117 and 413 have no common denominator, so 117/413 is it's simplest form
Answer: 87%
Solution:
87 correct questions over 100 = 87/100 = .87 = (change to percent by moving the decimal 2 places to the right) 87%
Since x is the number of seconds it took the rock to hit the water, x is the value that we are looking for. When the rock hits the water, it's height is 0, therefore, f(x) = 0. So, we can set the expression on the right equal to 0, and solve for 0. Let's do just that:

We can divide by -16, nothing will happen because 0 divided by anything is 0:

To factor any trinomial in standard form (given below), we must find two numbers that add to "b" and multiply to "c":

So, for this specific question, let's find two numbers that add to -8 and multiply to 9. These are clearly 9 and -1. We can write it in this way now:

Both answers would be valid, but there can't be negative time, so your answer is
"It takes 9 seconds for the rock to reach the water."
Answer: Expected value of the daily cost of operating the machine is 235.264.
Step-by-step explanation:
Since we have given that
E[x]= 0.96 repairs per day
And Var[x] = 0.96 repairs per day.

![E[c]=160+40E[x^2]\\\\E[c]=160+40(Var[x]+(E[x])^2)\\\\E[c]=160+40(0.96+0.96^2)\\\\E[c]=235.264](https://tex.z-dn.net/?f=E%5Bc%5D%3D160%2B40E%5Bx%5E2%5D%5C%5C%5C%5CE%5Bc%5D%3D160%2B40%28Var%5Bx%5D%2B%28E%5Bx%5D%29%5E2%29%5C%5C%5C%5CE%5Bc%5D%3D160%2B40%280.96%2B0.96%5E2%29%5C%5C%5C%5CE%5Bc%5D%3D235.264)
Hence, Expected value of the daily cost of operating the machine is 235.264.