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

Figure 15 gives the percent of persons 25 years and over who have completed four or more years of college.(a) Obtain the least-squares line that fits these data. (Let x = 0 correspond to 1989.)(b) Estimate the percent for the year 2012.(c) If the trend determined by the straight line in part (a)
Suppose that the line y = - 2x + 12 is used to fit the four data points in Table 5. Complete the table, and determine the sum-of-squares error E. Data Point Point on Line Vertical Distance (1, 11)............................................................................. (2,
Figure 16 gives the average college costs (in thousands of dollars) for public colleges in the U.S.(a) Obtain the least-squares line that fits these data. (Let x = 0 correspond to 2005.)(b) Estimate the average cost in 2010.(c) If the trend determined by the straight line in part (a) continues,
The following table is an abbreviated life expectancy table for U.S. males: Current Age Life
Two Harvard economists studied countries' relationships between the independence of banks and inflation rates from 1955 to 1990. The independence of banks was rated on a scale of -1.5 to 2.5, with -1.5, 0, and 2.5 corresponding to least, average, and most independence, respectively. The following
The following table gives the average price of a pound of spaghetti and macaroni in January of the given years. Year
Although greenhouse gases are essential to maintaining the temperature of the Earth, an excess of greenhouse gases can raise the temperature to dangerous levels. One of the most threatening greenhouse gases is carbon dioxide (CO2). The Mauna Loa atmospheric CO2 measurements constitute the longest
Find the sum-of-squares error E for the least-squares line fit to the four points in Fig. 11.
Find the sum-of-squares error E for the least-squares line fit to the five points in Fig. 12.
Complete Table 6, and find the values of m and b for the straight line that provides the least-squares fit to the data.
Complete Table 7, and find the values of m and b for the straight line that provides the least-squares fit to the data.
Consider the data points (1, 2), (2, 5), and (3, 11). Find the straight line that provides the least-squares fit to these data.
Consider the data points (1, 8), (2, 4), and (4, 3). Find the straight line that provides the least-squares fit to these data.
Consider the data points (1, 9), (2, 8), (3, 6), and (4, 3). Find the straight line that provides the least-squares fit to these data.
1. How do you determine the coordinates of a point in the plane? 2. What is meant by the graph of an equation in x and y?
1. What is the point-slope form of the equation of a line? 2. Describe how to find the equation for a line when you know the coordinates of two points on the line.
1. What can you say about the slopes of perpendicular lines? 2. What can you say about the slopes of parallel lines? 3. Describe how to obtain the point of intersection of two lines.
What is the least-squares line approximation to a set of data points?
What is the y-intercept of a line? How do you find the y-intercept from an equation of a line?
What is the x-intercept of a line? How do you find the x-intercept from an equation of a line?
1. What is the general form of a linear equation in x and y? 2. Define the slope of a line, and give a physical description. 3. What is the slope-intercept form of a non-vertical line?
Suppose that you know the slope and the coordinates of a point on a line. How could you draw the line without first finding its equation?
1. Table 1 can be used to obtain the demand curve for a monopolist who manufactures and sells a unique type of camera. The first column gives several production quantities in thousands of cameras, and the second column gives the corresponding prices per camera. For instance, in order to sell 200
1. What is the equation of the y-axis? 2. Graph the linear equation y = - 1/2x.
1. Find the y-intercept of the line passing through the point (4, 9) and having slope 1/2. 2. Cost of Moving The fee charged by a local moving company depends on the amount of time required for the move. If t hours are required, then the fee is y = 35t + 20 dollars. Give an interpretation of the
Are the points (1, 2), (2, 0), and (3, 1) on the same line?
1. Write an equation of the line with x-intercept (3, 0) and y-intercept (0, -2). 2. If x + 7y = 30 and x = -2y, then determine the value of y.
Solve the system of linear equations
Find the equation of the line through (1, 1) and the intersection point of the lines y = - x + 1 and y = 2x + 3.
Do the three graphs of the linear equations 2x - 3y = 1, 5x + 2y = 0, and x + y = 1 contain a common point?
Graph the equation x + 1/2y = 4, and give the slope and both intercepts.
Show that the lines with equations 2x - 3y = 1 and 3x + 2y = 4 are perpendicular.
Each of the lines L1, L2, and L3 in Fig. 1 is the graph of one of the equations (a), (b), and (c). Match each of the equations with its corresponding line.(a) 4x + y = 17 (b) y = x + 2 (c) 2x + 3y = 11
Consider the following four equations. p = .01q - 5 p = .005q + .5 p = - .01q - 10 p = - .01q + 5 One is the equation of a supply curve, and another is the equation of a demand curve. Identify the two equations, and then find the intersection point of those two curves.
Many of the nation's prominent public universities are shifting to admitting more out-of-state students. The number of out-of-state freshmen at the University of Alabama x years after 2004 is given approximately by the linear equation y = 3.6x + 28. (a) What interpretation can be given to the
For a certain manufacturer, the production and sale of each additional unit yields an additional profit of $10. The sale of 1000 units yields a profit of $4000. (a) Find the profit equation. (b) Find the y- and x-intercepts of the graph of the profit equation. (c) Draw the graph of the profit
One-day car rentals cost $50 plus 10 cents per mile from company A and $40 plus 20 cents per mile from company B. (a) For each company, give the linear equations for the cost, y, when x miles are driven. (b) Which company offers the best value when the car is driven for 80 miles? (c) Which company
In 2003, bacon cost an average of $3.20 per pound. In 2015, bacon cost an average of $5.45 per pound. (a) Assuming a linear increase in the price per pound of bacon, find the equation that relates the cost, y, to the number of years after 2003, x. (b) When did bacon cost an average of $4.60 per
According to the U.S. Department of Labor, medical assistant jobs are expected to increase from 591,300 in 2014 to 730,200 in 2024. Assuming that the number of medical assistant jobs increases linearly during that time, find the equation that relates the number of jobs, y, to the number of years
1. A furniture store offers its new employees a weekly salary of $200 plus a 3% commission on sales. After one year, employees receive $100 per week plus a 5% sales commission. For what weekly sales level will the two scales produce the same salary? 2. Soft Drinks According to Beverage Digest
1. Find the point of intersection of the pair of straight lines x - 5y = 6 and 3x = 6. 2. Find the slope of the line having equation 3x - 4y = 8.
According to the U.S. National Center of Education Statistics, 107,238 bachelor's degrees in education were awarded in 2006 and 104,647 were awarded in 2013. If the number of bachelor's degrees in education continues to decline linearly, how many bachelor's degrees in education will be awarded in
The following table gives the percentage of first-year students who were accepted by their first-choice college in recent years. (a) Use the method of least squares to obtain the straight line that best fits these data. (Let x = 0 represent 2012.) (b) If this trend continues, what percentage of
The following table gives the 2015 life expectancy at birth for several countries.(a) Use the method of least squares to obtain the straight line that best fits these data. (b) In Greece, the life expectancy of men is 77.8 years. Use the least-squares line from (a) to estimate the life expectancy
The following table gives the (age-adjusted) death rate per 100,000 women from breast cancer and the daily dietary fat intake (in grams per day) for various countries.(a) Use the method of least squares to obtain the straight line that best fits these data. (b) In Denmark, women consume an average
1. Consider a linear equation of the form y = mx + b. When the value of b remains fixed and the value of m changes, the graph rotates about the point (0, b). As the value of m increases, will the graph rotate in a clockwise or counterclockwise direction? 2. Consider an equation of the form y = mx +
1. Suppose that you have found the least-squares line for a collection of points and that you edit the data by adding a point on the line to the data. Will the expanded data have the same least-squares line? Explain the rationale for your conclusion, and then experiment to test whether your
1. Find the equation of the line having y-intercept (0, 5) and x-intercept (10, 0). 2. Find the point of intersection of the pair of straight lines 2x - y = 1 and x + 2y = 13.
1. Find the equation of the straight line passing through the point (15, 16) and parallel to the line 2x - 10y = 7. 2. Find the y-coordinate of the point having x-coordinate 1 and lying on the line y = 3x + 7.
1. Find the x-intercept of the straight line with equation x = 5.2. Solve the system of linear equations.
1. Operation 2: Multiply the first equation by 2.2. Operation 2: Multiply the second equation by -1. 3. Operation 3: Change the second equation by adding to it 5 times the first equation. Perform the indicated elementary row operation and give its abbreviation.
Write the system of linear equations corresponding to the matrix.1.2. 3. 4.
Describe in your own words the meaning of the notation with respect to a matrix. 1. 1/3 R2 2. R2 + (- 4)R1 3. R1 + 3R2 4. (- 1)R1 5. R2 ↔ R3 6. R1 ↔ R2
Carry out the indicated elementary row operation.1.2. 3. 4. 5. 6.
State the next elementary row operation that should be performed in order to put the matrix into diagonal form. Do not perform the operation.1.2. 3. 4. 5.
Two steps of the Gauss-Jordan elimination method are shown. Fill in the missing numbers.1.2.
Show a matrix, A, corresponding to a system of linear equations and the matrix rref(A) obtained after the Gauss-Jordan elimination method is applied to A. Write the system of linear equations corresponding to A, and use rref(A) to give the solution to the system of linear
1. Operation 3: Change the second equation by adding to it (- 1/2) times the first equation.2. Operation 3: Change the third equation by adding to it (-4) times the first equation. 3. Operation 3: Change the third equation by adding to it 3 times the second equation. Perform the indicated
Solve the linear system by the Gauss-Jordan elimination method.1.2.
A baked potato smothered with cheddar cheese weighs 180 grams and contains 10.5 grams of protein. If cheddar cheese contains 25% protein and a baked potato contains 2% protein, how many grams of cheddar cheese are there?
A high school math department purchased brand A calculators for $80 each and brand B calculators for $95 each. It purchased a total of 20 calculators at a total cost of $1780. How many brand A calculators did the department purchase?
A box of golf balls and a golf glove cost a total of $20. How much does the box of balls cost? Statement I: The golf glove costs three times as much as the box of golf balls. Statement II: The golf glove costs $15. Each exercise consists of a question and two statements that may or may not provide
I have four nickels and three pennies in my pocket. What is the total weight of these coins? Statement I: A nickel weighs twice as much as a penny. Statement II: The total weight of a nickel and two pennies is 10 grams. Each exercise consists of a question and two statements that may or may not
A street vendor has a total of 350 short- and long-sleeve T-shirts. If they sell the short-sleeve shirts for $10 each and the long-sleeve shirts for $14 each, how many of each did they sell if they sold all of their stock for $4300?
A grocery store carries two brands of bleach. A 30-ounce bottle of the national brand sells for $2.59, while the same-size bottle of the store brand sells for $2.09. How many bottles of each brand were sold if a total of 82 bottles were sold for $194.88?
A 275-seat movie theater charges $11.25 admission for adults and $8.50 for children. If the theater is full and $2860 is collected, how many adults and how many children are in the audience?
A baseball player's batting average is determined by dividing the number of hits by the number of times at bat and multiplying by 1000. (Batting averages are usually, but not necessarily, rounded to the nearest whole number.) For instance, if a player gets 2 hits in 5 times at bat, his batting
The United States and Canada are the largest of the 23 countries that make up North America. The bar graph in Fig. 5 shows their areas and that of the remaining North American countries in millions of square miles. The total area of North America is 9.5 million square miles. Canada is 200,000 sq.
1. Operation 3: Change the first row by adding to it 1/2 times the second row.2. Operation 3: Change the third row by adding to it (-4) times the second row. Perform the indicated elementary row operation and give its abbreviation.
The bar graph in Fig. 6 gives the intended majors of a group of 100 randomly selected college freshmen. (The biology category includes the biological and life sciences.) Six more students intend to major in biology than intend to major in business. The number of students intending to major in
A one-pound blend of coffee uses Brazilian (60 ¢ per ounce), Columbian (50 ¢ per ounce), and Peruvian (70 ¢ per ounce) coffee beans and costs $9.70. The blend contains twice the weight of Brazilian beans as Columbian beans. How many ounces of each type of bean does the blend contain?
A one-pound mixture of nuts contains cashews (70 ¢ per ounce), almonds (60 ¢ per ounce), and walnuts (80 ¢ per ounce) and costs $11.10. The mixture contains the same weight of cashews as walnuts. How many ounces of each type of nut does the mixture contain?
A bank wishes to invest a $100,000 trust fund in three sources: a bond fund paying 8%; a health sciences fund paying 7%; and a real estate fund paying 10%. The bank wishes to realize an $8000 annual income from the investment. A condition of the trust is that the total amount invested in the bond
A dietitian wishes to plan a meal around three foods. Each ounce of food I contains 10% of the daily requirements for carbohydrates, 10% for protein, and 15% for vitamin C. Each ounce of food II contains 10% of the daily requirements for carbohydrates, 5% for protein, and 0% for vitamin C. Each
A small candy store makes three types of party mixes. The first type contains 40% nonpareils and 60% peanut clusters, while the second type contains 30% peanut clusters and 70% chocolate-covered raisins. The third type consists of 40% nonpareils, 30% peanut clusters, and 30% chocolate-covered
New parents Jim and Lucy want to start saving for their son's college education. They have $5000 to invest in three different types of plans. A traditional savings account pays 1% annual interest, a certificate of deposit pays 3.6% annual interest, and a prepaid college plan pays 5.5% annual
Write the augmented matrix corresponding to the system of linear equations.1.2. 3. 4.
Pivot the matrix about the circled element.1.2. 3. 4. 5. 6. 7. 8.
Use the Gauss-Jordan elimination method to find all solutions of the system of linear equations.1.2. 3. 4.
Find three solutions to the system of equations.1.2.
In a laboratory experiment, a researcher wants to provide a rabbit with exactly 1000 units of vitamin A, exactly 1600 units of vitamin C, and exactly 2400 units of vitamin E. The rabbit is fed a mixture of three foods whose nutritional content is given by the accompanying table. How many grams of
Rework Exercise 41 with the requirement for vitamin E changed to 2000 units.In a laboratory experiment, a researcher wants to provide a rabbit with exactly 1000 units of vitamin A, exactly 1600 units of vitamin C, and exactly 2400 units of vitamin E. The rabbit is fed a mixture of three foods whose
The nutritional content of three foods is given by the accompanying table. Use the methods of this section to show that no combination of these three foods can contain 72 units of B-12, 68 calories, and 60 units of iron.
Refer to Exercise 43. Show that when the required units of iron are increased to 64 units, there are several combinations of the three foods that meet the requirement. Give two such combinations.The nutritional content of three foods is given by the accompanying table. Use the methods of this
A furniture manufacturer makes sofas, chairs, and ottomans. The accompanying table gives the number of hours of labor required for the carpentry and upholstery that goes into each item. Suppose that, each day, 380 labor-hours are available for carpentry and 450 laborhours are available for
An office manager placed an order for computers, printers, and scanners. Each computer cost $1000, each printer cost $100, and each scanner cost $400. She ordered 15 items for $10,200. Give two different combinations for the numbers of each type of item that she could have purchased.
Granny's Custom Quilts receives an order for a patchwork quilt made from square patches of three types: solid green, solid blue, and floral. The quilt is to be 8 squares by 12 squares, and there must be 15 times as many solid squares as floral squares. If Granny's charges $3 per solid square and $5
Amanda is decorating her new home and wants to buy some house plants. She is interested in three types of plants costing $7, $10, and $13. If she has budgeted exactly $150 for the plants and wants to buy exactly 15 of them, what are her options?
For what values(s) of k will the following system of linear equations have no solution? Infinitely many solutions?
For what value of k will the following system of linear equations have a solution?
1. Figure 5 shows the graphs of the equations from a system of three linear equations in two variables. How many solutions does the system have?2. Suppose that after the Gauss-Jordan elimination method has been applied to a matrix corresponding to a system of linear equations, the matrix has a row
Graph the three equations together and determine the number of solutions (exactly one, none, or infinitely many). If there is exactly one solution, estimate the solution.1.2.3.4.
Show a matrix, A, corresponding to a system of linear equations and the matrix rref(A) obtained after the Gauss-Jordan elimination method is applied to A. Write the system of linear equations corresponding to A, and use rref(A) to give all solutions to the system of linear equations.1.2.3.4.5.
Give the size and special characteristics of the given matrix (such as square, column, row, identity).1.2. 3. 4. 5. 6. [5]
Perform the indicated matrix calculation.1.2.3.4.5.
The sizes of two matrices are given. Tell whether or not the product AB is defined. If so, give its size. 1. A, 3 × 4; B, 4 × 5 2. A, 3 × 3; B, 3 × 4 3. A, 3 × 2; B, 3 × 2 4. A, 1 × 1; B, 1 × 1 5. A, 3 × 3; B, 3 × 1 6. A, 4 × 2; B, 3 × 4
Perform the multiplication.1.2. 3. 4. 5.
Give the system of linear equations that is equivalent to the matrix equation. Do not solve.1.2. 3. 4.
Write the given system of linear equations as a matrix equation.1.2. 3. 4.
The distributive law says that (A + B)C = AC + BC. That is, adding A and B and then multiplying on the right by C gives the same result as first multiplying each of A and B on the right by C and then adding.1.2.

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