Question 1

A new chocolate company is estimating how many candy bars per week college students will consume of their line of
products. The graph shows the probable number of candy bars students (age 18-22) will consume from year 0 to year 10.
B(x) gives the number of candy bars for boys, G(x) gives the number of candy bars for girls, and T(x) gives the total
number for both groups. Use the graph to answer the question. 
-The volume of water added to a circular drum of radius r is given by V $\mathrm { V } _ { \mathrm { w } } = 25 \mathrm { t } , \text { where } \mathrm { V } _ { \mathrm { w } }$ is volume in cu ft and t is time in sec. Find the depth of water in a drum of radius 6 ft after adding water for 18 sec. (Round result to
One decimal place.)
A) 8.0 ft
B) 2.0 ft
C) 12.6 ft
D) 4.0 ft

Accepted Answer

The volume of water added is $ V_w = 25t = 25 \times 18 = 450 $ cu ft. The volume of a cylinder is $ V = \pi r^2 h $. Solving for height $ h $, we have $ h = \frac{V}{\pi r^2} = \frac{450}{\pi \times 6^2} \approx 4.0 $ ft.

Question 2

Consider the function h as defined. Find functions f and g so tha $( f \circ g ) ( x ) = h ( x )$
-$$h ( x ) = \frac { 10 } { x ^ { 2 } } + 10$$
A) $f ( x ) = \frac { 10 } { x ^ { 2 } } , g ( x ) = 10$
B) $f ( x ) = x + 10 , g ( x ) = \frac { 10 } { x ^ { 2 } }$
C) $f ( x ) = x , g ( x ) = \frac { 10 } { x } + 10$
D) $f ( x ) = \frac { 1 } { x } , g ( x ) = \frac { 10 } { x } + 10$

Accepted Answer

Function $f(x) = x + 10$ adds 10 to its input, and function $g(x) = \frac{10}{x^2}$ computes the fraction $\frac{10}{x^2}$. When $g(x)$ is input into $f(x)$, the result is $f(g(x)) = \frac{10}{x^2} + 10$, which matches $h(x)$.

Question 3

Consider the function h as defined. Find functions f and g so tha $( f \circ g ) ( x ) = h ( x )$
-$$h ( x ) = ( - 6 x + 9 ) ^ { 2 }$$
A) $f ( x ) = ( - 6 x ) ^ { 2 } , g ( x ) = 9$
B) $f ( x ) = - 6 x ^ { 2 } , g ( x ) = x + 9$
C) $f ( x ) = x ^ { 2 } , g ( x ) = - 6 x + 9$
D) $f ( x ) = - 6 x + 9 , g ( x ) = x ^ { 2 }$

Accepted Answer

The correct choice is C because $f(x) = x^2$ and $g(x) = -6x + 9$ satisfy the composition requirement $(f \circ g)(x) = f(g(x)) = f(-6x + 9) = (-6x + 9)^2 = h(x)$.

Question 4

A new chocolate company is estimating how many candy bars per week college students will consume of their line of
products. The graph shows the probable number of candy bars students (age 18-22) will consume from year 0 to year 10.
B(x) gives the number of candy bars for boys, G(x) gives the number of candy bars for girls, and T(x) gives the total
number for both groups. Use the graph to answer the question. 
-Estimate B(7) and G(7) and use your estimates to estimate T(7).
A) 2.5; 4.0; 6.5
B) 2.2; 4.3; 6.5
C) 3.5; 4.2; 7.7
D) 2.3; 4.0; 6.3

Accepted Answer

The answer of A new chocolate company is estimating how...

Question 5

Consider the function h as defined. Find functions f and g so tha $( f \circ g ) ( x ) = h ( x )$
-$$h ( x ) = | 2 x + 2 |$$
A) $f ( x ) = - | x | , g ( x ) = 2 x + 2$
B) $f ( x ) = x , g ( x ) = 2 x + 2$
C) $f ( x ) = | x | , g ( x ) = 2 x + 2$
D) $f ( x ) = | - x | , g ( x ) = 2 x - 2$

Accepted Answer

The correct choice is C because $f(x) = |x|$ and $g(x) = 2x + 2$ satisfy the condition $(f \circ g)(x) = f(g(x)) = f(2x + 2) = |2x + 2| = h(x)$.

Question 6

A new chocolate company is estimating how many candy bars per week college students will consume of their line of
products. The graph shows the probable number of candy bars students (age 18-22) will consume from year 0 to year 10.
B(x) gives the number of candy bars for boys, G(x) gives the number of candy bars for girls, and T(x) gives the total
number for both groups. Use the graph to answer the question. 
-The radius $\mathrm { r }$ of a circle of known area $\mathrm { A }$ is given by $\mathrm { r } = \sqrt { \mathrm { A } / \pi }$, where $\pi \approx 3.1416$. Find the radius and circumference of a circle with an area of $48.71 \mathrm { sq } \mathrm { ft }$. (Round results to two decimal places.)
A) $\mathrm { r } = 15.52 \mathrm { ft } , \mathrm { C } = 97.52 \mathrm { ft }$
B) $\mathrm { r } = 3.94 \mathrm { ft } , \mathrm { C } = 24.76 \mathrm { ft }$
C) $\mathrm { r } = 3.94 \mathrm { ft } , \mathrm { C } = 24.76 \mathrm { sq } \mathrm { ft }$
D) $\mathrm { r } = 3.94 \mathrm { ft } , \mathrm { C } = 8.86 \mathrm { ft }$

Accepted Answer

First, calculate the radius using the formula $r = \sqrt{A/\pi}$, where $A = 48.71$. This gives $r \approx 3.94$ ft. Then, calculate the circumference using $C = 2\pi r$, which gives $C \approx 24.76$ ft.

Question 7

A new chocolate company is estimating how many candy bars per week college students will consume of their line of
products. The graph shows the probable number of candy bars students (age 18-22) will consume from year 0 to year 10.
B(x) gives the number of candy bars for boys, G(x) gives the number of candy bars for girls, and T(x) gives the total
number for both groups. Use the graph to answer the question. 
-Use the slopes of the line segments to decide in which period ( $0 - 5$ or $5 - 10 )$ the number of candy bars per week increased more rapidly.
A) 0-5
B) $5 - 10$
C) The number of candy bars increased at the same rate in both periods

Accepted Answer

The answer of A new chocolate company is estimating how...

Question 8

A new chocolate company is estimating how many candy bars per week college students will consume of their line of
products. The graph shows the probable number of candy bars students (age 18-22) will consume from year 0 to year 10.
B(x) gives the number of candy bars for boys, G(x) gives the number of candy bars for girls, and T(x) gives the total
number for both groups. Use the graph to answer the question. 
-A furniture store buys 45 footstools from a distributor at a cost of $230 each plus an overhead charge of $45 per order. The retail markup is 25% on the total price paid. Find the profit on the sale of one footstool.
A) $57.50
B) $57.25
C) $57.75
D) $5775.00

Accepted Answer

The answer of A new chocolate company is estimating how...

Question 9

Consider the function h as defined. Find functions f and g so tha $( f \circ g ) ( x ) = h ( x )$
-$$h ( x ) = \frac { 1 } { \sqrt { 2 x + 4 } }$$
A) $f ( x ) = \frac { 1 } { \sqrt { x } } , g ( x ) = 2 x + 4$
B) $f ( x ) = \sqrt { 2 x + 4 } , g ( x ) = 1$
C) $f ( x ) = \frac { 1 } { x } , g ( x ) = 2 x + 4$
D) $f ( x ) = 1 , g ( x ) = \sqrt { 2 + 4 }$

Accepted Answer

The answer of Consider the function h as defined. Find...

Question 10

A new chocolate company is estimating how many candy bars per week college students will consume of their line of
products. The graph shows the probable number of candy bars students (age 18-22) will consume from year 0 to year 10.
B(x) gives the number of candy bars for boys, G(x) gives the number of candy bars for girls, and T(x) gives the total
number for both groups. Use the graph to answer the question. 
-The cost of manufacturing clocks is given by $C ( x ) = 56 + 31 x - x ^ { 2 }$. Also, it is known that in thours the number of clocks that can be produced is given by $x = 12 t$, where $1 \leq t \leq 12$. Express $C$ as a function of $t$.
A) $C ( t ) = 56 + 31 t + t ^ { 2 }$
B) $C ( t ) = 56 + 372 t - 144 t ^ { 2 }$
C) $C ( t ) = 56 + 31 \mathrm { t } - 12$
D) $C ( t ) = 56 + 372 t - 144 t$

Accepted Answer

To express $C$ as a function of $t$, substitute $x = 12t$ into the given cost function $C(x) = 56 + 31x - x^2$, resulting in $C(t) = 56 + 31(12t) - (12t)^2 = 56 + 372t - 144t^2$.

Question 11

A new chocolate company is estimating how many candy bars per week college students will consume of their line of
products. The graph shows the probable number of candy bars students (age 18-22) will consume from year 0 to year 10.
B(x) gives the number of candy bars for boys, G(x) gives the number of candy bars for girls, and T(x) gives the total
number for both groups. Use the graph to answer the question. 
-Estimate B(4) and G(4) and use your estimates to estimate T(4).
A) 1.5; 2.5; 4.0
B) 1.8; 2.5; 4.3
C) 2.0; 2.8; 4.8
D) 2.0; 3.0; 5.0

Accepted Answer

B(4) = 2.0, G(4) = 2.8, and T(4) = 4.8

Quiz 3: Graphs and Functions

Consider the function h as defined. Find functions f and g so tha $( f \circ g ) ( x ) = h ( x )$ - $h ( x ) = \frac { 10 } { x ^ { 2 } } + 10$

Consider the function h as defined. Find functions f and g so tha $( f \circ g ) ( x ) = h ( x )$ - $h ( x ) = ( - 6 x + 9 ) ^ { 2 }$

Consider the function h as defined. Find functions f and g so tha $( f \circ g ) ( x ) = h ( x )$ - $h ( x ) = | 2 x + 2 |$

Consider the function h as defined. Find functions f and g so tha $( f \circ g ) ( x ) = h ( x )$ - $h ( x ) = \frac { 1 } { \sqrt { 2 x + 4 } }$

Quiz 3: Graphs and Functions

Consider the function h as defined. Find functions f and g so tha (f∘g) (x) =h(x) ( f \circ g ) ( x ) = h ( x ) (f∘g) (x) =h(x) - h(x) =10x2+10h ( x ) = \frac { 10 } { x ^ { 2 } } + 10h(x) =x210​+10

Consider the function h as defined. Find functions f and g so tha (f∘g) (x) =h(x) ( f \circ g ) ( x ) = h ( x ) (f∘g) (x) =h(x) - h(x) =(−6x+9) 2h ( x ) = ( - 6 x + 9 ) ^ { 2 }h(x) =(−6x+9) 2

Consider the function h as defined. Find functions f and g so tha (f∘g) (x) =h(x) ( f \circ g ) ( x ) = h ( x ) (f∘g) (x) =h(x) - h(x) =∣2x+2∣h ( x ) = | 2 x + 2 |h(x) =∣2x+2∣

Consider the function h as defined. Find functions f and g so tha (f∘g) (x) =h(x) ( f \circ g ) ( x ) = h ( x ) (f∘g) (x) =h(x) - h(x) =12x+4h ( x ) = \frac { 1 } { \sqrt { 2 x + 4 } }h(x) =2x+4​1​

Consider the function h as defined. Find functions f and g so tha $( f \circ g ) ( x ) = h ( x )$ - $h ( x ) = \frac { 10 } { x ^ { 2 } } + 10$

Consider the function h as defined. Find functions f and g so tha $( f \circ g ) ( x ) = h ( x )$ - $h ( x ) = ( - 6 x + 9 ) ^ { 2 }$

Consider the function h as defined. Find functions f and g so tha $( f \circ g ) ( x ) = h ( x )$ - $h ( x ) = | 2 x + 2 |$

Consider the function h as defined. Find functions f and g so tha $( f \circ g ) ( x ) = h ( x )$ - $h ( x ) = \frac { 1 } { \sqrt { 2 x + 4 } }$