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College Mathematics for Business Economics Life Sciences and Social Sciences 12th edition Raymond A. Barnett, Michael R. Ziegler, Karl E. Byleen - Solutions
Solve Problem using substitution or elimination by addition. 3x - 6y = -9 -2x + 4y = 12
Solve Problem using substitution or elimination by addition. 7m + 12n = -1 5m - 3n = 7
Solve Problem using substitution or elimination by addition. 2x + 4y = -8 x + 2y = 4
Solve Problem using substitution or elimination by addition. x + y = 1 0.5x - 0.4y = 0
In Problem, use a graphing calculator to find the solution to each system. Round any approximate solutions to tree decimal places y = -3x + 6 y = -3x + 9
In Problem, use a graphing calculator to find the solution to each system. Round any approximate solutions to tree decimal places 3x -7y = -20 2x + 5y = 8
In Problem, use a graphing calculator to find the solution to each system. Round any approximate solutions to tree decimal places 4.2x + 5.4 y = -12.9 6.4x + 3.7 y = -4.5
In Problem, graph the equations in the same coordinate system. Find the coordinates of any points where two or more lines intersect and discuss the nature of the solution set. x + y = 3 x + 3y = 15 3x - y = 5
In Problem, graph the equations in the same coordinate system. Find the coordinates of any points where two or more lines intersect and discuss the nature of the solution set. x - y = 6 x - 2y = 8 x + 4y = -4
In Problem, graph the equations in the same coordinate system. Find the coordinates of any points where two or more lines intersect and discuss the nature of the solution set. 2x + 3y = 18 2x - 6y = - 6 4x +6y = -24
Repeat Problem 55 for the following systems:(A) 6x - 5y = 10-13x + lly = -20(B) 6x - 5y = 10-13x + lOy = 20(C) 6x - 5y = 10 -12x + lOy = -20
Suppose that the supply and demand for printed baseball caps for a particular week are Price-supply equation Price-demand equation where p is the price in dollars and q is the quantity in hundreds. (A) Find the supply and demand (to the nearest unit) if baseball caps are $4 each. Discuss the
Solve Problem by graphing. 3x - 2y = 12 7x + 2y = 8
At $2.13 per bushel, the annual supply for corn in the Midwest is 8.9 billion bushels and the annual demand is 6.5 billion bushels. When the price falls to $1.50 per bushel, the annual supply decreases to 8.2 billion bushels arid the annual demand increases to 7.4 billion bushels. Assume that the
Repeat Problem 61 with the cost and revenue equations y = 65,000 +1,100x Cost equation y = 1,600x Cost equation Problem 61 Repeat Problem 61 with the cost and revenue equations y = 65,000 + 1,100x Cost equation y = 1,600x Revenue equation (A) How many units must be manufactured and sold each
Repeat Problem 63 if the monthly fixed costs increase to $27,200, the variable costs increase to $9.15, and the company raises the selling price of the DVDs to $21.95. Problem 63 A company markets exercise DVDs that sell for $19.95, including shipping and handling. The monthly fixed costs
Federated Shipping, a competing overnight delivery service, informs the customer in Problem 65 that they would ship the 5-pound package for $29.95 and the 20-pound package for $59.20. (A) If Federated Shipping computes its cost in the same manner as United Express, find the base price and the
Refer to Problem 67.(A) If the company decides to discontinue production of the robust blend and produce only the mild blend, how many pounds of the mild blend can the company produce? How many beans of each type will the company use? Are there any beans that are not used?(B) Repeat part (A) if the
A fruit grower uses two types of fertilizer in an orange grove, brand A and brand B. Each bag of brand A contains 8 pounds of nitrogen and 4 pounds of phosphoric acid. Each bag of brand B contains 7 pounds of nitrogen and 6 pounds of phosphoric acid. Tests indicate that the grove needs 720 pounds
Sausage. A company produces Italian sausages and bratwursts at plants in Green Bay and Sheboygan. The hourly production rates at each plant are given in the table. How many hours should each plant operate to exactly fill an order for 62,250 Italian sausages and 76,500 bratwursts?
Physics. Repeat Problem 73 if the object is 240 feet above the ground after 1 second and 192 feet above the ground after 2 seconds.
Sound waves. A ship using sound-sensing devices above and below water recorded a surface explosion 6 seconds sooner by its underwater device than its above-water device. Sound travels in air at 1,100 feet per second and in seawater at 5,000 feet per second. How long did it take each sound wave to
(A) what is size of F? (B) How many additional rows would E have to have to be a square matrix? (C) Find e14 and f31.
Solve Problem using augmented matrix methods. Graph each solution set. Discuss the difference between the graph of an equation in the system and the graph of the system's solution set x1 - 2x2 = 5 -2x1 + 4x2 = -10
Solve Problem using augmented matrix methods. Graph each solution set. Discuss the difference between the graph of an equation in the system and the graph of the system's solution set. x1 - 2x2 = 1 -2x1 + 5x2 = 2
Solve Problem using augmented matrix methods. Write the linear system represented by each augmented matrix in your solution, and solve each of these systems graphically Discuss the relationship among the solutions of these systems. x1 - x2 = 2 x1 + x2 = 6
Solve Problem using augmented matrix methods. x1 + 3x2 = 1 3x1 - 2x2 = 14
Solve Problem using augmented matrix methods. x1 - 3x2 = -5 -3x1 - x2 = 5
Solve Problem using augmented matrix methods. 2x1 + x2 = 0 x1 - 2x2 = -5
Solve Problem using augmented matrix methods. 2x1 - 3x2 = -2 -4x1 +6x2 = 7
Solve Problem using augmented matrix methods. -3x1 - x2 = -5 x1 + 3x2 = 5
Solve Problem using augmented matrix methods. 2x1 - 4x2 = -2 -3x1 + 6x2 = 3
Solve Problem using augmented matrix methods. -6x1 + 2x2 = 4 3x1 -x2 = -2
Solve Problem using augmented matrix methods. 2x1 - x2 = -8 2x1 + x2 = 8
Solve Problem using augmented matrix methods. -2x1 -4x2 = - 4 3x1 + 6x2 = 4
Solve Problem using augmented matrix methods. -2x1 + 4x2 = 4 3x1 -6x2 = -6
Solve Problem using augmented matrix methods. 2x1 - 3x2 = -8 5x1 + 3x2 = 1
Solve Problem using augmented matrix methods. 4x1 + 3x2 = 26 5x1 - 11x2 = -7
Solve Problem using augmented matrix methods. 0.3x1 - 0.6x2 = 0.18 0.5x1 - 0.2x2 = 0.54
Solve Problem using augmented matrix methods. Use a graphing calculator to perform the row operations 2.7x1 - 15.12x2 = 27 3.25x1 -18.52x2 = 33
Solve Problem using augmented matrix methods. Use a graphing calculator to perform the row operations 5.7x1 - 8.55x2 = -35.91 4.5x1 +5.73x2 = 76.17
Write the linear system corresponding to each reduced augmented matrix in problem and write the solution of the system.
Write the linear system corresponding to each reduced augmented matrix in problem and write the solution of the system.
Write the linear system corresponding to each reduced augmented matrix in problem and write the solution of the system. Discuss.
In Problem, if a matrix is in reduced form, say so, if not, explain why and indicate the row operation (s) necessary to transfrom the matrix into reduced form.
Write the linear system corresponding to each reduced augmented matrix in problem and write the solution of the system. Discuss in detail.
If the number of leftmost ones is less than the number of variables and the system is consistent, then the system has infinitely many solutions.
Use row operations to change each matrix in Problem reduced form.
Use row operations to change each matrix in Problem to reduce form.
Use row operations to change each matrix in Problem to reduce form.
Use row operations to change each matrix in Problem to reduce form.
Solve Problem using Gauss-Jordan elimination. 3x1 +5x2 -x3 = -7 x1 +x2 +x3 = -1 2x1 + 11x3 =7
Solve Problem using Gauss-Jordan elimination. 2x1 + 6x2 + 15x3 =-12 4x1 + 7x2 + 13x3 = -10 3x1 + 6x2 +12x3 = -9
Solve Problem using Gauss-Jordan elimination. 2x1 + 4x2 - 6x3 = 10 3x1 + 3x2 - 3x3 = 6
Solve Problem using Gauss-Jordan elimination. 2x1 - x2 = 0 3x1 + 2x2 = 7 x1 - x2 = -2
Solve Problem using Gauss-Jordan elimination. 3x1 + 7x2 -x3 = 11 x1 +2x2 - x3 = 3 2x1 + 4x2 - 2x3 = 10
Solve Problem using Gauss-Jordan elimination. 2x1 + 3x2 + 5x3 = 21 x1 - x2 -5x3 = -2 2x1 + x2 -x3 = 11
Solve Problem using Gauss-Jordan elimination. 3x1 - 9x2 + 12x3 = 6 -2x1 + 6x2 - 8x3 = -4
Solve Problem using Gauss-Jordan elimination. 4x1 - 2x2 + 2x3 = 5 -6x1 + 3x2 - 3x3 = -2 10x1 - 5x2 + 9x3 = 4
Consider a system of three linear equations in three variables. Give examples of two reduced forms that are not row-equivalent if the system is (A) Consistent and dependent (B) Inconsistent
Solve Problem using Gauss - Jordan elimination. 2x1 + 4x2 + 5x3 + 4x4 = 8 x1+ 2x2 + 2x3 + x4 = 3
In Problem, if a matrix is in reduced form, say so, if not, explain why and indicate the row operation (s) necessary to transfrom the matrix into reduced form.
Solve Problem using Gauss - Jordan elimination. x1 + x2 + 4x3 + x4 = 1.3 -x1+ x2 - x3 = 1.1 2x1 + x3 + 3x4 = -4.4 2x1 + 5x2 + 11x3 + 3x4 = 5.6
Solve Problem using Gauss - Jordan elimination. x1 - 3x2 + x3 + x4 + 2x5 = 2 -x1 + 5x2 + 2x3 + 2x4 - 2x5 = 0 2x1 - 6x2 + 2x3 + 2x4 + 4x5 = 4 -x1 + 3x2 - x3 + x5 = -3
Find a, b, and c so that the graph of the quadratic equation y = ax2 + bx + c passes through the points (-1, -5), (2,7), and (5,1).
Repeat Problem 65 assuming that the cutting, assembly, and packaging departments have available a maximum of 350, 330, and 115 labor-hours per week, respectively.Problem 65Boat production. A small manufacturing plant makes three types of inflatable boats: one-person, two-person, and four-person
Airplane leases. A corporation wants to lease a fleet of 12 airplanes with a combined carrying capacity of 220 passengers. The three available types of planes carry 10,15, and 20 passengers, respectively. How many of each type of plane should be leased?
Airplane leases. Refer to Problem 68. The cost of leasing a 10-passenger airplane is $8,000 per month, a 15-passenger airplane is $14,000 per month, and a 20-passenger airplane is $16,000 per month. Which of the solutions to Problem 68 would minimize the monthly leasing cost?
Repeat Problem 71 if local taxes are not al-lowed as a deduction for federal and state taxes. Problem 71 A corporation has a taxable income of $7,650,000. At this income level, the federal income tax rate is 50%, the state tax rate is 20%, and the local tax rate is 10%. If each tax rate is applied
Repeat Problem 73 if tax law is changed so that the taxable income of a company is defined to be all of its own annual net income plus its share of the taxable income of each of the other companies.Problem 73As a result of several mergers and acquisitions, stock in four companies has been
Repeat Problem 75 if the diet is to include exactly 400 units of calcium, 160 units of iron, and 240 units of vitamin A.Problem 75A dietitian in a hospital is to arrange a special diet composed of three basic foods. The diet is to include exactly 340 units of calcium. 180 units of iron, and 220
In a laboratory experiment, rats are to be fed 5 packets of food containing a total of 80 units of vitamin E. There are four different brands of food packets that can be used. A packet of brand A contains 5 units of vitamin E, a packet of brand B contains 10 units of vitamin E, a packet of brand C
In Problem, if a matrix is in reduced form, say so, if not, explain why and indicate the row operation (s) necessary to transfrom the matrix into reduced form.
Refer to Problem 78. The costs of the four brands are Brand A, $1.50; Brand B, $3.00; Brand C, $3.75; and Brand D, $2.25. Which of the solutions to Problem 78 would minimize the cost of the rat food? Problem 78 In a laboratory experiment, rats are to be fed 5 packets of food containing a total of
The population of California was approximately 24 million in 1980, 30 million in 1990, and 34 million in 2000. Construct a model for this data by finding a quadratic equation whose graph passes through the points (0,24), (10,30), and (20,34). Use this model to estimate the population in 2020. Do
The life expectancy for males born during 1980-1985 was approximately 70.7 years. This grew to 71.1 years during 1985-1990 and to 71.8 years during 1990-1995. Construct a model for this data by finding a quadratic equation whose graph passes through the points (0,70.7), (5,71.1), and (10,71.8). Use
Subsequent data indicated that life expectancy grew to 73.2 years for males born during 1995-2000 and to 74.3 years for males born during 2000-2005. Add the points (15,73.2) and (20,74.3) to the data set in Problem 84. Use a graphing calculator to find a quadratic regression model for all five data
Repeat Problem 87 if 650 telephone contacts and 350 house contacts are needed. Problem 87 Two sociologists have grant money to study school busing in a particular city. They wish to conduct an opinion survey using 600 telephone contacts and 400 house contacts. Survey company A has personnel to do
Refer to Problem 89. Closing Washington Avenue east of 6th Street for Construction changes the traffic flow for the network as indicated in the figure. Repeat parts (A)-(D) of Problem 89 for this traffic flow.Problem 89.(A) For a smooth traffic flow, the number of vehicles entering each
Problem refer to the following matrices:
Perform the indicated operation, if possible. BA
Perform the indicated operation, if possible. C2
Perform the indicated operation, if possible. C + DA
Perform the indicated operation, if possible (0.2)CD
Perform the indicated operations, if possible. (2)DB + (5)CD
Perform the indicated operations, if possible. CDA
Perform the indicated operation, if possible. BAD
If a and b are nonzero real numbers,Find Ab and BA
If a and b are nonzero real numbers andFind A2.
In Problem use a graphing calculator to calculate to calculate B,B2, B3,...and AB, AB2, AB3,....Describe any patterns you observe in each sequence of matrices.
Find w,x,y and z so that
Find a, b, c and d so that
Perform the indicated operations in Problem, if possible.
A square matrix is an upper triangular matrix if all elements below the principal diagonal are zero. So a 2 × 2 upper triangular matrix has the formwhere a, b and d are real numbers. Discuss the validity of each of the following statements. If the statement is always true, explain why.
If both labor and materials at plant X in Problem 65 are increased by 20%, find 1/2(1.2A + B), the new average cost of production for the two plantsProblem 65A company with two different plants manufactures guitars and banjos. Its production costs for each instrument are given in the following
Referring to Problem 67, what is the markup matrix resulting from a 20% increase in dealer invoice prices and an increase in retail prices of 15%? (Compute results to the nearest dollar.)Problem 67An import car dealer sells three models of a car. The retail prices and the current dealer invoice
A personal computer retail company sells five different computer models through three stores. The inventory of each model on hand in each store is summarized in matrix M.Wholesale (W) and retail (R)values of each model computer are summarized in matrix N.(A) what is the retail value of the
Gregor Mendel (1822-1884) made discoveries that revolutionized the science of genetics. In one experiment, he crossed dihybrid yellow round peas (yellow and round are dominant characteristics; the peas also contained genes for the recessive characteristics green and wrinkled) and obtained peas of
A teacher has given four tests to a class of five students and stored the results in the following matrixDiscuss methods of matrix multiplication that the teacher can use to obtain the information indicated below. In each case, state the matrices to be used and then perform the necessary
In Problem, find the matrix products. Product can be found mentally, without the use of a calculator or pencil - and - paper calculations.
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