Your heart beats about 72 times per minute. At that rate how many times will it beat in one hour? (Write an equation and solve the problem.)

Solve each inequality and graph the solutions.

$$2 d + 21 \leq 11$$

Use the table to relate each term in the sequence to its position.

$$\begin{matrix} \text{Position} & \text{1} & \text{2} & \text{3} & \text{4} & \text{5}\\ \text{Term} & \text{-2} & \text{-8} & \text{-18} & \text{-32} & \text{-50}\\ \end{matrix}$$

Draw dot diagrams for the following. a. silicon b. xenon c. calcium d. H2O

What phrase does the speaker of “The Pond” use to describe the croaking of frogs?

A matrix $A$ is given. Find $A^k$ for an arbitrary positive integer $k$.

$$\begin{bmatrix}5&&-6\\3&&-4\end{bmatrix}$$

Sketch a graph of the polar equation, and express the equation in rectangular coordinates. r = 2

For

$$x_n$$

given by the following formulas, establish either the convergence or the divergence of the sequence

$$X = (x_n).$$

$$\left(a\right)x_n:=\frac{n}{n+1},\left(b\right) x_n:= \frac {\left(-1\right)^nn} {n+1},\left(c\right)x_n:=\frac{n^2}{n+1},\left (d\right)x_n: =\frac{2n^2+3}{n^2+1}.$$

Find the product or quotient. -25(-30)

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Evaluate the iterated integral. ∫_0^2∫_y^2y (10 + 2x² + 2y²) dx dy

a. Use the definition of the derivative to show that

$$\frac { d } { d x } \left( x ^ { 2 } e ^ { x } \right) = e ^ { x } \cdot \lim _ { h \rightarrow 0 } \frac { \left( x ^ { 2 } + 2 x h + h ^ { 2 } \right) e ^ { n } - x ^ { 2 } } { h }$$

. b. Manipulate the limit in part (a) to arrive at f'(x)=

$$e ^ { x } \left( x ^ { 2 } + 2 x \right)$$

. (Hint: Use the fact that

$$\lim _ { h \rightarrow 0 } \frac { e ^ { h } - 1 } { h }$$

=1.)

Calculate the instantaneous speed (in m/s) at the 10-second mark for a car that accelerates at

$$2 m/s^2$$

from a position of rest.

A corporation with a 39% combined income tax rate is considering the following investment in research equipment.

$$\begin{matrix} \text{Year} & \text{Before-Tax Cash Flow}\\ \text{0} & \text{-\$7,500,000}\\ \text{1} & \text{650,000}\\ \text{2} & \text{950,000}\\ \text{3} & \text{2,750,000}\\ \text{4} & \text{1,900,000}\\ \text{5} & \text{800,000}\\ \text{6} & \text{450,000}\\ \text{ }\\ \end{matrix}$$

Prepare an after-tax cash flow table assuming MACRS depreciation. (a) What is the before-tax rate of return? (b) What is the after-tax rate of return?