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mathematics
college algebra graphs and models
College Algebra 7th Edition Robert F Blitzer - Solutions
The figure shows three one-way streets with intersections A, B, and C. Numbers indicate the average traffic flow in vehicles per minute. The variables x, y, and z denote unknown traffic flows that need to be determined for timing of stoplights. (a) If the number of vehicles per minute entering an
The following graph shows web page links.There is a 1 in row 4 column 4 of A2. What does this tell us? Page 1 Page 3 Page 2 Page 4
In the study of electrical circuits, the application of Kirchoff's rules frequently results in systems of linear equations. To determine the current I (in amperes) in each branch of the circuit shown in the figure, solve the system of linear equations. Round values to the nearest hundredth. 1₁ =
The following table shows the weight W, neck size N, and chest size C for a representative sample of black bears.(a) Find values for a, b, and c so that the equation W = a +bN+ cC models these data. (b) Estimate the weight of a bear with a 20-inch neck and a 31-inch chest size. (c) Explain why it
Solve the system, if possible. = 1 3x-y y=1
Each set of data can be modeled by the quadratic function f(x) = ax2 + bx + c. (a) Write a linear system whose solution represents values of a, b, and c. (b) Use technology to find the solution. (c) Graph f and the data in the same viewing rectangle. (d) Make your own prediction using f.The
The figure shows three one-way streets with intersections A, B, and C. Numbers indicate the average traffic flow in vehicles per minute. The variables x, y, and z denote unknown traffic flows that need to be determined for timing of stoplights. (a) If the number of vehicles per minute entering an
Three pumps are being used to empty a small swimming pool. The first pump is twice as fast as the second pump. The first two pumps can empty the pool in 8 hours, while all three pumps can empty it in 6 hours. How long would it take each pump to empty the pool individually?
Each set of data can be modeled by the quadratic function f(x) = ax2 + bx + c. (a) Write a linear system whose solution represents values of a, b, and c. (b) Use technology to find the solution. (c) Graph f and the data in the same viewing rectangle. (d) Make your own prediction using f.A large
Each set of data can be modeled by the quadratic function f(x) = ax2 + bx + c. (a) Write a linear system whose solution represents values of a, b, and c. (b) Use technology to find the solution. (c) Graph f and the data in the same viewing rectangle. (d) Make your own prediction using f.The
Suppose in Exercise 85 that the first pump is three times as fast as the third pump. the first and second pumps can empty the pool in 6 hours, and all three pumps can empty the pool in 8 hours. (a) Are these data realistic? Explain your reasoning. (b) Make a conjecture about a solution to
Each set of data can be modeled by the quadratic function f(x) = ax2 + bx + c. (a) Write a linear system whose solution represents values of a, b, and c. (b) Use technology to find the solution. (c) Graph f and the data in the same viewing rectangle. (d) Make your own prediction using f.Carbon
Find the current (in amperes) in each branch of the circuit shown in the figure by solving the system of linear equations. Round values to the nearest hundredth. 1₁ = 1₂ + 13 20 = 4/₁ + 713 10 + 713 = 61₂ 20v- 40 4₁ ww 13 70 YU 10v 60
Discuss how to use test points to solve a linear inequality. Give an example.
Discuss whether matrix multiplication is more like multiplication of functions or composition of functions. Explain your reasoning.
A sum of $5000 is invested in three mutual funds that pay 8%, 11%, and 14% annual interest rates. The amount of money invested in the fund paying 14% equals the total amount of money invested in the other two funds, and the total annual interest from all three funds is $595. (a) Write a system
Describe one application of matrices.
A sum of $10,000 is invested in three accounts that pay 3%, 4%, and 5% interest. Twice as much money is invested in the account paying 5% as in the account paying 3%, and the total annual interest from all three accounts is $421. (a) Write a system of equations whose solution gives the amount
Solve the system of linear equations (a) Numerically,(b) Graphically, (c) Symbolically. -2x + y = 0 7x - 2y = 3
Solve the system of linear equations (a) Numerically,(b) Graphically, (c) Symbolically. 2x + y = 1 x-2y = 3
Solve the system of linear equations (a) Numerically,(b) Graphically, (c) Symbolically. 3x + 2y = -2 2x - y = -6
Solve the system, if possible. 5x +4y = -3 3x - бу = -6 3х
Solve the system of linear equations (a) Numerically,(b) Graphically, (c) Symbolically. x - 4y = 15 4у 3x-2y = 15
Solve the system, if possible. -5x + 3y = -36 4x5y = 34
Solve the nonlinear system of equations (a) Symbolically and (b) Graphically. x² + y² = 2 - y = 0
A study investigated the relationship among annual tire sales T in thousands, automobile registrations A in millions, and personal disposable income I in millions of dollars. Representative data for three different years are shown in the table. The data were modeled by T = aA + bI + c, where a, b,
A linear equation in three variables can be represented by a flat plane. Describe geometrically situations that can occur when a system of three linear equations has either no solution or an infinite number of solutions.
Give an example of an augmented matrix in rowechelon form that represents a system of linear equations that has no solution. Explain your reasoning.
Break-Even Point The break-even point for a company is where costs equal revenues. Therefore the break-even point is the solution to a system of two equations. For each of the following, C represents cost in dollars to produce x items and R represents revenue in dollars from selling x items.The
Estimate, to the nearest tenth, the surface area of a person with weight w and height hw = 86 kilograms, h= 185 centimeters
Estimate, to the nearest tenth, the surface area of a person with weight w and height hW = 132 pounds, h = 62 inches
The quantity y of a product supplied is related to its price by the equation y = -17,500 + 8000x, where x is price in dollars. The quantity demanded y for the same product is represented by y = 35,000 2500.x. (a) Find the price at which this product is sold. (b) Find the quantity sold at
Estimate, to the nearest tenth, the surface area of a person with weight w and height h W = 220 pounds, h = 75 inches
Find the probability of drawing two cards, neither of which is an ace or a queen.
In a game of musical chairs, seven children will sit in six chairs arranged in a circle. One child will be left out. How many (different) ways can the children sit in the chairs?
Use technology to find the solution. Approximate values to the nearest thousandth. 53x + 95y + 12z = 108 81x57y24z = -92 -9x + 11y 78z = 21
The following graph shows web page links.There is a 2 in row 2 column 3 of A2. What does this tell us? Page 1 Page 3 Page 2 Page 4
Give the general form of a system of linear inequalities in two variables. Discuss what distinguishes a system of linear inequalities from a nonlinear system of inequalities.
Use technology to find the solution. Approximate values to the nearest thousandth. 0.1.x + 0.3y + 1.7z = 0.6 0.6x + 0.1y 3.1z = 6.2 2.4y+0.9z = 3.5
Find the sum of the infinite geometric series: 4 + + 4 + 4 81 +
In Exercises 10–22, solve each equation, inequality, or system of equations. √2x + 4√x + 3-1 = 0
In Exercises 11–24, use mathematical induction to prove that each statement is true for every positive integer n. 3 + 6 + 9 + . . . + 3n 3n(n + 1) 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 : 2 is a factor of n2 - n.
In Exercises 11–24, use mathematical induction to prove that each statement is true for every positive integer n.4 + 8 + 12 +.......+ 4n = 2n(n + 1)
The sequences in Exercises 13–18 are defined using recursion formulas. Write the first four terms of each sequence.a1 = 7 and an = an-1 + 5 for n ≥ 2
In Exercises 11–16, a die is rolled. Find the probability of getting an odd number.
In Exercises 11–24, use mathematical induction to prove that each statement is true for every positive integer n.1 + 3 + 5 + g + (2n - 1) = n2
In Exercises 9–16, use the formula for nCr to evaluate each expression.7C7
In Exercises 9–30, use the Binomial Theorem to expand each binomial and express the result in simplified form.(5x - 1)3
In Exercises 1–14, write the first six terms of each arithmetic sequence.an = an-1 - 0.4, a1 = 1.6
In Exercises 12–15, write the first six terms of each arithmetic sequence.a1 = 3/2, d = - 1/2
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 a30 when a1 = 8000, r = - 1/2.
In Exercises 10–22, solve each equation, inequality, or system of equations. |2x + 1| ≤ 1
The sequences in Exercises 13–18 are defined using recursion formulas. Write the first four terms of each sequence.a1 = 12 and an = an-1 + 4 for n ≥ 2
In Exercises 11–16, a die is rolled. Find the probability of getting a number greater than 3.
In Exercises 9–16, use the formula for nCr to evaluate each expression.4C4
In Exercises 9–30, use the Binomial Theorem to expand each binomial and express the result in simplified form.(4x - 1)3
In Exercises 1–14, write the first six terms of each arithmetic sequence.an = an-1 - 0.3, a1 = -1.7
Express 0.̅7̅3 in fractional notation.
In Exercises 12–15, write the first six terms of each arithmetic sequence.an+1 = an + 5, a1 = -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 = 1,000,000, r = 0.1.
The sequences in Exercises 13–18 are defined using recursion formulas. Write the first four terms of each sequence.a1 = 3 and an = 4an-1 for n ≥ 2
In Exercises 11–24, use mathematical induction to prove that each statement is true for every positive integer n.3 + 7 + 11 +.......+ (4n - 1) = n(2n + 1)
In Exercises 9–16, use the formula for nCr to evaluate each expression.5C0
In Exercises 9–30, use the Binomial Theorem to expand each binomial and express the result in simplified form.(2x + 1)4
In Exercises 15–22, find the indicated term of the arithmetic sequence with first term, a1, and common difference, d.Find a6 when a1 = 13, d = 4.
In Exercises 11–24, use mathematical induction to prove that each statement is true for every positive integer n. 2 + 7 + 12 +. + (5n - 3) = n(5n - 1) 2
Use mathematical induction to prove that for every positive integer n, 1 +4+7+ · .. + (3n - 2): = n(3n - 1) 2
A job pays $30,000 for the first year with an annual increase of 4% per year beginning in the second year. What is the total salary paid over an eight-year period? Round to the nearest dollar.
In Exercises 10–22, solve each equation, inequality, or system of equations. X x + 3 VI 0
In Exercises 10–22, solve each equation, inequality, or system of equations.6x2 - 6 < 5x
In Exercises 16–18, find the indicated term of the arithmetic sequence with first term, a1, and common difference, d.Find a6 when a1 = 5, d = 3.
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 = 40,000, r = 0.1.
The sequences in Exercises 13–18 are defined using recursion formulas. Write the first four terms of each sequence.a1 = 2 and an = 5an-1 for n ≥ 2
In Exercises 11–16, a die is rolled. Find the probability of getting a number greater than 7.
In Exercises 9–30, use the Binomial Theorem to expand each binomial and express the result in simplified form.(3x + 1)4
In Exercises 9–16, use the formula for nCr to evaluate each expression.6C0
In Exercises 15–22, find the indicated term of the arithmetic sequence with first term, a1, and common difference, d.Find a16 when a1 = 9, d = 2.
In Exercises 11–24, use mathematical induction to prove that each statement is true for every positive integer n. 1+3+32 +. ... +3n-1 = 31 2
In Exercises 16–18, find the indicated term of the arithmetic sequence with first term, a1, and common difference, d.Find a12 when a1 = -8, d = -2.
The sequences in Exercises 13–18 are defined using recursion formulas. Write the first four terms of each sequence.a1 = 4 and an = 2an-1 + 3 for n ≥ 2
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.3, 12, 48, 192,.......
In Exercises 17–20, you are dealt one card from a standard 52-card deck. Find the probability of being dealt a queen.
In Exercises 11–24, use mathematical induction to prove that each statement is true for every positive integer n.1 + 2 + 22 +.....+ 2n-1 = 2n - 1
In Exercises 9–30, use the Binomial Theorem to expand each binomial and express the result in simplified form.(x2 + 2y)4
In Exercises 15–22, find the indicated term of the arithmetic sequence with first term, a1, and common difference, d.Find a50 when a1 = 7, d = 5.
Use the Binomial Theorem to expand and simplify: (x2 - 1)5.
In Exercises 10–22, solve each equation, inequality, or system of equations.30e0.7x = 240
In Exercises 16–18, find the indicated term of the arithmetic sequence with first term, a1, and common difference, d.Find a14 when a1 = 14, d = -4.
The sequences in Exercises 13–18 are defined using recursion formulas. Write the first four terms of each sequence.a1 = 5 and an = 3an-1 - 1 for n ≥ 2
In Exercises 17–20, does the problem involve permutations or combinations? Explain your answer.A medical researcher needs 6 people to test the effectiveness of an experimental drug. If 13 people have volunteered for the test, in how many ways can 6 people be selected?
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.3, 15, 75, 375,.......
In Exercises 17–20, you are dealt one card from a standard 52-card deck. Find the probability of being dealt a diamond.
In Exercises 9–30, use the Binomial Theorem to expand each binomial and express the result in simplified form.(x2 + y)4
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 n!
In Exercises 15–22, find the indicated term of the arithmetic sequence with first term, a1, and common difference, d.Find a60 when a1 = 8, d = 6.
Use the Binomial Theorem to write the first three terms in the expansion and simplify: (x + y2)8.
A human resource manager has 11 applicants to fill three different positions. Assuming that all applicants are equally qualified for any of the three positions, in how many ways can this be done?
In Exercises 10–22, solve each equation, inequality, or system of equations. 4x² + 3y² = 48 (3x² + 2y² = 35
In Exercises 10–22, solve each equation, inequality, or system of equations.2x3 + 3x2 - 8x + 3 = 0
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