The table below shows the surface area y, in square feet, of a shrinking lake in x days:

time (x)
(days) 10 20 30 40
surface area (y)
(square feet) 100 90 80 70

part a: what is the most likely value of the correlation coefficient of the data in the table? based on the correlation coefficient, describe the relationship between time and surface area of the lake. [choose the value of the correlation coefficient from −1, −0.99, −0.5, −0.02.] (4 points)

part b: what is the value of the slope of the graph of surface area versus time between 20 and 30 days, and what does the slope represent? (3 points)

part c: does the data in the table represent correlation or causation? explain your answer. (3 points)

use the functions h(x) = 5x − 2 and t(x) = 4x + 6 to complete the function operations listed below.

part a: find (h + t)(x). show your work. (3 points)

part b: find (h ⋅ t)(x). show your work. (3 points)

part c: find h[t(x)]. show your work. (4 points)

part a: factor 3x2y2 − 2xy2 − 8y2. show your work. (4 points)

part b: factor x2 + 10x + 25. show your work. (3 points)

part c: factor x2 − 36. show your work. (3 points)

a quadratic equation is shown below:

4x2 − 12x + 10 = 0

part a: describe the solution(s) to the equation by just determining the radicand. show your work. (5 points)

part b: solve 2x2 − 13x + 21 = 0 by using an appropriate method. show the steps of your work, and explain why you chose the method used. (5 points)