If you have a parametric equation grapher, graph the equations over the given intervals. x = sec t (enter as 1/cos(t)), y = tan t (enter as sin(t)/cos(t)), over

$$\left. \begin{array} { l } a.{ - 1.5 \leq t \leq 1.5 } \\ b.{ - 0.5 \leq t \leq 0.5 } \\ c.{ - 0.1 \leq t \leq 0.1 } \end{array} \right.$$

$$\text { Find all subgroups of order } 3 \text { in } Z _ { 9 } \oplus Z _ { 3 }$$

Write out in words how to say each of the following:

$$( f \circ g ) ( 2 ) \quad g ( f ( - 8 ) )$$

Write the fraction as a decimal and a percent. $\frac{2}{5}$

An investment of $\$5000$ doubles in value every decade. The function $f(x)=5000\cdot 2^x$, where $x$ is the number of decades, models the growth of the value of the investment. How much is the investment worth after $30$ yr?

Find the general solution of the given system.

$$\mathbf{X}^{\prime}=\left(\begin{array}{rr}{12} & {-9} \\ {4} & {0}\end{array}\right) \mathbf{X}$$

Solve each problem, and express the answer in scientific notation. a. $\left(4 \times 10^{2}\right) \times\left(1 \times 10^{8}\right)$ b. $\left(2 \times 10^{-4}\right) \times\left(3 \times 10^{2}\right)$ c. $\left(6 \times 10^{2}\right) \div\left(2 \times 10^{\prime}\right)$ d. $\left(8 \times 10^{4}\right) \div\left(4 \times 10^{1}\right)$

describe how to transform the graph of y =ln x into the graph of the given function. Sketch the graph by hand and support your sketch with a grapher.

$$f(x)=ln(2-x)$$

Find $(f \cdot g)(-2)$ for the following functions.

$$\begin{array}{l}{f(x)=-x^{2}+2 x-2} \\ {g(x)=2 x+3}\end{array}$$

A. -20 B. 8 C. 120 D. 215

Let

$$F _ { 1 } \left( y _ { 1 } \right) \text { and } F _ { 2 } \left( y _ { 2 } \right)$$

be two distribution functions. For any

$$\alpha , - 1 \leq \alpha \leq 1$$

, consider

$$Y _ { 1 }$$

and

$$Y _ { 2 }$$

with joint distribution function

$$F \left( y _ { 1 } , y _ { 2 } \right) = F _ { 1 } \left( y _ { 1 } \right) F _ { 2 } \left( y _ { 2 } \right) \left[ 1 - \alpha \left\{ 1 - F _ { 1 } \left( y _ { 1 } \right) \right\} \left\{ 1 - F _ { 2 } \left( y _ { 2 } \right) \right\} \right]$$

. What is

$$F \left( y _ { 1 } , \infty \right)$$

, the marginal distribution function of

$$Y _ { 1 }$$

? [Hint: What is

$$F _ { 2 } ( \infty )$$

?]

Solve each inequality and graph the solution set on a number line.

$$- 3 \leq 2 x + 1 < 6$$

Is it possible to form a triangle with the given side lengths? If not, explain why not. 3 in., 4 in., 8 in.

A geosynchronous satellite orbits Earth at a distance of 42,250.0 km and has a period of 1 day. What is the centripetal acceleration of the satellite?

The center of a ring R is the subring defined by $\{c \in R: c r=r c$ for every $r \in R\}.$ Prove that the center of $M(2, \mathbb{Z})$ consists of all matrices of the form

$$\left[\begin{array}{ll}{a} & {0} \\ {0} & {a}\end{array}\right], \quad a \in \mathbb{Z}$$

Verify that this is not an ideal of $M(2, \mathbb{Z}).$