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All Textbook Solutions for Precalculus

9AYU 10AYU 11AYU 12AYU 13AYU In Problems 5-16, evaluate each expression. ( 60 20 )15AYU 16AYU In Problems 17-28, expand each expression using the Binomial Theorem. ( x+1 ) 5 In Problems 17-28, expand each expression using the Binomial Theorem. ( x1 ) 5 In Problems 17-28, expand each expression using the Binomial Theorem. ( x2 ) 6 In Problems 17-28, expand each expression using the Binomial Theorem. ( x+3 ) 5 In Problems 17-28, expand each expression using the Binomial Theorem. ( 3x+1 ) 4 In Problems 17-28, expand each expression using the Binomial Theorem. ( 2x+3 ) 5 In Problems 17-28, expand each expression using the Binomial Theorem. ( x 2 + y 2 ) 5 In Problems 17-28, expand each expression using the Binomial Theorem. ( x 2 y 2 ) 6 In Problems 17-28, expand each expression using the Binomial Theorem. ( x + 2 ) 6 In Problems 17-28, expand each expression using the Binomial Theorem. ( x 3 ) 4 In Problems 17-28, expand each expression using the Binomial Theorem. ( ax+by ) 5 In Problems 17-28, expand each expression using the Binomial Theorem. ( axby ) 4 In Problems 29-42, use the Binomial Theorem to find the indicated coefficient or term. The coefficient of x 6 in the expansion of ( x+3 ) 10 In Problems 29-42, use the Binomial Theorem to find the indicated coefficient or term. The coefficient of x 3 in the expansion of ( x3 ) 10 In Problems 29-42, use the Binomial Theorem to find the indicated coefficient or term. The coefficient of x 7 in the expansion of ( 2x1 ) 12 In Problems 29-42, use the Binomial Theorem to find the indicated coefficient or term. The coefficient of x 3 in the expansion of ( 2x+1 ) 12 In Problems 29-42, use the Binomial Theorem to find the indicated coefficient or term. The coefficient of x 7 in the expansion of ( 2x+3 ) 9 In Problems 29-42, use the Binomial Theorem to find the indicated coefficient or term. The coefficient of x 2 in the expansion of ( 2x3 ) 9 In Problems 29-42, use the Binomial Theorem to find the indicated coefficient or term. The 5th term in the expansion of ( x+3 ) 7 In Problems 29-42, use the Binomial Theorem to find the indicated coefficient or term. The 3rd terms in the expansion of ( x3 ) 7 In Problems 29-42, use the Binomial Theorem to find the indicated coefficient or term. The 3rd term in the expansion of ( 3x2 ) 9 In Problems 29-42, use the Binomial Theorem to find the indicated coefficient or term. The 6th term in the expansion of ( 3x+2 ) 8 In Problems 29-42, use the Binomial Theorem to find the indicated coefficient or term. The coefficient of x 0 in the expansion of ( x 2 + 1 x ) 12 40AYU 41AYU 42AYU 43AYU 44AYU Show that ( n n1 )=nand( n n )=1 .46AYU 47AYU 48AYU 49AYU 50AYU 1RE 2RE 3RE 4RE 5RE 6RE 7RE 8RE 9RE 10RE 11RE 12RE 13RE 14RE 15RE 16RE 17RE 18RE 19RE 20RE 21RE 22RE 23RE 24RE 25RE 26RE 27RE 28RE 29RE 30RE 31RE 32RE 33RE 34RE 35RE 36RE 37RE 38RE 39RE 40RE 1CT In Problems, a survey of college freshmen asked whether students planned to take biology, chemistry, or physics during their first year. Use the diagram to answer each question. How many of the surveyed students do not plan to take biology, chemistry, or physics during their first year? In Problems 14, a survey of 70college freshmen asked whether students planned to take biology, chemistry, or physics during their first year. Use the diagram to answer each question. How many of the surveyed studentsplan to takeonly biology and chemistry during their first year?In Problems 14, a survey of 70college freshmen asked whether students planned to take biology, chemistry, or physics during their first year. Use the diagram to answer each question. How many of the surveyed studentsplan to takeonly physics or chemistry during their first year?5CT 6CT 7CT MMs offers customers the opportunity to create their own color mix of candy. There are 21 colors to choose from, and customers are allowed to select up to 6 different colors. How many different color mixes are possible, assuming that no color is selected more than once and 6 different colors are chosen?9CT 10CT On February 20, 2004, the Ohio Bureau of Motor Vehicles unveiled the states new license plate format. The plate consists of three letters (AZ) followed by 4 digits (09). Assume that all letters and digits may be used, except that the third letter cannot be O,I or Z. If repetitions are allowed, how many different plates are possible?Kiersten applies for admission to the University of Southern California (USC) and Florida State University (FSU). She estimates that she has a 60 chance of being admitted to USC, a 70 chance of being admitted to FSU, and a 35 chance of being admitted to both universities. What is the probability that she will be admitted to either USC or FSU? What is the probability that she will not be admitted to FSU?A cooler contains 8 bottles of Pepsi, 5 bottles of Coke, 4 bottles of Mountain Dew, and 3 bottles of IBC. What is the probability that a bottle chosen at random is Coke? What is the probability that a bottle chosen at random is either Pepsi or IBC?14CT 15CT 16CT 1CR 2CR 3CR 4CR 5CR 6CR 7CR 8CR 9CR 10CR Graph: y=3sin(2x+)12CR 1AYU 2AYU True or false The intersection of two sets is always a subset of their union. (pp. 2-3)4AYU 5AYU 6AYU 7AYU 8AYU 9AYU 10AYU If n( A )=15 , n( B )=20 , and n( AB )=10 , find n( AB ) .If n( A )=30 , n( B )=40 , and n( AB )=45 , find n( AB ) .If n( AB )=50 , n( AB )=10 , and n( B )=20 , find n( A ) .If n( AB )=60 , n( AB )=40 , and n( A )=n( B ) , find n( A ) .In Problems 15-22, use ihe information given in the figure. How many are in set A ?In Problems 15-22, use ihe information given in the figure. How many are in set B ?In Problems 15-22, use ihe information given in the figure. How many are in set A or B ?In Problems 15-22, use ihe information given in the figure. How many are in set A or B ?In Problems 15-22, use ihe information given in the figure. How many are in set A or C ?In Problems 15-22, use ihe information given in the figure. How many are in A and B and C ?In Problems 15-22, use ihe information given in the figure. How many are in A and B and C ?In Problems 15-22, use ihe information given in the figure. How many are in A or B or C ?A man has shirts and ties. How many different shirt-and-tie arrangements can be wear? Blouses and Skirts A woman has 5 blouses and 8 skirts. How many different outfits can she wear?Four-digit Numbers How many four-digit numbers can be formed using the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 if the First digit cannot be 0? Repeated digits are allowed.Five-digit Numbers How many five-digit numbers can be formed using the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 if the first digit cannot be 0 or 1? Repeated digits are allowed.Analyzing Survey Data In a consumer survey of people, indicated that they would be buying a major appliance within the next month, indicated that they would buy a car, andsaid that they would purchase both a major appliance and a car. How many will purchase neither? How many will purchase only a car? Analyzing Survey Data In a student survey, 200 indicated that they would attend Summer Session I, and 150 indicated Summer Session II. If 75 students plan to attend both summer sessions, and 275 indicated that they would attend neither session, how many students participated in the survey?Analyzing Survey Data In a survey of 100 investors in the stock market, 50 owned shares in IBM 40 owned shares in AT&T 45 owned shares in GE 20 owned shares in both IBM and GE 15 owned shares in both AT&T and GE 20 owned shares in both IBM and AT&T a. How many of the investors surveyed did not have shares in any of the three companies? b. How many owned just IBM shares? c. How many owned just GE shares? d. I low many owned neither IBM nor GE? e. I low many owned either IBM or AT&T but no GE?Classifying Blood Types Human blood is classified as either Rh+ or Rh-. Blood is also classified by type: A, if it contains an A antigen but not a B antigen; B, if it contains a B antigen but not an A antigen; AB, if it contains both A and B antigens; and O, if it contains neither antigen. Draw a Venn diagram illustrating the various blood types. Based on this classification, how many different kinds of blood are there?Demographics The following data represent the marital status of males years old and older in the U.S. in. Determine the number of males years old and older who are widowed or divorced. Determine the number of males years old and older who are married , divorced, r separated. Demographics The following data represent the marital status of females years old and older in the U.S. in. Determine the number of females years old and older who are divorced or separated. Determine the number of females years old and older who are married, widowed or divorced. Stock Portfolios As a financial planner, you are asked to select one stock each from the following groups: 8 Dow Jones stocks, 15 NASDAQ stocks, and 4 global stocks. How many different portfolios are possible?34AYU 35AYU 0!= ; 1!= . (p. 642)2AYU A(n) __________ is an ordered arrangement of r objects chosen from n objects.A(n) ___________ is an arrangement of r objects chosen from n distinct objects, without repetition and without regard to order.P( n,r )= __________________.C( n,r )= _______________________.In Problems 7-14, find the value of each permutation. P( 6,2 )In Problems 7-14, find the value of each permutation. P( 7,2 )In Problems 7-14, find the value of each permutation. P( 4,4 )In Problems 7-14, find the value of each permutation. P( 8,8 )In Problems 7-14, find the value of each permutation. P( 7,0 )In Problems 7-14, find the value of each permutation. P( 9,0 )In Problems 7-14, find the value of each permutation. P( 8,4 )In Problems 7-14, find the value of each permutation. P( 8,3 )In Problems 15-22, use formula (2) to find the value of each combination. C( 8,2 )In Problems 15-22, use formula (2) to find the value of each combination. C( 8,6 )In Problems 15-22, use formula (2) to find the value of each combination. C( 7,4 )In Problems 15-22, use formula (2) to find the value of each combination. C( 6,2 )In Problems 15-22, use formula (2) to find the value of each combination. C( 15,15 )In Problems 15-22, use formula (2) to find the value of each combination. C( 18,1 )In Problems 15-22, use formula (2) to find the value of each combination. C( 26,13 )In Problems 15-22, use formula (2) to find the value of each combination. C( 18,9 )List all the ordered arrangements of 5 objects a , b , c , d , and e choosing 3 at a time without repetition. What is P( 5,3 ) ?List all the ordered arrangements of 5 objects a , b , c , d , and e choosing 2 at a time without repetition. What is P( 5,2 ) ?List all the ordered arrangements of 4 objects 1, 2, 3, and 4 choosing 3 at a time without repetition. What is P( 4,3 ) ?List all the ordered arrangements of 6 objects 1, 2, 3, 4, 5, and 6 choosing 3 at a time without repetition. What is P( 6,3 ) ?List all the combinations of 5 objects a , b , c , d , and e taken 3 at a time. What is C( 5,3 ) ?List all the combinationss of 5 objects a , b , c , d , and e taken 2 at a time. What is C( 5,2 ) ?List all the combinations of 4 objects 1, 2, 3, and 4 taken 3 at a time. What is C( 4,3 ) ?List all the combinationss of 6 objects 1, 2, 3, 4, 5, and 6 taken 3 at a time. What is C( 6,3 ) ?Forming Codes How many two-letter codes can be formed using the letters A , B , C , and D ? Repeated letters are allowed.Forming Codes How many two-letter codes can be formed using the letters A , B , C , D , and E ? Repeated letters are allowed.Forming Numbers How many three-digit numbers can be formed using the digits 0 and 1? Repeated digits are allowed.Forming Numbers How many three-digit numbers can be formed using the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9? Repeated digits are allowed.Lining People Up In how many ways can 4 people be lined up?Stacking Boxes In how many ways can 5 different boxes be stacked?Forming Codes How many different three-letter codes are there if only the letters A , B , C , D , and E can be used and no letter can be used more than once?Forming Codes How many different four-letter codes are there if only the letters A , B , C , D , E , and F can be used and no letter can be used more than once?Stocks on the NYSE Companies whose stocks are listed on the New York Stock Exchange (NYSE) have their company name represented by 1, 2, or 3 letters (repetition of letters is allowed). What is the maximum number of companies that can be listed on the NYSE?Stocks on the NASDAQ Companies whose stocks are listed on the NASDAQ stock exchange have their company name represented by either 4 or 5 letters (repetition of letters is allowed). What is the maximum number of companies that can be listed on the NASDAQ?Establishing Committees In how many ways can a committee of 4 students be formed from a pool of 7 students?Establishing Committees In how many ways can a committee of 3 professors be formed from a department that has 8 professors?Possible Answers on a True/False Test How many arrangements of answers are possible for a true/false test with 10 questions?Possible Answers on a Multiple-choice Test How many arrangements of answers are possible in a multiple-choice test with 5 questions, each of which has 4 possible answers?Arranging Books Five different mathematics books are to be arranged on a students desk. How many arrangements are possible?46AYU Birthday Problem In how many ways can 2 people each have different birthdays? Assume that there are 365 days in a year.48AYU 49AYU 50AYU Forming Words How many different 9-letter words (real or imaginary) can be formed from the letters in the word ECONOMICS?52AYU Selecting Objects An urn contains 7 white balls and 3 red balls. Three balls are selected. In how many ways can the 3 balls be drawn from the total of 10 balls: (a) If 2 balls are white and 1 is red? (b) If all 3 balls are white? (c) If all 3 balls are red?54AYU 55AYU 56AYU 57AYU 58AYU 59AYU 60AYU 61AYU 62AYU Combination Locks A combination lock displays 50 numbers. To open it, you turn clockwise to the first number of the combination, then rotate counterclockwise to the second number, and then rotate clockwise to the third number. (a) How many different lock combinations are there? (b) Comment on the description of such a lock as a combination lock.64AYU 65AYU 66AYU When the same probability is assigned to each outcome a sample space, the experiment is said to have _____________ outcomes.2AYU 3AYU 4AYU In a probability model, which of the following numbers could be the probability of an outcome? 00.010.350.411.4 6AYU Determine whether the following is a probability model.8AYU 9AYU 10AYU In Problems 11-16, construct a probability model for each experiment. Tossing a fair coin twice In Problems 11-16, construct a probability model for each experiment. Tossing two fair coins once In Problems 11-16, construct a probability model for each experiment. Tossing two fair coins and then a fair die 14AYU In Problems 11-16, construct a probability model for each experiment. Tossing three fair coins once In Problems 11-16, construct a probability model for each experiment. Tossing one fair coin three times In Problems 17-22, use the following spinners to construct a probability model for each experiment. Spin spinner I, then spinner II. What is the probability of getting a 2 or a 4, followed by Red?In Problems 17-22, use the following spinners to construct a probability model for each experiment. Spin spinner III, then spinner II. What is the probability of getting Forward, followed by Yellow or Green?In Problems 17-22, use the following spinners to construct a probability model for each experiment. Spin spinner I, then II, then III. What is the probability of getting a 1, followed by Red or Green, followed by Backward?In Problems 17-22, use the following spinners to construct a probability model for each experiment. Spin spinner II, then I, then III. What is the probability of getting Yellow, followed by a 2 or a 4, followed by Forward?In Problems 17-22, use the following spinners to construct a probability model for each experiment. Spin spinner I twice, then spinner II. What is the probability of getting a 2, followed by a 2 or a 4, followed by Red or Green?In Problems 17-22, use the following spinners to construct a probability model for each experiment. Spin spinner III, then spinner I twice. What is the probability of getting Forward, followed by a 1 or a 3, followed by a 2 or a 4?In Problems 23-26, consider the experiment of tossing a coin twice. The table lists six possible assignments of probabilities for this experiment. Using this table, answer the following questions. Which of the assignments of probabilities is(are) consistent with the definition of a probability model?In Problems 23-26, consider the experiment of tossing a coin twice. The table lists six possible assignments of probabilities for this experiment. Using this table, answer the following questions. Which of the assignments of probabilities should be used if the coin is known to be fair?25AYU 26AYU Assigning Probabilities A coin is weighted so that heads is four times as likely as tails to occur. What probability should be assigned to heads? to tails?Assigning Probabilities A coin is weighted so that tails is twice as likely as heads to occur. What probability should be assigned to heads? to tails?Assigning Probabilities A die is weighted so that an odd-numbered face is twice as likely to occur as an even-numbered face. What probability should be assigned to each face?Assigning Probabilities A die is weighted so that a six cannot appear. All the other faces occur with the same probability. What probability should be assigned to each face?For Problems 31-34, the sample space is S={ 1,2,3,4,5,6,7,8,9,10 } Suppose that the outcomes are equally likely. Compute the probability of the event E={ 1,2,3 }For Problems 31-34, the sample space is S={ 1,2,3,4,5,6,7,8,9,10 } Suppose that the outcomes are equally likely. Compute the probability of the event F={ 3,5,9,10 }For Problems 31-34, the sample space is S={ 1,2,3,4,5,6,7,8,9,10 } Suppose that the outcomes are equally likely. Compute the probability of the event E : an even number.For Problems 31-34, the sample space is S={ 1,2,3,4,5,6,7,8,9,10 } Suppose that the outcomes are equally likely. Compute the probability of the event F: an odd number.For Problems 35 and 36, an urn contains 5 white marbles, 10 green marbles, 8 yellow marbles, and 7 black marbles. If one marble is selected, determine the probability that it is white.For Problems 35 and 36, an urn contains 5 white marbles, 10 green marbles, 8 yellow marbles, and 7 black marbles. If one marble is selected, determine the probability that it is black.In Problems 37-40, assume equally likely outcomes. Determine the probability of having 3 boys in a 3-child family.In Problems 37-40, assume equally likely outcomes. Determine the probability of having 3 girls in a 3-child family.In Problems 37-40, assume equally likely outcomes. Determine the probability of having 1 girl and 3 boys in a 4-child family.In Problems 37-40, assume equally likely outcomes. Determine the probability of having 2 girls and 2 boys in a 4-child family.41AYU 42AYU 43AYU 44AYU 45AYU In Problems 45-48, find the probability of the indicated event if P( A )=0.25 and P( B )=0.45 P( AB )ifP( AB )=0.6 47AYU 48AYU 49AYU 50AYU Automobile Theft According to the Insurance Information Institute, in 2016 there was a probability that an automobile theft in the United States would be cleared by arrests. If an automobile theft case from 2016 is randomly selected, what is the probability that it was not cleared by an arrest? 52AYU Cat Ownership According to the American Pet Products Manufacturers Associations 2017-2018 National Pet Owners Survey, there is a 38% probability that a U.S. household owns a cat. If a U.S. household is randomly selected, what is the probability that it does not own a cat?Doctorate Degrees According to the National Science Foundation, in 2016 there was a 17.2% probability that a doctoral degree awarded at a U.S. university was awarded in engineering. If a 2016 U.S. doctoral recipient is randomly selected, what is the probability that his or her degree was not in engineering?55AYU 56AYU 57AYU 58AYU 59AYU 60AYU 61AYU 62AYU 63AYU 64AYU 65AYU 66AYU Surveys In a survey about the number of TV sets in a house, the following probability table was constructed: NumberofTVsets01234ormoreProbability0.050.240.330.210.17 Find the probability of a house having: 1 or 2 TV sets 1 or more TV sets 3 or fewer TV sets 3 or more TV sets Fewer than 2 TV sets Fewer than 1 TV sets 1,2 or 3 TV sets 2 or more TV sets 68AYU 69AYU 70AYU 71AYU 72AYU 73AYU 1RE 2RE 3RE 4RE 5RE 6RE 7RE 8RE 9RE 10RE 11RE 12RE 13RE 14RE 15RE 16RE

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