Pass the WGU Courses and Certificates Applied-Algebra Questions and answers with Dumpstech

We are told that the number of property sales this year is expected to be 8 times the number of property sales last year.

Let:

x= " number of properties sold last year "

and

H(x)= " number of property sales this year "

Since this year’s sales are 8 times last year’s sales, the function rule is:

H(x)=8x

The question says that last year’s property sales were:

x=360

Substitute 360into the function:

H(360)=8(360)

H(360)=2,880

So the correct notation is:

H(360)=2,880

This means: if 360 properties were sold last year, then 2,880 property sales are expected this year.

Therefore, the correct answer is:

▭ ( " C " )

The graph shows P(t), where:

t= " years since opening "

and

P(t)= " daily profit in hundreds of dollars "

The graph is a downward-opening curve, so its maximum value occurs at the highest point of the graph, also called the vertex.

From the graph, the highest point occurs at approximately:

t=9

So the maximum daily profit happened approximately:

9 " years after opening "

The vertical value at this maximum point is approximately:

P(t)=29

But the graph measures profit in hundreds of dollars, so:

29×100=2900

Therefore, the maximum daily profit was approximately:

$2,900

So the correct interpretation is:

" Approximately 9 years after opening, a maximum daily profit of approximately " $2,900 " was earned. "

The function is:

f(x)=330× 〖 1.15 〗 ^x

Because xrepresents the number of years since 2005:

2006 ⇒ x=1

2011 ⇒ x=6

The average yearly rate of change from 2006 to 2011 is:

(f(6)-f(1))/(6-1)

First, find f(1):

f(1)=330× 〖 1.15 〗 ^1

f(1)=330×1.15

f(1)=379.50

Now find f(6):

f(6)=330× 〖 1.15 〗 ^6

f(6)≈330×2.31306

f(6)≈763.31

Now calculate the average rate of change:

(763.31-379.50)/(6-1)

=383.81/5

=76.762

Rounded to two decimal places:

76.76

So the average yearly rate of change of the artifact’s value from 2006 to 2011 is approximately:

$76.76 " per year "

Therefore, the correct answer is:

▭ ( " A " )

The graph shows a linear relationship between the amount of red dye, r, and the amount of yellow dye, y.

The rate of change of a line is the slope:

" slope " =( " change in " y)/( " change in " r)

From the graph, the line goes through the origin and rises steeply. A clear point on the line is approximately:

(2│9)

This means when the amount of red dye is 2gallons, the amount of yellow dye is 9gallons.

So the rate of change is:

9/2

That means for every 2gallons of red dye, the factory uses 9gallons of yellow dye.

The relationship can be written as:

y=9/2 r

So the correct interpretation is:

" The amount of yellow dye must be " 9/2 " of the amount of red dye. "

Therefore, the correct answer is:

▭ ( " A " )

We are told that the number of people expected to audition this year is 4 times the number of people who auditioned last year.

Let:

t=number of people who auditioned last year

and

A(t)=number of people expected to audition this year

Since this year’s number is 4 times last year’s number, the function is:

A(t)=4t

The question says that 330 people auditioned last year, so:

t=330

Now substitute 330 into the function:

A(330)=4(330)

A(330)=1320

So, the correct function notation is:

A(330)=1,320

This means: when 330 people auditioned last year, 1,320 people are expected to audition this year.

Therefore, the correct answer is:

B

The graph compares the spread of two viruses over time.

The horizontal axis represents:

" time in months "

The vertical axis represents:

" percent of the population affected "

The graph shows:

Virus A as the solid blue curve.

Virus B as the dashed blue curve.

To determine which statement is correct, compare when each virus reaches the same population percentage.

At 20%, Virus A reaches that level earlier than Virus B. The solid curve is already at 20%before the dashed curve reaches 20%.

However, for higher percentages like 70%and 80%, Virus B reaches those levels before Virus A because the dashed curve becomes steeper and rises above the solid curve after about 50%.

So the correct conclusion is:

" Virus A affects " 20% " of the population before virus B does. "

Therefore, the correct answer is:

▭ ( " A " )

The function w(t)gives the number of workers at the job site thours after 6:00 a.m.

We need to find the difference between:

w(4)

and

w(8)

Because w(t)represents workers, the difference will be measured in workers, not hours.

First, evaluate w(4):

w(4)=0.03(4)^4-0.81(4)^3+7.55(4)^2-26.62(4)+44

w(4)=0.03(256)-0.81(64)+7.55(16)-106.48+44

w(4)=7.68-51.84+120.8-106.48+44

w(4)=14.16

Now evaluate w(8):

w(8)=0.03(8)^4-0.81(8)^3+7.55(8)^2-26.62(8)+44

w(8)=0.03(4096)-0.81(512)+7.55(64)-212.96+44

w(8)=122.88-414.72+483.2-212.96+44

w(8)=22.4

Now find the difference:

22.4-14.16=8.24

This is approximately:

8 " workers "

The function is:

p(m)=5m+5

This is a linear function in the form:

p(m)=mx+b

For a linear function, the average rate of change over any interval is the same as the slope.

The slope is the coefficient of m:

5

So the price increases at a constant rate of:

$5 " per month "

We can also verify using the average rate of change formula:

(p(10)-p(1))/(10-1)

Find p(10):

p(10)=5(10)+5=55

Find p(1):

p(1)=5(1)+5=10

Now calculate:

(55-10)/(10-1)

=45/9

=5

The model has:

r^2=0.42

This indicates a moderate fit, not a strong fit.

The prediction is being made at:

x=19.5

From the scatterplot, the observed data values appear to extend only to about:

x=16

So x=19.5is beyond the observed data range.

Because the model has only a moderate fit and the prediction is too far beyond the observed data, the prediction is not appropriate.

The correct interpretation is:

" No. The " r^2 " value indicates a moderate fit, but " x=19.5 " is more than " 25% " of the range beyond the maximum value. "

The function f(n) gives the distance traveled by vehicle B.

The input n represents the distance traveled by vehicle A.

The problem says vehicle B travels 17 more than vehicle A. The phrase “17 more than” means we add 17 to the amount traveled by vehicle A.

So the relationship is:

f(n)=n+17

For example, if vehicle A traveled 50 miles, then vehicle B traveled:

f(50)=50+17=67

So the correct function is:

f(n)=n+17

Therefore, the correct answer is:

B