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College Algebra 7th Edition Robert F Blitzer - Solutions
You are considering two job offers. Company A will start you at $19,000 a year and guarantee a raise of $2600 per year. Company B will start you at a higher salary, $27,000 a year, but will only guarantee a raise of $1200 per year. Find the total salary that each company will pay over a ten-year
In Exercises 66–69, determine whether each statement makes sense or does not make sense, and explain your reasoning.The probability that I will go to graduate school is 1.5.
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 70–71, find the term indicated in each expansion.(x + 2)5; fourth term
In Exercises 66–69, determine whether each statement makes sense or does not make sense, and explain your reasoning.When I toss a coin, the probability of getting heads or tails is 1, but the probability of getting heads and tails is 0.
A theater has 30 seats in the first row, 32 seats in the second row, increasing by 2 seats per row for a total of 26 rows. How many seats are there in the theater?
In Exercises 70–72, use the Binomial Theorem to find a polynomial expansion for each function. Then use a graphing utility and an approach similar to the one in Exercises 68 and 69 to verify the expansion.Data from Exercise 68In Exercises 68–69, graph each of the functions in the same viewing
The target in the figure shown contains four squares. If a dart thrown at random hits the target, find the probability that it will land in a yellow region. -12 in.- -9 in.- ←6 in.— 3 in.
In Exercises 70–72, use the Binomial Theorem to find a polynomial expansion for each function. Then use a graphing utility and an approach similar to the one in Exercises 68 and 69 to verify the expansion.Data from Exercise 68In Exercises 68–69, graph each of the functions in the same viewing
In Exercises 70–72, use the Binomial Theorem to find a polynomial expansion for each function. Then use a graphing utility and an approach similar to the one in Exercises 68 and 69 to verify the expansion.Data from Exercise 68In Exercises 68–69, graph each of the functions in the same viewing
A deposit of $6000 is made in an account that earns 6% interest compounded quarterly. The balance in the account after n quarters is given by the sequenceFind the balance in the account after five years. Round to the nearest cent. an = 6000 1 + 0.06 4 n n = 1, 2, 3, ....
A deposit of $10,000 is made in an account that earns 8% interest compounded quarterly. The balance in the account after n quarters is given by the sequence an n 10,000(1; 0.08)". 4 n = 1, 2, 3, ....
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 70–71, find the term indicated in each expansion.(2x - 3)6; fifth term
In Exercises 71–72, you save $1 the first day of a month, $2 the second day, $4 the third day, continuing to double your savings each day.What will your total savings be for the first 15 days?
A section in a stadium has 20 seats in the first row, 23 seats in the second row, increasing by 3 seats each row for a total of 38 rows. How many seats are in this section of the stadium?
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 72–75, evaluate each expression.8P3
In Exercises 71–72, you save $1 the first day of a month, $2 the second day, $4 the third day, continuing to double your savings each day.What will your total savings be for the first 30 days?
Suppose that it is a drawing in which the Powerball jackpot is promised to exceed $700 million. If a person purchases 292,201,338 tickets at $2 per ticket (all possible combinations), isn’t this a guarantee of winning the jackpot? Because the probability in this situation is 1, what’s wrong
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 a class of 50 students, 29 are Democrats, 11 are business majors, and 5 of the business majors are Democrats. If one student is randomly selected from the class, find the probability of choosinga. A Democrat who is not a business major.b. A student who is neither a Democrat nor a business major.
Use the capability of a graphing utility to calculate the sum of a sequence to verify any five of your answers to Exercises 45–50.Data from Answers of 45-5045.46.47.48.49. 17 Σ (5i+3)=(5+3)+(10+3)+(15+3)+...+(85+3)=8+13+18++88 i=1 $17 17 == 2 -(8+88)=816
In Exercises 72–75, evaluate each expression.9P5
What is an arithmetic sequence? Give an example with your explanation.
A job pays a salary of $24,000 the first year. During the next 19 years, the salary increases by 5% each year. What is the total lifetime salary over the 20-year period? Round to the nearest dollar.
Some three-digit numbers, such as 101 and 313, read the same forward and backward. If you select a number from all three digit numbers, find the probability that it will read the same forward and backward.
A pendulum swings through an arc of 20 inches. On each successive swing, the length of the arc is 90% of the previous length.After 10 swings, what is the total length of the distance the pendulum has swung? 20, 0.9(20), 0.9² (20), 0.9³ (20), ... 1st swing 2nd swing 3rd swing 4th swing
A pendulum swings through an arc of 16 inches. On each successive swing, the length of the arc is 96% of the previous length.After 10 swings, what is the total length of the distance the pendulum has swung? 16, 0.96(16), (0.96)²(16), (0.96)³(16),... 1st swing 2nd swing 3rd swing 4th swing
In Exercises 72–75, evaluate each expression.8C3
You are investigating two employment opportunities. Company A offers $30,000 the first year. During the next four years, the salary is guaranteed to increase by 6% per year. Company B offers $32,000 the first year, with guaranteed annual increases of 3% per year after that. Which company offers the
What is the common difference in an arithmetic sequence?
a. If two people are selected at random, the probability that they do not have the same birthday (day and month) is 365/365 . 364/365. Explain why this is so. (Ignore leap years and assume 365 days in a year.)b. If three people are selected at random, find the probability that they all have
What is a sequence? Give an example with your description.
Explain the Fundamental Counting Principle.
On New Year’s Eve, the probability of a person driving while intoxicated or having a driving accident is 0.35. If the probability of driving while intoxicated is 0.32 and the probability of having a driving accident is 0.09, find the probability of a person having a driving accident while
In Exercises 73–76, determine whether each statement makes sense or does not make sense, and explain your reasoning. In order to expand (x3 - y4)5, I find it helpful to rewrite the expression inside the parentheses as x3 + (-y4).
Explain how to find the general term of an arithmetic sequence.
In Exercises 72–75, evaluate each expression.3C11
In Exercises 73–76, determine whether each statement makes sense or does not make sense, and explain your reasoning.One of the terms in my binomial expansion is (3)x²4.
Explain how to write terms of a sequence if the formula for the general term is given.
Write an original problem that can be solved using the Fundamental Counting Principle. Then solve the problem.
In Exercises 73–76, determine whether each statement makes sense or does not make sense, and explain your reasoning.Without writing the expansion of (x - 1)6, I can see that the terms have alternating positive and negative signs.
Explain how to find the sum of the first n terms of an arithmetic sequence without having to add up all the terms.
What does the graph of a sequence look like? How is it obtained?
After a 20% reduction, a digital camera sold for $256. What was the price before the reduction?
What is a permutation?
In Exercises 76–82, solve by the method of your choice.A popular brand of pen comes in red, green, blue, or black ink. The writing tip can be chosen from extra bold, bold, regular, fine, or micro. How many different choices of pens do you have with this brand?
To save money for a sabbatical to earn a master’s degree, you deposit $2000 at the end of each year in an annuity that pays 7.5% compounded annually.a. How much will you have saved at the end of five years?b. Find the interest.
Use the SEQ (sequence) capability of a graphing utility and the formula you obtained for an to verify the value you found for a20 in any five exercises from Exercises 23–34.Data from Exercise 23In Exercises 23–34, write a formula for the general term (the nth term) of each arithmetic sequence.
What is a recursion formula?
Describe what nPr represents.
Find the average rate of change of f(x) = x2 - 1 from x1 = 1 to x2 = 2.
In Exercises 78–81, determine whether each statement makes sense or does not make sense, and explain your reasoning.Rather than performing the addition, I used the formula to find the sum of the first 30 terms of the sequence 2, 4, 8, 16, 32, . . . . Sn = (a₁ + an)
In Exercises 76–82, solve by the method of your choice.A stock can go up, go down, or stay unchanged. How many possibilities are there if you own five stocks?
Use the formula for the value of an annuity to solve Exercises 77–84. Round answers to the nearest dollar.To save money for a sabbatical to earn a master’s degree, you deposit $2500 at the end of each year in an annuity that pays 6.25% compounded annually.a. How much will you have saved at the
Explain how to find n! if n is a positive integer.
In Exercises 76–82, solve by the method of your choice.A club with 15 members is to choose four officers president, vice president, secretary, and treasurer. In how many ways can these offices be filled?
In Exercises 77–80, determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement.The binomial expansion for (a + b)n contains n terms.
Graph f(x) = x2. Then use the graph of f to obtain the graph of g(x) = (x + 2)2 - 1.
Write a word problem that can be solved by evaluating 7P3.
Explain the best way to evaluate 900!/899! without a calculator.
In Exercises 77–80, determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement.The Binomial Theorem can be written in condensed form as (a + b)" = n r=0 n ") a²-7b². r
The bar graph shows the differences among age groups on the Implicit Association Test that measures levels of racial prejudice. Higher scores indicate stronger bias.a. The data can be described by the following polynomial model of degree 3:In this polynomial model, S represents the score on the
In Exercises 83–90, evaluate each expression without using a calculator. 16 5 GIN
In Exercises 83–90, perform the indicated operation or operations. (5x - 3)6 (5r – 3)4
In Exercises 87–106, perform the indicated computations. Write the answers in scientific notation. If necessary, round the decimal factor in your scientific notation answer to two decimal places. (1.4 x 10¹5) (3 × 10-¹1) X
The bar graph shows the differences among political identification groups on the Implicit Association Test that measure levels of racial prejudice. Higher scores indicate stronger bias.a. The data can be described by the following polynomial model of degree 3:In this polynomial model, S represents
In Exercises 91–100, simplify using properties of exponents. (7x³) (2x²)
In Exercises 89–105, factor completely, or state that the polynomial is prime.15x3 + 3x2
In Exercises 87–106, perform the indicated computations. Write the answers in scientific notation. If necessary, round the decimal factor in your scientific notation answer to two decimal places. (6.1 x 10-8)(2 x 10-4)
In Exercises 85–96, simplify each algebraic expression.7(3y - 5) + 2(4y + 3)
In Exercises 65–92, factor completely, or state that the polynomial is prime.12x2 y - 27y - 4x2 + 9
In Exercises 87–106, perform the indicated computations. Write the answers in scientific notation. If necessary, round the decimal factor in your scientific notation answer to two decimal places. (5.1 x 10-8)(3 x 10-4)
In Exercises 91–100, simplify using properties of exponents. ele 3 X ) (4x4) (3x3
In Exercises 85–96, simplify each algebraic expression.4(2y - 6) + 3(5y + 10)
Explain how to divide rational expressions.
In Exercises 65–92, factor completely, or state that the polynomial is prime.2x3 - 8a2 x + 24x2 + 72x
In Exercises 89–105, factor completely, or state that the polynomial is prime.x2 - 11x + 28
Explain how to add rational expressions with different denominators. Use in your explanation. 3 x + 5 + 7 (x + 2)(x + 5)
In Exercises 87–106, perform the indicated computations. Write the answers in scientific notation. If necessary, round the decimal factor in your scientific notation answer to two decimal places. (4.3 × 108) (6.2 x 104)
In Exercises 93–102, factor and simplify each algebraic expression. ن را از X X
The volume, V, of a rectangular solid with length l, width w, and height h is given by the formula V = lwh. In Exercises 93–94, use this formula to write a polynomial in standard form that models, or represents, the volume of the open box. 8- 2x 10 - 2x X
In Exercises 91–100, simplify using properties of exponents. 20x² 1 5x4
In Exercises 85–96, simplify each algebraic expression.5(3y - 2) - (7y + 2)
Explain how to add or subtract rational expressions with the same denominators.
In Exercises 91–100, simplify using properties of exponents. 72x4 9x 3
In Exercises 65–92, factor completely, or state that the polynomial is prime.2x3 - 98a2 x + 28x2 + 98x
In Exercises 93–102, factor and simplify each algebraic expression. 314 .14
In Exercises 89–105, factor completely, or state that the polynomial is prime.15x2 - x - 2
In Exercises 87–106, perform the indicated computations. Write the answers in scientific notation. If necessary, round the decimal factor in your scientific notation answer to two decimal places. (8.2 x 108) (4.6 × 104) x
In Exercises 85–96, simplify each algebraic expression.4(5y - 3) - (6y + 3)
The volume, V, of a rectangular solid with length l, width w, and height h is given by the formula V = lwh. In Exercises 93–94, use this formula to write a polynomial in standard form that models, or represents, the volume of the open box. 8- 2x 5 - 2x X
In Exercises 89–105, factor completely, or state that the polynomial is prime.64 - x2
In Exercises 93–102, factor and simplify each algebraic expression. 4x 3 + 8x3
In Exercises 91–100, simplify using properties of exponents. (3 3
Describe two ways to simplify 3 X 1 x2 + 2 2 X² I's 2 X
In Exercises 95–96, write a polynomial in standard form that models, or represents, the area of the shaded region. x + 3 x+1 -x + 9- -x+ 5-
In Exercises 87–106, perform the indicated computations. Write the answers in scientific notation. If necessary, round the decimal factor in your scientific notation answer to two decimal places. 8.4 x 108 4 x 105
In Exercises 85–96, simplify each algebraic expression.7 - 4[3 - (4y - 5)]
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