Anytime in math that it says the word "of" it means multiplication. So, in this situation, we are multiplying:
(5/8) x 64.
But, when you are multiplying a fraction by a number, you are actually dividing instead of multiplying. Think of it this way: the question is asking you 5/8 <em>of</em> 64, meaning you must find how many is 5/8 <em>of</em> the amount of students that gave their speeches is. Also, that slash between the 5 and the 8 in the fraction is actually a division symbol. So, by placing 5/8 into 64, we get:
(5/8) x 64 = 40.
I'm quite sure why it asked for "simplest form" when the answer is not a decimal or fraction, but this is the answer to the problem that you have posted.
Let , where is the quantity of insecticide, measured in hundreds of liters, and is the total manufacturing cost as a function of the quantity of the insecticide, measured in US dollars. A possible approach to determine which regions of are decreasing and increasing by means of the first derivative and graphing tools. The first derivative of the function is:
(1)
Please notice that regions where C(x) is increasing has , whereas when .
We notice that is increasing in two regions: (i) and (ii) . Besides, decreases in .