die is rolled 18 times and two threes come up. A) B) C) D) ) The probability that a radish seed will germinate is 0.7. The gardener plants 20 seeds and she harvests 16 radishes. A) B) C) D) Find the expected value for the random variable. 29) A business bureau gets complaints as shown in the following table. Find the expected number of complaints per day. Complaints per Day Probability A) 2.98 B) 2.73 C) 2.85 D)

11 30) A business bureau gets complaints as shown in the following table. Find the expected number of complaints per day. Complaints per Day Probability A) 2.98 B) 3.01 C) 2.85 D) 2.73 At one high school, girls can run the 100-yard dash in an average of 15.2 seconds with a standard deviation of 0.9 second. The times are very closely approximated by a normal curve. Find the percent of times that are: 31) Greater than 15.2 seconds A) 48% B) 68% C)50% D) 34% 32) Less than 17 seconds A) 97.7% B) 2.5% C) 84% D) 99% 33) Between 16.1 and 17.0 seconds A) 27% B) 12% C) 13.6% D) 34% 34) At least 14.3 seconds A) 16% B) 13.5% C) 50% D) 84% 11

12 Solve the problem. 35) If the life, in years, of a washing machine is normally distributed with a mean of 16 years and a standard deviation of 3 years, what should be the guarantee period if the company wants less than 1% of the machines to fail while under warranty? A) Less than 9.01 years B) More than 9.01 years C)More than years D) Less than years 12

13 Answer Key Testname: MATH 235 PRACTICE TEST 41 1) B 2) C 3) A 4) D 5) C 6) A 7) C 8) D 9) D 10) D 11) B 12) C 13) C 14) B 15) B 16) B 17) B 18) D 19) B 20) C 21) B 22) A 23) D 24) C 25) B 26) A 27) A 28) B 29) A 30) D 31) C 32) A 33) C 34) D 35) A 13