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mathematics
mathematical applications for the management

Questions and Answers of Mathematical Applications for the Management

In Problem, solve each equation using the quadratic formula. Give real answers (a) Exactly (b) Rounded to two decimal places.7 - 2x - x2 = 0
The total cost function for a product is C(x) = 30x + 1200, and the total revenue is R(x) = 38x, where x is the number of units produced and sold.(a) Find the marginal cost.(b) Find the profit
A small business sells custom oak moldings in 12-foot lengths. One molding type has the revenue functionR(x) = 69xand the cost functionC(x) = 1400 + 55xFind the number of 12-foot lengths of this
A cake manufacturer boxes Swiss chocolate and German chocolate cakes at one site. A box of Swiss chocolate cake contains 0.55 lb of a sugar mixture and 0.45 lb of flour. A box of German chocolate
A freight company has shipping orders for two products. The first product has a unit volume of 10 cu ft and weighs 50 lb. The second product’s unit volume is 3 cu ft, and it weighs 40 lb. If the
Use the left-to-right elimination method to solve the systems in Problems. х — Зу — z%3 0 х — 2у + z 3 8 2х — бу + 2z3D6
In Problems, solve each system by elimination or by any convenient method. бх — 4у 3D 16 9х — бу 3D 24
In Problems, solve each system by elimination or by any convenient method. [ (0.5x + y = 3 (0.3х + 0.2у %3D6
The selling price for each item of a product is $50, and the total cost is given by C(x) = 10x + 18,000, where x is the number of items.(a) Write the revenue function.(b) Find C(100) and write a
In Problems, solve each system by elimination or by any convenient method. Sx- 3y = -1 7. 8х + 3у — 11
The supply function for a product is p = 5q + 1500, and the demand function is p = – 3q + 3100. Find the quantity and price that give market equilibrium.
In Problems, solve each system by elimination or by any convenient method. Sx - y = 1 l3x – y = 1
In Problem solve each equation by factoring.x = x2
Amanda plans to invest $20,000, part of it at a 9% interest rate and part of it in a safer fund that pays 6%. How much should be invested in each fund to yield an annual return of $1560?
An airline has 360 seats on a plane for one of its flights. If 90% of the people making reservations actually buy a ticket, how many reservations should the airline accept to be confident that it
A building is depreciated by its owner, with the value y of the building after x months given by y = 720,000 – 2000x.(a) Find the y-intercept of the graph of this function and explain what it
In Problems, solve each system by elimination or by any convenient method. S4x + 6y = 4 |2x + 3y = 2
If a line is horizontal, then its slope is _______.
If a line is vertical, then its slope is _______.
What is the rate of change of the function whose graph is a line passing through (3, 2) and (-1, 2)?
What is the rate of change of the function whose graph is a line passing through (11, -5) and (-9, -4)?
In Problems, find the slope and y-intercept and then graph each equation.y = 7/3x - 1/4
In Problems, find the slope and y-intercept and then graph each equation.y = 4/3x + 1/2
In Problems, find the slope and y-intercept and then graph each equation.y = -2
In Problems, find the slope and y-intercept and then graph each equation.x = -8
In Problems, find the slope and y-intercept and then graph each equation.x = -1/2
In Problems, find the slope and y-intercept and then graph each equation.2x + 3y = 6
In Problems, find the slope and y-intercept and then graph each equation.3x - 2y = 18
In Problems, write the slope-intercept form of the equation of the line that has the given slope and y-intercept. Then graph the line.Slope 1/2 and y-intercept -3
In Problems, write the slope-intercept form of the equation of the line that has the given slope and y-intercept. Then graph the line.Slope 4 and y-intercept 2
In Problems, write the slope-intercept form of the equation of the line that has the given slope and y-intercept. Then graph the line.Slope -2 and y-intercept 1/2
In Problems, write the slope-intercept form of the equation of the line that has the given slope and y-intercept. Then graph the line.Slope -2/3 and y-intercept -1
In Problems, write the equation of the line that passes through the given point and has the given slope. Then graph the line.(2, 0) with slope -5
In Problems, write the equation of the line that passes through the given point and has the given slope. Then graph the line.(1, 1) with slope -1/3
In Problems, write the equation of the line that passes through the given point and has the given slope. Then graph the line.(-1, 4) with slope -3/4
In Problems, write the equation of the line that passes through the given point and has the given slope. Then graph the line.(3, -1) with slope 1
In Problems, write the equation of the line that passes through the given point and has the given slope. Then graph the line.(-1, 1) with undefined slope
In Problems, write the equation of the line that passes through the given point and has the given slope. Then graph the line.(1, 1) with 0 slope
In Problems, write the equation of each line described or shown. y 4 -6 3 6 -12 -16
In Problems, write the equation of each line described or shown. + + 2 4 6 8 1012 -1十 -2 + す 2.
Write the equation of the line passing through (-2, -7) that is parallel to 3x + 5y = 11.
Write the equation of the line passing through (6, -4) that is parallel to 4x - 5y = 6.
Write the equation of the line passing through (3, 1) that is perpendicular to 5x - 6y = 4.
The dollars per capita of federal tax burden T can be modeled byT = 2.11x3 - 93.01x2 + 1373.9x + 394where x is the number of years past 1990.(a) Graph this function for values of x that correspond to
Using data from 2000 and projected to 2025, the percent p of the U.S. population that uses the Internet can be described byp = 1.19x + 58.0where x is the number of years after 1990 (Source:Nation and
Using U.S. Department of Energy data from 2010 and projected to 2032, the millions of metric tons of carbon dioxide emissions from biomass energy combustion, y, in the United States can be modeled
Using data from 2014 and projected to 2019, the percent of people in the world who are Internet users can be described by p = 2.14x + 32.2 where x is the number of years after 2010 (Source:
For adults, the desired heart rate to achieve weight loss during exercise is given by the linear function H = -0.650t + 143 where t equals the person’s age and H equals the heart rate in beats per
In Problems, find the slope of the line passing through the given pair of points.(-4, 2) and (-4, -2)
In Problems, find the slope of the line passing through the given pair of points.(3, 2) and (-1, 2)
A couple seeking to buy a home decides that a monthly payment of $1600 fits their budget. The amount they can borrow, A, is a function of the time t, in years, it will take to repay the debt. If we
Suppose y = g(x) has the graph in Problem 6(b).(a) Find g(0).(b) How many x-values in the domain of this function satisfy g(x) = 0? 10 6. 4. 2. -8 -4 6 8 10 2 -4 -6 -8 -10+
Disposable income, the amount left after taxes have been paid, is one measure of the health of the economy. Using U.S. Energy Information Administration data for selected years from 2015 and
Data and projections from the Centers for Medicare and Medicaid Services from 2010 to 2024 indicate that the annual per capita out-of-pocket expenses for health care can be approximated byy = 39.6x +
Using data from 2010 and projected to 2020, the population of the United Kingdom (y, in millions) can be approximated by the equation 10.0y – 4.55x = 581 where x is the number of years after 2000
Burnem Inc. manufactures thumb drives and sells them to a distributor. Burnem’s total cost and total revenue (in dollars) for x thumb drives are given by Total cost = 2x + 7920 and Total
In Problem solve each inequality and graph the solution. 4x 5x 3> 2 3 12
In Problem solve each inequality and graph the solution. 3x 2(x – 1) 6. 3 4,
In Problem solve each inequality and graph the solution.– 2x/5 ≤ – 10 – x
In Problem solve each inequality and graph the solution.– 3x/2 > 3 – x
In Problem solve each inequality and graph the solution.7x + 4 ≤ 2(x – 1)
In Problem solve each inequality and graph the solution.2(x – 1) – 3 > 4x + 1
In Problem, solve each inequality. x - 1 -+ 1>x +1 2.
In Problem, solve each inequality. 3(x 1)
In Problem, solve each inequality.17 – x < – 4
Using data from 2010 and projected to 2050, the number of millions of U.S. adults with diabetes, y, can be approximated by the formulawhere t is the number of years after 2000 (Source: Centers for
Use the following factorization formulas involving cubes to factor each expression in Problems27 + 8x3 Factorizations with Cubes Perfect cube a? + 3a?b + 3ab? + b3 = (a + b)³ Perfect cube a? -
In Problem, simplify the expression with a exponents positive.54/(5-2 · 53)
In Problems, write an inequality that describes each interval or graph. +o+ 4 5 6 8. 2.
In many applications, it is necessary to write expressions in the form cxn, where c is a constant and n is an integer. In Problems, write the expressions in this form.1/4x2
Using data from 2014 and projected to 2019, the percent of people in the world who are Internet users can be approximated accurately by(1) y = 2.14t + 32.2 or by(2) y = 0.00536t2 + 2.07t + 32.4with t
In rationalize each denominator and then simplify.3√m2x / 3√mx5
In Problem, perform the indicated operations and simplify.(2x – 3)3
Use the following factorization formulas involving cubes to factor each expression in Problemsx3 – 64 Factorizations with Cubes Perfect cube a? + 3a?b + 3ab? + b3 = (a + b)³ Perfect cube a? - 3a?b
In many applications, it is necessary to write expressions in the form cxn, where c is a constant and n is an integer. In Problems, write the expressions in this form.3/2x4
In rationalize each denominator and then simplify.4√mx3 / 4√y2z5
In Problem, perform the indicated operations and simplify.(3x + 4)3
Use the following factorization formulas involving cubes to factor each expression in Problems8x3 – 1 Factorizations with Cubes Perfect cube a? + 3a?b + 3ab? + b3 = (a + b)³ Perfect cube a? - 3a?b
In many applications, it is necessary to write expressions in the form cxn, where c is a constant and n is an integer. In Problems, write the expressions in this form. 3 X-
Use the following federal tax table for a single person claiming one personal exemption.(a) Write the last three taxable income ranges as inequalities.(b) If an individual has a taxable income of
Blood types are determined by the presence or absence of three antigens: A antigen, B antigen, and an antigen called the Rh factor. The resulting blood types are classified as follows:type A if the A
In Problem, perform the indicated operations and simplify.(x3 + x – 1) ÷ (x + 2)
In many applications, it is necessary to write expressions in the form cxn, where c is a constant and n is an integer. In Problems, write the expressions in this form. X- 3
In Problem, perform the indicated operations and simplify.(x5 + 5x – 7) ÷ (x + 1)
Use the following factorization formulas involving cubes to factor each expression in Problemsa3 + 216 Factorizations with Cubes Perfect cube a? + 3a?b + 3ab? + b3 = (a + b)³ Perfect cube a? - 3a?b
In Problem, perform the indicated operations and simplify.(x4 + 3x3 – x + 1) ÷ (x2 + 1)
In Problem, perform the indicated operations and simplify.(x3 + 5x2 – 6) ÷ (x2 – 2)
The total U.S. personal income I (in billions of dollars) from 1960 and projected to 2024 can be approximated by I = 533.6(1.065)t where t is the number of years after 1960 (Source: U.S. Bureau
In Problem factor each expression completely.4(x2 + 1)2 – 2(x2 + 1)3
For the years 2013 through 2020, the estimated annual production of shale-natural gas in China, in billions of cubic feet, can be approximated by the formula y = 0.012(1.75)t where t is the
In Problem, perform the indicated operations with expressions involving fractional exponents and radicals and then simplify. (√x + 3)(√x – 3)
Life expectancy in the United States can be approximated with the equation L = 29x0.22 where x is the number of years the birth year is past 1900 (Source: National Center for Health
In Problem, perform the indicated operations with expressions involving fractional exponents and radicals and then simplify. (x1/5 + x1/2)(x1/5 – x1/2)
In Problem, perform the indicated operations with expressions involving fractional exponents and radicals and then simplify.(2x + 1)1/2[(2x + 1)3/2 – (2x + 1)–1/2]
For the years after 1965, the percent of people who say they trust the government always or most of the time can be approximated by y = 154 / x0.5 where x is the number of years after 1960.(a)
In Problem, perform the indicated operations with expressions involving fractional exponents and radicals and then simplify.(4x – 3)–5/3[(4x – 3)8/3 +3(4x – 3)5/3]
The half-life of strontium-90 is 25 years. Find the amount of strontium-90 remaining after 10 years if q0 = 98 kg.In use the fact that the quantity of a radioactive substance after t years is given
A company sells its product for $55 per unit. Write an expression for the amount of money received (revenue) from the sale of x units of the product.
The half-life of carbon-14 is 5730 years. Find the amount of carbon-14 remaining after 10,000 years if q0 = 40.0 g.In use the fact that the quantity of a radioactive substance after t years is given
Suppose the formula for the growth of the population of a city for the next 10 years is given byP = P0(2.5)htwhere P0 is the population of the city at the present time and P is the population t years

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