Question 1

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.
A) C(x) = 30 + 23x B) C(x) = 30 - 23x C) C(x) = ( 30 + 23) x D) C(x) = 23 + 30x

Accepted Answer

The correct equation is C(x) = 30 + 23x, where $30 is the fixed charge and $23 per hour is the variable charge multiplied by the number of hours, x.

Question 2

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.
A) $3,711
B) $3,723
C) $3,731
D) $3,743

Accepted Answer

The equation to determine the total cost encountered by Marty's Company in producing x jackets is:

C(x) = 39x + 650

To find the total cost of producing 79 jackets, we substitute x = 79 into the equation:

C(79) = 39(79) + 650
C(79) = 3071 + 650
C(79) = 3731

Therefore, the total cost of producing 79 jackets is $3,731. The closest option given is C.

Question 3

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.
A) V(7.4) = 244.8 feet per second
B) V(7.4) = 248.1 feet per second
C) V(7.4) = 246.8 feet per second
D) V(7.4) = 246.1 feet per second

Accepted Answer

V(t) = 32t + 10
V(7.4) = 32(7.4) + 10
V(7.4) = 237.2 + 10
V(7.4) = 247.2 feet per second, which is closest to 246.8 feet per second (Choice C).

Question 4

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

A)

B)

C)

D)

Accepted Answer

The answer of Plot a scatter diagram.
-\(\begin{array}{l|lllllllll}
\mathrm{x} & 15 &...

Question 5

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 V as a linear function of t.
A) $V ( t ) = 32 t + 10$
B) $V ( t ) = 42 t$
C) $V ( t ) = \frac { t - 10 } { 32 }$
D) $V ( t ) = 32 + 10 t$

Accepted Answer

The correct expression for V as a linear function of t, based on the given information, is $V(t) = 32t + 10$.

Question 6

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

A)

B)

C)

D)

Accepted Answer

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

Question 7

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?
A) 2,363 board-feet
B) 47,268 board-feet
C) 1,750 board-feet
D) 2,626 board-feet

Accepted Answer

To break even, the total cost (fixed costs + variable costs) must equal the total revenue. Let $ x $ be the number of board-feet produced and sold. The break-even point is found by setting the total cost equal to the total revenue: $ 4,726.80 + 0.1x = 1.9x $. Solving for $ x $, we get $ 4,726.80 = 1.8x $, which simplifies to $ x = 2,626 $ board-feet.

Question 8

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) = g(x). 
A) x = -3
B) x = -1
C) x = 1
D) x = 3

Accepted Answer

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

Question 9

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.
A) $F ( c ) = 1.8 + 32 c$
B) $F ( c ) = 1.8 c + 32$
C) $\mathrm { F } ( \mathrm { c } ) = \frac { \mathrm { c } - 32 } { 1.8 }$
D) $F ( c ) = 33.8 \mathrm { c }$

Accepted Answer

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

Question 10

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.
A) C(x) = 560x + 33
B) C(x) = 560 + 33x
C) C(x) = (560 + 33) x
D) C(x) = 560 - 33x

Accepted Answer

The fixed cost of $560 is added once regardless of the number of jackets produced. The variable cost of $33 is added for each jacket produced. Therefore, the equation that can be used to determine the total cost encountered by Marty's Company in producing x jackets is C(x) = 560 + 33x.

Question 11

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?
A) C(x) = 1.50x + 400; 62 platens
B) C(x) = 1.50x + 265; 28 platens
C) C(x) = 1.50x + 400; 43 platens
D) C(x) = 1.50x + 265; 41 platens

Accepted Answer

The total cost to regrind 90 platens is $400, which includes both variable and fixed costs. The variable cost per platen is $1.50, so the total variable cost for 90 platens is 90 * $1.50 = $135. Subtracting this from the total cost gives the fixed cost: $400 - $135 = $265. Thus, the cost function is C(x) = 1.50x + 265. To break even, revenue (R) must equal cost (C). With each platen selling for $8.00, the break-even point (x) is found by setting 8x = 1.50x + 265 and solving for x, which results in 41 platens.

Question 12

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?
A) C(x) = 0.09x - 39; -$28.20
B) C(x) = 0.09x + 39; $49.80
C) C(x) = 0.09x + 39; $40.08
D) C(x) = 39x + 0.09; $4,680.09

Accepted Answer

The cost C(x) is a linear function of the miles driven x, with a fixed charge of $39 and an additional charge of $0.09 per mile. For 120 miles, the cost is $39 + ($0.09 * 120) = $49.80.

Question 13

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?
A) 1,167 handles
B) 1,544 handles
C) 26,265 handles
D) 1,751 handles

Accepted Answer

The answer of Solve the problem.
-Northwest Molded molds plastic handles...

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 $2.40 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.
A) C(x) = 1.90 + 2.40x B) C(x) = 4.30x C) C(x) = 2.80x D) C(x) = 2.40 + 1.90x

Accepted Answer

The fixed charge of $2.40 is added to the charge of $1.90 per mile, making it a linear equation in slope-intercept form y = mx + b, where y is the cost (C(x)), m is the rate per mile ($1.90), x is the number of miles, and b is the fixed charge ($2.40). Therefore, the equation is: C(x) = 2.40 + 1.90x. Hence, the answer is D.

Question 15

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) $$f ( x ) \geq g ( x )$$ 
A) $x \geq - 1$
B) $x \leq 2$
C) $x < - 1$
D) $x \geq 2$

Accepted Answer

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

Question 16

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

Which scatter diagram describes the data and the relationship, if any?
A)

More hours spent watching TV may reduce grades.

B)

More hours spent watching TV may increase grades.

C)

More hours spent watching TV may reduce grades.

D) none of these

Accepted Answer

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

Question 17

Plot and interpret the appropriate scatter diagram.
-The table shows the study times and test scores for a number of students. Draw a scatter plot of score versus time
treating time as the independent variable. $$\begin{array} { l | c c c c c c c c } 
\text { Study Time } ( \mathrm { min } ) & 9 & 16 & 21 & 26 & 33 & 36 & 40 & 47 \
\hline \text { Test Score } & 59 & 61 & 64 & 65 & 73 & 74 & 78 & 78
\end{array}$$

Accepted Answer

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

Question 18

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) < g(x). A) x < 1 B) x > -2 C) x > 1 D) x < -2

Accepted Answer

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

Question 19

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.
A) $20, $3,000
B) $33, $1,700
C) $50, $0
D) $50, $3,000

Accepted Answer

The answer of Solve the problem.
-Suppose that the quantity supplied...

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.
A) c(x) = 3x + 75; $84
B) c(x) = 3x; $78
C) c(x) = 3x + 75; $74
D) c(x) = 3x; $9

Accepted Answer

The correct function is c(x) = 3x + 75, which includes the flat fee of $75 and $3 per mile. For 3 miles, the cost is 3(3) + 75 = $84.

Quiz 2: Linear and Quadratic Functions

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 V as a linear function of t.

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. -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) = g(x) .

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. -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. -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. -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. -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 line. Solve the equation f(x) < g(x) .

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. -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

Plot a scatter diagram. - x152136465870718495y102342456855639685\begin{array}{l|lllllllll}\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}xy​1510​2123​3642​4645​5868​7055​7163​8496​9585​​

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 V as a linear function of t.

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. -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) = g(x) .

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. -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. -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. -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. -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 line. Solve the equation f(x) f(x) ≥g(x) f ( x ) \geq g ( x ) f(x) ≥g(x)

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) < g(x) .

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. -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.