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1.
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Solve the system by the method of
substitution.
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2.
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Solve the system graphically.
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3.
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Solve the system by the method of elimination and
check any solutions algebraically.
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4.
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Solve the system by the method of
elimination.
a. | | b. | (dependent) | c. | | d. | inconsistent | e. | |
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5.
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Find the least squares regression line for the points
by solving the system for a and
b.
Points:
a. | y = 3.93x
–4.21 | b. | y =
2.80x –3.20 | c. | y =
–2.66x +2.80 | d. | y =
–3.47x –4.21 | e. | y =
–3.20x +2.80 |
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6.
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Use back-substitution to solve the system of linear
equations.
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7.
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Find the equation of the circle
that passes through the points.
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8.
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Find values of x, y, and that satisfy the system. These systems arise in certain optimization problems in
calculus, and is called a Lagrange multiplier.
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9.
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A chemist needs 10 liters of a 25% acid solution.
The solution is to be mixed from three solutions whose concentrations are 10%, 20%, and 50%. How
many liters of each solution will satisfy each condition? Use 2 liters of the 50%
solution.
a. | 2 L of 10%, 7 L of 20%, 1 L of 50%
| b. | 7 L of 10%, 7 L of 20%, 2 L of 50%
| c. | 7 L of 10%, 1 L of 20%, 2 L of 50%
| d. | 1 L of 10%, 2 L of 20%, 7 L of
50% | e. | 1 L of 10%, 7 L of 20%, 2 L of 50%
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10.
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Write the form of the partial fraction
decomposition of the rational expression. Do not solve for the constants.
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11.
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Write the partial fraction decomposition of the
rational expression. Check your result algebraically.
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12.
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Write the partial fraction decomposition of the
rational expression. Check your result algebraically.
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13.
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Write the partial fraction decomposition of the
rational expression.
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14.
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Select the correct graph of the
inequality.
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15.
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Find the consumer surplus and producer
surplus.
Demand
Supply
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16.
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Find the minimum value of the objective function
and where they occur, subject to the indicated constraints.
Objective function:
Constraints:
a. | Minimum at | b. | Minimum at | c. | Minimum at | d. | Minimum at | e. | Minimum at |
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17.
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Select the region determined by the constraints.
Then find the minimum value of the objective function (if possible) and where they occur, subject to
the indicated constraints.
Objective function:
Constraints:
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18.
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Find the maximum value of the objective function
and where they occur, subject to the constraints:
Objective function:
Constraints:
a. | Maximum at 80 | b. | Maximum at | c. | No maximum | d. | Maximum at | e. | Maximum at |
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19.
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The linear programming problem has an unusual
characteristic. Select a graph of the solution region for the problem and describe the unusual
characteristic. Find the maximum value of the objective function (if possible) and where they
occur.
Objective function:
Constraints:
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20.
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An accounting firm has 780 hours of staff time and
272 hours of reviewing time available each week. The firm charges for an audit
and for a tax return. Each audit requires 60
hours of staff time and 16 hours of review time. Each tax return requires 10 hours of staff time and
4 hours of review time. What numbers of audits and tax returns will yield an optimal revenue? What is
the optimal revenue?
a. | 0 audit 16 tax returns Optimal revenue: | b. | 13 audits 0 tax
return Optimal revenue: | c. | 16 audits 0 tax return Optimal revenue: | d. | 0 audit 13 tax
returns Optimal revenue: | e. | 10 audits 10 tax returns Optimal revenue: |
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