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mathematics
calculus with applications
Calculus With Applications 12th Edition Margaret L. Lial - Solutions
Suppose that the supply function for walnuts is p = S(q) = 0.25q + 3.6, where p is the price in dollars per pound and q is the quantity in bushels. Suppose also that the equilibrium price is $5.85, and the demand is 4 bushels when the price is $7.60. Find an equation for the demand function,
Graph each linear equation defined as follows.y = 4x + 3
In Exercises, find an equation for each line in the form ax + by = c, where a, b, and c are integers with no factor common to all three and a ≥ 0.The line with y-intercept 4 and perpendicular to x + 5y = 7
Producing x units of tacos costs C(x) = 5x + 20; revenue is R(x) = 15x, where C(x) and R(x) are in dollars.(a) What is the break-even quantity?(b) What is the profit from 100 units?(c) How many units will produce a profit of $500?
Graph each linear equation defined as follows.y = 6 - 2x
To produce x units of a religious medal costs C(x) = 12x + 39. The revenue is R(x) = 25x. Both C(x) and R(x) are in dollars.(a) Find the break-even quantity.(b) Find the profit from 250 units.(c) Find the number of units that must be produced for a profit of $130.
In Exercises, find an equation for each line in the form ax + by = c, where a, b, and c are integers with no factor common to all three and a ≥ 0.The line with x-intercept -2/3 and perpendicular to 2x - y = 4
Graph each linear equation defined as follows.3x - 5y = 15
Do the points (4, 3), (2, 0), and (-18, -12) lie on the same line? Explain why or why not.
Johana sells silk-screened T-shirts at community festivals and craft fairs. Her marginal cost to produce one T-shirt is $3.50. Her total cost to produce 60 T-shirts is $300, and she sells them for $9 each.(a) Find the linear cost function for Johana’s T-shirt production.(b) How many T-shirts must
Find k so that the line through (4, -1) and (k, 2) is(a) Parallel to 2x + 3y = 6,(b) Perpendicular to 5x - 2y = -1.
Graph each linear equation defined as follows.4x + 6y = 12
Alberto owns a small publishing house specializing in Latin American poetry. His fixed cost to produce a typical poetry volume is $525, and his total cost to produce 1000 copies of the book is $2675. His books sell for $4.95 each.(a) Find the linear cost function for Alberto’s book production.(b)
Graph each linear equation defined as follows.x - 3 = 0
Use slopes to show that the quadrilateral with vertices at (1, 3), (-5/2, 2), (-7/2, 4), and (2, 1) is a parallelogram.
The manager of a restaurant found that the cost to produce 100 cups of coffee is $11.02, while the cost to produce 400 cups is $40.12. Assume the cost C(x) is a linear function of x, the number of cups produced.(a) Find a formula for C(x).(b) What is the fixed cost?(c) Find the total cost of
Graph each linear equation defined as follows.y = 1x + 3y = 0
Use slopes to show that the square with vertices at (-2, 5), (4, 5), (4, -1), and (-2, -1) has diagonals that are perpendicular.
In deciding whether to set up a new manufacturing plant, company analysts have decided that a linear function is a reasonable estimation for the total cost C(x) in dollars to produce x items. They estimate the cost to produce 10,000 items as $547,500, and the cost to produce 50,000 items as
Graph each linear equation defined as follows.y = 2x
For the lines in exercises which of the following is closest to the slope of the line? (a) 1 (b) 2 (c) 3 (d) 21 (e) 22(f) - 3 2 2 X
The percent of U.S. households with telephonelandlines has decreased at a roughly linear rate, as shown bythe following table.(a) Find the equation of the least squares line, letting x equal the number of years since 2000.(b) Based on your answer to part (a), at approximately what rate is the
The total amount of consumer credit has been increasing steadily in recent years. The following table gives the total U.S. outstanding consumer credit (in billions of dollars).(a) Find an equation for the least squares line, letting x equal the number of years since 2000.(b) Based on your answer to
For exercises, let f (x) = 7 – 5x and g(x) – 2x – 3.Find the following.ƒ(t)
The mean earnings (in dollars) of workers 18 years and over, by educational attainment, have increased steadily over the years and are given in the following table. Let x equal the number of years since 2000.(a) Plot the data for high school graduates and for workers with a bachelor’s degree. Do
Find the slope for each line that has a slope.Through the origin and (11, -2)
Find the slope of each line.A line perpendicular to 8x = 2y - 5
Using Expedia, a discount travel website, the American Airline prices for a one-way flight from New York City to various cities were recorded. The following table gives the distances from New York City to 14 selected cities, along with the airfare to each of these cities.(a) Plot the data. Do the
For exercises, let f (x) = 7 – 5x and g(x) – 2x – 3.Find the following.g(k2)
Find the slope for each line that has a slope.Through the origin and 10, 72
In exercises, find an equation in slope-intercept form for each line.Through 11, 32, m = -2
Describe what fixed costs and marginal costs mean to a company.
Find the slope for each line that has a slope.4x + 3y = 6
The following table shows the number of new jobs gained per year in the private sector in the U.S. in recent years.(a) Find an equation for the least squares line, letting x be the number of years since 2000.(b) Find the correlation coefficient for these data.(c) Sketch a scatterplot of these data,
In exercises, find an equation in slope-intercept form for each line.Through 12, 42, m = -1
The following table shows the seasonally adjusted unemployment rate in the U.S. in recent years.(a) Find the least squares line through these data, letting x be the number of years since 2000.(b) Find the correlation coefficient for these data.(c) Sketch a scatterplot of these data, and include the
In a few sentences, explain why the price of a commodity not already at its equilibrium price should move in that direction.
Find the slope for each line that has a slope.4x - y = 7
In exercises, find an equation in slope-intercept form for each line.Through 1-5, -72, m = 0
Explain why a linear function may not be adequate for describing the supply and demand functions.
The average length and width of various bird eggs are given in the following table.(a) Plot the points, putting the length on the y-axis and the width on the x-axis. Do the data appear to be linear?(b) Find the least squares line, and plot it on the same graph as the data.(c) Suppose there are
Find the slope for each line that has a slope.y + 4 = 9
In exercises, find an equation in slope-intercept form for each line.Through 1-8, 12, with undefined slope
In your own words, describe the break-even quantity, how to find it, and what it indicates.
Find the slope for each line that has a slope.3y - 1 = 14
A Lake Tahoe resort charges a snowboard rental fee of $10 plus $2.25 per hour.Write a linear cost function for each situation. Identify all variables used.
In exercises, find an equation in slope-intercept form for each line.Through 14, 22 and 11, 32The line goes through (4. 2) and (1. 3). Find the slope, then use point-slope form with either of tile two given points.
Find the slope for each line that has a slope.y = 5x + 4
In the 1960s, the famous researcher Jane Goodall observed that chimpanzees hunt and eat meat as part of their regular diet. Sometimes chimpanzees hunt alone, while other times they form hunting parties. The following table summarizes research on chimpanzee hunting parties, giving the size of the
Biologists have observed a linear relationship between the temperature and the frequency with which a cricket chirps. The following data were measured for the striped ground cricket.(a) Find the equation for the least squares line for the data.(b) Use the results of part (a) to determine how many
An Internet site for downloading music charges a $10 registration fee plus 99 cents per downloaded song.Write a linear cost function for each situation. Identify all variables used.
Find the slope for each line that has a slope.x = 5y
The following table gives the national average pupil-teacher ratio in public schools over selected years.(a) Find the equation for the least squares line. Let x correspond to the number of years since 1990 and let y correspond to the average number of pupils per teacher.(b) Use your answer from
In exercises, find an equation in slope-intercept form for each line.Through 12/3, 1/22 and 11/4, -22
Find an equation in the form y = mx + b for each line.Through (5, -1); slope = 2/3
In exercises, find an equation in slope-intercept form for each line.Through 1-2, 3/42 and 12/3, 5/22
For a one-day rental, a car rental firm charges $44 plus 28 cents per mile.Write a linear cost function for each situation. Identify all variables used.
The following table lists how poverty level income cutoffs (in dollars) for a family of four have changed over time.Let x represent the year, with x = 0 corresponding to 1990, and y represent the income in thousands of dollars.(a) Plot the data. Do the data appear to lie along a straight line?(b)
A parking garage charges 2 dollars plus 75 cents per hour.Write a linear cost function for each situation. Identify all variablesused.
Find an equation in the form y = mx + b for each line.Through (8, 0); slope = -1/4
In exercises, find an equation in slope-intercept form for each line.Through 1-8, 42 and 1-8, 62
In an introductory statistics course at Cornell University, 147 undergraduates were asked their own height and the ideal height for their ideal spouse or partner. For this exercise, we are including the data for only a representative sample of 10 of the students, as given in the following table.
Assume that each situation can be expressed as a linear cost function. Find the cost function in each case.Fixed cost: $100; 50 items cost $1600 to produce.
Find an equation in the form y = mx + b for each line.Through (-6, 3) and (2, -5)
In exercises, find an equation in slope-intercept form for each line.Through 1-1, 32 and 10, 32
Assume that each situation can be expressed as a linear cost function. Find the cost function in each case.Fixed cost: $35; 8 items cost $395 to produce.
At Hofstra University, all students take the math SAT before entrance, and most students take a mathematics placement test before registration. Recently, one professor collected the following data for 19 students in his Finite Mathematics class:(a) Find an equation for the least squares line. Let x
Find an equation in the form y = mx + b for each line.Through (2, -3) and (-3, 4)
In Exercises, find an equation for each line in the form ax + by = c, where a, b, and c are integers with no factor common to all three and a ≥ 0.x-intercept -6, y-intercept -3
Assume that each situation can be expressed as a linear cost function. Find the cost function in each case.Marginal cost: $75; 50 items cost $4300 to produce.
Find the slope of each line.4x + 7y = 1
Determine whether each statement is true or false, and explain why.A correlation coefficient of zero indicates a perfect fit with the data.
Consider the following table of data.(a) Calculate the least squares line and the correlation coefficient.(b) Repeat part (a), but this time delete the last point.(c) Draw a graph of the data, and use it to explain the dramatic difference between the answers to parts (a) and (b). X 1 1 y 1
For exercises, let f (x) = 7 – 5x and g(x) – 2x – 3.Find the following.ƒ(-3)
Find the slope of each line.5x - 9y = 11
Determine whether each statement is true or false, and explain why.The function ƒ(x) = (x) + 3 represents a linear function.
Find the slope of each line.Through (1, 5) and (-2, 5)
Determine whether each statement is true or false, and explain why.The marginal cost is the rate of change of the cost function.
Find the slope of each line.y = x
Determine whether each statement is true or false, and explain why.The function ƒ(x) = πx + 4 represents a linear function.
Find the slope of each line.Through (8, 4) and (8, -7)
Determine whether each statement is true or false, and explain why.The x-intercept of the line y = 8x + 9 is 9.
Determine whether each statement is true or false, and explain why.According to the Law of Demand, a linear demand function ordinarily has a negative slope.
Find the slope of each line.Through (5, -4) and (1, 3)
Given a set of points, the least squares line formed by letting x be the independent variable will not necessarily be the same as the least squares line formed by letting y be the independent variable. Give an example to show why this is true.
Determine whether each statement is true or false, and explain why.The variable x in the linear function ƒ(x) = 3x + 4 is the dependent variable.
Determine whether each statement is true or false, and explain why.The line that intersects the points (4, 6) and (5, 6) is a horizontal line.
Determine whether each statement is true or false, and explain why.The line that intersects the points (2, 32 and (2, 5) is a horizontal line.
If two lines are vertical, the product of their slopes is -1.Determine whether each statement is true or false, and explain why.
Determine whether each statement is true or false, and explain why.The correlation coefficient must always be between -1 and 1 (or equal to -1 or 1).
Determine whether each statement is true or false, and explain why.The line y = -2x + 5 intersects the point (3, -1).
Find the slope of each line.A line parallel to 6x - 3y = 12
The number of nonmobile broadband subscriptions per 100 inhabitants of the U.S. in recent years is given in the following table.(a) Find an equation for the least squares line, letting x be the number of years since 2000.(b) Based on your answer to part (a), at approximately what rate is the number
Find the slope for each line that has a slope.Through (4, -1) and (3, -3)
For exercises, let f (x) = 7 – 5x and g(x) – 2x – 3.Find the following.g(-3/4)
The number of banks in the United States has been dropping steadily since 1984, and the trend in recent years has been roughly linear. The annual data for the years 2009 through 2018 can be summarized as follows, where x represents the years since 2000 and y the number of banks, in thousands, in
Find the slope of each line.y = -6
Find the slope for each line that has a slope.Through (-3, 7) and (2, 12)
For exercises, let f (x) = 7 – 5x and g(x) – 2x – 3.Find the following.g(-1/2)
The total value of consumer durable goods (goods purchased by households for their nonbusiness use with a life expectancy of at least three years) has grown at an approximately linear rate in recent years. The annual data for the years 2008 through 2017 can be summarized as follows, where x
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