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College Algebra 7th Edition Robert F Blitzer - Solutions
In Exercises 1–8, evaluate the given binomial coefficient. 12 1
In Exercises 1–12, write the first four terms of each sequence whose general term is given.an = 3n
The figure shows the graph of y = f(x) and its vertical asymptote. Use the graph to solve Exercises 1–9.Is f even, odd, or neither? 200 y = f(x) -5-4-3-2-1 17 H cr |||| 2 3 4 5 T HH X
Write the second term of each sequence. an = 5n - 6______ .
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 : 2 is a factor of n2 - n.
Fill in each blank so that the resulting statement is true.Consider the statement 3 + 7 + 11 + g+ (4n - 1) = n(2n + 1).If n = 1, the statement is 3 = 1(2 + 1).If n = 2, the statement is 3 + 7 = 2(4 + 1).If n = 3, the statement is________ .If n = k + 1, the statement before the algebra is simplified
Fill in each blank so that the resulting statement is true.The number of possible permutations if r objects are taken from n items is nPr =_________ .
Fill in each blank so that the resulting statement is true.The sum, Sn, of the first n terms of the sequence described in Exercise 1 is given by the formula Sn =_____ , where a1 is the______ and r is the______ , r ≠ 1.
Fill in each blank so that the resulting statement is true.The theoretical probability of event E, denoted by_______ , is the________ divided by the_________ .
Fill in each blank so that the resulting statement is true.The sum, Sn, of the first n terms of the sequence described in Exercise 1 is given by the formula Sn =________ , where a1 is the_______ and an is the______ .
In Exercises 1–14, write the first six terms of each arithmetic sequence.a1 = -7, d = 4
In Exercises 1–8, use the formula for nPr to evaluate each expression.8P5
In Exercises 1–6, write the first four terms of each sequence whose general term is given. . an || (-1)^²+1 2"
In Exercises 1–8, write the first five terms of each geometric sequence.a1 = 24, r = 1/3
Fill in each blank so that the resulting statement is true. an = (-1)n/4n - 1_______ .
In Exercises 1–12, write the first four terms of each sequence whose general term is given. 3 n
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 2–4, find each indicated sum. 15 Σ(-2) 1-1
In Exercises 1–8, evaluate the given binomial coefficient. 11 1
Fill in each blank so that the resulting statement is true.The first term of _______ . and the last term is_______ . 20 Σ(6 – 4) i=1
Fill in each blank so that the resulting statement is true.A sequence of equal payments made at equal time periods is called a/an_______ . Its value, A, after t years is given by the formulawhere_______ is the deposit made at the end of each compounding period at_______ percent annual interest
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 is a factor of n3 - n.
Fill in each blank so that the resulting statement is true.Consider the statement 2 is a factor of n2 + 3n.If n = 1, the statement is 2 is a factor of_______ .If n = 2, the statement is 2 is a factor of_______ .If n = 3, the statement is 2 is a factor of________ .If n = k + 1, the statement before
Fill in each blank so that the resulting statement is true.A standard bridge deck has________ cards with four suits:________ and_______ are red, and________ and_______ are black.
In Exercises 1–6, write the first four terms of each sequence whose general term is given. a1 = 9 and an 2 3an-1 for n ≥ 2
Fill in each blank so that the resulting statement is true.The number of possible combinations if r objects are taken from n items is nCr =_________ .
Fill in each blank so that the resulting statement is true.The sum of the exponents on a and b in each term is______ . (a + b)" = n an + an-26² + an-lb + an-363 + + bn
In Exercises 5–7, evaluate each expression.
Fill in each blank so that the resulting statement is true.The first three terms of are______ ,________ , and______ . The common difference is________ . 17 i=1 (5i + 3)
In Exercises 1–8, use the formula for nPr to evaluate each expression.10P4
In Exercises 1–14, write the first six terms of each arithmetic sequence.a1 = -8, d = 5
In Exercises 1–8, evaluate the given binomial coefficient.
In Exercises 1–8, write the first five terms of each geometric sequence.an = -4an-1, a1 = 10
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 = (-3)n
Fill in each blank so that the resulting statement is true.an = 2an-1 - 4, a1 = 3_____ .
In Exercises 1–6, write the first four terms of each sequence whose general term is given. a1 4 and an 2an-13 for n ≥ 2
In Exercises 5–10, a statement Sn about the positive integers is given. Write statements Sk and Sk+1, simplifying statement Sk+1 completely.Sn : 4 + 8 + 12 +......+ 4n = 2n(n + 1)
The figure shows the graph of y = f(x) and its vertical asymptote. Use the graph to solve Exercises 1–9.Find (f ° f)(-4). 200 y = f(x) -5-4-3-2-1 17 H cr |||| 2 3 4 5 T HH X
In Exercises 1–12, write the first four terms of each sequence whose general term is given. a an || 3 n
In Exercises 1–8, evaluate the given binomial coefficient. 15 2
In Exercises 5–10, a statement Sn about the positive integers is given. Write statements Sk and Sk+1, simplifying statement Sk+1 completely. Sn: 3+ 4+ 5+ + (n + 2) n(n + 5) 2
Fill in each blank so that the resulting statement is true.The probability of winning a lottery with one lottery ticket is the number of ways of winning, which is precisely_______ , divided by the total number of possible__________ .
Fill in each blank so that the resulting statement is true.The first four terms of are________ ,__________ ,______, and_________ . The common ratio is___________ . 6 Σ2 i=1
In Exercises 1–8, use the formula for nPr to evaluate each expression.6P6
Fill in each blank so that the resulting statement is true.An infinite sum of the form a1 + a1r + a1r2 + a1r3 +...... is called a/an______ . If -1 < r < _____, its sum, S, is given by the formula S =______ . The series does not have a sum if________ .
In Exercises 1–14, write the first six terms of each arithmetic sequence.a1 = 300, d = -90
Fill in each blank so that the resulting statement is true.The formula for nCr has the same numerator as the formula for nPr but contains an extra factor of_______ in the denominator.
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
The figure shows the graph of y = f(x) and its vertical asymptote. Use the graph to solve Exercises 1–9.Use arrow notation to complete this statement: 200 y = f(x) -5-4-3-2-1 17 H cr |||| 2 3 4 5 T HH X
In Exercises 1–8, write the first five terms of each geometric sequence.an = -3an-1, a1 = 10
Fill in each blank so that the resulting statement is true.The (r + 1)st term of the expansion of (a + b)n is______ . n r
Fill in each blank so that the resulting statement is true.5!, called 5______ , is the product of all positive integers from_______ down through_______ . By definition, 0! =_______ .
In Exercises 5–7, evaluate each expression.10P3
In Exercises 1–8, use the formula for nPr to evaluate each expression.9P9
Fill in each blank so that the resulting statement is true.The formula in Exercise 5 is called the_______ Theorem.
The figure shows the graph of y = f(x) and its vertical asymptote. Use the graph to solve Exercises 1–9.Graph g(x) = f(x - 2) + 1. 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.Because P(E) + P(not E) = 1, then P(not E) =_______ and P(E) =_________ .
In Exercises 1–8, evaluate the given binomial coefficient. 100 2
In Exercises 1–14, write the first six terms of each arithmetic sequence.a1 = 200, d = -60
In Exercises 1–8, write the first five terms of each geometric sequence.an = -5an-1, a1 = -6
Evaluate: 40!/4!38!
In Exercises 1–12, write the first four terms of each sequence whose general term is given.an = (-1)n(n + 3)
In Exercises 5–10, a statement Sn about the positive integers is given. Write statements Sk and Sk+1, simplifying statement Sk+1 completely.Sn : 3 + 7 + 11 +......+ (4n - 1) = n(2n + 1)
Fill in each blank so that the resulting statement is true. (n + 3)!/(n + 2)! = ______ .
In Exercises 8–9, find each indicated sum. 5 Σ (212 – 3) i=1
In Exercises 5–7, evaluate each expression.10C3
Fill in each blank so that the resulting statement is true.If it is impossible for events A and B to occur simultaneously, the events are said to be_______ . For such events, P(A or B) =________ .
In Exercises 1–8, use the formula for nPr to evaluate each expression.8P0
In Exercises 1–14, write the first six terms of each arithmetic sequence.a1 = 5/2, d = - 1/2
In Exercises 1–8, write the first five terms of each geometric sequence.an = -6an-1, a1 = -2
Fill in each blank so that the resulting statement is true.Determine whether each sequence is arithmetic or geometric.4, 8, 12, 16, 20, . . ._______
In Exercises 1–12, write the first four terms of each sequence whose general term is given.an = (-1)n+1(n + 4)
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 5–10, a statement Sn about the positive integers is given. Write statements Sk and Sk+1, simplifying statement Sk+1 completely. Sn: 2 + 7 + 12 + . . + (5n - 3) = n(5n - 1) 2
In Exercises 1–8, evaluate the given binomial coefficient. 100 98
Fill in each blank so that the resulting statement is true.If it is possible for events A and B to occur simultaneously, then P(A or B) =_________ .
In Exercises 1–8, use the formula for nPr to evaluate each expression.6P0
Express the sum using summation notation. Use i for the index of summation. 2 3 + 3 4 4 + +10 5 + + 21 22
The figure shows the graph of y = f(x) and its vertical asymptote. Use the graph to solve Exercises 1–9.Graph h(x) = -f(2x). 200 y = f(x) -5-4-3-2-1 17 H cr |||| 2 3 4 5 T HH X
In Exercises 8–9, find each indicated sum. 4 Σ(-1)+1;! i=0
In Exercises 1–12, write the first four terms of each sequence whose general term is given. an 2n n + 4
In Exercises 1–14, write the first six terms of each arithmetic sequence.a1 = 3/4, d = - 1/4
In Exercises 10–11, express each sum using summation notation. Use i for the index of summation. + + 214 +
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 9–16, use the formula for the general term (the nth term) of a geometric sequence to find the indicated term of each sequence with the given first term, a1, and common ratio, r.Find a8 when a1 = 6, r = 2.
In Exercises 1–12, write the first four terms of each sequence whose general term is given. an 3n n + 5
Fill in each blank so that the resulting statement is true.Determine whether each sequence is arithmetic or geometric.4, 8, 16, 32, 64, . . ._______ .
In Exercises 5–10, a statement Sn about the positive integers is given. Write statements Sk and Sk+1, simplifying statement Sk+1 completely.Sn : 2 is a factor of n2 - n + 2.
In Exercises 9–16, use the formula for nCr to evaluate each expression.9C5
In Exercises 9–30, use the Binomial Theorem to expand each binomial and express the result in simplified form.(x + 2)3
In Exercises 10–11, express each sum using summation notation. Use i for the index of summation. 4³ +53 +6³ +...+13³
In Exercises 1–12, write the first four terms of each sequence whose general term is given. an (−1)n+1 2" - 1
In Exercises 1–14, write the first six terms of each arithmetic sequence.an = an-1 + 6, a1 = -9
Fill in each blank so that the resulting statement is true.If the occurrence of one event has no effect on the probability of another event, the events are said to be_______ . For such events P(A and B) =________ .
In Exercises 9–10, write a formula for the general term (the nth term) of each sequence. Do not use a recursion formula. Then use the formula to find the twelfth term of the sequence.4, 9, 14, 19, . . .
In Exercises 11–24, use mathematical induction to prove that each statement is true for every positive integer n. 3+ 4+ 5+ + (n + 2) = = n(n + 5) 2
In Exercises 10–22, solve each equation, inequality, or system of equations.-2(x - 5) + 10 = 3(x + 2)
In Exercises 9–16, use the formula for the general term (the nth term) of a geometric sequence to find the indicated term of each sequence with the given first term, a1, and common ratio, r.Find a8 when a1 = 5, r = 3.
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