A student is assessing the correlation between the average number of hours of internet browsing and average score on a math test. The table below shows the data: Number of hours of internet browsing (x) 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 Score on math test (y) 95 94 93 92 91 90 89 88 87 86 Part A: Is there any correlation between the average number of hours of internet browsing and average score on the math test? 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 100 POINTS AND BRAINLIEST

A) yes, there is a clear correlation: "The more hours the Internet browsing, the lower the score in the math test."

B)  y = -2 x + 95

C) slope is: number of units of test score that go down for every browsing hour

y-intercept is: the maximum test score reported

Step-by-step explanation:

Part A)

There is clearly a correlation between the number of hours of Internet browsing and the scores on a math test. The more hours the Internet browsing, the lower the score in the math test. If we plot the data in pairs (x, y) we observe a clear tendency with the shape of a line (representing the scores) going down as the number of hours of Internet browsing increases. (See attached image)

Part B)

We can run a regression analysis on these points, or simple observe that for every half hour increase of browsing time, the scores go down in one unit.

The equation for this line of best fit is given by:

y = - 2 x + 95

being "x" the number of hours of Internet browsing, and "Y" the math test scores.

the slope "-2" is the number of units of test score that go down for every browsing hour.

The y=intercept is the maximum test score (95) reported

step-by-step explanation:

1. when "a" is a root of a polynomial, (x -a) is a factor of it. for the three roots given, the factors of the desired polynomial are (x +2)(x -1/2)(x -3).

in order to make the leading coefficient be negative, we need to multiply this product by a negative number. any negative number will do, but we choose a small (magnitude) value that will eliminate the fraction: -2.

then

f(x) = -2(x +2)(x -1/2)(x -3) = -(x +2)(2x -1)(x -3)

= -(2x² +3x -2)(x -3)

= -(2x³ -3x² -11x +6)

f(x) = -2x³ +3x² +11x -6

2. a graph created by the desmos on-line graphing calculator is shown, and the zeros are highlighted.

3. as indicated in part 1, the multiplier of this equation can be anything and the zeros will remain the same. you want a negative leading coefficient, so the "anything" is restricted to any of the infinite number of numbers that will make that be the case.