Miss Rose teaches three ballet classes. Her students' data are shown in the

Answer:

The equation for the line is

Step-by-step explanation:

Let A denote Area and C stand for Cost, we can deduce that:

For an area of square feet, the cost amounts to

If , then,

Since the cost equation represents a function of area, this establishes a linear connection, necessitating the formulation of the line's equation.

Where:

m denotes the slope of the line

b indicates the intercept with the C axis..

We possess two coordinates:

(700, 30000)

(1500, 54000)

Using these points, we calculate the slope via the formula:

Consequently, the equation concludes with:

To find b, we substitute the point (700, 30000) into the equation

Thus

The linear equation's graph is depicted in the provided image

Answer:

Domain = [0, 50]

Range   = [0, 3250]

Step-by-step explanation:

A function illustrates the relationship between two variables (independent and dependent). The independent variable depends on nothing else, serving as the function's input, while the dependent variable relies on the independent variable, acting as the output.

The domain of a function includes all possible input variables (independent variable), and the range encompasses all potential output variables (dependent variables).

For the function C(p) = 65p, p represents the independent variable and C(p) constitutes the dependent variable.

As the hall accommodates a maximum of 50 individuals, the domain of this function is defined as [0, 50]

C(0) results in 65(0) = 0 and C(50) results in 65(50) = 3250

Thus, the range of this function is [0, 3250]

Response:

Her brother catches up to her at 11 am + 4 hours = 15 p.m

Detailed explanation:

Provided information;

Ariel's speed = 45 mph

She departed at 9 a.m

Her brother's speed = 60 mph

He began at 11 a.m

Inferred from the question: Since Ariel's speed is 45 mph, after two hours she is ahead by 90 miles.

Meanwhile, her brother travels at 60 mph, hence he is traveling (60 - 45) = 15 mph faster

Therefore, with this speed, he will catch up to her in = 4 hours.

So her brother catches up with her at 11 am + 4 hours = 15 p.m