Soda Tak claims that Diet Tak has 40mg of sodium per can. You work for a consumer organization that tests such claims. You take a random sample of 60 cans and find that the mean amount of sodium in the sample is 42.4 mg. The population standard deviation in all cans is 5.2 mg. You suspect there is more than 40 mg of sodium per can. What is the z-score?

-0.461

Step-by-step explanation:

By formula we know that z is equal to:

z = (x - m) / sd

of the statement we have the following information:

x is the reference value which is 40 mg

m = the sample mean is 42.4 mg,

sd = the standard deviation in all cans is 5.2 mg.

Replacing we have:

z = (40 - 42.4) /5.2

z = -0.461

Therefore the value of z is -0.461

step-by-step explanation:

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