Lauren supplies costumes to a number of theater companies. She recently provided 8 top hats and 14 other hats. Considering this data, how many of the next 33 hats requested
from Lauren's inventory should you expect to be top hats?

12 Top Hats.

Step-by-step explanation:

We can easily solve this problem by setting up a proportion.

Before we do this, we should first gather the information we know. We know that there were 22 hats provided in total (14 + 8 = 22), and out of those 22 there were 8 that were top hats.

Next, we know that out of the next 33 hats in total, there are an unknown number of top hats. So, we should mark the top hats as the variable x, since it is unknown.

Finally, we can setup the proportion: it would be 8 (original number of top hats) over 22 (total number of top hats) is equal to x (unknown number of new top hats) over 33 (total number of new hats). So, 8/22 = x/33, after cross multiplying, we get 22x = 264, from simplifying (by dividing 264 by 22), we receive x = 12.

So, x = 12. 12 is the number of top hats we should expect.

step-by-step explanation:

to determine whether a given function is even, we simply substitute x with -x in the expression. if the result after simplification is identical to the original equation, then the function is said to be even other wise odd.

f(-x) = (-x)^2 - (-x) + 8

      = x^2 + x +8

the resulting function is not identical to the original one;

f(-x) ≠ f(x)

therefore, f(x) is not an even function