Order the expressions by choosing langle ,rangle ,or equiv 7^-2square 7^-1 ((1)/(7))^-1square 7^-2 ((1)/(7))^-2square ((1)/(7))^-1

Simplify each expression. $\frac {1}{6c^{2}d}+\frac {3}{4cd^{3}}$ $\frac {2cd^{2}+9cd}{12c^{3}d^{4}}$ $\frac {11cd^{2}}{12c^{2}d^{3}}$ $\frac {2d^{2}+9c}{12c^{2}d^{3}}$ $\frac {4}{6c^{3}d^{4}}$

Write the expression below as a single logarithm in simplest form. $log_{b}9-log_{b}3$ Answer Attemptiout of 2 $log_{b}(\square )$

Use the formula for the cosine of the difference of two angles to find the exact value of the expression $cos(\frac {\pi }{4}-\frac {5\pi }{6})$ Rewrite the expression using a sum or difference formula. Choose the correct answer below. A. $sin\frac {5\pi }{6}cos\frac {5\pi }{6}-sin\frac {\pi }{4}cos\frac {\pi }{4}$ B. $cos\frac {\pi }{4}cos\frac {5\pi }{6}+sin\frac {\pi }{4}sin\frac {5\pi }{6}$ C $cos\frac {\pi }{4}cos\frac {5\pi }{6}-sin\frac {\pi }{4}sin\frac {5\pi }{6}$ D. $sin\frac {\pi }{4}cos\frac {5\pi }{6}+cos\frac {\pi }{4}sin\frac {5\pi }{6}$ Find the exact value of the expression. $cos(\frac {\pi }{4}-\frac {5\pi }{6})=\square $

2. Which of the following sets is invertible? $\{ (-6,3),(-4,7),(-2,3),(0,8)\} $ $\{ (-5,8),(-2,12),(8,-5),(12,14)\} $ $\{ (0,1),(1,1),(2,1),(3,1)\} $ $\{ (-3,5),(-3,6),(-3,7),(-3,8)\} $

Evaluate the following definite integral to two decimal places. $\int _{0}^{30}e^{0.03t}e^{0.05(30-t)}dt$ $\int _{0}^{30}e^{0.03t}e^{0.05(30-t)}dt=\square $ (Round to two decimal places as needed.)

Samantha charges $\$ 20$ for 8 bracelets . At the same rate how much would she charge for 2 bracelets? $\$ 20$ $\$ 8$ $\$ 2$ $\$ 5$

3. Which is a solution of $2x+6\gt 12$ $x\gt 5$ $x\gt -1$ $x\gt 0$ $x\gt 3$

If $r(x)=3x-1$ and $s(x)=2x+1$ $\frac {3(6)-1}{2(6)+1}$ $\frac {(6)}{2(6)+1}$ $\frac {36-1}{26+1}$ $\frac {(6)-1}{(6)+1}$

Use dimensional analysis to convert the quantity to the indicated units. 27,540 ft to mi $27,540ft=\square mi$ (Round to the nearest hundredth as needed.)

14. (11 pts) The profit P (in thousands of dollars) for a company spending an amount s (in thousands of dollars) on advertising is given by the equation: $P(s)=-\frac {1}{10}s^{3}+9s^{2}+400$ a. Find the amount of money the company should spend on advertising in order to make a maximum profit. Also, what is the maximum profit the company makes? If the company spends $\$ \underline {\quad }on$ advertising the maximum profit is $\$ \underline {\quad }.$ b. The point of diminishing returns is the point at which the rate of growth of the profit begins to decline. Find the point of diminishing returns. $\square $ The point of diminishing returns is $\$ \underline {\quad }$