Courses and Certificates Applied-Algebra WGU Study Notes

This question asks us to compare the heights of two balls at a specific time:

t=0.9

The graph shows:

Ball 1 as the solid blue curve.

Ball 2 as the dashed blue curve.

To determine which ball was lower at t=0.9, we look at the vertical positions of both curves when the time is 0.9seconds.

At approximately t=0.9:

" height of Ball 1 " < " height of Ball 2 "

This means Ball 1 is lower than Ball 2 at that time.

The correct reasoning must say both:

Ball 1 was lower, and

Ball 1’s height was less than Ball 2’s height at t=0.9.

That matches option A.

The graph shows customer visits by day.

To determine which days likely featured new releases, we should look for the days with unusually high customer counts.

From the graph:

Day 8 has about 40customers.

Day 11 also has about 40customers.

These are the highest values shown on the graph.

Since the problem says more customers show up on days when new releases are featured, the days with the highest customer counts are the most likely new-release days.

Therefore, the correct answer is:

▭ ( " D " )

The coefficient of determination, r

2

, measures how well a regression model fits the data. A value close to 1 indicates a strong fit, while a lower value indicates that the model does not explain the data as reliably. Here, r

2

=0.45, which is below 0.7. That means the model does not have a strong enough fit for reliable extrapolation in this question. Extrapolation means using the model to predict values outside the observed data range, which is riskier than interpolation. Because the model fit is not strong, choosing an extended range of x-values would not be appropriate. The correct reason is that extrapolation is not appropriate because r

2

< 0.7. Therefore, the answer is D.

The function is:

P(t)=462-35t

This is a linear function in the form:

P(t)=mt+b

where:

m= " rate of change "

and

b= " initial value "

In this function:

m=-35

The negative sign means the fish population is decreasing.

The number 35tells us the amount of decrease per month.

So the fish population is decreasing by:

35 " fish per month "

The value 462is not the rate of change. It represents the starting fish population at the beginning of the year, when t=0:

P(0)=462

Therefore, the correct interpretation is:

" The number of fish in the lake is decreasing at a constant rate of 35 fish per month. "

So the correct answer is:

▭ ( " D " )