Question 1

Plot a scatter diagram.
-$$\begin{array} { l | l l l l l l l l l } 
\mathrm { x } & 18 & 25 & 29 & 47 & 59 & 67 & 74 & 83 & 85 \
\hline \mathrm { y } & 13 & 27 & 35 & 46 & 69 & 52 & 66 & 95 & 75
\end{array}$$

A)

B)

C)

D)

Accepted Answer

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

Question 2

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 ≥ 1
C) x ≥ -1
D) x ≤1

Accepted Answer

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

Question 3

Solve the problem.
-A lumber yard has fixed costs of $1384.90 per day and variable costs of $0.56 per board-foot produced. Lumber sells for $1.66 per board-foot. How many board-feet must be produced and sold daily to break even?
A) 623 board-feet
B) 2473 board-feet
C) 1259 board-feet
D) 839 board-feet

Accepted Answer

To break even, total costs must equal total revenue. The fixed cost is $1384.90, and the variable cost per board-foot is $0.56. The selling price per board-foot is $1.66. The break-even point is calculated as: $1384.90 / ($1.66 - $0.56) = 1259 board-feet.

Question 4

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 = -4
B) x = 4
C) x = -3
D) x = 3

Accepted Answer

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

Question 5

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

Accepted Answer

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

Question 6

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(2.2), the velocity of the object at time t = 2.2 seconds.
A) V(2.2) = 81.7 feet per second
B) V(2.2) = 79.7 feet per second
C) V(2.2) = 78.4 feet per second
D) V(2.2) = 80.4 feet per second

Accepted Answer

The answer of Solve the problem.
-If an object is dropped...

Question 7

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) = 3230 - 90p and D(p) = 100p, where p is the price. Find the equilibrium price for
Caps at the game. Then find the equilibrium quantity.
A) $32, $350
B) $10, $2330
C) $17, $1700
D) $10, $1700

Accepted Answer

The equilibrium price occurs when quantity supplied equals quantity demanded: S(p) = D(p). Solving 3230 - 90p = 100p gives p = 17. Substituting p = 17 into either function gives the equilibrium quantity: 1700.

Question 8

Solve the problem.
-Linda needs to have her car towed. Little Town Auto charges a flat fee of $45 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 14
Miles.
A) c(x) = 3x + 45; $77
B) c(x) = 3x; $48
C) c(x) = 3x; $42
D) c(x) = 3x + 45; $87

Accepted Answer

The function for the towing cost is c(x) = 3x + 45. For 14 miles, the cost is 3(14) + 45 = $87.

Question 9

Solve the problem.
-Regrind, Inc. regrinds used typewriter platens. The variable cost per platen is $1.50. The total cost to regrind 70 platens is $400. Find the linear cost function to regrind platens. If reground platens sell for $8.40 each, how
Many must be reground and sold to break even?
A) C(x) = 1.50x + 295; 30 platens
B) C(x) = 1.50x + 400; 41 platens
C) C(x) = 1.50x + 295; 43 platens
D) C(x) = 1.50x + 400; 58 platens

Accepted Answer

The total cost for 70 platens is $400, which includes both variable and fixed costs. The variable cost is $1.50 per platen, so for 70 platens, the variable cost is 70 * $1.50 = $105. Subtracting this from the total cost gives the fixed cost: $400 - $105 = $295. Thus, the cost function is C(x) = 1.50x + 295. To break even, revenue must equal cost. The revenue per platen is $8.40. Setting the revenue equal to the cost gives $8.40x = 1.50x + 295. Solving for x gives the number of platens needed to break even, which is 43.

Question 10

Plot a scatter diagram.
-$$\begin{array} { c | c c c c c c c c c c } 
\mathrm { x } & 22 & - 10 & 10 & - 11 & - 6 & 12 & 4 & 13 & 5 & - 4 \
\hline \mathrm { y } & 53 & 17 & 43 & - 15 & - 2 & 38 & 7 & 68 & - 4 & 3
\end{array}$$  
A)

B)

C)

D)

Accepted Answer

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

Question 11

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. $\begin{array} { l | c c c c c c c c } 
\text { Study Time (min) } & 9 & 16 & 21 & 26 & 33 & 36 & 40 & 47 \
\hline \text { Test Score } & 59 & 61 & 64 & 65 & 73 & 74 & 78 & 78
\end{array}$

Accepted Answer

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

Question 12

Solve the problem.
-In a certain city, the cost of a taxi ride is computed as follows: There is a fixed charge of $2.95 as soon as you get in the taxi, to which a charge of $1.60 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.
A) $10.25
B) $9.23
C) $9.53
D) $9.35

Accepted Answer

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

Question 13

Solve the problem.
-A truck rental company rents a moving truck one day by charging $29 plus $0.11 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 180 miles?
A) C(x) = 0.11x + 29; $48.80
B) C(x) = 0.11x - 29; -$9.20
C) C(x) = 29x + 0.11; $5220.11
D) C(x) = 0.11x + 29; $30.98

Accepted Answer

The correct linear equation is C(x) = 0.11x + 29, which represents a base charge of $29 plus $0.11 per mile. For 180 miles, the cost is $29 + (0.11 * 180) = $48.80.

Question 14

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 $690 to set up for production, and variable costs of $28 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 121 jackets.
A) $4090
B) $4078
C) $4058
D) $4070

Accepted Answer

The answer of Solve the problem.
-Marty's Tee Shirt & Jacket...

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) < 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 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 $580 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.
A) C(x) = (580 + 39) x
B) C(x) = 580x + 39
C) C(x) = 580 - 39x
D) C(x) = 580 + 39x

Accepted Answer

The total cost C(x) consists of a fixed cost ($580) plus the variable cost per jacket ($39) multiplied by the number of jackets (x), which is represented by the equation C(x) = 580 + 39x.

Question 17

Solve the problem.
-In a certain city, the cost of a taxi ride is computed as follows: There is a fixed charge of $2.95 as soon as you get in the taxi, to which a charge of $2.25 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) = 2.95 + 2.25x
B) C(x) = 3.70x
C) C(x) = 2.25 + 2.95x
D) C(x) = 5.20x

Accepted Answer

The cost of a taxi ride consists of a fixed charge ($2.95) and a variable charge based on the distance traveled ($2.25 per mile). Therefore, the total cost, C(x), for an x-mile ride is the sum of the fixed charge and the variable charge, which is represented by the equation C(x) = 2.95 + 2.25x.

Question 18

Solve the problem.
-Northwest Molded molds plastic handles which cost $0.50 per handle to mold. The fixed cost to run the molding machine is $7200 per week. If the company sells the handles for $3.50 each, how many handles must be
Molded and sold weekly to break even?
A) 1800 handles
B) 14,400 handles
C) 1600 handles
D) 2400 handles

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. The revenue is the selling price per handle times the number of handles. Setting these equal: $7200 + $0.50x = $3.50x. Solving for x gives x = 2400 handles.

Question 19

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) = 42t
B) V(t) = 32 + 10t
C) V(t) = 32t + 10 $$\text { D) } V ( t ) = \frac { t - 10 } { 32 }$$

Accepted Answer

The correct expression is obtained by multiplying t by 32 and then adding 10, which is represented as V(t) = 32t + 10.

Question 20

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

More hours spent watching TV may increase grades.
D) none of these

Accepted Answer

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

Quiz 2: Linear and Quadratic Functions

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. -A lumber yard has fixed costs of $1384.90 per day and variable costs of $0.56 per board-foot produced. Lumber sells for $1.66 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. -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) = 3230 - 90p and D(p) = 100p, 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 $45 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 14 Miles.

Solve the problem. -Regrind, Inc. regrinds used typewriter platens. The variable cost per platen is $1.50. The total cost to regrind 70 platens is $400. Find the linear cost function to regrind platens. If reground platens sell for $8.40 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 $29 plus $0.11 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 180 miles?

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. -In a certain city, the cost of a taxi ride is computed as follows: There is a fixed charge of $2.95 as soon as you get in the taxi, to which a charge of $2.25 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. -Northwest Molded molds plastic handles which cost $0.50 per handle to mold. The fixed cost to run the molding machine is $7200 per week. If the company sells the handles for $3.50 each, how many handles must be Molded and sold weekly 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 V as a linear function of t.