91Ó°ÊÓ

A catering company estimates that, if it has \(x\) customers in a typical week, its expenses will be approximately \(C(x)=550 x+6500\) dollars, and its revenue will be approximately \(R(x)=1200 x\) dollars. (a) How much profit will the company earn in 1 week when it has 12 customers? (b) How much profit is the company making each week if the weekly costs are running at a level of $$\$ 14,750$$ ?

$$ \begin{array}{l} \text { Find the points of intersection of the pairs of curves in Exercises }\\\ \end{array} $$ $$ y=3 x^{2}+9, y=2 x^{2}-5 x+3 $$

Sketch the graphs of the following functions. $$ f(x)=\left\\{\begin{array}{ll} \frac{1}{2} x & \text { for } 0 \leq x<4 \\ 2 x-3 & \text { for } 4 \leq x \leq 5 \end{array}\right. $$

Use the laws of exponents to compute the numbers. \((125 \cdot 27)^{1 / 3}\)

Evaluate each of the functions in Exercises \(37-42\) at the given value of \(x\). $$ f(x)=|x|, x=\pi $$

Evaluate each of the functions in Exercises \(37-42\) at the given value of \(x\). $$ f(x)=|x|, x=-\frac{2}{3} $$

In Exercises \(43-46\), use your graphing calculator to find the value of the given function at the indicated values of \(x\). $$ f(x)=3 x^{3}+8 ; x=-11, x=10 $$

Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. \(\left(\frac{x^{4}}{y^{2}}\right)^{3}\)

In Exercises \(53-56\), compute \(f(1), f(2)\), and \(f(3)\). $$ f(x)=\left\\{\begin{array}{ll} \sqrt{x} & \text { for } 0 \leq x<2 \\ 1+x & \text { for } 2 \leq x \leq 5 \end{array}\right. $$

Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. \(\left(16 x^{8}\right)^{-3 / 4}\)