A student is assessing the correlation between the number of workers in a factory and the number of units produced daily. The table 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. (4 points) Part B: Write a function that best fits the data. (3 points) Part C: What does the slope and y-intercept of the plot indicate? (3 points)

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

Part B: The equation of the function that best fits the data is

Part C: The slope is  which indicates the rate of change of number of units produced daily over the change in number of workers. The y - intercept is  which indicates the number of units produced by number of workers.

Explanation:

Part A: To determine the correlation coefficient, first we shall find the slope and y - intercept.

Let us substitute the coordinates  and  in the slope formula, to find the value of slope.

Hence, we have,

Thus, the slope is

The y - intercept is the value of y when the value of x is equal to 0.

Thus, from the table , we can see that when , the value of y is 2

Hence, the y - intercept is

Substituting the values  and  in the slope intercept form  , we get,

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

Part B: To find the function that best fits the data, let us substitute the value of slope and y - intercept in the slope intercept formula.

Since, we have already found slope  and y - intercept

Substituting these values in the slope intercept form  , we get,

Thus, the function that best fits the data is

Part C:

The slope is

The slope indicates that the rate of change of number of units produced daily over the change in number of workers.

The y - intercept is

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

Learn more:

(1) Slope of a linear regression line is 1.5, and when x is 10 y takes the value of 8. determine the intercept of the regression line.

(2) Explain Linear Regression Equation.

Step-by-step explanation:

check above link.

graphically?   well, you graph them both, the solutions is where they both intersect each other, since there are two solutions, meaning they will meet twice, or namely the linear will run into the quadratic curve twice, and where they meet, those x,y coordinates are the solutions to the system.