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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

Find the derivatives of the functions in Problem. Simplify and express the answer using positive exponents only.y = (x3 - 4x)10/10
In Problem, find the third derivative.y = 1/x
Differentiate the functions in Problem. 3 f(s) = (2s5 + 1)4
In Problem, find each limit, if it exists. 4x3 lim x-2 4x 8x² 16x
Find the derivatives of the functions in Problem.w = z7 - 3z6 + 13
In Problem, find the indicated derivatives and simplify.dp/dq for p = q2 + 3/2q - 1
In Problem, use derivative formulas to find the derivative of each function. Simplify, except for Problem 10.g(x) = 3/4/(2x5 + 7x3 - 5)12
Find the derivatives of the functions in Problem. Simplify and express the answer using positive exponents only.C(w) = 1 + w2 - w4/1 + w4
In Problem, use the graph of y = f (x) and the given c-value to find the following, whenever they exist.(a) lim x→c- f (x)(b) limx→c+ f (x)(c) limx→c f (x)(d) f (c)c = 4 1/2 y -9. -6 -3 3 y f(x) ... -3· +-6
In Problem, find the third derivative.f (x) = 3x5 - x6
Differentiate the functions in Problem.p = (q3 + 1)-5
Find the derivatives of the functions in Problem.y = 3x5 - 5x3 - 8x + 8
In Problem, use derivative formulas to find the derivative of each function.f(x) = (3x5 - 2x + 3)(4x10 + 10x4 - 17)
Find the derivatives of the functions in Problem. Simplify and express the answer using positive exponents only.f(u) = u3 + 1/u2
In Problem, use the graph of y = f (x) and the given c-value to find the following, whenever they exist.(a) limx→c- f (x)(b) limx→c+ f (x)(c) limx→c f (x)(d) f (c)c = 2 у 2 3 -1 y = f(x) -3
In Problem, find the third derivative.f (x) = 2x9 - 6x6
Differentiate the functions in Problem.g (x) = (x4 - 5x)-2
Find the derivatives of the functions in Problem.y = 10x5 - 3x3 + 5x - 11
In Problem, use derivative formulas to find the derivative of each function. Simplify, except for Problem 10. 3x y = 2х + 11
Find the derivatives of the functions in Problem. Simplify and express the answer using positive exponents only.y = (x3 - 5x2 + 1)(x3 - 3)
In Problem, determine whether each function is continuous or discontinuous at the given x-value. Examine the three conditions in the definition of continuity. S² + 1 2x2 - 1 ifx>1’ if x < 1 f(x) = x = 1
Differentiate the functions in Problem.p(q) = 4(3q2 - 1)4 - 13q
In Problem, total revenue is in dollars and x is the number of units. Suppose the total revenue for a certain product is given by R(x) = 25x - 0.05x2.(a) Graph the marginal revenue function for this product.(b) Determine the number of units that must be sold to maximize total revenue.(c) What is
Find the derivatives of the functions in Problem.f(x) = 3x4 - x9
In Problem, find the derivative but do not simplify your answer.y = (x2 + x + 1)(3√x - 2√x + 5)
In Problem, use derivative formulas to find the derivative of each function. Simplify, except for Problem 10.p = 9t10 - 6t7 - 17t + 23
Find the derivatives of the functions in Problem. Simplify and express the answer using positive exponents only.y = (x2 - 2)(x + 4)
In Problem, determine whether each function is continuous or discontinuous at the given x-value. Examine the three conditions in the definition of continuity. x - 3 if x < 2 f(x) x = 2 4x – 7 — 7 if x> 2'
Differentiate the functions in Problem.s(t) = 5t - 3(2t4 + 7)3
Find the derivatives of the functions in Problem.f(x) = 3x4 - x6
In Problem, find the derivative but do not simplify your answer.y = (5√x - 24√x + 1)(x3 - 5x - 7)
In Problem, use derivative formulas to find the derivative of each function. Simplify, except for Problem 10.B = 0.523W - 5176
Find the derivatives of the functions in Problem. Simplify and express the answer using positive exponents only.y = 3x2 + 4√x
In Problem, determine whether each function is continuous or discontinuous at the given x-value. Examine the three conditions in the definition of continuity. 6x + 8 f(x) x + x – 20 x = 4
In Problem, a graph of y = f (x) is shown and a c-value is given. For each problem, use the graph to find the following, whenever they exist.(a) limx→c f(x) and(b) f(c) c = -8 y = f(x) -12 -8 -4 -8
In Problem, find the second derivative.y = 3x2 - 3√x2
Differentiate the functions in Problem.k(x) = 5/7 (2x3 - x + 6)14
In Problem, use the graph of y = f (x) in Figure 9.40 to find the functional values and limits, if they exist.(a) f (2)(b) limx→2 f(x) y 2 y = f(x) 2 4
Find the derivatives of the functions in Problem.y = 12 + 2x - 7x3
Let f(x) = 4x/x2 - 8x. Identify all x-values where f (x) is not continuous.
Find the derivatives of the functions in Problem. Simplify and express the answer using positive exponents only.g (x) = 5x3 + 4/x
In Problem, a graph of y = f (x) is shown and a c-value is given. For each problem, use the graph to find the following, whenever they exist.(a) limx→c f(x) (b) f(c)c = -2 y= f(x)
In Problem, find the second derivative.y = x3 - √x
In Problem, total revenue is in dollars and x is the number of units.Suppose that demand for local cable TV service is given byp = 120 - 0.4xwhere p is the monthly price per subscriber in dollars and x is the number of subscribers (in hundreds).(a) Find the total revenue as a function of the number
Find the derivatives of the functions in Problem.y = 6 - 8x + 2x2
(a) Write the limit definition for f'(x).(b) Use the definition from (a) to find f'(x) for f(x) = 3x2 - x + 9.
In Problem, find the second derivative.h(x) = x2 - 1/x2
In Problem, total revenue is in dollars and x is the number of units.Suppose that the total revenue function for a commodity is R(x) = 44x - 0.05x2.(a) Find R(50) and tell what it represents.(b) Find the marginal revenue function.(c) Find the marginal revenue at x = 50 and tell what it predicts
In Problem, for each given function, find the average rate of change over each specified interval.For f (x) given in the table, over(a) [3, 3.5] and(b) [2, 6] X 1 2 3 3.5 3.7 6. f(x) 40 25 18 15 18 38
In Problem, find the derivative and simplify.f(x) = (x12 + 3x4 + 4)(2x3 - 1)
In Problem, evaluate the limits, if they exist. Use algebraic methods. 5x – 25 lim x-5 x + 5
In Problem, a graph of y = f (x) is shown and a c-value is given. For each problem, use the graph to find the following, whenever they exist.(a) limx→c f(x) and(b) f(c)c = -10 y 15- 10- y=f(x) -15 -10 -5 ++
In Problem, find the second derivative.g (x) = x3 - 1/x
In Problem, total revenue is in dollars and x is the number of units.Suppose that the total revenue function for a commodity is R = 64x - 0.02x2.(a) Find R(100) and tell what it represents.(b) Find the marginal revenue function.(c) Find the marginal revenue at x = 100 and tell what it predicts
In Problem, for each given function, find the average rate of change over each specified interval.For f (x) given by the table, over(a) [2, 5] and(b) [3.8, 4] 2.5 3 3.8 4 f(x) 14 20 22 19 17 16 30
In Problem, find the derivative and simplify.y = (3x7 + 4)(8x6 - 6x4 - 9)
In Problem, evaluate the limits, if they exist. Use algebraic methods. - 5х — 14 lim x+7 бх — 7
In Problems, find dy/du, du/dx, and dy/dx.(a) y = u4 and u = x2 + 4x(b) y = u10 and u = x2 + 5x
In Problem, evaluate the limits, if they exist. Use algebraic methods. 8x lim x-0 2 + x - 5x2 4х + 1
In Problem, total revenue is in dollars and x is the number of units.(a) If the total revenue function for a product is R(x) = 4x, what is the marginal revenue function for that product?(b) What does this marginal revenue function tell us?
In Problems, find dy/du, du/dx, and dy/dx.(a) y = u3 and u = x2 + 1(b) y = u4 and u = 4x2 - x + 8
In Problem, evaluate the limits, if they exist. Use algebraic methods. 4x lim х>-2 4х — 8
A home improvement warehouse, HIW, has 15 sump pumps in stock. The company sells these pumps for $150 each, with a double-your-money-back guarantee for any defective pump. Suppose the probability of any pump being defective is 0.08 and each pump’s quality is independent.(a) Find the mean and
Suppose a birth control pill is 99% effective in preventing pregnancy. What number of women would be expected to get pregnant out of 100 women using this pill?
Suppose that when an oil company drills a well, there is a 15% chance that it will produce oil. Assume that the outcomes of the drillings are independent and the company drills 12 wells.(a) Find the mean and standard deviation of the number of successful wells.(b) Find the probability that at most
The probability that a manufacturer produces defective faucets is 0.001. What is the expected number of defective faucets in a shipment of 3000?
Islands Realty estimates that 5% of the families who inquire about time-share villas will purchase one. If this is true, what is the probability that no more than 20 of 500 families who inquire about time-share villas will make a purchase?
Suppose that a particular Walgreens estimates that it will earn 10% of the printer ink business by offering an ink cartridge refill program. If the estimate is correct, what is the probability that more than 800 of the 7500 persons who need ink will use this Walgreens program?
The table gives the private school enrollments as percents of total school enrollment (actual and projected) for selected school years from 1899–1900 to 2021–2022. Find the mean and standard deviation of the percents of private school enrollments for the given school years. School Year %
Forty-eight percent of accountants taking a CPA exam fail the first time. If 1000 candidates take the exam for the first time, what is the expected number that will pass?
In a family with 2 children, the probability that both children will be boys is 1/4. Suppose 1200 families with two children are selected at random.(a) How many of the families would we expect to have 2 boys?(b) What is the standard deviation of the number of families with 2 boys?(c) Suppose that
A candidate claims that 60% of the voters in his district will vote for him.(a) If his district contains 100,000 voters, how many votes does he expect to get from his district?(b) What is the standard deviation of the number of these votes?(c) If the number of votes the candidate gets is 2 standard
Suppose it has been determined that the probablity is 0.6 that a rat injected with cancerous cells will live. If 35 rats are injected, how many would be expected to die?
Disposable income is the amount left after taxes have been paid. The following table gives the U.S. per capita disposable income (in thousands of dollars) for selected years from 2016 and projected to 2030. For these data, find the (a) Mean (b) Standard deviation. Per Capita Disposable
The following table gives the total value (in millions of dollars) of shipments of beet sugar manufactured in the United States from 2008 and projected to 2020. Construct a frequency histogram of the values, using intervals of $500 million and starting at $3000 million. Year $million Year $million
Suppose a youth has a part-time job in an ice cream shop. He receives $80 if he is called to work a full day and $40 if he is called to work a half-day. Over the past year, he has been called to work a full day an average of 8 days per month and a half-day an average of 14 days per month. How much
The aged dependency ratio, the ratio of the U.S. population ages 65 or over to that of ages 20–64, can be used to estimate the number of Medicare enrollees per worker. The following table shows Social Security Administration data for this ratio every 5 years from 1945 and projected to 2050.
The amount spent monthly, x, for maintenance and repairs at XONIX, LLC, is normally distributed with a mean of $2000 and standard deviation of $120. If x is the amount budgeted for next month, find x to the nearest $10 so that the probability of being over-budget for maintenance and repairs is 0.05.
A car owner must decide whether she should take out a $500-deductible collision policy in addition to her liability insurance policy. Records show that each year in her area, 8% of the drivers have one accident that is their fault or for which no fault is assigned and that the average cost of
Suppose you live in a neighborhood with a few expensive homes and many modest homes. Which measure would you give as the “average” property value(a) if you wanted to impress people with the neighborhood where you lived? Explain.(b) if you wanted to convince the property tax committee that
The Rent-to-Own Company estimates that 35% of its rentals result in the sale of the product, with an average revenue of 100% of revenue R, 56% of the rentals are returned in good condition, with an average revenue of 35% of R on these rentals, and the remainder of the rentals are stolen or returned
The following table shows the U.S. population (in thousands) of individuals age 100 years or older for selected years from 2010 and projected to 2050.(a) Display these data with a bar graph.(b) Find the mean and standard deviation of these data for the U.S. population of centenarians. Centenarians
A nonprofit organization sells chances for a $40,000 classic Mustang at $100 per ticket. It sells 1500 tickets and offers four prizes, summarized in the table. What are the expected winnings (or loss) for each ticket?Prizes AmountFirst
In Problems, find the mean and standard deviation of the sample data in each table. 6 7 8 9 10 11 12 13 14 15 f(x) 2 1 0 2 5 3 1 2 4 3.
In Problems, find the mean and standard deviation of the sample data in each table. 4 5 7 8 9 10 11 12 f(x) 6 0 5 3 4 3 2 1 0 4
Empirical records show that the probability is 0.06 that a driver insured with Riders Insurance Company will have an accident during 2019 in which he or she is at fault. If the company has 12,000 drivers insured in Century City, what is the probability that at most 800 will have an at-fault
If the probability of an automobile part being defective is 0.02, find the probability of getting exactly 3 defective parts in a sample of 12.
What is the area under the standard normal curve between z = -1.6 and z = 1.9?
In the following problems, use a normal approximation to the binomial. An airport announced a plan to make a special security checkpoint so that first-class passengers would have priority passing through security. Airlines supported this plan, assuming that 25% of passengers would like the idea and
It has been determined empirically that the probability that a given cell will survive for a given period of time is 0.4. Find the probability that 3 out of 6 of these cells will survive for this period of time if the survival of the cells is independent.
A juice manufacturer sells several kinds of juice in 59-oz containers. A machine fills the containers, and the amount dispensed by the machine is normally distributed with a mean of 59 oz and standard deviation of 0.5 oz. Overfilling the container wastes juice, and underfilling it risks consumer
Find the modes, medians, and means of the scores in Problem.1.14, 2.28, 7.58, 6.32, 5.17
In a certain school district, 3% of the faculty use none of their sick days in a school year. Find the probability that 5 faculty members selected at random used no sick days in a given year.
Hargray Communications offered a bundled package of television cable, broadband Internet, and basic telephone service for $99.99 for the first 3 months. If the company expects that 1% of the viewers of the ad will purchase the service, what is the probability that at least 120 of 11,000 viewers of
Find the modes, medians, and means of the scores in Problem.2.8, 6.4, 5.3, 5.3, 6.8
A new light bulb has an expected life of 18,620 hours, with a standard deviation of 4012 hours. If the hours of life of these bulbs are normally distributed, find the probability that one of these bulbs chosen at random will last(a) Less than 10,000 hours.(b) More than 24,000 hours.(c) Between
Find the modes, medians, and means of the scores in Problem.3.2, 3.2, 3.5, 3.7, 3.4
For the probability distribution shown, find the expected value E(x). X 1 2 3 4 Pr(x) 0.4 0.3 0.2 0.1
If spermicides and male latex condoms are used correctly by a group of 30 couples, how many of the 30 women could be expected to become pregnant in a year? Assume that these uses are independent events.The table gives the percent of women who become pregnant during 1 year of use with different
If a group of 30 women use diaphragms typically, how many of these 30 women could be expected to become pregnant in a year?The table gives the percent of women who become pregnant during 1 year of use with different types of contraceptives. The “Typical Use” column includes failures from

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