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mathematics
mathematical applications for the management
Mathematical Applications For The Management, Life And Social Sciences 12th Edition Ronald J. Harshbarger, James J. Reynolds - Solutions
In Problem find the real solutions to each quadratic equation.46.3x – 117 – 0.5x2 = 0
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 functions will be helpful. if x< -1 ーX ソ= 1 if -1 1
Solve 1 + 2x = 1. x + 1 +. 3.
In Problem determine whether each function’s vertex is a maximum point or a minimum point and find the coordinates of this point. Find the zeros, if any exist, and the y-intercept. Then sketch the graph of the function.1/2 x2 + x - y = 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 functions will be helpful.y = √x – 2 -4- (а) (b) 2 4 6 (c) (d) -6 -4 4 6 (e) (f) 1234 (g) (h)
Which of the following three graphs is that of g(x) = 3x – 12 / x + 2? Explain your choice.a.b.c. 2 -2 4 十+ 6 4 6,
In Problem determine whether each function’s vertex is a maximum point or a minimum point and find the coordinates of this point. Find the zeros, if any exist, and the y-intercept. Then sketch the graph of the function.x2 + x + 2y = 5
The profit function for a firm making widgets is P(x) = 88x - x2 - 1200. Find the number of units at which maximum profit is achieved and find the maximum profit.
Find the horizontal and vertical asymptotes of the graph ofF(x) = 8/2x – 10
In Problem find the equation of the function of the specified type that is the best fit for the given data. Plot the data and the equation. cubic y -4 -72 -3 -31 -2 -10 -1 -3 -4 1 -7 2 -6
In Problem find the equation of the function of the specified type that is the best fit for the given data. Plot the data and the equation. cubic y -3 -22 -2 -6 -1 -2 -4 1 -6 2 -2 3 14
In Problem match each equation with the correct graph among those labeled (a)–(h) by recognizing shapes and features of polynomial and rational functions. Use a graphing utility to confirm your choice.y = x3 – x 2468 10 10 (c) (e) +++ (b)
Choose the type of function that models each of the following graphs.a.b. 3 -5 5 - 10
In Problem find the equation of the function of the specified type that is the best fit for the given data. Plot the data and the equation. power y 1 2 2 2.8284 3.4641 4 4 5 4.4721 6 4.899
Solve x2 + ax + b = 0 for x.
In Problem match each equation with the correct graph among those labeled (a)–(h) by recognizing shapes and features of polynomial and rational functions. Use a graphing utility to confirm your choice.y = (x – 3)2(x + 1) 2468 10 10 (c) (e) +++ (b)
(a) Make a scatter plot and develop a model for the following data.(b) What does the model predict for x = 40?(c) When does the model predict f (x) = 0? 4 6 8 10 12 14 16 18 20 y 20.1 19.2 18.8 17.5 17.0 15.8 16.0 14.9 13.8 13.7 13.0
In Problem find the equation of the function of the specified type that is the best fit for the given data. Plot the data and the equation. power y 1 3 2 8.4853 3 15.588 4 24 33.541 6. 44.091
Solve xr2 – 4ar – x2c = 0 for r.
In Problem match each equation with the correct graph among those labeled (a)–(h) by recognizing shapes and features of polynomial and rational functions. Use a graphing utility to confirm your choice.y = 16x2 – x4 2468 10 10 (c) (e) +++ (b)
Suppose the supply and demand functions for a product are given by 6p – q = 180 and (p + 20)q = 30,000, respectively. Find the equilibrium price and quantity.
In Problem match each equation with the correct graph among those labeled (a)–(h) by recognizing shapes and features of polynomial and rational functions. Use a graphing utility to confirm your choice.y = x4 – 3x2 – 4 2468 10 10 (c) (e) +++ (b)
Suppose a company’s total cost for a product is given by C(x) = 15,000 + 35x + 0.1x2 and the total revenue for the product is given by R(x) = 285x – 0.9x2, where x is the number of units produced and sold.(a) Find the profit function.(b) Determine the number of units at which the profit for the
In Problem match each equation with the correct graph among those labeled (a)–(h) by recognizing shapes and features of polynomial and rational functions. Use a graphing utility to confirm your choice.y = x2 + 7x 2468 10 10 (c) (e) +++ (b)
The following table gives the total revenues of Cablenet Communications for selected years.Year Total Revenues (millions)2012 ............................. $63.132013 ............................. 62.912014
In Problem match each equation with the correct graph among those labeled (a)–(h) by recognizing shapes and features of polynomial and rational functions. Use a graphing utility to confirm your choice.y = 7x – x2 2468 10 10 (c) (e) +++ (b)
The U.S. total annual out-of-pocket health care costs (actual and projected in billions of dollars) for selected years from 2003 and projected to 2024 are given in the following table.(a) Plot the data, with x representing the number of years after 2000 and y representing the expenses.(b) Find a
Assume that sales revenues for Continental Divide Mining can be modeled byR(t) = 20.031t2 + 0.776t + 0.179where t is the number of years past 2007.(a) Use the function to determine the year in which maximum revenue occurs and the maximum revenue it predicts.(b) Check the result from (a) against the
In Problem match each equation with the correct graph among those labeled (a)–(h) by recognizing shapes and features of polynomial and rational functions. Use a graphing utility to confirm your choice.y = x – 3 / x + 1 2468 10 10 (c) (e) +++ (b)
In Problem (a) Plot the given points, (b) Determine what type of function best models the data, (c) Find the equation that is the best fit for the data. X y -2 19 -1 8 1 1 -2 2 -1 3 4 4 13
Find the maximum revenue for the revenue functionR(x) = 396x - 0.9x2.
In Problem find the average rate of change of the function between the given values of x.y = - 5x - x2 between x = - 1 and x = 1
Assume that costs and expenses for Continental Divide Mining can be modeled byC(t) = - 0.012t2 + 0.492t + 0.725where t is the number of years past 2007.(a) Use R(t) as given in Problem 20 and form the profit function (as a function of time).(b) Use the function from (a) to find the year in which
In Problem match each equation with the correct graph among those labeled (a)–(h) by recognizing shapes and features of polynomial and rational functions. Use a graphing utility to confirm your choice.y = 1 – 3x / 2x + 5 2468 10 10 (c) (e) +++ (b)
In Problem (a) Plot the given points, (b) Determine what type of function best models the data, (c) Find the equation that is the best fit for the data. y -4 37 -3 19 -2 -1 1 1 1 7 19
In Problem find the average rate of change of the function between the given values of x.y = 8 + 3x + 0.5x2 between x = 2 and x = 4
In Problem (a) Plot the given points, (b) Determine what type of function best models the data, (c) Find the equation that is the best fit for the data. y -3 -11 -2 3 -1 1 1 -3 2 -1 3 13
For each function in Problem find the vertex and determine if it is a maximum or minimum point, find the y-intercept and the zeros if they exist, and sketch the graph.y = x2 + 6x + 9
In Problem (a) Plot the given points, (b) Determine what type of function best models the data, (c) Find the equation that is the best fit for the data. y -3 - 54 -2 -14 -1 1 -2 2 6 3 36
For each function in Problem find the vertex and determine if it is a maximum or minimum point, find the y-intercept and the zeros if they exist, and sketch the graph.y = 12x – 9 – 4x2
In Problem graph the function. x' + 2 ソ= if x 1
In Problem graph the function. x' + 2 ソ= if x 1
If F (x) = x2 – 1/x, find the following.(a) F(–1/3(b) F(10)(c) F(0.001)(d) Is F(0) defined?
In Problem use a graphing calculator to graph each function. Use the vertex and zeros to determine an appropriate window. Be sure to label the maximum or minimum point.y = 20x – 0.1x2
If H(x) = |x – 1|, find the following.(a) H(–1)(b) H(1)(c) H(0)(d) Does H(–x) = H(x)?
In Problem use a graphing calculator to graph each function. Use the vertex and zeros to determine an appropriate window. Be sure to label the maximum or minimum point.y = 50 – 1.5x + 0.01x2
If f (x) = x3/2, find the following.(a) f (16)(b) f (1)(c) f (100)(d) f (0.09)
The monthly profit from the sale of x units of a product is given by P = 16x - 0.01x2 - 900 dollars.(a) What level of production maximizes profit?(b) What is the maximum possible profit?
Find the average rate of change of f (x) = 100x – x2 from x = 30 to x = 50.
Iffind the following.(a) k(–0.1)(b) k(0.1)(c) k(3.9)(d) k(4.1) [4 – 2x if x
In Problem use any method to find the exact real solutions, if they exist.10y2 – y – 65 = 0
The monthly profit from the sale of x units of a product is P = 80x - 0.04x2 - 12,000 dollars.(a) What level of production maximizes profit?(b) What is the maximum possible profit?
Iffind the following.(a) k(–5)(b) k(0)(c) k(1)(d) k(20.001) if x
In Problem use any method to find the exact real solutions, if they exist.(x – 1)(x + 5) = 7
Iffind the following.(a) g(–4)(b) g(1)(c) g(7)(d) g(3.9) 0.5x + 4 if x 4 8(x) = 4 - x
In Problem use any method to find the exact real solutions, if they exist.(x – 3)(1 – x) = 1
In Problem use any method to find the exact real solutions, if they exist.5x2 = 2x + 6
In Problem use any method to find the exact real solutions, if they exist.3x2 = –6x – 2
In Problem(a) Graph each function with a graphing utility;(b) Classify each function as a polynomial function, a rational function, or a piecewise defined function;(c) Identify any asymptotes; and(d) Use the graphs to locate turning points.f (x) = x – 2 / 3 + 2
In Problem(a) Graph each function with a graphing utility;(b) Classify each function as a polynomial function, a rational function, or a piecewise defined function;(c) Identify any asymptotes; and(d) Use the graphs to locate turning points. f(x) = 5x if x0
Iffind the following.(a) f (–2) (b) f (0) (c) f (1) (d) f (2) if x < 1 f(x) = 3x - 2 ifx>1 - 2 ifx>1'
In Problem(a) Graph each function with a graphing utility;(b) Classify each function as a polynomial function, a rational function, or a piecewise defined function;(c) Identify any asymptotes; and(d) Use the graphs to locate turning points. [2x – 1 if x
In Problem graph each function. if x 1
In Problem graph each function.(a) f (x) = (x – 2)2(b) f (x) = (x + 1)3
Latin American Internet use Using data from 2013 and projected to 2019, the number of Internet users (in millions) in Latin America can be modeled byy = 200.8x0.30with x equal to the number of years after 2010 (Source: eMarketer).(a) Does the graph of this function bend upward or downward?(b) Graph
The owner of an apartment building can rent all 50 apartments if she charges $1800 per month, but she rents one fewer apartment for each $60 increase in monthly rent.(a) Construct a table that gives the revenue generated if she charges $1800, $1860, and $1920.(b) Does her revenue from the rental of
Consider the data given in the table.(a) Make a scatter plot.(b) Fit a linear function to the data.(c) Try other function types and find one that fits better than a linear function. 3 10 15 20 25 30 y 100 150 200 220 250 210 190
In a given year, the U.S. federal income tax owed by a married couple filing jointly can be found from the following table (Source: Internal Revenue Service, Form 1040 Instructions).(a) For incomes up to $151,900, write the piecewise defined function T with input x that models the federal tax
The average monthly sales volume (in thousands of dollars) for a company depends on the number of hours of training x of its sales staff, according to(a) Combine the terms of this function over a common denominator to create a rational function.(b) Graph the rational function. 50 S== + 10 + 10
The Municipal Water Authority of Bella Isla used the following function to determine charges for water.where C(x) is the cost in dollars for x thousand gallons of water.(a) Find the monthly charge for 12,000 gallons of water.(b) Find the monthly charge for 825,000 gallons of water. if 0
In Problem use any method to find the exact real solutions, if they exist.16z2 + 16z – 21 = 0
In Problem use any method to find the exact real solutions, if they exist.y2/2 – 11/6 y + 1 = 0
In Problem use any method to find the exact real solutions, if they exist.w2/8 – w/2 – 4 = 0
Using data from 2002 and with projections to 2024, total annual expenditures for national health care (in billions of dollars) can be described byE = 4.61x2 + 43.4x + 1620where x is the number of years past 2000 (Source: U.S. Centers for Medicare and Medicaid Services). If the pattern indicated by
The global spending on travel and tourism (in billions of dollars) can be described by the equationy = 1.48x2 – 25.23x + 416.91where x equals the number of years past 1990 (Source: World Tourism Organization). Find the year after 1990 in which spending is projected to reach $1968 billion.
Using Social Security Administration data for selected years from 2012 and projected to 2050, the U.S. consumer price index (CPI) can be described by the equationC = 0.068t2 + 1.8t + 96where t is the number of years past 2010. With 2012 as the reference year, a year in which the CPI = 120.56 means
Profit Suppose the profit from the sale of x units of a product is P = 50x – 300 – 0.01x2.(a) What level(s) of production will yield a profit of $250?(b) Can a profit of more than $250 be made?
Profit If the profit from the sale of x units of a product is P = 16x – 0.1x2 – 100, what level(s) of production will yield a profit of $180?
In Problem, solve each equation using a graphing utility.6.8z2 – 4.9z – 2.6 = 0
In Problem, solve each equation using a graphing utility.25.6x2– 16.1x – 1.1 = 0
A manufacturer of DVD players has weekly fixed costs of $1540 and variable costs of $12.50 per unit for one particular model. The company sells this model to dealers for $19.50 each.(a) For this DVD player, write the function for weekly total costs.(b) Write the function for total revenue.(c) Write
In Problem solve each equation by factoring.7x2 - x = 26
Solve the equations in Problems. 6/3x - 5 = 6/2x + 3
Suppose that the total cost function for a Bluetooth dock is linear, that the marginal cost is $54, and that the total cost for 50 Bluetooth docks is $8700. Write the equation of this cost function and then graph it.
In Problem solve each equation by factoring.5x2 + 6 = 11x
In Problem solve each equation by factoring.49z2 + 14z + 1 = 0
Stutz Department Store will buy 10 pairs of sunglasses if the price is $75 per pair and 30 pairs if the price is $25. The supplier of the sunglasses is willing to provide 35 pairs if the price is $80 per pair but only 5 pairs if the price is $20. Assuming that the supply and demand functions for
A linear cost function is C(x) = 27.55x + 5180.(a) What are the slope and the C-intercept?(b) What is the marginal cost, and what does it mean?(c) What are the fixed costs?(d) How are your answers to parts (a), (b), and (c) related?(e) What is the cost of producing one more item if 50 are currently
In Problem solve each equation by factoring.4t2 - 4t + 1 = 0
Retailers will buy 45 Wi-Fi routers from a wholesaler if the price is $10 each but only 20 if the price is $60. The wholesaler will supply 56 routers at $42 each and 70 at $50 each. Assuming that the supply and demand functions are linear, find the market equilibrium point.
A linear cost function is C(x) = 5x + 250.(a) What are the slope and the C-intercept?(b) What is the marginal cost, and what does it mean?(c) What are the fixed costs?(d) How are your answers to parts (a), (b), and (c) related?(e) What is the cost of producing one more item if 50 are currently
In Problem solve each equation by factoring.t2 - 4t = 3t2
Complete Problems using the accompanying figure, which shows a supply function and a demand function.Will a price below the equilibrium price result in a market surplus or shortage? 40 30 10 10 20 30 40 50 60 20
In Problem, find the exact real solutions to each equation, if they exist.(x + 1)2 = 2
In Problem, find the exact real solutions to each equation, if they exist.(x + 4)2 = 25
Suppose a certain outlet chain selling appliances has found that for one brand of home theater, the monthly demand is 240 when the price is $900. However, when the price is $850, the monthly demand is 315. Assuming that the demand function for this system is linear, write the equation for the
Suppose a television manufacturer has the total cost function C(x) = 210x + 3300 and the total revenue function R(x) = 430x.(a) What is the equation of the profit function for this commodity?(b) What is the profit on 500 items?
Bacteria of species A and species B are kept in a single environment, where they are fed two nutrients. Each day the environment is supplied with 10,600 units of the first nutrient and 19,650 units of the second nutrient. Each bacterium of species A requires 2 units of the first nutrient and 3
If the demand function and supply function for Z-brand juicers are p + 2q = 100 and 35p - 20q = 350, respectively, compare the quantity demanded and the quantity supplied when p = 14. Are there surplus juicers or not enough to meet demand?
In Problem, solve each equation using the quadratic formula. Give real answers (a) Exactly (b) Rounded to two decimal places.6x - 2 = 3x2
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