An appliance dealer sells three different models of upright freezers having 14.5, 15.9, and 20.1 cubic feet of storage space. Let x = the amount of storage space purchased by the next customer to buy a freezer. Suppose that x has the following probability distribution. x p(x) 14.5 0.2 15.9 0.5 20.1 0.3 (a) Calculate the mean and standard deviation of x. (Round your answers to three decimal places.) mean cubic ft standard deviation cubic ft (b) If the price of the freezer depends on the size of the storage space, x, such that Price = 25x − 8.5, what is the mean price paid by the next customer?

Step-by-step explanation:

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let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1