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college algebra graphs and models
College Algebra 7th Edition Robert F Blitzer - Solutions
The table shows the population of Florida for 2000 and 2010, with estimates given by the U.S. Census Bureau for 2001 through 2009.a. Divide the population, for each year by the population in the preceding year. Round to two decimal places and show that Florida has a population increase that is
Exercises 49–51 will help you prepare for the material covered in the next section. Each exercise involves observing a pattern in the expanded form of the binomial expression (a + b)n.Describe the pattern for the sum of the exponents on the variables in each term. (a + b)¹ = a + b (a + b)² =
Use the formula for nCr to solve Exercises 49–56.A four-person committee is to be elected from an organization’s membership of 11 people. How many different committees are possible?
In Exercises 43–54, express each sum using summation notation. Use 1 as the lower limit of summation and i for the index of summation 4 + 2 + 3 + 4" | n
Use the graphs of the arithmetic sequences {an} and {bn} to solve Exercises 51–58.Find a16 + b18. bn "D 100 PA LOO CN 00 C n n 910 G menja ह्म प्रै HH
In Exercises 50–51, express each repeating decimal as a fraction in lowest terms.0.6̅
In Exercises 53–54, find and simplify.f(x) = x4 + 7 f(x +h)-f(x) h
In Exercises 49–52, a single die is rolled twice. Find the probability of rollingan even number the first time and a number greater than 2 the second time.
Use the formula for nCr to solve Exercises 49–56.Of 12 possible books, you plan to take 4 with you on vacation. How many different collections of 4 books can you take?
In Exercises 43–54, express each sum using summation notation. Use 1 as the lower limit of summation and i for the index of summation 1 9 + 2 92 + 3 + + n 9n
Use the graphs of the arithmetic sequences {an} and {bn} to solve Exercises 51–58.If {an} is a finite sequence whose last term is -83, how many terms does {an} contain? bn "D 100 PA LOO CN 00 C n n 910 G menja ह्म प्रै HH
In Exercises 51–56, the general term of a sequence is given. Determine whether the sequence is arithmetic, geometric, or neither. If the sequence is arithmetic, find the common difference; if it is geometric, find the common ratio.an = n + 5
In Exercises 50–51, express each repeating decimal as a fraction in lowest terms.0.4̅7̅
In Exercises 49–52, a single die is rolled twice. Find the probability of rolling an odd number the first time and a number less than 3 the second time.
Use the graphs of the arithmetic sequences {an} and {bn} to solve Exercises 51–58.If {bn} is a finite sequence whose last term is 93, how many terms does {bn} contain? bn "D 100 PA LOO CN 00 C n n 910 G menja ह्म प्रै HH
Use the formula for nCr to solve Exercises 49–56.There are 14 standbys who hope to get seats on a flight, but only 6 seats are available on the plane. How many different ways can the 6 people be selected?
In Exercises 53–54, find and simplify.f(x) = x5 + 8 f(x +h)-f(x) h
In Exercises 51–56, the general term of a sequence is given. Determine whether the sequence is arithmetic, geometric, or neither. If the sequence is arithmetic, find the common difference; if it is geometric, find the common ratio.an = n - 3
The probability that South Florida will be hit by a major hurricane (category 4 or 5) in any single year is 1 1/6.a. What is the probability that South Florida will be hit by a major hurricane two years in a row?b. What is the probability that South Florida will be hit by a major hurricane in three
If you toss a fair coin six times, what is the probability of getting all heads?
Use the formula for nCr to solve Exercises 49–56.You volunteer to help drive children at a charity event to the zoo, but you can fit only 8 of the 17 children present in your van. How many different groups of 8 children can you drive?
Find the middle term in the expansion of 3 X + 3 X 10
In Exercises 51–56, the general term of a sequence is given. Determine whether the sequence is arithmetic, geometric, or neither. If the sequence is arithmetic, find the common difference; if it is geometric, find the common ratio.an = 2n
Use the graphs of the arithmetic sequences {an} and {bn} to solve Exercises 51–58.Find the difference between the sum of the first 14 terms of {bn} and the sum of the first 14 terms of {an}. bn "D 100 PA LOO CN 00 C n n 910 G menja ह्म प्रै HH
In Exercises 43–54, express each sum using summation notation. Use 1 as the lower limit of summation and i for the index of summation1 + 3 + 5 + g+ (2n - 1)
A job pays $32,000 for the first year with an annual increase of 6% per year beginning in the second year. What is the salary in the sixth year? What is the total salary paid over this six-year period? Round answers to the nearest dollar.
Use the graphs of the arithmetic sequences {an} and {bn} to solve Exercises 51–58.Find the difference between the sum of the first 15 terms of {bn} and the sum of the first 15 terms of {an}. bn "D 100 PA LOO CN 00 C n n 910 G menja ह्म प्रै HH
If you toss a fair coin seven times, what is the probability of getting all tails?
In Exercises 54–55, use the formula for the value of an annuity and round to the nearest dollar.You spend $10 per week on lottery tickets, averaging $520 per year. Instead of buying tickets, if you deposited the $520 at the end of each year in an annuity paying 6% compounded annually,a. How much
Use the formula for nCr to solve Exercises 49–56.Of the 100 people in the U.S. Senate, 18 serve on the Foreign Relations Committee. How many ways are there to select Senate members for this committee (assuming party affiliation is not a factor in selection)?
Find the middle term in the expansion of 12 ( 1² - x²) ¹₁².
In Exercises 51–56, the general term of a sequence is given. Determine whether the sequence is arithmetic, geometric, or neither. If the sequence is arithmetic, find the common difference; if it is geometric, find the common ratio.an = (1/2)n
In Exercises 43–54, express each sum using summation notation. Use 1 as the lower limit of summation and i for the index of summationa + ar + ar2 + g+ arn-1
The graph shows that U.S. smokers have a greater probability of suffering from some ailments than the general adult population. Exercises 57–58 are based on some of the probabilities, expressed as decimals, shown to the right of the bars. In each exercise, use a calculator to determine the
In Exercises 54–55, use the formula for the value of an annuity and round to the nearest dollar.To save for retirement, you decide to deposit $100 at the end of each month in an IRA that pays 5.5% compounded monthly.a. How much will you have from the IRA after 30 years?b. Find the interest.
Use the formula for nCr to solve Exercises 49–56.To win at LOTTO in the state of Florida, one must correctly select 6 numbers from a collection of 53 numbers (1 through 53). The order in which the selection is made does not matter. How many different selections are possible?
In Exercises 51–56, the general term of a sequence is given. Determine whether the sequence is arithmetic, geometric, or neither. If the sequence is arithmetic, find the common difference; if it is geometric, find the common ratio.an = n2 + 5
In Exercises 55–60, express each sum using summation notation. Use a lower limit of summation of your choice and k for the index of summation.5 + 7 + 9 + 11 +.....+ 31
Use the graphs of the arithmetic sequences {an} and {bn} to solve Exercises 51–58.Write a linear function f(x) = mx + b, whose domain is the set of positive integers, that represents {an}. bn "D 100 PA LOO CN 00 C n n 910 G menja ह्म प्रै HH
The graph shows that U.S. smokers have a greater probability of suffering from some ailments than the general adult population. Exercises 57–58 are based on some of the probabilities, expressed as decimals, shown to the right of the bars. In each exercise, use a calculator to determine the
In Exercises 57–61, use mathematical induction to prove that each statement is true for every positive integer n. 1 + 4 + 4² + · +42-1 4" - 1 3
Use the graphs of the arithmetic sequences {an} and {bn} to solve Exercises 51–58.Write a linear function g(x) = mx + b, whose domain is the set of positive integers, that represents {bn}. bn "D 100 PA LOO CN 00 C n n 910 G menja ह्म प्रै HH
Use the formula for nCr to solve Exercises 49–56.To win in the New York State lottery, one must correctly select 6 numbers from 59 numbers. The order in which the selection is made does not matter. How many different selections are possible?
In Exercises 57–61, use mathematical induction to prove that each statement is true for every positive integer n. 5 + 10 + 15 + ... + 5n 5n(n+1) 2
In Exercises 51–56, the general term of a sequence is given. Determine whether the sequence is arithmetic, geometric, or neither. If the sequence is arithmetic, find the common difference; if it is geometric, find the common ratio.an = n2 - 3
In Exercises 55–60, express each sum using summation notation. Use a lower limit of summation of your choice and k for the index of summation.6 + 8 + 10 + 12 +......+ 32
Describe the difference between theoretical probability and empirical probability.
A factory in an isolated town has an annual payroll of $4 million. It is estimated that 70% of this money is spent within the town, that people in the town receiving this money will again spend 70% of what they receive in the town, and so on. What is the total of all this spending in the town each
In Exercises 57–66, solve by the method of your choice.In a race in which six automobiles are entered and there are no ties, in how many ways can the first four finishers come in?
In Exercises 57–62, let{an} = -5, 10, -20, 40, . . . ,{bn} = 10, -5, -20, -35, . . . ,{cn} = -2, 1, - 1/2, 1/4, . . . .Find a10 + b10.
Give an example of an event whose probability must be determined empirically rather than theoretically.
In Exercises 55–60, express each sum using summation notation. Use a lower limit of summation of your choice and k for the index of summation.a + ar + ar2 +.....+ ar12
In Exercises 57–61, use mathematical induction to prove that each statement is true for every positive integer n. 1.3+2 4+3·5+ ··· + n(n + 2) = ... = n(n + 1)(2n + 7) 6
In Exercises 57–61, use mathematical induction to prove that each statement is true for every positive integer n. 2 + 6 + 10 + . + (4n - 2) = 2n²
In Exercises 57–66, solve by the method of your choice.A book club offers a choice of 8 books from a list of 40. In how many ways can a member make a selection?
Explain how to evaluate Provide an example with your explanation. n r
In Exercises 55–60, express each sum using summation notation. Use a lower limit of summation of your choice and k for the index of summation.a + ar + ar2 + g+ ar14
In Exercises 57–62, let{an} = -5, 10, -20, 40, . . . ,{bn} = 10, -5, -20, -35, . . . ,{cn} = -2, 1, - 1/2, 1/4, . . . .Find a11 + b11.
Write a probability word problem whose answer is one of the following fractions: 1/6 or 1/4 or 1/3.
The bar graph shows changes in the percentage of college graduates for Americans ages 25 and older from 1990 to 2010. Exercises 61–62 involve developing arithmetic sequences that model the data.In 1990, 18.4% of American women ages 25 and older had graduated from college. On average, this
In Exercises 61–68, use the graphs of {an} and {bn} to find each indicated sum. The Graph of {a} an -1 1. 23 st 50 ITT 20 3 4 5 HA n The Graph of {b} b₁ 4 1 1 -2 ….….……….…….….…….……………… +5 2 3 4 5 n
In Exercises 57–66, solve by the method of your choice.A medical researcher needs 6 people to test the effectiveness of an experimental drug. If 13 people have volunteered for the test, in how many ways can 6 people be selected?
In Exercises 61–68, use the graphs of {an} and {bn} to find each indicated sum. The Graph of {a} an -1 1. 23 st 50 ITT 20 3 4 5 HA n The Graph of {b} b₁ 4 1 1 -2 ….….……….…….….…….……………… +5 2 3 4 5 n
Use a system of two equations in two variables, a1 and d, to solve Exercises 59–60.Write a formula for the general term (the nth term) of the arithmetic sequence whose second term, a2, is 4 and whose sixth term, a6, is 16.
In Exercises 55–60, express each sum using summation notation. Use a lower limit of summation of your choice and k for the index of summation.a + (a + d) + (a + 2d) + g+ (a + nd)
In Exercises 57–62, let{an} = -5, 10, -20, 40, . . . ,{bn} = 10, -5, -20, -35, . . . ,{cn} = -2, 1, - 1/2, 1/4, . . . .Find the difference between the sum of the first 10 terms of {an} and the sum of the first 10 terms of {bn}.
Explain how to find the probability of an event not occurring. Give an example.
The bar graph shows changes in the percentage of college graduates for Americans ages 25 and older from 1990 to 2010. Exercises 61–62 involve developing arithmetic sequences that model the data.In 1990, 24.4% of American men ages 25 and older had graduated from college. On average, this
In Exercises 57–66, solve by the method of your choice.Fifty people purchase raffle tickets. Three winning tickets are selected at random. If first prize is $1000, second prize is $500, and third prize is $100, in how many different ways can the prizes be awarded?
In Exercises 61–68, use the graphs of {an} and {bn} to find each indicated sum. The Graph of {a} an -1 1. 23 st 50 ITT 20 3 4 5 HA n The Graph of {b} b₁ 4 1 1 -2 ….….……….…….….…….……………… +5 2 3 4 5 n
Use a system of two equations in two variables, a1 and d, to solve Exercises 59–60.Write a formula for the general term (the nth term) of the arithmetic sequence whose third term, a3, is 7 and whose eighth term, a8, is 17.
In Exercises 55–60, express each sum using summation notation. Use a lower limit of summation of your choice and k for the index of summation.(a + d) + (a + d2) + g+ (a + dn)
In Exercises 57–62, let{an} = -5, 10, -20, 40, . . . ,{bn} = 10, -5, -20, -35, . . . ,{cn} = -2, 1, - 1/2, 1/4, . . . .Find the difference between the sum of the first 11 terms of {an} and the sum of the first 11 terms of {bn}.
What are mutually exclusive events? Give an example of two events that are mutually exclusive.
Use one of the models in Exercises 65–66 and the formula for Sn to find the total dormitory charges for your undergraduate education. How well does the model describe your anticipated costs?Data from Exercise 65The bar graph shows the average dormitory charges at public and private four-year U.S.
Describe the pattern in the exponents on a in the expansion of (a + b)n.
In Exercises 61–68, use the graphs of {an} and {bn} to find each indicated sum. The Graph of {a} an -1 1. 23 st 50 ITT 20 3 4 5 HA n The Graph of {b} b₁ 4 1 1 -2 ….….……….…….….…….……………… +5 2 3 4 5 n
In Exercises 57–66, solve by the method of your choice.From a club of 20 people, in how many ways can a group of three members be selected to attend a conference?
In Exercises 62–63, evaluate the given binomial coefficient. 11 8
In Exercises 57–62, let{an} = -5, 10, -20, 40, . . . ,{bn} = 10, -5, -20, -35, . . . ,{cn} = -2, 1, - 1/2, 1/4, . . . .Find the product of the sum of the first 6 terms of {an} and the sum of the infinite series containing all the terms of {cn}.
In Exercises 57–61, use mathematical induction to prove that each statement is true for every positive integer n.2 is a factor of n2 + 5n.
Explain how to find or probabilities with mutually exclusive events. Give an example.
The table shows the population of California for 2000 and 2010, with estimates given by the U.S. Census Bureau for 2001 through 2009.a. Divide the population for each year by the population in the preceding year. Round to two decimal places and show that California has a population increase that is
Describe the pattern in the exponents on b in the expansion of (a + b)n.
The bar graph at the top of the next column shows the average number of hours per day that U.S. adult users spent on digital media (desktop/laptop, mobile, and other devices) from 2008 through 2014.Let an represent the average number of hours per day that U.S. adult users spent on digital media n
In Exercises 57–66, solve by the method of your choice.Fifty people purchase raffle tickets. Three winning tickets are selected at random. If each prize is $500, in how many different ways can the prizes be awarded?
In Exercises 57–62, let{an} = -5, 10, -20, 40, . . . ,{bn} = 10, -5, -20, -35, . . . ,and {cn} = -2, 1, - 1/2, 1/4, . . . .Find the product of the sum of the first 9 terms of {an} and the sum of the infinite series containing all the terms of {cn}.
The table shows the population of Texas for 2000 and 2010, with estimates given by the U.S. Census Bureau for 2001 through 2009.a. Divide the population for each year by the population in the preceding year. Round to two decimal places and show that Texas has a population increase that is
Explain how to find or probabilities with mutually exclusive events. Give an example.
The bar graph shows the number of Americans who renounced their U.S. citizenship, many over tax laws, from 2010 through 2014.Let an represent the number of Americans who gave up their U.S. citizenship n years after 2009. Number of People Renouncing Their U.S.
What is true about the sum of the exponents on a and b in any term in the expansion of (a + b)n?
In Exercises 57–66, solve by the method of your choice.How many different four-letter passwords can be formed from the letters A, B, C, D, E, F, and G if no repetition of letters is allowed?
In Exercises 68–69, graph each of the functions in the same viewing rectangle. Describe how the graphs illustrate the Binomial Theorem. fi(x) = (x + 2)³ f3(x) = x³ + 6x²2 f₂(x) = x³ f4(x) = x³ + 6x² + 12x 3 fs(x) = x³ + 6x² + 12x + 8 Use a [-10, 10, 1] by [-30, 30, 10] viewing rectangle.
In Exercises 68–69, graph each of the functions in the same viewing rectangle. Describe how the graphs illustrate the Binomial Theorem. fi(x) = (x + 1)4 f3(x) = x² + 4x³ f₂(x) = x² f4(x) = x4 + 4x³ + 6x² fs(x) = x² + 4x³ + 6x² + 4x f(x) = x² + 4x³ + 6x² + 4x + 1 Use a [-5, 5, 1] by
Explain how to find or probabilities with events that are not mutually exclusive. Give an example.
Exercises 67–72 are based on the following jokes about books:• “Outside of a dog, a book is man’s best friend. Inside of a dog, it’s too dark to read.”—Groucho Marx• “I recently bought a book of free verse. For $12.” —George Carlin• “If a word in the dictionary was
In Exercises 64–67, use the Binomial Theorem to expand each binomial and express the result in simplified form.(x - 2)6
In Exercises 66–69, determine whether each statement makes sense or does not make sense, and explain your reasoning.Assuming the next U.S. president will be a Democrat or a Republican, the probability of a Republican president is 0.5.
Exercises 67–72 are based on the following jokes about books:• “Outside of a dog, a book is man’s best friend. Inside of a dog, it’s too dark to read.”—Groucho Marx• “I recently bought a book of free verse. For $12.” —George Carlin• “If a word in the dictionary was
In Exercises 68–69, write the first three terms in each binomial expansion, expressing the result in simplified form.(x - 3)9
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