Question 1

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

Accepted Answer

A)  ( 0, 0 ), ( 7, 0 ), ( 0, 6 ), ( 4, 3 ), ( 13, 1 ) 
B)  ( 7, 0 ), ( 0, 6 ), ( 4, 3 ) 
C)  ( 13, 1 ), ( 7, 0 ), ( 0, 6 ), ( 4, 3 ) 
D)  ( 0, 0 ), ( 8, 0 ), ( 0, 7 ), ( 4, 3 ) 
E)  ( 0, 0 ), ( 7, 0 ), ( 0, 6 ), ( 4, 3 ) 
A)  ( 0, 0 ), ( 7, 0 ), ( 0, 6 ), ( 4, 3 ), ( 13, 1 ) 
B)  ( 7, 0 ), ( 0, 6 ), ( 4, 3 ) 
C)  ( 13, 1 ), ( 7, 0 ), ( 0, 6 ), ( 4, 3 ) 
D)  ( 0, 0 ), ( 8, 0 ), ( 0, 7 ), ( 4, 3 ) 
E)  ( 0, 0 ), ( 7, 0 ), ( 0, 6 ), ( 4, 3 )

Question 2

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

Accepted Answer

A)  ​   
B)  ​   
C)  ​   
D)    
E)  ​   
A)  ​   
B)  ​   
C)  ​   
D)    
E)  ​

Question 3

Sociologists often study the dominance of one group over another. Suppose in a certain society there are four classes which we will call: abigweel, aweel, upancomer, and pon. Hint: These are pronounced "A big wheel," "A wheel," "Up and comer," and "peon."
​
Abigweel dominate aweel, upancomer, and pon.
Aweel dominate upancomer and pon.
Upancomer dominate pon.
​
Matrix [ D ] represent these dominance relationships. We say that an individual has two-stage dominance over another if 1 appears in the matrix [ D ] 2 for those individuals. Write the two-stage dominance matrix.
​

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 4

The Seedy Vin Company produces Riesling, Charbono, and Rose wines. There are three procedures for producing each wine (the procedures for production affect the cost of the final product). One procedure allows an outside company to bottle the wine; a second allows the wine to be produced and bottled at the winery; a third allows the wine to be estate bottled. The amount of wine produced by the Seedy Vin Company by each method is shown by the matrix [ W ]. Suppose the cost for each method of production is given by the matrix [ C ]. Find the cost of producing each of the three types of wine. ​
Hint: This is [ C ][ W ].
​   ​

Accepted Answer

A)  Riesling, 21; Charbono, 24; Rose, 48 
B)  Riesling, 22; Charbono, 27; Rose, 42 
C)  Riesling, 25; Charbono, 27; Rose, 48 
D)  Riesling, 22; Charbono, 23; Rose, 48 
E)  Riesling, 25; Charbono, 23; Rose, 42 
A)  Riesling, 21; Charbono, 24; Rose, 48 
B)  Riesling, 22; Charbono, 27; Rose, 42 
C)  Riesling, 25; Charbono, 27; Rose, 48 
D)  Riesling, 22; Charbono, 23; Rose, 48 
E)  Riesling, 25; Charbono, 23; Rose, 42

Question 5

Given the matrix, perform elementary row operation to obtain zeros under the 1 in the first column. ​   ​

Accepted Answer

A)  ​   ​
​  
​ 
B)  ​
​   ​  
​ 
C)  ​
​   ​  
​ 
D)  ​   ​
​  
​ 
E)  ​
​   ​  
​
​ 
A)  ​   ​
​  
​ 
B)  ​
​   ​  
​ 
C)  ​
​   ​  
​ 
D)  ​   ​
​  
​ 
E)  ​
​   ​  
​
​

Question 6

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: each had how many pistoles? ​

Accepted Answer

A)  (21, 13) 
B)  (   ,   ) 
C)  (   , 16) 
D)  (   , 17) 
E)  inconsistent 
A)  (21, 13) 
B)  (   ,   ) 
C)  (   , 16) 
D)  (   , 17) 
E)  inconsistent

Question 7

Given the matrix, perform elementary row operations to obtain a zeros above and below the 1 in the second column without changing the entries in the first column.
​

Accepted Answer

*Row+(-6, [C], 2, 1)

Question 8

Suppose Ingredient I is made up of 80% micoden and 20% water, Ingredient II is made up of 30% micoden, 60% bixon, and 10% water, and these ingredients are mixed together. How much micoden is in the mixture? Round to one decimal place, if required.   ​
__________ lb micoden

Accepted Answer

The answer of Suppose Ingredient I is made up of...

Question 9

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

Accepted Answer

The answer of Solve the system for all real solutions,...

Question 10

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

Accepted Answer

The answer of Find the corner points for the set...

Question 11

Find the inverse of matrix, if it exists. ​   ​

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 12

The box contains twenty-five more dimes than nickels. How many of each type of coin is there if the total value is $6.40?
​
__________ nickels __________ dimes

Accepted Answer

The answer of The box contains twenty-five more dimes than...

Question 13

How many gallons of 27% butterfat cream must be mixed with 500 gallons of 3% butterfat milk to obtain a 7% butterfat milk?
​
__________ gallons of 27% butterfat cream.

Accepted Answer

The answer of How many gallons of 27% butterfat cream...

Question 14

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

Accepted Answer

A)    
B)    
C)    
D)    
E)  inconsistent 
A)    
B)    
C)    
D)    
E)  inconsistent

Question 15

Graph the solution of the system. ​   ​

Accepted Answer

A)  ​   
B)    
C)    
D)    
E)    
A)  ​   
B)    
C)    
D)    
E)

Question 16

Given the matrix, perform elementary row operations to obtain a zeros above and below the 1 in the second column without changing the entries in the first column. ​   ​

Accepted Answer

A)  ​  
​ 
B)  ​  
​ 
C)  ​
​  
​ 
D)  ​  
​ 
E)  ​
​  
​ 
A)  ​  
​ 
B)  ​  
​ 
C)  ​
​  
​ 
D)  ​  
​ 
E)  ​
​  
​

Question 17

Solve the system by solving the corresponding matrix equation with an inverse, if possible.
​   ​
Enter the answer in the form   ,   ,   .

Accepted Answer

The answer of Solve the system by solving the corresponding...

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

Solve the system by solving the corresponding matrix equation with an inverse, if possible.

Given the matrix, perform elementary row operation to obtain zeros under the 1 in the first column.

Given the matrix, perform elementary row operations to obtain a zeros above and below the 1 in the second column without changing the entries in the first column.

Suppose Ingredient I is made up of 80% micoden and 20% water, Ingredient II is made up of 30% micoden, 60% bixon, and 10% water, and these ingredients are mixed together. How much micoden is in the mixture? Round to one decimal place, if required. __________ lb micoden

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

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

Find the inverse of matrix, if it exists.

The box contains twenty-five more dimes than nickels. How many of each type of coin is there if the total value is $6.40? nickels dimes

How many gallons of 27% butterfat cream must be mixed with 500 gallons of 3% butterfat milk to obtain a 7% butterfat milk? __________ gallons of 27% butterfat cream.

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

Graph the solution of the system.

Given the matrix, perform elementary row operations to obtain a zeros above and below the 1 in the second column without changing the entries in the first column.

Solve the system by solving the corresponding matrix equation with an inverse, if possible. Enter the answer in the form , , .

The Nature of Problem Solving

The Nature of Sets

The Nature of Logic

The Nature of Numeration Systems

The Nature of Numbers

The Nature of Algebra

The Nature of Geometry

The Nature of Measurement

The Nature of Networks and Graph Theory

The Nature of Growth

The Nature of Sequences, Series, and Financial Management

The Nature of Counting

The Nature of Probability

The Nature of Statistics

The Nature of Graphs and Functions

The Nature of Voting and Apportionment

Filters

Exam 16: The Nature of Mathematical Systems

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

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

Given the matrix, perform elementary row operation to obtain zeros under the 1 in the first column. ​ ​

Given the matrix, perform elementary row operations to obtain a zeros above and below the 1 in the second column without changing the entries in the first column. ​

Suppose Ingredient I is made up of 80% micoden and 20% water, Ingredient II is made up of 30% micoden, 60% bixon, and 10% water, and these ingredients are mixed together. How much micoden is in the mixture? Round to one decimal place, if required. ​ __________ lb micoden

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

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

Find the inverse of matrix, if it exists. ​ ​

The box contains twenty-five more dimes than nickels. How many of each type of coin is there if the total value is $6.40? ​ __________ nickels __________ dimes

How many gallons of 27% butterfat cream must be mixed with 500 gallons of 3% butterfat milk to obtain a 7% butterfat milk? ​ __________ gallons of 27% butterfat cream.

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

Graph the solution of the system. ​ ​

Given the matrix, perform elementary row operations to obtain a zeros above and below the 1 in the second column without changing the entries in the first column. ​ ​

Solve the system by solving the corresponding matrix equation with an inverse, if possible. ​ ​ Enter the answer in the form , , .

The Nature of Problem Solving

The Nature of Sets

The Nature of Logic

The Nature of Numeration Systems

The Nature of Numbers

The Nature of Algebra

The Nature of Geometry

The Nature of Measurement

The Nature of Networks and Graph Theory

The Nature of Growth

The Nature of Sequences, Series, and Financial Management

The Nature of Counting

The Nature of Probability

The Nature of Statistics

The Nature of Graphs and Functions

The Nature of Voting and Apportionment

Filters

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

Solve the system by solving the corresponding matrix equation with an inverse, if possible.

Given the matrix, perform elementary row operation to obtain zeros under the 1 in the first column.

Given the matrix, perform elementary row operations to obtain a zeros above and below the 1 in the second column without changing the entries in the first column.

Suppose Ingredient I is made up of 80% micoden and 20% water, Ingredient II is made up of 30% micoden, 60% bixon, and 10% water, and these ingredients are mixed together. How much micoden is in the mixture? Round to one decimal place, if required. __________ lb micoden

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

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

Find the inverse of matrix, if it exists.

The box contains twenty-five more dimes than nickels. How many of each type of coin is there if the total value is $6.40? nickels dimes

How many gallons of 27% butterfat cream must be mixed with 500 gallons of 3% butterfat milk to obtain a 7% butterfat milk? __________ gallons of 27% butterfat cream.

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

Graph the solution of the system.

Given the matrix, perform elementary row operations to obtain a zeros above and below the 1 in the second column without changing the entries in the first column.

Solve the system by solving the corresponding matrix equation with an inverse, if possible. Enter the answer in the form , , .