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College Algebra 7th Edition Robert F Blitzer - Solutions
Fill in each blank so that the resulting statement is true.Determine whether each sequence is arithmetic or geometric.1, -3, 9, -27, 81, . . . _________ .
In Exercises 9–16, use the formula for nCr to evaluate each expression.10C6
In Exercises 9–30, use the Binomial Theorem to expand each binomial and express the result in simplified form.(x + 4)3
In Exercises 1–14, write the first six terms of each arithmetic sequence.an = an-1 + 4, a1 = -7
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.16, 4, 1, 1/4, . . .
In Exercises 10–22, solve each equation, inequality, or system of equations.3x2 - 6x + 2 = 0
In Exercises 10–22, solve each equation, inequality, or system of equations. 1 x² - 6x² + 8 = 0
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 a12 when a1 = 5, r = -2.
Fill in each blank so that the resulting statement is true.Determine whether each sequence is arithmetic or geometric.1, 1, 3, 5, 7, . . . _______ .
In Exercises 11–16, a die is rolled. Find the probability of getting a 4.
In Exercises 11–16, a die is rolled. Find the probability of getting a 5.
In Exercises 9–16, use the formula for nCr to evaluate each expression.12C5
In Exercises 9–30, use the Binomial Theorem to expand each binomial and express the result in simplified form.(x + 3y)3
In Exercises 1–14, write the first six terms of each arithmetic sequence.an = an-1 - 20, a1 = 50
In Exercises 11–12, use a formula to find the sum of the first ten terms of each sequence.-7, -14, -21, -28, . . .
In Exercises 12–15, write the first six terms of each arithmetic sequence.a1 = -4, d = -5
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 a40 when a1 = 1000, r = - 1/2.
In this summation notation, i is called the_______ of summation, n is the_________ of summation, and 1 is the______ of summation. WI = +. + 1 + · +
In Exercises 9–16, use the formula for nCr to evaluate each expression.11C4
In Exercises 9–30, use the Binomial Theorem to expand each binomial and express the result in simplified form.(3x + y)3
In Exercises 1–14, write the first six terms of each arithmetic sequence.an = an-1 - 10, a1 = 30
In Exercises 11–12, use a formula to find the sum of the first ten terms of each sequence.7, -14, 28, -56, . . .
In Exercises 10–22, solve each equation, inequality, or system of equations.log2 x + log2(2x - 3) = 1
In Exercises 1–12, write the first four terms of each sequence whose general term is given. an (-1)^²+1 2" + 1
In Exercises 12–15, write the first six terms of each arithmetic sequence.a1 = 7, d = 4
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 a12 when a1 = 4, r = -2.
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
Explain how to find and probabilities with independent events. Give an example.
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 63–64, find a2 and a3 for each geometric sequence.2, a2, a3, -54
In Exercises 64–67, use the Binomial Theorem to expand each binomial and express the result in simplified form.(2x + 1)3
Explain how to use the Binomial Theorem to expand a binomial. Provide an example with your explanation.
How do you determine how many terms there are in a binomial expansion?
In Exercises 62–63, evaluate the given binomial coefficient. 90 2
Company A pays $24,000 yearly with raises of $1600 per year. Company B pays $28,000 yearly with raises of $1000 per year. Which company will pay more in year 10? How much more?
In Exercises 63–64, find a2 and a3 for each geometric sequence.8, a2, a3, 27
In Exercises 57–66, solve by the method of your choice.Nine comedy acts will perform over two evenings. Five of the acts will perform on the first evening and the order in which the acts perform is important. How many ways can the schedule for the first evening be made?
Company A pays $23,000 yearly with raises of $1200 per year. Company B pays $26,000 yearly with raises of $800 per year. Which company will pay more in year 10? How much more?
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
The bar graph shows the average dormitory charges at public and private four-year U.S. colleges. Use the information displayed by the graph to solve Exercises 65–66.a. Use the numbers shown by the bar graph to find the total dormitory charges at public colleges for a four-year, period from the
The probability that Jill will win the election is 0.7 and the probability that she will not win is 0.4.
Use the formula for the general term (the nth term) of a geometric sequence to solve Exercises 65–68.In Exercises 65–66, suppose you save $1 the first day of a month, $2 the second day, $4 the third day, and so on. That is, each day you save twice as much as you did the day before.What will you
In Exercises 64–67, use the Binomial Theorem to expand each binomial and express the result in simplified form.(x2 - 1)4
In Exercises 57–66, solve by the method of your choice.Using 15 flavors of ice cream, how many cones with three different flavors can you create if it is important to you which flavor goes on the top, middle, and bottom?
Explain how to find a particular term in a binomial expansion without having to write out the entire expansion.
The president of a large company with 10,000 employees is considering mandatory cocaine testing for every employee. The test that would be used is 90% accurate, meaning that it will detect 90% of the cocaine users who are tested, and that 90% of the nonusers will test negative. This also means that
In Exercises 57–66, solve by the method of your choice.Baskin-Robbins offers 31 different flavors of ice cream. One of its items is a bowl consisting of three scoops of ice cream, each a different flavor. How many such bowls are possible?
The bar graph shows the average dormitory charges at public and private four-year U.S. colleges. Use the information displayed by the graph to solve Exercises 65–66.a. Use the numbers shown by the bar graph to find the total dormitory charges at private colleges for a four-year period from the
Describe how you would use mathematical induction to proveWhat happens when n = 1? Write the statement that we assume to be true. Write the statement that we must prove. What must be done to the left side of the assumed statement to make it look like the left side of the statement that must be
In Exercises 64–67, use the Binomial Theorem to expand each binomial and express the result in simplified form.(x + 2y)5
Use the formula for the general term (the nth term) of a geometric sequence to solve Exercises 65–68.In Exercises 65–66, suppose you save $1 the first day of a month, $2 the second day, $4 the third day, and so on. That is, each day you save twice as much as you did the day before.What will you
Use the formula for the general term (the nth term) of a geometric sequence to solve Exercises 65–68.A professional baseball player signs a contract with a beginning salary of $3,000,000 for the first year and an annual increase of 4% per year beginning in the second year. That is, beginning in
Use the formula for the sum of an infinite geometric series to solve Exercises 85–87.If the shading process shown in the figure is continued indefinitely, what fractional part of the largest square will eventually be shaded?
Suppose that a survey of 350 college students is taken. Each student is asked the type of college attended (public or private) and the family’s income level (low, middle, high). Use the data in the table to solve Exercises 83–88. Express probabilities as simplified fractions.Find the
Among all pairs of numbers whose sum is 24, find a pair whose product is as large as possible. What is the maximum product?
Use the graph of f to determine each of the following. Where applicable, use interval notation. ·2- T y -4-3-2-14 PT 2 3 X y = f(x) A
Solve: 6|1 - 2x|- 7 = 11.
Solve: log2(x + 9) - log2 x = 1.
In Exercises 83–86, determine whether each statement makes sense or does not make sense, and explain your reasoning.I used the permutations formula to determine the number of ways people can select their 9 favorite baseball players from a team of 25 players.
In Exercises 87–90, determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement.The number of ways to choose four questions out of ten questions on an essay test is 10P4.
Exercises 88–90 will help you prepare for the material covered.Use the formula an = a13n-1 to find the seventh term of the sequence 11, 33, 99, 297, . . . .
Exercises 89–91 will help you prepare for the material covered.You can choose from two pairs of jeans (one blue, one black) and three T-shirts (one beige, one yellow, and one blue), as shown in the diagram. True or false: The diagram shows that you can form 2 × 3, or 6, different outfits.
Many graphing utilities have a sequence-graphing mode that plots the terms of a sequence as points on a rectangular coordinate system. Consult your manual; if your graphing utility has this capability, use it to graph each of the sequences in Exercises 89–92. What appears to be happening to the
Suppose that a survey of 350 college students is taken. Each student is asked the type of college attended (public or private) and the family’s income level (low, middle, high). Use the data in the table to solve Exercises 83–88. Express probabilities as simplified fractions.Find the
Many graphing utilities have a sequence-graphing mode that plots the terms of a sequence as points on a rectangular coordinate system. Consult your manual; if your graphing utility has this capability, use it to graph each of the sequences in Exercises 89–92. What appears to be happening to the
Exercises 88–90 will help you prepare for the material covered in the next section.Consider the sequence 1, -2, 4, -8, 16, . . . . Find and a5/a4 . What do you observe? a2 a3 a4 аг aj az az
As n increases, the terms of the sequenceget closer and closer to the number e (where e ≈ 2.7183). Use a calculator to find a10, a100, a1000, a10,000, and a100,000, comparing these terms to your calculator’s decimal approximation for e. an 1 + 1) " n
Exercises 88–90 will help you prepare for the material covered in the next section.Consider the sequence whose nth term is an = 3 . 5n. Find and a5/a4. What do you observe? το A2 A3 A4 απ' αγ' αξ 92
Exercises 89–91 will help you prepare for the material covered in the next section. Evaluate n! (n − r)! - for n 20 and r = 3.
Exercises 89–91 will help you prepare for the material covered in the next section. Evaluate n! (n - r)!r! for n 8 and r = = 3.
Many graphing utilities have a sequence-graphing mode that plots the terms of a sequence as points on a rectangular coordinate system. Consult your manual; if your graphing utility has this capability, use it to graph each of the sequences in Exercises 89–92. What appears to be happening to the
In Exercises 89–90, a die is rolled. Find the probability of getting a number less than 5.
What is a geometric sequence? Give an example with your explanation.
In Exercises 87–90, determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement.If r > 1, nPr is less than nCr.
In Exercises 97–100, determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. n! (n − 1)! 1 n - 1
What is the common ratio in a geometric sequence?
In Exercises 89–90, a die is rolled. Find the probability of getting a number less than 3 or greater than 4.
Many graphing utilities have a sequence-graphing mode that plots the terms of a sequence as points on a rectangular coordinate system. Consult your manual; if your graphing utility has this capability, use it to graph each of the sequences in Exercises 89–92. What appears to be happening to the
In Exercises 87–90, determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement.7P3 = 3!7C3
Explain how to find the general term of a geometric sequence.
In Exercises 91–92, you are dealt one card from a 52-card deck. Find the probability of Getting an ace or a king.
Use the SEQ (sequence) capability of a graphing utility and the formula you obtained for an to verify the value you found for a7 in any three exercises from Exercises 17–24.Data from exercise 17-2417.18.19. a7 = 3(4) = 12,288
In Exercises 93–96, determine whether each statement makes sense or does not make sense, and explain your reasoning.Now that I’ve studied sequences, I realize that the joke in this cartoon is based on the fact that you can’t have a negative number of sheep. an+ 1 low > ап 11A An-1² 13:00
If f(x) = 4x2 - 5x - 2, find and simplify f(x +h)-f(x) h h = 0
In Exercises 87–90, determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement.The number of ways to pick a winner and first runner-up in a talent contest with 20 contestants is 20C2.
Explain how to find the sum of the first n terms of a geometric sequence without having to add up all the terms.
In Exercises 93–95, it is equally probable that the pointer on the spinner shown will land on any one of the six regions, numbered 1 through 6, and colored as shown. If the pointer lands on a borderline, spin again. Find the probability ofstopping on green on the first spin and stopping on a
In Exercises 91–92, you are dealt one card from a 52-card deck. Find the probability of getting a queen or a red card.
In Exercises 93–96, determine whether each statement makes sense or does not make sense, and explain your reasoning.It makes a difference whether or not I use parentheses around the expression following the summation symbol, because the value of but the value of is 43. 8 Σ (i + 7) is 92, i=1
Five men and five women line up at a checkout counter in a store. In how many ways can they line up if the first person in line is a woman and the people in line alternate woman, man, woman, man, and so on?
Exercises 98–100 will help you prepare for the material covered in the next section. The figure shows that when a die is rolled, there are six equally likely outcomes: 1, 2, 3, 4, 5, or 6. Use this information to solve each exercise.What fraction of the outcomes is less than 5?
What is an annuity?
In Exercises 93–95, it is equally probable that the pointer on the spinner shown will land on any one of the six regions, numbered 1 through 6, and colored as shown. If the pointer lands on a borderline, spin again. Find the probability of not stopping on yellow.
How many four-digit odd numbers less than 6000 can be formed using the digits 2, 4, 6, 7, 8, and 9?
What is the difference between a geometric sequence and an infinite geometric series?
Exercises 98–100 will help you prepare for the material covered in the next section. The figure shows that when a die is rolled, there are six equally likely outcomes: 1, 2, 3, 4, 5, or 6. Use this information to solve each exercise.What fraction of the outcomes is not less than 5?
In Exercises 93–95, it is equally probable that the pointer on the spinner shown will land on any one of the six regions, numbered 1 through 6, and colored as shown. If the pointer lands on a borderline, spin again. Find the probability of stopping on red or a number greater than 3.
In Exercises 93–96, determine whether each statement makes sense or does not make sense, and explain your reasoning.Without writing out the terms, I can see that (-1)2n in causes the terms to alternate in sign. an (-1)²n 3п
Solve and determine whether 8(x - 3) + 4 = 8x - 21 is an identity, a conditional equation, or an inconsistent equation.
A lottery game is set up so that each player chooses five different numbers from 1 to 20. If the five numbers match the five numbers drawn in the lottery, the player wins (or shares) the top cash prize. What is the probability of winning the prizea. with one lottery ticket?b. with 100 different
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