An economist for a sporting goods company estimates the revenue and cost functions for the production of a new snowboard. these functions are r (x) = -x^2+10x and c (x) = 4x+5, respectively, where x is the number of snowboards produced, in thousands. the average profit is defined by the function ap(x) =p(x) / x, where p(x) is the profit function. determine the production levels that make ap(x) > 0

Between 1000 and 5000 snowboards will make the function AP(x) >0.

Step-by-step explanation:

Since x can only take possitive values, we have that AP(x) = P(x)/x > 0 if and only if P(x) > 0.

In order to find when P(x) > 0, we find the values from where it is 0 and then we use the Bolzano Theorem.

P(x) = R(x) - C(x) = -x²+10x - (4x+5) = -x²+6x - 5. the roots of P can be found using the quadratic formula:

Therefore, P(1) = P(5) = 0. Lets find intermediate values to apply Bolzano Theorem:

The production levels that make AP(x) >0 are between 1000 and 5000 snowboards (because we take x by thousands)

i think it's b

step-by-step explanation:

because the graph is 2 above (0,0)

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below: