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All Textbook Solutions for College Algebra (MindTap Course List)
58E59E60ESelf Check Write the first five terms of a geometric sequence whose first term is 2 and whose common ratio is 3. Find the 10th term.2SCSelf Check Insert two geometric means between -3 and 192.4SC5SC6SC7SC8SCFill in the blanks. A geometric sequence is a sequence of the form a,ar,ar2,ar3,.... The nth term is a(_).2E3E4E5E6E7E8E9EPractice Write the first four terms of each geometric sequence with the given properties. a=3;r=211EPractice Write the first four terms of each geometric sequence with the given properties. a=64;r=1213E14E15E16EFind the requested term of each geometric sequence. Find the sixth term of the geometric sequence whose first three terms are 14, 1, and 4.Find the requested term of each geometric sequence. Find the eighth term of the geometric sequence whose second and fourth terms are 0.2 and 5.Find the requested term of each geometric sequence. Find the fifth term of a geometric sequence whose second term is 6 and whose third term is 18.20E21E22ESolve each problem. Insert four geometric means between 2 and 2048.Solve each problem. Insert three geometric means between 162 and 2. There are two possibilities25E26E27E28E29EFind the sum of indicated terms of each geometric series. n=1612(12)n131E32E33E34E35E36E37E38E39E40E41E42E43E44E45E46E47E48EApplications Use a calculator to help solve each problem. 49. Population study If the population of the Earth were to double every 30 years, approximately how many people would there be in the year 3020? Consider the population in the year 2000 to be 5 billion and use 2000 as the base year.50E51E52E53E54E55E56E57E58E59E60E61E62E63E64E65E66E67E68E69E70E71E72E73E74E75E76E77E78E1SC2SC3SC1E2E3E4E5E6E7E8E9E10E11E12E13E14E15E16E17E18E19E20E21EProve each formula by mathematical induction, if possible. 13+29+427++1323n-1=1-23n23E24E25EProve by induction that n2n.27E28E29E30E31EProve by induction that 1+2n3n for n1.Prove by induction that if r is a real number where r1, then 1+r+r2++rn=1-rn+11-rProve the formula for the sum of the first n terms of an arithmetic series: a+a+d+a+2d+a+n-1d=na+an2 where an=a+n-1d.35E36E37E38E39ETower of Hanoi The result in Exercise 39 suggest that the minimum number of moves required to transfer n disks from one peg to another is given by the formula 2n1. Use the following outline to prove that this result is correct using mathematical induction. a Verify the formula for n=1. b Write the induction hypothesis. c How many moves are needed to transfer all but the largest of k+1 disks to another peg? d How many moves are needed to transfer the largest disk to an empty peg? e How many moves are needed to transfer the first k disks back onto the largest one? f How many moves are needed to accomplish steps c, d, and e? g Show that part f can be written in the form 2(k+1)1. h Write the conclusion of the proof.41E42E43EDetermine if the statement is true or false. If the statement is false, then correct it and make it true. 3n3n+1 is true for all natural numbers n greater than 2.If a man has 4 sweaters and 5 pairs of slacks, how many different outfit can he wear?How many different signals can be sent, when three flags are used, if two of the 9 flags are missing?3SC4SCIn how many ways can 5 people stand in a line if one person demands to be first?6SC7SC8SC9SC10SC1E2E3E4E5E6E7E8E9E10E11E12E13E14E15EEvaluate each expression. C(8,3)17E18E19E20E21E22E23E24E25E26E27E28E29E30E31E32E33EApplications Arranging letters with restrictions In how many ways can the letters of the word number be arranged if the e and r cannot be side by side?35EApplications Arranging letters with repetitions How many ways can six Scrabble tiles bearing the letters, B, E, E, E, F, and L be arranged to spell the word feeble?37EPlacing people in line In how many arrangements can 5 women and 5 men be placed in a line if the women and men alternate?39E40E41ECombination locks How many permutations does a combination lock have if each combination has 3 numbers, no two numbers of the combination are the same, and the lock dial has 100 notches?43E44ESeating at a table In how many ways can 6 people be seated at a round table if 2 of the people insist on sitting together?46E47E48E49ESelecting surfboards In how many ways can 6 surfboards be selected from 24 different surfboards?Circuit wiring A wiring harness containing a red, a green, a white, and a black wire must be attached to a control panel. In how many different orders can the wires be attached?52E53E54E55E56E57E58E59E60E61E62E63E64E65E66E67E68E69E70E71E72E73E74E75E76E77E78E79E80E81E82E83E84E85E86E87E88E89E90E91E92E93E94ESelf Check How many pairs in the above sample space have a sum of 7? 1, 1 1, 2 1, 3 1, 4 1, 5 1, 6 2, 1 2, 2 2, 3 2, 4 2, 5 2, 6 3, 1 3, 2 3, 3 3, 4 3, 5 3, 6 4, 1 4, 2 4, 3 4, 4 4, 5 4, 6 5, 1 5, 2 5, 3 5, 4 5, 5 5, 6 6, 1 6, 2 6, 3 6, 4 6, 5 6, 6Self Check Find the probability of rolling a sum of 10.Self Check Find the probability of drawing 6 cards, all hearts, from the deck.Finding the Probability of an Event Example 4 A box contains 40 wooden blocks of the same size. Of these blocks, 17 are red, 13 are blue, and the rest are yellow. If 2 blocks are drawn at random, without replacement, find the probability that 2 yellow blocks will be drawn. Self check Find the probability that 2 blue blocks will be drawn.Self Check Using the Multiplication Property of Probabilities to find the probability of drawing 6 cards, all hearts, from the deck.6SC1E2E3EFill in the blanks. P(AB)=List the sample space of each experiment. Rolling one die and tossing one coinList the sample space of each experiment. Tossing three coinsList the sample space of each experiment. Selecting a letter of the alphabetList the sample space of each experiment. Picking a one-digit numberAn ordinary die is rolled. Find the probability of each event. Rolling a 2An ordinary die is rolled. Find the probability of each event. Rolling a number greater than 4An ordinary die is rolled. Find the probability of each event. Rolling a number greater than 1 but less than 612E13EBalls numbered from 1 to 42 are placed in a container. If one is drawn at random, find the probability of each result. The number is less than 50.15E16EIf the spinner shown below is spun, find the probability of each event. Assume that the spinner never stops on a line. The spinner stops on red.If the spinner shown below is spun, find the probability of each event. Assume that the spinner never stops on a line. The spinner stops on green.If the spinner shown below is spun, find the probability of each event. Assume that the spinner never stops on a line. The spinner stops on orange.If the spinner shown below is spun, find the probability of each event. Assume that the spinner never stops on a line. The spinner stops on yellow.21E22E23EFind the probability of each event. Drawing two aces from a card deck without replacing the card after the first draw25EFind the probability of each event. Getting 2 red eggs in a single scoop from a bucket containing 5 red eggs and 7 yellow eggs27E28E29E30E31E32EFind the probability of each event. Drawing 5 orange cubes from a bowl containing 5 orange cubes and 1 beige cubesFind the probability of each event. Rolling a sum of 4 on one roll of three diceFind the probability of each event. Rolling a sum of 11 on one roll of three dice36E37EFind the probability of each event. Tossing 5 heads in 5 tosses of a fair coinAssume that the probability that an airplane engine will fail during a torture test is 12and that the aircraft in question has 4 engines. Construct a sample space for the torture test. Use S for survive and F for fail.Assume that the probability that an airplane engine will fail during a torture test is 12and that the aircraft in question has 4 engines. Find the probability that all engines will survive the test.41E42E43E44EAssume that the probability that an airplane engine will fail during a torture test is 12and that the aircraft in question has 4 engines. 40. Find the probability that all engines will survive the test. 41. Find the probability that exactly 1 engine will survive. 42. Find the probability that exactly 2 engines will survive. 43. Find the probability that exactly 3 engines will survive. 44. Find the probability that no engines will survive. Find the sum of the probabilities in Exercises 40 through 44.Assume that a survey of 282 people is taken to determine the opinions of doctors, teachers, and lawyers on a proposed piece of legislation, with the results as shown in the table. A person is chosen at random from those surveyed. Refer to the table to find each probability. Number that favor Number that Oppose Number with No Opinion Total Doctors 70 32 17 119 Teachers 83 24 10 117 Lawyers 23 15 8 46 Total 176 71 35 282 The person favors the legislation.Assume that a survey of 282 people is taken to determine the opinions of doctors, teachers, and lawyers on a proposed piece of legislation, with the results as shown in the table. A person is chosen at random from those surveyed. Refer to the table to find each probability. Number that favor Number that Oppose Number with No Opinion Total Doctors 70 32 17 119 Teachers 83 24 10 117 Lawyers 23 15 8 46 Total 176 71 35 282 A doctor opposes the legislation.48E49EMedicine Out of a group of 9 patients treated with a new drug, 4 suffered a relapse. Find the probability that 3 patients of this group, chosen at random, will remain disease-free.Use the Multiplication Property of Probabilities. If P(A)=0.3 and P(BA)=0.6, find P(AB).Use the Multiplication Property of Probabilities. If P(AB)=0.3 and P(BA)=0.6, find P(A).53EConditional probability If 40 of the population have completed college, and 85 of college graduates are registered to vote, what percent of the population are both college graduates and registered voters?