Let f(x) = 3x + 1 and

$$g ( t ) = t ^ { 2 } - 2 t + 1$$

. Find the value. f(r + 8)

Multistep A business is worth $10 ^ { 6 }$ dollars this year. The business expects to be $10 ^ { 3 }$ more valuable in five years a. Simplify $10 ^ { 3 }$ to determine how many times more valuable the business will be. b. What will the business be worth in five years? Express your answer in exponential form, then simplify your answer.

Choose the most appropriate type of graph for each set of data. Then on a separate sheet of paper, construct the graphs from the data.

$$\begin{matrix} \text{Number of Hits Per game}\\ \text{Game} & \text{No. of Students}\\ \text{1} & \text{11}\\ \text{2} & \text{9}\\ \text{3} & \text{8}\\ \text{4} & \text{11}\\ \text{5} & \text{12}\\ \text{6} & \text{15}\\ \text{7} & \text{16}\\ \end{matrix}$$

What is the importance of common traits in Cattell's theory? What are Cattell's source traits?

Jerry randomly selects 20 boxes of crayons from the shelf and finds 2 boxes with at least one broken crayon. If the shelf holds 130 boxes, how many would you expect to have at least one broken crayon?

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. Most car leasing agreements have yearly mileage limits.

Find the next three terms in each sequence.

$$2187,729,243,81, \cdots, \cdots,\cdots$$

Consider a rabbit population $P(t)$ satisfying the logistic equation $d P / d t = a P - b P ^ { 2 }$, where $B = a P$ is the time rate at which births occur and $D = b P ^ { 2 }$ is the rate at which deaths occur. If the initial population is $240$ rabbits and there are $9$ births per month and $12$ deaths per month occurring at time $t = 0$, how many months does it take for $P(t)$ to reach $105\%$ of the limiting population $M$?

Recall that if

$$f ( t ) \geq g ( t )$$

for

$$t \geq 0,$$

then for all

$$x \geq 0, \quad \int _ { 0 } ^ { x } f ( t ) d t \geq \int _ { 0 } ^ { x } g ( t ) d t$$

The inequality

$$e ^ { t } \geq 1$$

holds for

$$t \geq 0$$

because e > 1. Use the inequality above to prove that

$$e ^ { x } \geq 1 + x$$

for

$$x \geq 0.$$

Then prove, by successive integration, the following inequalities (for

$$x \geq 0 ):$$

$$e ^ { x } \geq 1 + x + \frac { 1 } { 2 } x ^ { 2 } , \quad e ^ { x } \geq 1 + x + \frac { 1 } { 2 } x ^ { 2 } + \frac { 1 } { 6 } x ^ { 3 }$$

Find the derivative of the function. Assume a, b, and c are constants. $f ( \alpha ) = \cos \alpha + 3 \sin \alpha$

How does Odysseus escape from Polyphemus?

$$\begin{array} { l } { \text { In the left regular representation for } D _ { 4 } , \text { write } T _ { R _ { \infty _ { 0 } } } \text { and } T _ { H } \text { in matrix } } \\ { \text { form and in cycle form. } } \end{array}$$

Evaluate each expression, or indicate that the root is not a real number.

$$\sqrt [ 3 ] { 125 }$$

Simplify

$$\left( - 2 a ^ { - 2 } b ^ { - 6 } \right) \left( - 3 a ^ { - 1 } b ^ { 8 } \right)$$