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mathematics
college algebra graphs and models
College Algebra 7th Edition Robert F Blitzer - Solutions
Exercises 104–106 will help you prepare for the material covered in the first section of the next chapter.Evaluate i2 + 1 for all consecutive integers from 1 to 6, inclusive. Then find the sum of the six evaluations.
Fill in each blank so that the resulting statement is true.is called a/an________ coefficient. (1)
Exercises 104–106 will help you prepare for the material covered in the first section of the next chapter.Find the product of all positive integers from n down through 1 for n = 5.
In Exercises 1–8, write the first five terms of each geometric sequence.a1 = 5, r = 3
In Exercises 1–6, write the first four terms of each sequence whose general term is given.an = 7n - 4
The figure shows the graph of y = f(x) and its vertical asymptote. Use the graph to solve Exercises 1–9.For what value(s) of x is f(x) = 1? 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.an = 3n + 2
Fill in each blank so that the resulting statement is true.{an} = a1, a2, a3, a4, . . . , an, . . . represents an infinite________ , a function whose domain is the set of positive________ . The function values a1, a2, a3, . . . are called the_______ .
Fill in each blank so that the resulting statement is true.The principle of mathematical__________ states that a statement involving positive integers is true for all positive integers when two conditions have been satisfied: The first condition states that the statement is true for the positive
In Exercises 1–8, use the formula for nPr to evaluate each expression.7P3
Fill in each blank so that the resulting statement is true.Probability that is based on situations in which we observe how frequently an event occurs is called_________ probability.
Fill in each blank so that the resulting statement is true.A sequence in which each term after the first differs from the preceding term by a constant amount is called a/an________ sequence. The difference between consecutive terms is called the _________ of the sequence.
Fill in each blank so that the resulting statement is true.If you can choose one item from a group of M items and a second item from a group of N items, then the total number of two-item choices is_________ .
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 21–28, evaluate each expression. 46! 10C3 6C4 44!
In Exercises 23–28, evaluate each factorial expression. (n + 2)! n!
In Exercises 25–27, use the formula for the sum of the first n terms of an arithmetic sequence to find the indicated sum. 30 Σ (51) i=1
In Exercises 21–28, evaluate each expression. 4C2.6C1 18C3
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 + 3n.
In Exercises 11–16, a die is rolled. Find the probability of getting a number greater than 4.
In 2014, the average ticket price for top rock concerts, adjusted for inflation, had increased by 77% since 1995. This was greater than the percent increase in the cost of tuition at private four-year colleges during the same time period. The bar graph shows the average ticket price, in 2015
In Exercises 23–28, evaluate each factorial expression. (2n + 1)! (2n)!
In Exercises 9–30, use the Binomial Theorem to expand each binomial and express the result in simplified form.(x - 2)5
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)=√x + 4 and fl -1
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.a1 = 9, d = 2
One card is randomly selected from a deck of 52 cards. Find the probability of selecting a black card or a picture card.
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 - 4x - 5
In Exercises 21–28, evaluate each expression. 5C1.7C2 12C3
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 11 terms of the geometric sequence: 3, -6, 12, -24, . . . .
Mega Millions is a multi-state lottery played in most U.S. states. As of this writing, the top cash prize was $656 million, going to three lucky winners in three states. Players pick five different numbers from 1 to 56 and one number from 1 to 46. Use this information to solve Exercises 27–30.
In Exercises 25–34, use mathematical induction to prove that each statement is true for every positive integer n.6 is a factor of n(n + 1)(n + 2).
In Exercises 9–30, use the Binomial Theorem to expand each binomial and express the result in simplified form.(3x - y)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.a1 = 6, d = 3
A group of students consists of 10 male freshmen, 15 female freshmen, 20 male sophomores, and 5 female sophomores. If one person is randomly selected from the group, find the probability of selecting a freshman or a female.
In Exercises 29–42, find each indicated sum. 9 Σ i=1 5i
In Exercises 25–34, use mathematical induction to prove that each statement is true for every positive integer n. n 1=1 5.6¹ 6(61) =
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 11 terms of the geometric sequence: 4, -12, 36, -108, . . . .
Mega Millions is a multi-state lottery played in most U.S. states. As of this writing, the top cash prize was $656 million, going to three lucky winners in three states. Players pick five different numbers from 1 to 56 and one number from 1 to 46. Use this information to solve Exercises 27–30.
If the spinner shown is spun twice, find the probability that the pointer lands on red on the first spin and blue on the second spin. yellow green red blue blue red green yellow
In Exercises 25–34, use mathematical induction to prove that each statement is true for every positive integer n.3 is a factor of n(n + 1)(n - 1).
In Exercises 9–30, use the Binomial Theorem to expand each binomial and express the result in simplified form.(x - 3y)5
In Exercises 29–42, find each indicated sum. 6 i=1 7i
Exercises 31–32 involve a deck of 52 cards. If necessary, refer to the picture of a deck of cards, Figure 8.12.A poker hand consists of five cards.a. Find the total number of possible five-card poker hands.b. A diamond flush is a five-card hand consisting of all diamonds. Find the number of
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.a1 = -20, d = -4
A quiz consisting of four multiple-choice questions has four available options (a, b, c, or d) for each question. If a person guesses at every question, what is the probability of answering all questions correctly?
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) = log2 x and g(x) = -log2(x + 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 14 terms of the geometric sequence: - 3/2, 3, -6, 12, . . . .
A company offers a starting salary of $31,500 with raises of $2300 per year. Find the total salary over a ten-year period.
Mega Millions is a multi-state lottery played in most U.S. states. As of this writing, the top cash prize was $656 million, going to three lucky winners in three states. Players pick five different numbers from 1 to 56 and one number from 1 to 46. Use this information to solve Exercises 27–30.
In Exercises 25–34, use mathematical induction to prove that each statement is true for every positive integer n. n i=1 7.8¹ = 8(81)
In Exercises 30–31, let f(x) = -x2 - 2x + 1 and g(x) = x - 1. Find f(x +h)-f(x) h and simplify.
In Exercises 9–30, use the Binomial Theorem to expand each binomial and express the result in simplified form.(2a + b)6
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.a1 = -70, d = -5
In Exercises 29–42, find each indicated sum. 4 Σ 212 i=1
In Exercises 30–31, let f(x) = -x2 - 2x + 1 and g(x) = x - 1.Find (f ° g)(x) and (g ° f)(x).
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 14 terms of the geometric sequence: - 1/24, 1/12, - 1/6, 1/3, . . . .
Use the Fundamental Counting Principle to solve Exercises 29–40.The model of the car you are thinking of buying is available in nine different colors and three different styles (hatchback, sedan, or station wagon). In how many ways can you order the car?
In Exercises 31–36, find the indicated sum. Use the formula for the sum of the first n terms of a geometric sequence. 8 Σ3 i=1
Mega Millions is a multi-state lottery played in most U.S. states. As of this writing, the top cash prize was $656 million, going to three lucky winners in three states. Players pick five different numbers from 1 to 56 and one number from 1 to 46. Use this information to solve Exercises 27–30.
A theater has 25 seats in the first row and 35 rows in all. Each successive row contains one additional seat. How many seats are in the theater?
In Exercises 9–30, use the Binomial Theorem to expand each binomial and express the result in simplified form.(a + 2b)6
Exercises 31–32 involve a deck of 52 cards. If necessary, refer to the picture of a deck of cards, Figure 8.12.If you are dealt 3 cards from a shuffled deck of 52 cards, find the probability that all 3 cards are picture cards. A 12 AD 44 CVD 24 24 3 3 34 34 5 6 7 5 8. 13 Diamonds 6 7 8 9 56. 9 13
In Exercises 31–36, find the indicated sum. Use the formula for the sum of the first n terms of a geometric sequence. 9 Σ4 i=1
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.an = an-1 + 3, a1 = 4
In Exercises 29–42, find each indicated sum. 5 i=1
Find the partial fraction decomposition for 2x²10x + 2 (x-2)(x² + 2x + 2)
IfA = 4 1 0 2 -1 -1 and B 5 24 -[31]. = find AB - 4A. A = 4 1 0 2 -1 -1 and B 5 24 -[31]. = find AB - 4A.
In Exercises 31–34, write the first five terms of each geometric sequence.a1 = 3, r = 2
Use the Fundamental Counting Principle to solve Exercises 29–40.A popular brand of pen is available in three colors (red, green, or blue) and four writing tips (bold, medium, fine, or micro). How many different choices of pens do you have with this brand?
In Exercises 25–34, use mathematical induction to prove that each statement is true for every positive integer n.n + 2 > n
In Exercises 31–38, write the first three terms in each binomial expansion, expressing the result in simplified form.(x + 2)8
In Exercises 31–36, find the indicated sum. Use the formula for the sum of the first n terms of a geometric sequence. 10 Σ5·2 i=1
The table shows the educational attainment of the U.S. population, ages 25 and over. Use the data in the table, expressed in millions, to solve Exercises 33–38.Find the probability, expressed as a simplified fraction, that a randomly selected American, age 25 or over, has not completed four years
In Exercises 29–42, find each indicated sum. 5 Σκ(k + 4) k=1
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.an = an-1 + 5, a1 = 6
In Exercises 31–34, write the first five terms of each geometric sequence.a1 = 1/2, r = 1/2
Use the Fundamental Counting Principle to solve Exercises 29–40.An ice cream store sells two drinks (sodas or milk shakes), in four sizes (small, medium, large, or jumbo), and five flavors (vanilla, strawberry, chocolate, coffee, or pistachio). In how many ways can a customer order a drink?
In Exercises 25–34, use mathematical induction to prove that each statement is true for every positive integer n.If 0 < x < 1, then 0 < xn < 1.
In Exercises 31–38, write the first three terms in each binomial expansion, expressing the result in simplified form.(x + 3)8
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.an = an-1 - 10, a1 = 30
In Exercises 29–42, find each indicated sum. 4 Σ (κ – 3)(k + 2) k=1
In Exercises 25–34, use mathematical induction to prove that each statement is true for every positive integer n. a b n = an Bn
In Exercises 31–36, find the indicated sum. Use the formula for the sum of the first n terms of a geometric sequence. 7 Σ 4-3) i=1
In Exercises 31–34, write the first five terms of each geometric sequence.a1 = 16, r = - 1/2
The table shows the educational attainment of the U.S. population, ages 25 and over. Use the data in the table, expressed in millions, to solve Exercises 33–38.Find the probability, expressed as a simplified fraction, that a randomly selected American, age 25 or over, has not completed four years
In Exercises 25–34, use mathematical induction to prove that each statement is true for every positive integer n.(ab)n = anbn
Use the formula for the sum of the first n terms of an arithmetic sequence to find 50 Σ (4i – 25). i=1
In Exercises 31–36, find the indicated sum. Use the formula for the sum of the first n terms of a geometric sequence. 6 Σ (3)i+1 i=1
In Exercises 31–38, write the first three terms in each binomial expansion, expressing the result in simplified form.(x - 2y)10
In Exercises 29–42, find each indicated sum. 화 4 i=1 (-1)
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.an = an-1 - 12, a1 = 24
The table shows the educational attainment of the U.S. population, ages 25 and over. Use the data in the table, expressed in millions, to solve Exercises 33–38.Find the probability, expressed as a simplified fraction, that a randomly selected American, age 25 or over, has not completed four years
Expand and simplify: (x3 + 2y)5.
In Exercises 29–42, find each indicated sum. i=2 3
In Exercises 31–34, write the first five terms of each geometric sequence.an = -5an-1, a1 = -1
Use the Fundamental Counting Principle to solve Exercises 29–40.You are taking a multiple-choice test that has five questions. Each of the questions has three answer choices, with one correct answer per question. If you select one of these three choices for each question and leave nothing blank,
Use the Fundamental Counting Principle to solve Exercises 29–40.You are taking a multiple-choice test that has eight questions. Each of the questions has three answer choices, with one correct answer per question. If you select one of these three choices for each question and leave nothing blank,
The table shows the educational attainment of the U.S. population, ages 25 and over. Use the data in the table, expressed in millions, to solve Exercises 33–38.Find the probability, expressed as a simplified fraction, that a randomly selected American, age 25 or over, has not completed four years
In Exercises 31–38, write the first three terms in each binomial expansion, expressing the result in simplified form.(x - 2y)9
In Exercises 31–36, find the indicated sum. Use the formula for the sum of the first n terms of a geometric sequence. 6 Σ (3)+1 i=1
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