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mathematics
mathematical applications for the management
Questions and Answers of
Mathematical Applications for the Management
The following tables give the capital expenditures and gross operating costs of manufacturing establishments for pollution abatement, in millions of dollars.(a) Use a calculator or spreadsheet to
In Problems, use inverse matrices to find the solution of the systems of equations. -X2 X4 0.7 X1 + X2 - X3 - 1.5x4 0.5x5 = -1.6 0.5x1 + 1.75x2 - x3 - 1.25x4 - 0.25x5 1.275 -0.5x1 X2 + x3 + X4 1.15
In Problems, find the inverse of each matrix. 7 -1 -10 2
In Problems, use inverse matrices to find the solution of the systems of equations. 2х + 3x2 + X4 + 3x5 = + 2х; + 3x4 + Xs — X1 27 + 2x4 + 3x5 = -15 + 2х3 + 2x4 + Xs — X2 X1 24 X1 + 3x5 = -24
In Problems, find the inverse of each matrix. 2 3 4 -1 1 1
In Problem use technology to solve each system of equations, if a solution exists. X1 + 2x2 + 3x3 + 4x4 = 2 X1 + 2x2 + 4x3 + 3x4 = 2 2x1 + 4x2 + Sx3 + 8x4 = 4 X1 + 4x2 + 3x3 %3D = 4
In Problems, find the inverse of each matrix. 3 3 2 -1 4 2 5 3. 2.
In Problem use technology to solve each system of equations, if a solution exists. X1 + 3x2 + 4x3 - x4 + 2x5 = 1 X1 - x2 - 2x3 + x4 X1 + 2x2 + 3x3 + x4 + 4xs = 0 + X4 = 3 %3D 2x1 + 2x2 + 2x3 + 2x5 = 4
The following table gives the years of life expectancy at birth for Blacks and Whites born in the United States for selected years projected to 2060.(a) Make a matrix A containing the information for
In Problem use technology to solve each system of equations, if a solution exists. 2x1 - x2 + x3 + 3x4 + 3x5 = X1 + x2 + x3 + 2x4 + 2x5 2x1 + x2 - x3 + x4 + x5 = -3 4x1 - X2 - 3x3 + X4 + x5 = 1
The following table shows the 2024 projected U.S. health expenditures of various types (both total and per capita).(a) Use the data to make a 2 x 4 matrix E with each column representing a type of
SolveThis gives a formula for solving two equations in two variables for x. Sax + biy = c1, for x. lazx + bay = c2
In Problems,(a) Evaluate each determinant (b) Use the determinant to decide whether each matrix has an inverse. Use technology in Problems. 3 2 -1 2 0 1 1 1,
Solve This gives a formula for solving two equations in two variables for y. Sajx + biy = lazx + bzy = c2 for y.
Does the following matrix have an inverse? 1 4 -4 1 -2 2. 2.
Ace, Baker, and Champ are being purchased by ALCO, Inc., and their outstanding debts must be paid by the purchaser. The following matrix gives the amounts of debt in dollars and the terms for the
In Problems, (a) Evaluate each determinant (b) Use the determinant to decide whether each matrix has an inverse. Use technology in Problems. 1 2 3 1 -1 -2 2.
A sales associate’s expense account for the first week of a certain month has the daily expenses (in dollars) shown in matrix A.(a) The associate finds that expenses for the second week are 5% more
In Problems, (a) Evaluate each determinant (b) Use the determinant to decide whether each matrix has an inverse. Use technology in Problems. 1 3 1 4 -1 3.
When a firm buys another company, the company frequently has some outstanding debt that the purchaser must pay. Consider three companies, A, B, and C, that are purchased by Maxx Industries. The
In Problems, (a) Evaluate each determinant (b) Use the determinant to decide whether each matrix has an inverse. Use technology in Problems. 3 1 4 -1 2 5 4 3 -1 0 4 2 2.
The Burr Cabinet Company manufactures bookcases and filing cabinets at two plants, A and B. Matrix M gives the production for the two plants during June, and matrix N gives the production for July.
Over the period of time 2009–2018, the return (per dollar invested) on Maura stock was 0.013469 per month, the return on Ward was 0.013543 per month, and the return on Goldsmith was 0.006504 per
Ace Trucking Company has an order for three products (A, B, and C) for delivery. The table gives the volume in cubic feet, the weight in pounds, and the value for insurance in dollars for a unit of
In Problems, solve each system of equations. x + 2y + 3z = 5 y + 11z = 21 5y + 9z = 13
The average annual cost per consumer for health care can be modeled by A = 476x + 5830 where x is the number of years from 2005 and projected to 2024.(a) Is A a linear function of x?(b) Find the
In problem solve the equations.10 – 2(2x – 9) – 4(6 + x) = 52
In problem solve the equations.4x – 3 = x/2 + 6
In problem solve the equations. 4x 3 + 4 = x + 1
In problem solve the equations. Зх — 1 5 3x 4x 7 ||
For f (x) = 7 + 5x – 2x2, find and simplify f(x + h) – f(x) h
Solve 1 + 2/3x ≤ 3x + 22 and graph the solution.
Solve for y: 3(y - 2) = -2(x + 5)
In Problem find the intercepts and graph the7x + 5y = 21
Consider the function f (x) = √4x + 16.(a) Find the domain and range.(b) Find f (3).(c) Find the y-coordinate on the graph of y = f (x) when x = 5.
Write the equation of the line passing through (–1, 2) and (3, – 4). Write your answer in slope-intercept form.
In Problems, solve the inequality and graph the solution.5x + 1 ≥ 2/3(x - 6)
Find the slope and the y-intercept of the graph of 5x + 4y = 15.
Write the equation of the line through (–3, –1) that(a) Has undefined slope(b) Is perpendicular to x = 4y – 8.
Which of the following relations [(a), (b), (c)] are functions of x? Explain.(a)(b) x y 1
Graph y = x2 – 12x(a) In the standard window and(b) In x-min = – 10, x-max = 30; y-min = – 40, y–max = 40.
What are the domain and range of the functiony = √9 - x ?
Solve the system Зх + 2у 3D—2 4х + 5у %3
In Problems, solve each system by elimination or by any convenient method. S-4x + 3y = -5 | 3x – 2y = 4
Given f (x) = 5x2 – 3x and g(x) = x + 1, find(a) (fg)(x)(b) g(g(x))(c) (f°g)(x)
If g(x) = x2 + 1/x, find the following.(a) g(-1)(b) g(1/2)(c) g(0.1)
In Problems, solve each system by elimination or by any convenient method. х+ 2у 3 3 3x + 6y = 6 ||
Using U.S. Bureau of Labor Statistics data for selected years from 1950 and projected to 2050, the number of men in the U.S. workforce (in millions) can be approximated byM = 0.59x + 43.2where x
In Problems, solve each system by elimination or by any convenient method. S0.2x – 0.3y = 4 12.3x – y = 1.2
The following table defines y as a function of x, denoted y = f(x).Use the table to complete the following.(a) Identify the domain and range of y = f(x).(b) Find f(4).(c) Find all x-values for which
In Problems, find the intercepts and graph.x = -2
In Problems, find the slope and y-intercept of each line.2x + 5y = 10
In Problems, find the slope and y-intercept of each line.x = -3/4 y + 3/2
In Problems, write the equation of each line described.Through (-1, 8) and (-1, -1)
In Problems, write the equation of each line described.Through (1, 6) and parallel to y = 4x - 6
In Problems, write the equation of each line described.Through (-1, 2) and perpendicular to 3x + 4y = 12
Use a graphing calculator and the x-intercept method to approximate the solution of 7x - 2 = 0.
In Problems, solve each system of equations. 4х — 2у — 6 Зх + 3у 3 9
In Problems, solve each system of equations. 2х + у3D 19 х — 2у 3D 12
In Problems, solve each system of equations. S3x + 2y = 5 |2x – 3y = 2х — Зу %3D 12
Using Social Security Administration data for selected years from 2012 and projected to 2050, the U.S. consumer price index (CPI) can be modeled by the functiony = 0.0682x2 + 1.76x + 96.0where x is
Write the equation of the line passing through (-2, -8) that is perpendicular to x = 4y + 3.
In Problems, solve each system of equations. 4х — Зу — 253 13х + 2у 3D —12
In Problems, solve each system of equations. х+ у — 2%3D 12 = 12 2y – 3z = -7 Зх + Зу — 7z 3D 0
When a couple purchases a home, one of the first questions they face deals with the relationship between the amount borrowed and the monthly payment. In particular, if a bank offers 25-year loans at
For many species of fish, the weight W is a function of the length L that can be expressed by W = W(L) = kL3 k = constantSuppose that for a particular species, k = 0.03 and that for this
Body-heat loss due to convection depends on a number of factors. If Hc is body-heat loss due to convection, Ac is the exposed surface area of the body, Ts - Ta is skin temperature minus air
Write the equation of the linear relationship between temperature in Celsius (C) and Fahrenheit (F) if water freezes at 0°C and 32°F and boils at 100°C and 212°F.
The amount y of photosynthesis that takes place in a certain plant depends on the intensity x of the light present according toy = 120x2 - 20x3 for x ≥ 0(a) Graph this function
A retired couple have $600,000 to invest and want to earn $60,000 per year in interest. The safer investment yields 9.5%, but they can supplement their earnings by investing some of their money at
A certain commodity sells for $52 per unit and has the following costs for a period.Fixed cost: $1500Variable cost per unit:
Suppose that for a certain product, the supply and demand functions prior to any taxation areSupply: p = q/10 + 8Demand: 10p + q = 1500If a tax of $2 per item is levied on the supplier and is passed
In Problem find the real solutions to each quadratic equation.(x – 1)(x + 3) = – 8
Find the average rate of change off(x) = x2 – 30x + 22over the interval [10, 50].
In Problem match each of the functions with one of the graphs labeled (a)–(l) shown following these functions. Recognizing special features of certain types of functions and plotting points for the
Sketch a graph of each of the following functions.(a) f (x) = x4(b) g(x) = |x|(c) h(x) = –1(d) k(x) = √x
In Problem match each of the functions with one of the graphs labeled (a)–(l) shown following these functions. Recognizing special features of certain types of functions and plotting points for the
The following figures show graphs of the power function y = xb. Which is the graph for b > 1? Which is the graph for 0 < b < 1?a.b. y
In Problem match each of the functions with one of the graphs labeled (a)–(l) shown following these functions. Recognizing special features of certain types of functions and plotting points for the
If f (x) = ax2 + bx + c and a < 0, sketch the shape of the graph of y = f (x).
In Problem match each of the functions with one of the graphs labeled (a)–(l) shown following these functions. Recognizing special features of certain types of functions and plotting points for the
Graph:(a) f (x) = (x + 1)2 – 1(b) f (x) = (x – 2)3 + 1
In Problem match each of the functions with one of the graphs labeled (a)–(l) shown following these functions. Recognizing special features of certain types of functions and plotting points for the
Which of the following three graphs is the graph of f (x) = x3 – 4x2? Explain your choice.a.b.c. 8. 6. 4 -2 2 4 6 8 10 -4
In Problem (a) Find the vertex of the graph of the equation, (b) Determine whether the vertex is a maximum or minimum point, (c) Determine what value of x gives the optimal value of
In Problem match each of the functions with one of the graphs labeled (a)–(l) shown following these functions. Recognizing special features of certain types of functions and plotting points for the
LetFind the following:(a) The y-coordinate of the point on the graph of y = f (x) where x = 16(b) f (–2)(c) f (13) 8x + 1/x if x
In Problem (a) Find the vertex of the graph of the equation, (b) Determine whether the vertex is a maximum or minimum point, (c) Determine what value of x gives the optimal value of
In Problem find the real solutions to each quadratic equation.4x2 = 3
In Problem match each of the functions with one of the graphs labeled (a)–(l) shown following these functions. Recognizing special features of certain types of functions and plotting points for the
Sketch the graph of if x < 1 8(x) = 4-x if x> 1
In Problem find the real solutions to each quadratic equation.20x2 + 3x = 20 – 15x2
In Problem match each of the functions with one of the graphs labeled (a)–(l) shown following these functions. Recognizing special features of certain types of functions and plotting points for the
Find the y-intercept, vertex, and zeros (if they exist) and sketch the graph of f (x) = 21 – 4x – x2.
In Problem find the real solutions to each quadratic equation.8x2 + 8x = 1 – 8x2
In Problem match each of the functions with one of the graphs labeled (a)–(l) shown following these functions. Recognizing special features of certain types of functions and plotting points for the
Solve 3x2 + 2 = 7x.
In Problem find the real solutions to each quadratic equation.7 = 2.07x – 0.02x2
If in a monopoly market the demand for a product is p = 175 - 0.50x and the revenue function is R = px, where x is the number of units sold, what price will maximize revenue?
In Problem match each of the functions with one of the graphs labeled (a)–(l) shown following these functions. Recognizing special features of certain types of functions and plotting points for the
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