Question 1

Solve the problem.
-Marty's Tee Shirt & Jacket Company is to produce a new line of jackets with a embroidery of a Great Pyrenees dog on the front. There are fixed costs of $650 to set up for production, and variable costs of $39 per jacket. Write
An equation that can be used to determine the total cost, C(x), encountered by Marty's Company in producing x
Jackets, and use the equation to find the total cost of producing 79 jackets.

Accepted Answer

C(x) = 650 + 39x. For 79 jackets, C(79) = 650 + 39(79) = 650 + 3081 = $3,731.

Question 2

Plot a scatter diagram.
-$$\begin{array} { l | c c c c c c c c c } 
\mathrm { x } & 15 & 21 & 36 & 46 & 58 & 70 & 71 & 84 & 95 \
\hline \mathrm { y } & 10 & 23 & 42 & 45 & 68 & 55 & 63 & 96 & 85
\end{array}$$

Accepted Answer

The answer of Plot a scatter diagram.
-\[\begin{array} { l |...

Question 3

Solve the problem.
-The cost for labor associated with fixing a washing machine is computed as follows: There is a fixed charge of $30 for the repairman to come to the house, to which a charge of $23 per hour is added. Find an equation that
Can be used to determine the labor cost, C(x), of a repair that takes x hours.

Accepted Answer

The correct equation is C(x) = 30 + 23x, representing a fixed charge of $30 plus $23 for each hour of labor.

Question 4

Solve the problem.
-In a certain city, the cost of a taxi ride is computed as follows: There is a fixed charge of $2.40 as soon as you get in the taxi, to which a charge of $1.90 per mile is added. Find an equation that can be used to determine the cost,
C(x), of an x-mile taxi ride.

Accepted Answer

The cost of the taxi ride consists of a fixed charge of $2.40 and an additional charge of $1.90 per mile. Therefore, the equation that represents the total cost C(x) for an x-mile ride is C(x) = 2.40 + 1.90x.

Question 5

Plot a scatter diagram.
-$$\begin{array} { c | c c c c c c c c c c } 
\mathrm { x } & 24 & - 13 & 7 & - 10 & - 6 & 17 & 6 & 18 & 10 & 1 \
\hline \mathrm { y } & 56 & 26 & 41 & - 12 & - 2 & 29 & 7 & 71 & - 9 & 5
\end{array}$$

Accepted Answer

The answer of Plot a scatter diagram.
-\[\begin{array} { c |...

Question 6

Solve the problem.
-Let $f ( x )$ be the function represented by the dashed line and $g ( x )$ be the function represented by the solid lin Solve the equation $f ( x ) = g ( x )$.

Accepted Answer

The answer of Solve the problem.
-Let $f ( x )$...

Question 7

Plot and interpret the appropriate scatter diagram.
-The table gives the times spent watching TV and the grades of several students. $$\begin{array} { l | c c c c c c } 
\text { Weekly TV } ( \mathrm { h } ) & 6 & 12 & 18 & 24 & 30 & 36 \
\hline \text { Grade (\%) } & 92.5 & 87.5 & 72.5 & 77.5 & 62.5 & 57.5
\end{array}$$ Which scatter diagram describes the data and the relationship, if any?

Accepted Answer

The answer of Plot and interpret the appropriate scatter diagram.
-The...

Question 8

Solve the problem.
-Regrind, Inc. regrinds used typewriter platens. The variable cost per platen is $1.50. The total cost to regrind 90 platens is $400. Find the linear cost function to regrind platens. If reground platens sell for $8.00 each, how
Many must be reground and sold to break even?

Accepted Answer

The total cost to regrind 90 platens is $400, which includes both variable and fixed costs. The variable cost is $1.50 per platen, so for 90 platens, the variable cost is 90 * $1.50 = $135. Subtracting this from the total cost, $400 - $135 = $265, gives us the fixed cost. Therefore, the cost function is C(x) = 1.50x + 265. To break even, revenue (R) must equal cost (C), so at $8.00 per platen, 8x = 1.50x + 265. Solving for x gives x = 265 / (8 - 1.5) = 41 platens.

Question 9

Solve the problem.
-Let $f ( x )$ be the function represented by the dashed line and $g ( x )$ be the function represented by the solid line. Solve the equation $f ( x ) \geq g ( x )$.

Accepted Answer

The answer of Solve the problem.
-Let $f ( x )$...

Question 10

Solve the problem.
-If an object is dropped off of a tower, the velocity, $V$, of the object after $t$ seconds can be obtained by multiplying $t$ by 32 and adding 10 to the result. Express $\mathrm { V }$ as a linear function of $\mathrm { t }$.

Accepted Answer

The problem states that the velocity $V$ after $t$ seconds is found by multiplying $t$ by 32 and then adding 10, which directly translates to the equation $V(t) = 32t + 10$.

Question 11

Solve the problem.
-Northwest Molded molds plastic handles which cost $0.20 per handle to mold. The fixed cost to run the molding machine is $5,253 per week. If the company sells the handles for $3.20 each, how many handles must
Be molded and sold weekly to break even?

Accepted Answer

To break even, the total cost must equal the total revenue. The total cost is the fixed cost plus the variable cost per handle times the number of handles, and the total revenue is the selling price per handle times the number of handles. Setting these equal gives: $5,253 + $0.20x = $3.20x$. Solving for x gives x = 1,751 handles.

Question 12

Solve the problem.
-If an object is dropped from a tower, then the velocity, V (in feet per second), of the object after t seconds can be obtained by multiplying t by 32 and adding 10 to the result. Find V as a linear function of t, and use this
Function to evaluate V(7.4), the velocity of the object at time t = 7.4 seconds.

Accepted Answer

The velocity function is V(t) = 32t + 10. Substituting t = 7.4 gives V(7.4) = 32(7.4) + 10 = 246.8 feet per second.

Question 13

Solve the problem.
-To convert a temperature from degrees Celsius to degrees Fahrenheit, you multiply the temperature in degrees Celsius by $1.8$ and then add 32 to the result. Express $F$ as a linear function of $c$.

Accepted Answer

The correct formula to convert Celsius to Fahrenheit is $F(c) = 1.8c + 32$, which matches choice B.

Question 14

Solve the problem.
-In a certain city, the cost of a taxi ride is computed as follows: There is a fixed charge of $2.15 as soon as you get in the taxi, to which a charge of $1.90 per mile is added. Find an equation that can be used to determine the cost,
C(x), of an x-mile taxi ride, and use this equation to find the cost of a 4-mile taxi ride.

Accepted Answer

The answer of Solve the problem.
-In a certain city, the...

Question 15

Solve the problem.
-A truck rental company rents a moving truck one day by charging $39 plus $0.09 per mile. Write a linear equation that relates the cost C, in dollars, of renting the truck to the number x of miles driven. What is the cost
Of renting the truck if the truck is driven 120 miles?

Accepted Answer

The correct linear equation is C(x) = 0.09x + 39, which represents a $39 flat fee plus $0.09 per mile. For 120 miles, the cost is $39 + (0.09 * 120) = $39 + $10.80 = $49.80.

Question 16

Solve the problem.
-Marty's Tee Shirt & Jacket Company is to produce a new line of jackets with an embroidery of a Great Pyrenees dog on the front. There are fixed costs of $560 to set up for production, and variable costs of $33 per jacket. Write
An equation that can be used to determine the total cost, C(x), encountered by Marty's Company in producing x
Jackets.

Accepted Answer

The total cost C(x) consists of a fixed cost ($560) plus a variable cost per jacket ($33) multiplied by the number of jackets (x), hence C(x) = 560 + 33x.

Question 17

Solve the problem.
-Let $\mathrm { f } ( \mathrm { x } )$ be the function represented by the dashed line and $g ( x )$ be the function represented by the solid li Solve the equation $f ( x ) < g ( x )$.

Accepted Answer

The answer of Solve the problem.
-Let \(\mathrm { f }...

Question 18

Solve the problem.
-Suppose that the quantity supplied S and quantity demanded D of baseball caps at a major league game are given by the functions S(p) = 5,000 - 100p and D(p) = 150p, where p is the price. Find the equilibrium price for
Caps at the game. Then find the equilibrium quantity.

Accepted Answer

The equilibrium price occurs when quantity supplied equals quantity demanded: 5,000 - 100p = 150p. Solving for p gives p = $20. Substituting p = $20 into either function gives the equilibrium quantity: 3,000 caps.

Question 19

Solve the problem.
-A lumber yard has fixed costs of $4,726.80 per day and variable costs of $0.1 per board-foot produced. Lumber sells for $1.90 per board-foot. How many board-feet must be produced and sold daily to break even?

Accepted Answer

To break even, the total cost (fixed costs + variable costs) must equal total revenue. Let $ x $ be the number of board-feet produced and sold. The break-even point occurs when $ 1.90x = 4,726.80 + 0.1x $. Solving for $ x $, we subtract $ 0.1x $ from both sides to get $ 1.80x = 4,726.80 $. Dividing both sides by 1.80 gives $ x = 2,626 $ board-feet.

Question 20

Solve the problem.
-Linda needs to have her car towed. Little Town Auto charges a flat fee of $75 plus $3 per mile towed. Write a function expressing Linda's towing cost, c, in terms of miles towed, x. Find the cost of having a car towed 3
Miles.

Accepted Answer

The correct function is c(x) = 3x + 75, representing the $75 flat fee plus $3 per mile. For 3 miles, the cost is 3(3) + 75 = 9 + 75 = $84.

Quiz 2: Linear and Quadratic Functions

Solve the problem. -In a certain city, the cost of a taxi ride is computed as follows: There is a fixed charge of $2.40 as soon as you get in the taxi, to which a charge of $1.90 per mile is added. Find an equation that can be used to determine the cost, C(x) , of an x-mile taxi ride.

Solve the problem. -Let $f ( x )$ be the function represented by the dashed line and $g ( x )$ be the function represented by the solid lin Solve the equation $f ( x ) = g ( x )$ .

Solve the problem. -Regrind, Inc. regrinds used typewriter platens. The variable cost per platen is $1.50. The total cost to regrind 90 platens is $400. Find the linear cost function to regrind platens. If reground platens sell for $8.00 each, how Many must be reground and sold to break even?

Solve the problem. -If an object is dropped off of a tower, the velocity, $V$ , of the object after $t$ seconds can be obtained by multiplying $t$ by 32 and adding 10 to the result. Express $\mathrm { V }$ as a linear function of $\mathrm { t }$ .

Solve the problem. -Northwest Molded molds plastic handles which cost $0.20 per handle to mold. The fixed cost to run the molding machine is $5,253 per week. If the company sells the handles for $3.20 each, how many handles must Be molded and sold weekly to break even?

Solve the problem. -To convert a temperature from degrees Celsius to degrees Fahrenheit, you multiply the temperature in degrees Celsius by $1.8$ and then add 32 to the result. Express $F$ as a linear function of $c$ .

Solve the problem. -A truck rental company rents a moving truck one day by charging $39 plus $0.09 per mile. Write a linear equation that relates the cost C, in dollars, of renting the truck to the number x of miles driven. What is the cost Of renting the truck if the truck is driven 120 miles?

Solve the problem. -Suppose that the quantity supplied S and quantity demanded D of baseball caps at a major league game are given by the functions S(p) = 5,000 - 100p and D(p) = 150p, where p is the price. Find the equilibrium price for Caps at the game. Then find the equilibrium quantity.

Solve the problem. -A lumber yard has fixed costs of $4,726.80 per day and variable costs of $0.1 per board-foot produced. Lumber sells for $1.90 per board-foot. How many board-feet must be produced and sold daily to break even?

Solve the problem. -Linda needs to have her car towed. Little Town Auto charges a flat fee of $75 plus $3 per mile towed. Write a function expressing Linda's towing cost, c, in terms of miles towed, x. Find the cost of having a car towed 3 Miles.

Quiz 2: Linear and Quadratic Functions

Solve the problem. -In a certain city, the cost of a taxi ride is computed as follows: There is a fixed charge of $2.40 as soon as you get in the taxi, to which a charge of $1.90 per mile is added. Find an equation that can be used to determine the cost, C(x) , of an x-mile taxi ride.

Solve the problem. -Let f(x) f ( x ) f(x) be the function represented by the dashed line and g(x) g ( x ) g(x) be the function represented by the solid lin Solve the equation f(x) =g(x) f ( x ) = g ( x ) f(x) =g(x) .

Solve the problem. -Regrind, Inc. regrinds used typewriter platens. The variable cost per platen is $1.50. The total cost to regrind 90 platens is $400. Find the linear cost function to regrind platens. If reground platens sell for $8.00 each, how Many must be reground and sold to break even?

Solve the problem. -Let f(x) f ( x ) f(x) be the function represented by the dashed line and g(x) g ( x ) g(x) be the function represented by the solid line. Solve the equation f(x) ≥g(x) f ( x ) \geq g ( x ) f(x) ≥g(x) .

Solve the problem. -If an object is dropped off of a tower, the velocity, VVV , of the object after ttt seconds can be obtained by multiplying ttt by 32 and adding 10 to the result. Express V\mathrm { V }V as a linear function of t\mathrm { t }t .