Find the sum. Use a graphing utility to verify your result. $\sum_{i=1}^{10} 5\left(-\frac{1}{3}\right)^{i-1}$

The polynomial

$$3.675 v + 0.096 v ^ { 2 }$$

is used by transportation officials to estimate the stopping distance in feet for a car whose speed is v miles per hour on flat, dry pavement. What is the stopping distance for a car traveling at 30 miles per hour?

Convert each rectangular equation to a polar equation that expresses r in terms of

$$\theta.$$

$$x ^ { 2 } + y ^ { 2 } = 9$$

The following data represent the average monthly temperatures for Baltimore, Maryland. (a) Draw a scatter diagram of the data for one period. (b) Find a sinusoidal function of the form $y=A \sin (\omega x-\phi)+B$ that models the data. (c) Draw the sinusoidal function found in part (b) on the scatter diagram. (d) Use a graphing utility to find the sinusoidal function of best fit. (e) Graph the sinusoidal function of best fit on a scatter diagram of the data.

$$\begin{matrix} \text{Month, x} & \text{Average Monthly}\\ \text{ } & \ {Temperature, ^{\circ} \mathrm{F}}\\ \text{January, 1} & \text{31.8}\\ \text{February, 2} & \text{34.8}\\ \text{March, 3} & \text{44.1}\\ \text{April, 4} & \text{53.4}\\ \text{May, 5} & \text{63.4}\\ \text{June, 6} & \text{72.5}\\ \text{July, 7} & \text{77.0}\\ \text{August, 8} & \text{75.6}\\ \text{September, 9} & \text{68.5}\\ \text{October, 10} & \text{56.6}\\ \text{November, 11} & \text{46.8}\\ \text{December, 12} & \text{36.7}\\ \end{matrix}$$

Construct a truth table for the statement. (p∧~q)vr

Use a vertical shift to graph one period of the function. y = sin x + 2

Perform the multiplication or division and simplify. $\frac{4 y-16}{5 y+15} \div \frac{4-y}{2 y+6}$

Which character did you side with in the conflict over the quilts? Why?

Given two terms of each arithmetic sequence, find $a_{1}$ and d. $a_{4}=8 \text { and } a_{7}=20$

Calculate each expression, giving the answer as a whole number or a fraction in lowest terms. $-\left(\frac{8(1-4)^{2}}{-9(5-1)^{2}}\right)$

Find the vertex, value of p, axis of symmetry, focus, and directrix of the parabola, and then graph.

$$y = \frac { 1 } { 32 } ( x + 2 ) ^ { 2 }$$

A standard number cube is tossed. Find each probability. P(odd or greater than 2)

Simplify the expression. Assume that no denominator equals 0.

$$\frac{p^4t^{-2}}{r^{-5}}$$

Along the curve

$$\mathbf { r } ( t ) = ( \cos t ) \mathbf { i } + ( \sin t ) \mathbf { j } - ( \cos t ) \mathbf { k } , 0 \leq t \leq \pi,$$

evaluate each of the following integrals.

$$\int _ { C } x z\ d x$$