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Finite Mathematics and Its Applications 12th edition Larry J. Goldstein, David I. Schneider, Martha J. Siegel, Steven Hair - Solutions

The percentage, y, of college freshmen who entered college intending to major in general biology increased steadily from the year 2000 to the year 2014 and can be approximated by the linear equation y = .2x + 4.1 where x represents the number of years since 2000. Thus, x = 0 represents 2000, x = 1
The percentage, y, of college freshmen who smoke cigarettes decreased steadily from the year 2004 to the year 2014 and can be approximated by the linear equation y = -.46x + 6.32 where x represents the number of years since 2004. Thus, x = 0 represents 2004, x = 1 represents 2005, and so on.(a)
Average tuition (including room and board) for all institutions of higher learning in year x can be approximated by y = 461x + 16,800 dollars, where x = 0 corresponds to 2004, x = 1 corresponds to 2005, and so on. (a) Approximately what was the average tuition in 2011? (b) Assuming that the formula
The number of bachelor's degrees conferred in mathematics and statistics in year x can be approximated by y = 667x + 12,403, where x = 0 corresponds to 2003, x = 1 corresponds to 2004, and so on. (a) Approximately how many bachelor's degrees in mathematics and statistics were awarded in 2007? (b)
Find an equation of the line having x-intercept (16, 0) and y-intercept (0, 8).
Find an equation of the line having x-intercept (.6, 0) and y-intercept (0, .9).
Find an equation of the line having y-intercept (0, 5) and x-intercept (4, 0).
1. Find an equation of the line having x-intercept (5, 0) and parallel to the y-axis. 2. What is the equation of the x-axis?
1. Can a line other than the x-axis have more than one x-intercept? 2. What is the general form of the equation of a line that is parallel to the y-axis? 3. What is the general form of the equation of a line that is parallel to the x-axis?
Find a general form of the given equation. 1. y = 2x + 3 2. y = 3x - 4 3. y = - 2/3x - 5 4. y = 4x - 56
Show that the straight line with x-intercept (a, 0) and y-intercept (0, b), where a and b are not zero, has bx + ay = ab as a general form of its equation.
Use the result of Exercise 61 to find a general form of the equation of the line having x-intercept (5, 0) and y-intercept (0, 6).
Give the equation of a line having the stated property. Note: There are many answers to each exercise. 1. x-intercept (9, 0) 2. y-intercept (0, 10) 3. Passes through the point (-2, 5) 4. Passes through the point (3, -3) 5. Crosses the positive part of the y-axis 6. Passes through the origin 7.
The lines with equations y = 2/3x - 2 and y = - 4x + c have the same x-intercept. What is the value of c?
The lines with equations 6x - 3y = 9 and y = 4x + b have the same y-intercept. What is the value of b?
(a) Graph the line, (b) Use the utility to determine the two intercepts, (c) Use the utility to find the y-coordinate of the point on the line with x-coordinate 2. 1. y = -3x + 6 2. y = .25x - 2
Determine an appropriate window, and graph the line. 1. 2y + x = 100 2. x - 3y = 60
1. What are the coordinates of the point Q in Fig. 7? 2. What are the coordinates of the point P in Fig. 7?
Find the slope of the line having the given equation. 1. y = 2/3x + 7 2. y = -4 3. y - 3 = 5(x + 4) 4. 7x + 5y = 10
1. What is the slope of any line parallel to the y-axis? 2. Why doesn't it make sense to talk about the slope of the line between the two points (2, 3) and (2, -1)? 3. (4, 17), (- 2, 17) Plot each pair of points, draw the straight line through them, and find its slope.
Graph the three lines y = 2x + 1, y = x + 1, and y = .5x + 1 together, and then identify each line without using trace.
Repeat Exercise 99 for the line y = .7x - 2, using up instead of down and .7 instead of .5. Graph the three lines y = 2x + 1, y = x + 1, and y = .5x + 1 together, and then identify each line without using trace.
Graph the given linear equation by beginning at the y-intercept, and moving 1 unit to the right and m units in the y-direction. 1. y = -2x + 1 2. y = 4x - 2 3. y = 3x 4. y = -2
Find the equation of line L.1.2. 3.
Give the slope-intercept form of the equation of the line.1.2. 3. 4.
1. Find the equation of the line passing through the point (2, 3) and parallel to the x-axis. 2. Find the equation of the line passing through the point (2, 3) and parallel to the y-axis.
1. Find the y-intercept of the line passing through the point (5, 6) and having slope 3/5. 2. Find the y-intercept of the line passing through the points (-1, 3) and (4, 6).
1. Find the equation of the line passing through (0, 4) and having undefined slope. 2. Find the equation of the line passing through the point (1, 4) and having y-intercept (0, 4). 3. Cost Curve A manufacturer has fixed costs (such as rent and insurance) of $2000 per month. The cost of producing
The price p that must be set in order to sell q items is given by the equation p = -3q + 1200. (a) Find and interpret the p-intercept of the graph of the equation. (b) Find and interpret the q-intercept of the graph of the equation. (c) Find and interpret the slope of the graph of the equation. (d)
At sea level, water boils at a temperature of 212°F. As the altitude increases, the boiling point of water decreases. For instance, at an altitude of 5000 feet, water boils at about 202.8°F. (a) Find a linear equation giving the boiling point of water in terms of altitude. (b) At what temperature
Biologists have found that the number of chirps that crickets of a certain species make per minute is related to the temperature. The relationship is very close to linear. At 68°F, those crickets chirp about 124 times a minute. At 80°F, they chirp about 172 times a minute. (a) Find the linear
Suppose that the cost of making 20 cell phones is $6800 and the cost of making 50 cell phones is $9500. (a) Find the cost equation. (b) What is the fixed cost? (c) What is the marginal cost of production? (d) Draw the graph of the equation.
Suppose that the total cost y of making x coats is given by the formula y = 40x + 2400. (a) What is the cost of making 100 coats? (b) How many coats can be made for $3600? (c) Find and interpret the y-intercept of the graph of the equation. (d) Find and interpret the slope of the graph of the
Suppose that the total revenue y from the sale of x coats is given by the formula y = 100x. (a) What is the revenue if 300 coats are sold? (b) How many coats must be sold to have a revenue of $6000? (c) Find and interpret the y-intercept of the graph of the equation. (d) Find and interpret the
Consider a coat factory with the cost and revenue equations given in Exercises 40 and 41. (a) Find the equation giving the profit y resulting from making and selling x coats. (b) Find and interpret the y-intercept of the graph of the profit equation. (c) Find and interpret the x-intercept of the
An apartment complex has a storage tank to hold its heating oil. The tank was filled on January 1, but no more deliveries of oil will be made until sometime in March. Let t denote the number of days after January 1, and let y denote the number of gallons of fuel oil in the tank. Current records
A corporation receives payment for a large contract on July 1, bringing its cash reserves to $2.3 million. Let y denote its cash reserves (in millions) t days after July 1. The corporation's accountants estimate that y and t will be related by the equation y = 2.3 - .15t. (a) Graph the equation y =
1. A furniture salesperson earns $220 a week plus 10% commission on her sales. Let x denote her sales and y her income for a week. (a) Express y in terms of x. (b) Determine her week's income if she sells $2000 in merchandise that week. (c) How much must she sell in a week in order to earn $540? 2.
Find an equation for each of the following lines. 1. Slope is - 1/2; y-intercept is (0, 0). 2. Slope is 3; y-intercept is (0, -1). 3. Slope is - 13; (6, - 2) on line.
We specify a line by giving the slope and one point on the line. We give the first coordinate of some points on the line. Without deriving an equation of the line, find the second coordinate of each of the points. 1. Slope is 2, (1, 3) on line; (2, ); (0, ); (-1, ). 2. Slope is -3, (2, 2) on line;
Each of the lines (A), (B), (C), and (D) in Fig. 9 is the graph of one of the linear equations (a), (b), (c), and (d). Match each line with its equation.(a)(b) (c) (d) (a) x + y = 1 (b) x - y = 1 (c) x + y = -1 (d) x - y = -1
The table that follows gives several points on the line Y1 = mx + b. Find m and b.
Give an equation of a line with the stated property. 1. Rises as you move from left to right 2. Falls as you move from left to right 3. Has slope 0 4. Slope not defined 5. Parallel to the line 2x + 3y = 4 6. Perpendicular to the line 5x + 6y = 7
Plot each pair of points, draw the straight line through them, and find its slope. 1. (3, 4), (7, 9) 2. (- 2, 1), (3, - 3)
Celsius and Fahrenheit temperatures are related by a linear equation. Use the fact that 0°C = 32°F and 100°C = 212°F to find an equation.
An archaeologist dates a bone fragment discovered at a depth of 4 feet as approximately 1500 B.C. and dates a pottery shard at a depth of 8 feet as approximately 2100B.C. Assuming that there is a linear relationship between depths and dates at this archeological site, find the equation that relates
The average college tuition and fees at four-year public colleges increased from $3735 in 2001 to $8312 in 2013. (See Fig. 10.) Assuming that average tuition and fees increased linearly with respect to time, find the equation that relates the average tuition and fees, y, to the number of years
Two-year college enrollments increased from 5.9 million in 2000 to 7.0 million in 2013. (See Fig. 11.) Assuming that enrollments increased linearly with respect to time, find the equation that relates the enrollment, y, to the number of years after 2000, x. When was the enrollment 6.5 million?
A certain car gets 25 miles per gallon when the tires are properly inflated. For every pound of pressure that the tires are underinflated, the gas mileage decreases by 12 mile per gallon. Find the equation that relates miles per gallon, y, to the amount that the tires are underinflated, x. Use the
According to the U.S. Department of Labor, home health aide jobs are expected to increase from 913,500 in 2014 to 1,261,900 in 2024. Assuming that the number of home health aide jobs increases linearly during that time, find the equation that relates the number of jobs, y, to the number of years
According to the U.S. National Center of Education Statistics, 263,515 bachelor's degrees in business were awarded in 2001 and 360,823 were awarded in 2013. If the number of bachelor's degrees in business continues to grow linearly, how many bachelor's degrees in business will be awarded in 2020?
According to Pizza Marketing Quarterly, the number of U.S. Domino's Pizza stores grew from 4818 in 2001 to 4986 in 2013. If the number of stores continues to grow linearly, when will there be 5100 stores?
The average cost of a 30-second advertising slot during the Super Bowl increased linearly from $3.5 million in 2012 to $4.5 million in 2015. Find the equation that relates the cost (in millions of dollars) of a 30-second slot, y, to the number of years after 2012, x. What was the average cost in
Suppose that 5 million tons of apples will be supplied at a price of $3000 per ton and 6 million tons of apples will be supplied at a price of $3400 per ton. Find the equation for the supply curve and draw its graph. Let the units for q be millions of tons and the units for p be thousands of
Suppose that 5 million tons of apples will be demanded at a price of $3000 per ton and 4.5 million tons of apples will be demanded at a price of $3100 per ton. Find the equation for the demand curve and draw its graph. Let the units for q be millions of tons and the units for p be thousands of
Show that the points (1, 3), (2, 4), and (3, -1) are not on the same line.
For what value of k will the three points (1, 5), (2, 7), and (3, k) be on the same line?
Find the value of a for which the line through the points (a, 1) and (2, -3.1) is parallel to the line through the points (-1, 0) and (3.8, 2.4)
Rework Exercise 85, where the word parallel is replaced by the word perpendicular. Find the value of a for which the line through the points (a, 1) and (2, -3.1) is parallel to the line through the points (-1, 0) and (3.8, 2.4)
Prove the parallel property. If y = mx + b and y = m'x + b' are the equations of two lines, then the two lines have a point in common if and only if the equation mx + b = m'x + b' has a solution for x.
Prove the perpendicular property. Without loss of generality, assume that both lines pass through the origin. Use the point-slope formula, the Pythagorean theorem, and Fig. 12.
Figure 13 gives the conversion of temperatures from Celsius to Fahrenheit. What is the Fahrenheit equivalent of 30°C?
Figure 14 gives the cost of shipping a package from coast to coast. What is the cost of shipping a 20-pound package?
A T-shirt company has fixed costs of $25,000 per year. Each T-shirt costs $8.00 to produce and sells for $12.50. How many T-shirts must the company produce and sell each year in order to make a profit of $65,000?
A company produces a single product for which variable costs are $100 per unit and annual fixed costs are $1,000,000. If the product sells for $130 per unit, how many units must the company produce and sell in order to attain an annual profit of $2,000,000?
1. Demand and Revenue Suppose that the quantity q of a certain brand of mountain bike sold each week depends on price according to the equation q = 800 - 4p. What is the total weekly revenue if a bike sells for $150? 2. Demand and Revenue Suppose that the number n of singleuse cameras sold each
During 2015, a manufacturer produced 50,000 items that sold for $100 each. The manufacturer had fixed costs of $600,000 and made a profit before income taxes of $400,000. In 2016, rent and insurance combined increased by $200,000. Assuming that the quantity produced and all other costs were
Rework Exercise 95 with a 2015 fixed cost of $800,000 and a profit before income taxes of $300,000.
Graph the three lines y = 2x - 3, y = 2x, and y = 2x + 3 together, and then identify each line without using trace.
Graph the two lines y = .5x + 1 and y = - 2x + 9 in the standard window [-10, 10] by [-10, 10]. Do they appear perpendicular? If not, use ZSquare to obtain true aspect, and look at the graphs.
Graph the line y = - .5x + 2 with the window ZDecimal. Without pressing TRACE, move the cursor to a point on the line. Then move the cursor one unit to the right and down .5 unit to return to the line. If you start at a point on the line and move 2 units to the right, how many units down will you
Find the point of intersection of the given pair of straight lines.1.2. 3.
Find the coordinates of the labeled points.1.2.
The supply curve for a certain commodity is p = .0001q + .05. (a) What price must be offered in order for 19,500 units of the commodity to be supplied? (b) What prices result in no units of the commodity being supplied?
The demand curve for a certain commodity is p = - .001q + 32.5. (a) At what price can 31,500 units of the commodity be sold? (b) What quantities are so large that all units of the commodity cannot possibly be sold no matter how low the price?
Suppose that supply and demand for a certain commodity are described by the supply and demand curves of Exercises 17 and 18. Determine the equilibrium quantity of the commodity that will be produced and the selling price.
A discount book seller has determined that the supply curve for a certain author's newest paperback book is p = 1/300 q + 13. The demand curve for this book is p = -.03q + 19. What quantity of sales would result in supply exactly meeting demand, and for what price should the book be sold?
Suppose that the demand curve for corn has the equation p = -.15q + 6.925 and the supply curve for corn has the equation p = .2q + 3.6, where p is the price per bushel in dollars and q is the quantity (demanded or produced) in billions of bushels. (a) Find the quantities supplied and demanded when
Suppose that the demand curve for soybeans has the equation p = -2.2q +19.36 and the supply curve for soybeans has the equation p = 1.5q + 9, where p is the price per bushel in dollars and q is the quantity (demanded or produced) in billions of bushels. (a) Find the quantities supplied and demanded
The formula for converting Fahrenheit degrees to Celsius degrees is C = 5/9 (F - 32). For what temperature are the Celsius and Fahrenheit values the same?
The precise formula for converting Celsius degrees to Fahrenheit degrees is F = 9/5 C + 32. An easier-to-use formula that approximates the conversion is F = 2C + 30. (a) Compare the values given by the two formulas for a temperature of 5°C. (b) Compare the values given by the two formulas for a
A clothing store can purchase a certain style of dress shirt from either of two manufacturers. The first manufacturer offers to produce shirts at a cost of $1200 plus $30 per shirt. The second manufacturer charges $500 plus $35 per shirt. Write the two equations that show the total cost y of
A plant supervisor must apportion her 40-hour workweek between hours working on the assembly line and hours supervising the work of others. She is paid $12 per hour for working and $15 per hour for supervising. If her earnings for a certain week are $504, how much time does she spend on each task?
A calling card offers two methods of paying for a phone call. Method A charges 1 cent per minute, but has a 45-cent connection fee. Method B charges 3.5 cents per minute, but has no connection fee. Write the equations that show the total cost, y, of a call of x minutes for methods A and B, and
Sun Towing Company charges $50 plus $3 per mile to tow a car, whereas Star Towing Company charges $60 plus $2.50 per mile. Write the equations that show the total cost y of towing a car x miles for each company. For what number of miles will the two companies charge the same amount? What is that
Find the area of the shaded triangle. Each triangle has its base on one of the axes. The area of a triangle is one-half the length of its base times its height.1.2.
In a wrestling competition, the total weight of the two contestants is 700 pounds. If twice the weight of the first contestant is 275 pounds more than the weight of the second contestant, what is the weight (in pounds) of the first contestant?
An appliance store sells a 42 TV for $400 and a 55 TV of the same brand for $730. During a one-week period, the store sold 5 more 55 TVs than 42 TVs and collected $26,250. What was the total number of TV sets sold?
Graph the lines and estimate the point of intersection to two decimal places.1.2.3.
1. Does (6, 4) satisfy the following system of linear equations?2. Does (12, 4) satisfy the following system of linear equations?
Solve the systems of linear equations.1.2.
Suppose that the line y = 3x + 1 is used to fit the four data points in Table 4. Complete the table, and determine the sum-of-squares error E. Data Point Point on Line Vertical Distance (1, 3)...................................................................... (2, 6)
Consider the data points (1, 5), (2, 7), (3, 6), and (4, 10). Find the straight line that provides the least-squares fit to these data.
Consider the data points (5, 4) and (7, 3). (a) Find the straight line that provides the least-squares fit to these data. (b) Use the method from Section 1.2 to find the equation of the straight line passing through the two points. (c) Explain why we could have predicted that the straight line in
According to Example 2, the sum-of-squares error for the least-squares fit to the data points (1, 6), (4, 5), and (6, 14) is E = 22.13. (a) Find the equation of the straight line through the two points (1, 6) and (6, 14). (b) What is the sum-of-squares error when the line in (a) is used to fit the
According to Example 2, the sum-of-squares error for the least-squares fit to the data points (1, 6), (4, 5), and (6, 14) is E = 22.13. (a) Find the equation of the straight line through the two points (4, 5) and (6, 14). (b) What is the sum-of-squares error when the line in (a) is used to fit the
The following table gives the city and highway miles per gallon for four hybrid cars:(a) Obtain the least-squares line that fits these data. (b) Use the equation from (a) to estimate the highway mpg for a hybrid car that gets 47 mpg in city driving. (c) Use the equation from (a) to estimate the
The following table gives the number of stores and the amount of sales (in millions of dollars) for the leading U.S. pizza chains in 2013.(a) Obtain the least-squares line that fits these data. (Let x represent the number of stores in thousands.)(b) Use the equation from (a) to estimate the 2013
The following table gives the crude male death rate for lung cancer in 1950 and the per capita consumption of cigarettes in 1930 in various countries. Figure 13 shows the least-squares line for the data.(a) Obtain the equation of the line in Fig. 13. (b) In 1930, the per capita cigarette
The percentage of college freshmen who smoke-declined substantially from the year 2004 to the year 2014. Figure 14 shows the percentage of college freshmen who smoked during six of the years of that time period and the least-squares line for the data, where x represents the number of years after

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