(( PLZ HELP))

A student is assessing the correlation between the number of workers in a factory in the number of units produced daily. The table below shows the data:

Number of workers (x): 0 10 20 30 40 50 60 70 80 90

Number of units (y): 2 52 102 152 202 252 302 352 402 452

Part A: Is there any correlation between the number of workers in a factory and the number of units produced daily? Justify your answer.

Part B: Write a function which best fits the data.

Part C: What does the slope and y-intercept of the plot indicate?

Part A: There is a correlation between the number of workers in a factory and the number of units produced daily.

Part B: The function that best fits the data is

Part C: The slope indicates the rate of change of number of units produced daily(y) over change in number of workers(x). The y-intercept of the plot indicates the number of units produced by number of workers.

Explanation:

Part A:  Let us determine it using the slope formula which is given by,

Substituting, the coordinates and .

Thus, we have,

Thus, slope = 5

The y-intercept can be determined when the value of x is zero.

Hence, y-intercept b = 2

Substituting these values in the slope-intercept formula,

Thus, there is a correlation between the number of workers in a factory and the number of units produced daily.

Part B: The function that best fits the data is given by

The explanation for the function equation is provided above.

Part C:

The slope is

The slope indicates the rate of change of number of units produced daily(y) over change in number of workers(x).

The y-intercept is

The y-intercept indicates the number of units produced by number of workers.

since we know that the two functions are equal, f (x) = g

(x), therefore when we equate the two equations the result should be similar to

3x = x – 4:

a. f(x) = 3x, g(x) = x – 4

equating the two functions:

3x = x – 4             (correct)

so we now got our answer (a)