Exam 16: The Nature of Mathematical Systems

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Find the corner points for the set of feasible solutions for the constraints given in problem. ​ ​ Find the corner points for the set of feasible solutions for the constraints given in problem. ​ ​   ​

(Multiple Choice)
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Solve the system for all real solutions, using any suitable method. ​ Solve the system for all real solutions, using any suitable method. ​   ​

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Solve the system for all real solutions, using any suitable method. ​ Solve the system for all real solutions, using any suitable method. ​

(Essay)
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Maximize Maximize   subject to the constraints. ​   ​ T = ____ at ( ____, ____ ) subject to the constraints. ​ Maximize   subject to the constraints. ​   ​ T = ____ at ( ____, ____ ) ​ T = ____ at ( ____, ____ )

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Find the corner points for the set of feasible solutions for the constraints given in problem. ​ Find the corner points for the set of feasible solutions for the constraints given in problem. ​   ​

(Multiple Choice)
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Solve the system by the addition method. ​ Solve the system by the addition method. ​

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Find the matrix [ A ] ( [ B ] + [ C ] ), if ​ Find the matrix [ A ] ( [ B ] + [ C ] ), if ​   ,   ,   ​ , Find the matrix [ A ] ( [ B ] + [ C ] ), if ​   ,   ,   ​ , Find the matrix [ A ] ( [ B ] + [ C ] ), if ​   ,   ,   ​

(Multiple Choice)
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Solve the system by the addition method. ​ Solve the system by the addition method. ​   ​

(Multiple Choice)
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Find the sum [ A ] + [ B ], if ​ Find the sum [ A ] + [ B ], if ​   ​

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Solve the system by the substitution method. ​ Solve the system by the substitution method. ​   ​

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Solve the system by the substitution method. ​ Solve the system by the substitution method. ​   ​

(Multiple Choice)
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Suppose Ingredient I is made up of 40% micoden and 60% water, Ingredient II is made up of 10% micoden, 30% bixon, and 60% water, and these ingredients are mixed together. What is the percentage of water in mixture below? Suppose Ingredient I is made up of 40% micoden and 60% water, Ingredient II is made up of 10% micoden, 30% bixon, and 60% water, and these ingredients are mixed together. What is the percentage of water in mixture below?

(Multiple Choice)
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The following problem was written by Leonhard Euler: "Two persons owe conjointly 32 pistoles; they both have money, but neither of them enough to enable him, singly, to discharge this common debt." The first debtor says therefore to the second, "If you give me The following problem was written by Leonhard Euler: Two persons owe conjointly 32 pistoles; they both have money, but neither of them enough to enable him, singly, to discharge this common debt. The first debtor says therefore to the second, If you give me   of your money, I can immediately pay the debt. The second answers that he also could discharge the debt, if the other would give him   of his money. Required, how many pistoles each had? of your money, I can immediately pay the debt." The second answers that he also could discharge the debt, if the other would give him The following problem was written by Leonhard Euler: Two persons owe conjointly 32 pistoles; they both have money, but neither of them enough to enable him, singly, to discharge this common debt. The first debtor says therefore to the second, If you give me   of your money, I can immediately pay the debt. The second answers that he also could discharge the debt, if the other would give him   of his money. Required, how many pistoles each had? of his money. Required, how many pistoles each had?

(Essay)
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The demand for a product varies from 100,000 units at $130 per unit to 250,000 at $40 per unit. Also, 150,000 could be supplied at $30 per unit, whereas only 250,000 could be supplied for $110 each. Find the equilibrium point for the system (p, n).

(Short Answer)
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Solve the system by graphing. ​ Solve the system by graphing. ​   ​  Solve the system by graphing. ​   ​

(Essay)
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Solve the system by solving the corresponding matrix equation with an inverse, if possible. ​ Solve the system by solving the corresponding matrix equation with an inverse, if possible. ​   ​

(Multiple Choice)
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Find the inverse of matrix, if it exists. ​ Find the inverse of matrix, if it exists. ​

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Find the corner points for the set of feasible solutions for the constraints. ​ Find the corner points for the set of feasible solutions for the constraints. ​

(Essay)
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Suppose Ingredient I is made up of 80% micoden and 20% water, Ingredient II is made up of 30% micoden, 50% bixon, and 20% water, and these ingredients are mixed together. How much micoden is in the mixture? INGREDIENT I INGREDIENT II MIXTURE 2 lb 11 lb 13 lb ​

(Multiple Choice)
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Solve the system by the Gauss-Jordan method. ​ ​ Solve the system by the Gauss-Jordan method. ​ ​   ​

(Multiple Choice)
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