Find the exact value of each quadrantal angle. If any are not defined, write undefined. $\sin \left( - 1530 ^ { \circ } \right)$

Solve each equation and check your solution. $\frac{6}{5} x=-1$

Use any analytical method to find the first four nonzero terms of the Taylor series centered at 0 for the following functions. You do not need to use the definition of the Taylor series coefficients.

Consider the function $f(x)=\frac{3 x-2}{x+3}$. Find $f^{\prime}(x)$ and draw its sign diagram.

Describe each of the events below as impossible, unlikely, as likely as not, likely, or certain a. Joshua rolls an odd number on a standard number cube. b. Maria's birthday is September 31st. c. The basketball team has won 11 of their last 12 games. The team will win the next game.

Solve the following cryptarithms. Assume that no leading digit is a 0.

$$AT \\ EAST \\ \frac{+WEST}{SOUTH}$$

Guess the requested limit.

$$\lim _{n \rightarrow \infty} \frac{n+1}{2 n}$$

The table shows the results of a customer satisfaction survey of 100 randomly selected shoppers at a mall. They were asked if they would shop at an earlier time if the mall opened earlier.

$$\begin{matrix} & \mathrm{Ages\ 10-20} & \mathrm{Ages\ 21-45} & \mathrm{Ages\ 46-65} & \mathrm{65\ and\ Older} & \mathrm{Total}\\ \mathrm{Yes} & \mathrm{0.13} & \mathrm{0.02} & \mathrm{0.08} & \mathrm{0.24} & \mathrm{0.47}\\ \mathrm{No} & \mathrm{0.25} & \mathrm{0.1} & \mathrm{0.15} & \mathrm{0.03} & \mathrm{0.53}\\ \mathrm{Total} & \mathrm{0.38} & \mathrm{0.12} & \mathrm{0.23} & \mathrm{0.27} & \mathrm{1}\\ \end{matrix}$$

What is the probability that a person aged 46-65 answered yes?

Differentiate the given function. $y=\frac{x^{5}-4 x^{2}}{x^{3}}$ [Hint: Divide first.]

Name the structure that makes up the body of a fungus.

Find an equation in terms of x and y for the line tangent to the curve given by

$$x=t^{2}-2 t-1, y=t^{4}-4 t^{2}+2$$

at the point where t = 1.

Ricardo weighs 2 pounds more than twice his sister's weight. The function rule, 2x+2 where x is his sister"s weight. can be used to find Ricardo's weight. Make a table of values that show Ricardo's weight when his sister is 20, 30, and 40 pounds. Then graph the function.

The process that release energy from food in the presence of oxygen is: a. synthesis b. cellular respiration c. ATP synthase d. photosynthesis

Find the general solution of the differential equation. In the case assume $x>0$

$$x^2y''-3xy'+4y=0$$