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Solve Problem using augmented matrix methods.0.2x1 – 0.5x2 = 0.070.8x1 – 0.3x2 = 0.79
Solve Problem using augmented matrix methods.0.3x1 – 0.6x2 = 0.180.5x1 – 0.2x2 = 0.54
The population of California was approximately 30 million in 1990, 34 million in 2000, and 37 million in 2010. Construct a model for this data by finding a quadratic equation whose graph passes
In Step 2 of Example 1, (0, 0) was used as a test point in graphing a linear inequality. Describe those linear inequalities for which (0, 0) is not a valid test point. In that case, how would you
Graph 2x – 3y ≤ 6.
Graph 6x – 3y > 18.
Solve the following system of linear inequalities graphically:x + y ≥ 62x – y ≥ 0
A manufacturer of lightweight mountain tents makes a standard model and an expedition model. Each standard tent requires 1 labor-hour from the cutting department and 3 labor-hours from the assembly
Is the point (3, 5) on the line y = 2x + 1?
Graph each inequality.x > 2y – 3
A manufacturing plant makes two types of inflatable boats—a two-person boat and a four-person boat. Each two-person boat requires 0.9 labor-hour from the cutting department and 0.8 labor-hour from
Refer to the feasible region S shown in Figure 3.(A) Let P = x + y. Graph the constant-profit lines through the points (5, 5) and (10, 10). Place a straightedge along the line with the smaller profit
Determine whether the solution region of each system of linear inequalities is bounded or unbounded. (A) y ≤ 1 x ≥ 0 y=0 (B) x 100 200 y ≤ x ≥ 0 y = 0 (C) x ≤ y y ≤ x x ≥ 0 y ≥ 0
Refer to the following system of linear inequalities:Is the point (3, 5) in the solution region? 4x + y = 20 3x + 5y = 37 x ≥ 0 y ≥ 0
(A) Minimize and maximize subject to(B) Minimize and maximize subject to z=3x + y 2x + y ≤ 20 10x + y ≥ 36 2х + 5y ≥ 36 x, y ≥ 0
Solve the following system of linear inequalities graphically:3x + y ≤ 21x – 2y ≤ 0
If necessary, review Theorem 1. In Problem the feasible region is the set of points on and inside the rectangle with vertices (0, 0), (12, 0), (0, 5), and (12, 5). Find the maximum and minimum values
Solve the following system of linear inequalities graphically and find the corner points: 2x + y ≤ 22 x + y ≤ 13. 2x + 5y = 50 x 20 y ≥ 0
Is the point (7, 9) on the line y = 3x – 11?
Graph each inequality.3y – 5x ≤ 30
If necessary, review Theorem 1. In Problem the feasible region is the set of points on and inside the rectangle with vertices (0, 0), (12, 0), (0, 5), and (12, 5). Find the maximum and minimum values
Find the linear inequality whose graph is given in Figure 13. Write the boundary line equation in the form Ax + By = C, where A, B, and C are integers, before stating the inequality. 10 SI Figure
Find the linear inequality whose graph is given in Figure 14. Write the boundary line equation in the form Ax + By = C, where A, B, and C are integers, before stating the inequality. Figure
A patient on a brown rice and skim milk diet is required to have at least 800 calories and at least 32 grams of protein per day. Each serving of brown rice contains 200 calories and 5 grams of
A hospital patient is required to have at least 84 units of drug A and 120 units of drug B each day (assume that an overdose of either drug is harmless). Each gram of substance M contains 10 units of
Is the point (3, 5) in the solution set of y ≤ 2x + 1?
Refer to the following system of linear inequalities:Is the point (3, 6) in the solution region? 4x + y = 20 3x + 5y = 37 x ≥0 y ≥ 0
A manufacturing plant makes two types of inflatable boats—a two-person boat and a four-person boat. Each two-person boat requires 0.9 labor-hour in the cutting department and 0.8 labor-hour in the
A chicken farmer can buy a special food mix A at 20¢ per pound and a special food mix B at 40¢ per pound. Each pound of mix A contains 3,000 units of nutrient N1 and 1,000 units of nutrient N2;
If necessary, review Theorem 1. In Problem the feasible region is the set of points on and inside the rectangle with vertices (0, 0), (12, 0), (0, 5), and (12, 5). Find the maximum and minimum values
A concert promoter wants to book a rock group for a stadium concert. A ticket for admission to the stadium playing field will cost $125, and a ticket for a seat in the stands will cost $175. The
A food vendor at a rock concert sells hot dogs for $4 and hamburgers for $5. How many of these sandwiches must be sold to produce sales of at least $1,000? Express the answer as a linear inequality
Refer to the following system of linear inequalities:Is the point (2, 6) in the solution region? 4x + y = 20 3x + 5y ≤ 37 x ≥ 0 y ≥ 0
Is the point (7, 9) in the solution set of y ≤ 3x – 11?
If necessary, review Theorem 1. In Problem the feasible region is the set of points on and inside the rectangle with vertices (0, 0), (12, 0), (0, 5), and (12, 5). Find the maximum and minimum values
Refer to the following system of linear inequalities:Is the point (5, 3) in the solution region? 5x + y = 32 7x + 4y = 45 x ≥ 0 y = 0
Refer to the following system of linear inequalities:Is the point (4, 3) in the solution region? 5x + y = 32 7x + 4y = 45 x ≥ 0 y = 0
If necessary, review Theorem 1. The feasible region is the set of points on and inside the triangle with vertices (0, 0), (8, 0), and (0, 10). Find the maximum and minimum values of the objective
If necessary, review Theorem 1. The feasible region is the set of points on and inside the triangle with vertices (0, 0), (8, 0), and (0, 10). Find the maximum and minimum values of the objective
Is the point (10, 12) on the line 13x – 11y = 2?
If necessary, review Theorem 1. The feasible region is the set of points on and inside the triangle with vertices (0, 0), (8, 0), and (0, 10). Find the maximum and minimum values of the objective
Refer to the following system of linear inequalities:Is the point (5, 2) in the solution region? 5x + y = 32 7x + 4y = 45 x ≥ 0 y = 0
Is the point (21, 25) on the line 30x – 27y = 1?
Is the point (10, 12) in the solution set of 13x – 11y ≥ 2?
If necessary, review Theorem 1. The feasible region is the set of points on and inside the triangle with vertices (0, 0), (8, 0), and (0, 10). Find the maximum and minimum values of the objective
In Problem solve each system of linear inequalities graphically. x - 2y = 12 2x + y = 4
In Problem solve each system of linear inequalities graphically. 3x + 4y = 12 y ≥ −3
In Problem solve each system of linear inequalities graphically. 3x + y = 6 x ≤ 4
In Problem solve each system of linear inequalities graphically. 2x + 5y = 20 x - 5y = -5
Graph each inequality in Problem.x ≥ –4
Graph each inequality in Problem.6x + 4y ≥ 24
Solve the linear programming problems stated in Problem. Maximize subject to P = 10x + 75y x + 8y = 24 x, y = 0
Graph each inequality in Problem.5x ≤ –2y
Solve the linear programming problems stated in Problem. Maximize subject to P = 30x + 12y 3x + y ≤ 18 x, y = 0
Solve the linear programming problems stated in Problem. Minimize subject to C = 8x + 9y 5x + 6y ≥ 60 x, y ≥ 0
In Problem.2x + 3y < 18(A) Graph the set of points that satisfy the inequality.(B) Graph the set of points that do not satisfy the inequality.
Solve the linear programming problems stated in Problem. Minimize subject to C = 15x + 25y 4x + 7y ≥ 28 x, y = 0
Solve the linear programming problems stated in Problem. Maximize subject to P = 30x + 40y 2x + y ≤ 10 x + y ≤ 7 x + 2y ≤ 12 x, y = 0
Solve the linear programming problems stated in Problem. Minimize and maximize z = 10x + 30y subject to 2x + y ≥ 16 = x + y = 12 x + 2y = 14 x, y = 0
In Problem.5x – 2y ≥ 20(A) Graph the set of points that satisfy the inequality.(B) Graph the set of points that do not satisfy the inequality.
Solve the linear programming problems stated in Problem. Minimize and maximize P = 30x + 10y subject to 2x + 2y = 4 6x + 4y = 36 2x + y ≤ 10 x, y = 0
Refer to the bounded feasible region with corner points O = (0, 0), A = (0, 5), B = (4, 3), and C = (5, 0) that is determined by the system of inequalitiesIf P = ax + 10y, find all numbers a such
Refer to the bounded feasible region with corner points O = (0, 0), A = (0, 5), B = (4, 3), and C = (5, 0) that is determined by the system of inequalitiesIf P = ax + 10y, find all numbers a such
Refer to the bounded feasible region with corner points O = (0, 0), A = (0, 5), B = (4, 3), and C = (5, 0) that is determined by the system of inequalitiesIf P = ax + 10y, find all numbers a such
Refer to the bounded feasible region with corner points O = (0, 0), A = (0, 5), B = (4, 3), and C = (5, 0) that is determined by the system of inequalitiesIf P = ax + 10y, find all numbers a such
A manufacturing company makes two types of water skis, a trick ski and a slalom ski. The trick ski requires 6 labor-hours for fabricating and 1 labor-hour for finishing. The slalom ski requires 4
Refer to Problem 51. The company makes a profit of $50 on each trick ski and a profit of $60 on each slalom ski.(A) If the company makes 10 trick skis and 10 slalom skis per day, the daily profit
In Problem graph each inequality subject to the nonnegative restrictions.40x – 55y > 0, x ≥ 0, y ≥ 0
In Problem graph each inequality subject to the nonnegative restrictions.25x + 75y < –600, x ≥ 0, y ≥ 0
A farmer can buy two types of plant food, mix A and mix B. Each cubic yard of mix A contains 20 pounds of phosphoric acid, 30 pounds of nitrogen, and 5 pounds of potash. Each cubic yard of mix B
In Problem express your answer as a linear inequality with appropriate nonnegative restrictions and draw its graph.Seed costs for a farmer are $90 per acre for corn and $70 per acre for soybeans. How
In Problem express your answer as a linear inequality with appropriate nonnegative restrictions and draw its graph.Labor costs for a farmer are $120 per acre for corn and $100 per acre for soybeans.
A farmer can buy two types of plant food, mix A and mix B. Each cubic yard of mix A contains 20 pounds of phosphoric acid, 30 pounds of nitrogen, and 5 pounds of potash. Each cubic yard of mix B
Refer to the following system of linear inequalities:Is the point (6, 2) in the solution region? 5x + y = 32 7x + 4y = 45 x ≥ 0 y = 0
What is the present value of an annuity that pays $200 per month for 5 years if money is worth 6% compounded monthly?
What is the value of an annuity at the end of 10 years if $1,000 is deposited every 6 months into an account earning 8% compounded semiannually? How much of this value is interest?
What amount will an account have after 2 years if $5,000 is invested at an annual rate of 8%(A) Compounded daily?(B) Compounded continuously?Compute answers to the nearest cent.
In Problem find the sum of the finite geometric series a + ar + ar2 + g+ arn – 1.1 + 5 + 25 + 125 + · · · + 58
What amount will an account have after 1.5 years if $8,000 is invested at an annual rate of 9%(A) Compounded weekly? (B) Compounded continuously?Compute answers to the nearest cent.
If you want to earn an annual rate of 10% on your investments, how much (to the nearest cent) should you pay for a note that will be worth $5,000 in 9 months?
(A) A family has an $85,000, 30-year mortgage at 9.6% compounded monthly. Show that the monthly payments are $720.94.(B) Explain why the equationgives the unpaid balance of the loan after x years.(C)
In Problem solve the equation for the unknown quantity.2,652.25 = P(1.03)2
(A) Which would be the better way to invest $1,000: at 9% simple interest for 10 years, or at 7% compounded monthly for 10 years?(B) Explain why the graph of future value as a function of time is a
A company estimates that it will have to replace a piece of equipment at a cost of $800,000 in 5 years. To have this money available in 5 years, a sinking fund is established by making equal monthly
Refer to Example 3 and Matched Problem 3. What was the total amount Jane deposited in order to have $143,785.10 at retirement? What was the total amount Mary deposited in order to have the same
Refer to Example 2. If $2,000 is deposited annually for the first 25 years, how much can be withdrawn annually for the next 20 years?Data from Example 2Lincoln Benefit Life offered an ordinary
In Problem find the sum of the finite geometric series a + ar + ar2 + · · · + arn – 1. Write the answer as a quotient of integers. 1 + -15 + 25 125 + - 57
If your state sales tax rate is 8.25%, what is the total cost of a motor scooter that sells for $1,349.95?
Lincoln Benefit Life offered an ordinary annuity that earned 6.5% compounded annually. A person plans to make equal annual deposits into this account for 25 years and then make 20 equal annual
A bond issue is approved for building a marina in a city. The city is required to make regular payments every 3 months into a sinking fund paying 5.4% compounded quarterly. At the end of 10 years,
Repeat Example 2 with a time period of 6 months.Data from Example 2If you want to earn an annual rate of 10% on your investments, how much (to the nearest cent) should you pay for a note that will be
Repeat Example 3, assuming that you pay $9,828.74 for the T-bill.Data from Example 3T-bills (Treasury bills) are one of the instruments that the U.S. Treasury Department uses to finance the public
How much should you invest now at 10% to have $8,000 toward the purchase of a car in 5 years if interest is(A) compounded quarterly?(B) compounded continuously?
In Problem find the sum of the finite geometric series a + ar + ar2 + g+ arn – 1.a = 30, r = 1, n = 100
How much should new parents invest at 8% to have $80,000 toward their child’s college education in 17 years if interest is(A) Compounded semiannually? (B) Compounded continuously?
T-bills (Treasury bills) are one of the instruments that the U.S. Treasury Department uses to finance the public debt. If you buy a 180-day T-bill with a maturity value of $10,000 for $9,893.78, what
In Problem solve the equation for the unknown quantity.12x3 = 58,956
Jane deposits $2,000 annually into a Roth IRA that earns 6.85% compounded annually. (The interest earned by a Roth IRA is tax free.) Due to a change in employment, these deposits stop after 10 years,
Replace each question mark with either 6 or 7.(A) 3 ? 5 (B) –6 ? –2 (C) 0 ? – 10
Use the profit equation from Matched Problem 3:(A) Sketch a graph of the profit function in a rectangular coordinate system.(B) Break-even points occur when P(x) = 0. Find the break-even points

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