A manager is assessing the correlation between the number of employees in a plant and the number of products produced monthly. The table below shows the data: Number of employees (x) 0 10 20 30 40 50 60 70 80 Number of products (y) 120 200 280 360 440 520 600 680 760 Part A: Is there any correlation between the number of employees in the plant and the number of products produced monthly? Justify your answer. (4 points) Part B: Write a function which best fits the data. (3 points) Part C: What does the slope and y-intercept of the plot indicate? (3 points)

A) In the table, we can see that from one pair (x,y) to the next one, x-variable increase in 10 units and y-variable increase in 80 units. This is valid for all pairs (x,y), which mean that there is a linear relationship between these variables.

B) slope (m) = y-variable increment / x-variable increment = 80/10 = 8

the coordintae (0, 120) indicates that 120 is the y-intercept (b) of the line

Equation of a line in the slope y-intercept form:

y = mx + b

y = 8x + 120

C) The y-intercept indicates the number of products produced monthly without employees.

The slope indicates how much the production increase with a new employee.

Part A: Yes there is a correlation because every new month there are 10 new employees, and every 10 new employees, 80 new products are produced monthly. This shows a linear function throughout the table because the data is increasing at the same amount every month.

Part B: A linear function uses the function (y = mx + b). To find m, you need to use the equation (y2 -y1/x2 -x1), like so, (200-120/1-0) = (80,10) = (8). To find out what b equals in the equation (y = mx + b), I need to put in what I already know, which is (y = 8x + b). Then I’m going to substitute the y and x for numbers from the data to find out what b is (don’t worry, I am not going to keep the numbers there, this is only to find out what b is.) I’ll go with the numbers (10, 200), (200 = 8 times 10 + b) = (200 = 80 + b) next step is to get ride of the 80, so that the b is alone, (200 - 80 = b) = (120 = b). You can chose another pair of (x,y) to check my number. The finale function is, (y = 8x + 120).

Part C: The y- Intercept indicates the number of products produces monthly without employees and the slope indicates the increasing value of products going up monthly for every new employee.

Step-by-step explanation:

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step-by-step explanation:

true

so firstly, we need to isolate the y variables to be able to solve these inequalities. firstly, add 0.5x on both sides of the first inequality and subtract 1.5x on both sides of the second inequality:

now since the slope is positive for the first inequality, this means that the line going upwards belongs to the first inequality, and the line going downwards belongs to the second inequality.

next, since y ≥ in the first inequality, this means that the shaded region will be above the first inequality's line, thus shading regions a and b.

next, since y ≤ in the second inequality, this means that the shaded region is going to be below this line, thus shading regions a and c.

since both lines shade region a, this means that region a is the solution.

step-by-step explanation:

mark brainliest!