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College Algebra 7th Edition Robert F Blitzer - Solutions
In Exercises 17–20, does the problem involve permutations or combinations? Explain your answer.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
In Exercises 19–21, write a formula for the general term (the nth term) of each arithmetic sequence. Do not use a recursion formula. Then use the formula for an to find a20, the 20th term of the sequence.-7, -3, 1, 5,.....
In Exercises 19–22, the general term of a sequence is given and involves a factorial. Write the first four terms of each sequence. an (n + 1)! n2
In Exercises 11–24, use mathematical induction to prove that each statement is true for every positive integer n. 2 + 1 4 + 100 8 + . . + + 1 2n = 1 1 2n
In Exercises 17–24, write a formula for the general term (the nth term) of each geometric sequence. Then use the formula for an to find a7, the seventh term of the sequence.18, 6, 2, 2/3, . . . .
In Exercises 17–20, you are dealt one card from a standard 52-card deck. Find the probability of being dealt a picture card.
In Exercises 11–24, use mathematical induction to prove that each statement is true for every positive integer n.2 + 4 + 8 +........+ 2n = 2n+1 - 2
In Exercises 9–30, use the Binomial Theorem to expand each binomial and express the result in simplified form.(y - 3)4
In Exercises 15–22, find the indicated term of the arithmetic sequence with first term, a1, and common difference, d.Find a200 when a1 = -40, d = 5.
In Exercises 10–22, solve each equation, inequality, or system of equations. (Use matrices.) x - 2y + z = 16 14 2x y z = - - 3x + 5y - 4z = -10
From the ten books that you’ve recently bought but not read, you plan to take four with you on vacation. How many different sets of four books can you take?
In Exercises 11–24, use mathematical induction to prove that each statement is true for every positive integer n. 1.2 +2.3 + 3.4 + ... + n(n+1) n(n + 1)(n + 2) 3
In Exercises 19–21, write a formula for the general term (the nth term) of each arithmetic sequence. Do not use a recursion formula. Then use the formula for an to find a20, the 20th term of the sequence.a1 = 200, d = -20
In Exercises 17–20, does the problem involve permutations or combinations? Explain your answer.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 21–28, evaluate each expression. 7P3 3! 7C3
In Exercises 9–30, use the Binomial Theorem to expand each binomial and express the result in simplified form.(y - 4)4
In Exercises 17–24, write a formula for the general term (the nth term) of each geometric sequence. Then use the formula for an to find a7, the seventh term of the sequence.12, 6, 3, 3/2, . . . .
In Exercises 17–20, you are dealt one card from a standard 52-card deck. Find the probability of being dealt a card greater than 3 and less than 7.
In Exercises 10–22, solve each equation, inequality, or system of equations. [x - y = 1 √x² - x - y = 1
In Exercises 15–22, find the indicated term of the arithmetic sequence with first term, a1, and common difference, d.Find a150 when a1 = -60, d = 5.
A class is collecting data on eye color and gender. They organize the data they collected into the table shown. Numbers in the table represent the number of students from the class that belong to each of the categories. Use the data to solve Exercises 22–25. Express probabilities as simplified
In Exercises 11–24, 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 19–21, write a formula for the general term (the nth term) of each arithmetic sequence. Do not use a recursion formula. Then use the formula for an to find a20, the 20th term of the sequence.an = an-1 - 5, a1 = 3
In Exercises 17–20, does the problem involve permutations or combinations? Explain your answer.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 19–22, the general term of a sequence is given and involves a factorial. Write the first four terms of each sequence.an = 2(n + 1)!
In Exercises 17–24, write a formula for the general term (the nth term) of each geometric sequence. Then use the formula for an to find a7, the seventh term of the sequence.1.5, -3, 6, -12, . . .
How many seven-digit local telephone numbers can be formed if the first three digits are 279?
In Exercises 21–22, a fair coin is tossed two times in succession. The sample space of equally likely outcomes is {HH, HT, TH, TT}. Find the probability of getting two heads.
In Exercises 9–30, use the Binomial Theorem to expand each binomial and express the result in simplified form.(2x3 - 1)4
In Exercises 21–28, evaluate each expression. 20P2 2! 20€₂
In Exercises 23–28, evaluate each factorial expression. 17! 15!
In Exercises 15–22, find the indicated term of the arithmetic sequence with first term, a1, and common difference, d.Find a60 when a1 = 35, d = -3.
A class is collecting data on eye color and gender. They organize the data they collected into the table shown. Numbers in the table represent the number of students from the class that belong to each of the categories. Use the data to solve Exercises 22–25. Express probabilities as simplified
Find the sum of the first 22 terms of the arithmetic sequence: 5, 12, 19, 26, . . . .
In Exercises 11–24, use mathematical induction to prove that each statement is true for every positive integer n. 1 + 1.2 1 + 2.3 1 + 3.4 + 1 n(n + 1) n n + 1
In Exercises 19–22, the general term of a sequence is given and involves a factorial. Write the first four terms of each sequence.an = -2(n - 1)!
In Exercises 17–24, write a formula for the general term (the nth term) of each geometric sequence. Then use the formula for an to find a7, the seventh term of the sequence.5, -1, 1/5, - 1/25, . . . .
In Exercises 21–22, a fair coin is tossed two times in succession. The sample space of equally likely outcomes is {HH, HT, TH, TT}. Find the probability of getting the same outcome on each toss.
A class is collecting data on eye color and gender. They organize the data they collected into the table shown. Numbers in the table represent the number of students from the class that belong to each of the categories. Use the data to solve Exercises 22–25. Express probabilities as simplified
In Exercises 9–30, use the Binomial Theorem to expand each binomial and express the result in simplified form.(2x5 - 1)4
In Exercises 15–22, find the indicated term of the arithmetic sequence with first term, a1, and common difference, d.Find a70 when a1 = -32, d = 4.
In Exercises 21–28, evaluate each expression. 1 3P2 4P3
In Exercises 23–28, evaluate each factorial expression. 18! 16!
In Exercises 23–34, write a formula for the general term (the nth term) of each arithmetic sequence. Do not use a recursion formula. Then use the formula for an to find a20, the 20th term of the sequence.1, 5, 9, 13,......
In Exercises 11–24, use mathematical induction to prove that each statement is true for every positive integer n. 1 + 2.3 1 + 3.4 1 4.5 + . + 1 (n + 1)(n + 2) n 2n + 4
In Exercises 23–29, graph each equation, function, or system in a rectangular coordinate system. If two functions are indicated, graph both in the same system.100x2 + y2 = 25
In Exercises 23–29, graph each equation, function, or system in a rectangular coordinate system. If two functions are indicated, graph both in the same system. f(x) = x² - 1 X x 2
Find the sum of the first 15 terms of the arithmetic sequence: -6, -3, 0, 3, . . . .
In Exercises 17–24, write a formula for the general term (the nth term) of each geometric sequence. Then use the formula for an to find a7, the seventh term of the sequence.0.0004, -0.004, 0.04, -0.4, . . .
A class is collecting data on eye color and gender. They organize the data they collected into the table shown. Numbers in the table represent the number of students from the class that belong to each of the categories. Use the data to solve Exercises 22–25. Express probabilities as simplified
In Exercises 23–24, you select a family with three children. If M represents a male child and F a female child, the sample space of equally likely outcomes is {MMM, MMF, MFM, MFF, FMM, FMF, FFM, FFF}. Find the probability of selecting a family withat least one male child.
In Exercises 23–29, graph each equation, function, or system in a rectangular coordinate system. If two functions are indicated, graph both in the same system.4x2 - 9y2 - 16x + 54y - 29 = 0
In Exercises 9–30, use the Binomial Theorem to expand each binomial and express the result in simplified form.(c + 2)5
In Exercises 21–28, evaluate each expression. 1 5P3 10P4
In Exercises 23–28, evaluate each factorial expression. 16! 2!14!
In Exercises 23–34, write a formula for the general term (the nth term) of each arithmetic sequence. Do not use a recursion formula. Then use the formula for an to find a20, the 20th term of the sequence.2, 7, 12, 17,.......
In Exercises 25–27, use the formula for the sum of the first n terms of an arithmetic sequence to find the indicated sum. 16 Σ (3i + 2) i=1
In Exercises 25–26, a single die is rolled twice. The 36 equally likely outcomes are shown as follows:Find the probability of gettingtwo numbers whose sum is 4. First Roll Second Roll (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)
Find 3 + 6 + 9 +......+ 300, the sum of the first 100 positive multiples of 3.
In Exercises 17–24, write a formula for the general term (the nth term) of each geometric sequence. Then use the formula for an to find a7, the seventh term of the sequence.0.0007, -0.007, 0.07, -0.7, . . .
In Exercises 23–24, you select a family with three children. If M represents a male child and F a female child, the sample space of equally likely outcomes is {MMM, MMF, MFM, MFF, FMM, FMF, FFM, FFF}. Find the probability of selecting a family with At least two female children.
In Exercises 23–29, graph each equation, function, or system in a rectangular coordinate system. If two functions are indicated, graph both in the same system. 2x - y = 4 x ≤ 2
In Exercises 9–30, use the Binomial Theorem to expand each binomial and express the result in simplified form.(c + 3)5
In Exercises 21–28, evaluate each expression. 98! 7C3 5C4 96!
In Exercises 23–28, evaluate each factorial expression. 20! 2!18!
In Exercises 23–34, write a formula for the general term (the nth term) of each arithmetic sequence. Do not use a recursion formula. Then use the formula for an to find a20, the 20th term of the sequence.7, 3, -1, -5,.......
In Exercises 25–27, use the formula for the sum of the first n terms of an arithmetic sequence to find the indicated sum. 25 Σ (2i + 6) i=1
Use the formula for the sum of the first n terms of a geometric sequence to solve Exercises 25–30.Find the sum of the first 12 terms of the geometric sequence: 2, 6, 18, 54, . . . .
In Exercises 25–34, use mathematical induction to prove that each statement is true for every positive integer n.2 is a factor of n2 - n.
In Exercises 9–30, use the Binomial Theorem to expand each binomial and express the result in simplified form.(x - 1)5
In Exercises 23–34, write a formula for the general term (the nth term) of each arithmetic sequence. Do not use a recursion formula. Then use the formula for an to find a20, the 20th term of the sequence.6, 1, -4, -9,......
A lottery game is set up so that each player chooses six different numbers from 1 to 15. If the six numbers match the six numbers drawn in the lottery, the player wins (or shares) the top cash prize. What is the probability of winning the prize with 50 different lottery tickets?
Use the formula for the sum of the first n terms of a geometric sequence to solve Exercises 25–30.Find the sum of the first 12 terms of the geometric sequence: 3, 6, 12, 24, . . . .
In Exercises 25–26, a single die is rolled twice. The 36 equally likely outcomes are shown as follows:Find the probability of gettingtwo numbers whose sum is 6. First Roll Second Roll (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)
Write the first five terms of the sequence whose general term is an (-1)"+1 се
In Exercises 1–8, evaluate the given binomial coefficient. 3
In Exercises 1–6, write the first four terms of each sequence whose general term is given. n+ an − (−1)n¹ + 2 n+ 1
The figure shows the graph of y = f(x) and its vertical asymptote. Use the graph to solve Exercises 1–9.Does f have a relative maximum or a relative minimum? What is this relative maximum or minimum and where does it occur? 200 y = f(x) -5-4-3-2-1 17 H cr |||| 2 3 4 5 T HH X
Shown again is the table indicating the marital status of the U.S. population in 2010. Numbers in the table are expressed in millions. Use the data in the table to solve Exercises 1–10. Express probabilities as simplified fractions and as decimals rounded to the nearest hundredth.If one person is
In Exercises 1–4, a statement Sn about the positive integers is given. Write statements S1, S2, and S3, and show that each of these statements is true. Sn: 3+ 4+ 5+ + (n + 2) ... n(n + 5) 2
In Exercises 1–4, a statement Sn about the positive integers is given. Write statements S1, S2, and S3, and show that each of these statements is true.Sn : 1 + 3 + 5 + g + (2n - 1) = n2
In Exercises 2–4, find each indicated sum. 5 Σ (2 + 10) i=1
In Exercises 1–8, use the formula for nPr to evaluate each expression.9P4
In Exercises 1–14, write the first six terms of each arithmetic sequence.a1 = 200, d = 20
Fill in each blank so that the resulting statement is true.A sequence in which each term after the first is obtained by multiplying the preceding term by a fixed nonzero constant is called a/an_______ sequence. The amount by which we multiply each time is called the___________ of the sequence.
In Exercises 1–8, evaluate the given binomial coefficient. 2
In Exercises 1–8, write the first five terms of each geometric sequence.a1 = 4, r = 3
In Exercises 1–6, write the first four terms of each sequence whose general term is given. an || 1 (n-1)!
Shown again is the table indicating the marital status of the U.S. population in 2010. Numbers in the table are expressed in millions. Use the data in the table to solve Exercises 1–10. Express probabilities as simplified fractions and as decimals rounded to the nearest hundredth.If one person is
In Exercises 1–12, write the first four terms of each sequence whose general term is given.an = 4n - 1
Fill in each blank so that the resulting statement is true. The nth term of a sequence, represented by an, is called the term_______.
The figure shows the graph of y = f(x) and its vertical asymptote. Use the graph to solve Exercises 1–9.Find the interval on which f is decreasing. 200 y = f(x) -5-4-3-2-1 17 H cr |||| 2 3 4 5 T HH X
Fill in each blank so that the resulting statement is true.Consider the statement 2 + 4 + 6 + g + 2n = n(n + 1).If n = 1, the statement is 2 = 1(1 + 1).If n = 2, the statement is 2 + 4 = 2(2 + 1).If n = 3, the statement is________ .If n = k + 1, the statement is_________ .
Fill in each blank so that the resulting statement is true.The set of all possible outcomes of an experiment is called the________ of the experiment.
Fill in each blank so that the resulting statement is true.The nth term of the sequence described in Exercise 1 is given by the formula an =_______ , where a1 is the______ and d is the_______ of the sequence.
In Exercises 1–14, write the first six terms of each arithmetic sequence.a1 = 300, d = 50
In Exercises 2–4, find each indicated sum. 20 Σ (3i – 4) i=1
Fill in each blank so that the resulting statement is true.The number of ways in which a series of successive things can occur is found by_______ the number of ways in which each thing can occur. This is called the_________ Principle.
Fill in each blank so that the resulting statement is true.The nth term of the sequence described in Exercise 1 is given by the formula an =_______ , where a1 is the_______ and r is the______ of the sequence.
In Exercises 1–8, write the first five terms of each geometric sequence.a1 = 20, r = 1/2
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