Courses and Certificates Applied-Algebra Exam Dumps

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 " )

The function M(t)represents the company’s market share after tyears.

The horizontal axis represents:

t= " time in years "

The vertical axis represents:

M(t)= " market share percentage "

We need to find when the market share reaches:

40%

From the graph, locate 40on the vertical axis. Then move horizontally to the blue curve and read the corresponding value on the horizontal axis.

The curve reaches 40%at approximately:

t=7.4

So the company should expect to have a market share of 40%after about:

7.4 " years "

Therefore, the correct answer is:

▭ ( " C " )

The regression model has:

r^2=0.99

This means the model is a very strong fit for the data because 0.99is close to 1.

However, a strong r^2value does not automatically make every prediction appropriate. We also have to check whether the x-value is within a reasonable extrapolation range.

The data shown on the graph appear to extend to about:

x=11

The prediction is for:

x=16.4

This is far beyond the observed data range. Even though the model fits the known data very well, predicting too far beyond the data can be unreliable.

The correct statement is that the r^2value indicates a strong fit, but x=16.4is more than 50%of the range beyond the maximum observed value.

Therefore, the correct answer is:

▭ ( " A " )

The average rate of change tells us how much the output changes, on average, for each 1-unit increase in the input.

Here:

x= " hours after 7:00 a.m. "

and

y= " estimated wait time in minutes "

From the graph, point Ais approximately:

A=(5,88.3)

and point Bis approximately:

B=(9,65)

Now use the average rate of change formula:

" Average rate of change " =(y_2-y_1)/(x_2-x_1 )

Substitute the values:

(65-88.3)/(9-5)

=(-23.3)/4

=-5.825

Rounded to two decimal places:

-5.83

The negative sign means the estimated wait time is decreasing from point Ato point B.

So the average rate of change is approximately:

-5.83 " minutes per hour "