Question

Haruka owns an umbrella factory. The revenue, RRR, she makes from selling nnn umbrellas is given by the function R(n)=18nR(n)=18nR, left parenthesis, n, right parenthesis, equals, 18, n, and the profit, PPP, that she makes from selling nnn umbrellas is given by the function P(n)=17n-5P(n)=17n−5P, left parenthesis, n, right parenthesis, equals, 17, n, minus, 5.

Let EEE be the expenses that Haruka incurs from producing nnn umbrellas.
Write a formula for E(n)E(n)E, left parenthesis, n, right parenthesis in terms of R(n)R(n)R, left parenthesis, n, right parenthesis and P(n)P(n)P, left parenthesis, n, right parenthesis.
\qquad E(n)=E(n)=space, E, left parenthesis, n, right parenthesis, equals
Write a formula of E(n)E(n)E, left parenthesis, n, right parenthesis in terms of nnn.
\qquad E(n)= E(n)=space, E, left parenthesis, n, right parenthesis, equals

Answer 1

E(n)= R(n)-p(n)

E(n)= n+5

Step-by-step explanation:

Since R(n)=18n and P(n)=17n-5 it follows that:

E(n)=R(n)-P(n)

=18n−(17n−5)

=18n−17n+5

=n+5

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Answer 2

E(n) = n + 5

Step-by-step explanation:

The profit is the difference between the amount of money received as a revenue and the amount of money spent as expenses.

This means that:

Profit = Revenue - Expenses

Rearrange the formula to solve for the expenses, we get:

Expenses = Revenue - Profit

We are given that:

Revenue = R(n) = 18n

Profit = P(n) = 17n - 5

Substitute in the above formula to get the formula for expenses as follows:

E(n) = R(n) - P(n)

E(n) = 18n - (17n-5)

E(n) = 18n - 17n + 5

E(n) = n + 5

Hope this helps :)