Describe and solve a real-life problem that involves finding the circumference of a circle.

Complete each step. Linearize the data according to the given model. Logarithmic

$$\begin{array}{|c|c|} \hline x & and \\ \hline 2 & 80.0 \\ \hline 4 & 83.5 \\ \hline 6 & 85.5 \\ \hline 8 & 87.0 \\ \hline 10 & 88.1 \\ \hline 12 & 89.0 \\ \hline 14 & 90.0 \\ \hline 16 & 90.5 \\ \hline \end{array}$$

Respond to each of the items using the following time series data.

$$\begin{array}{|cc|cc|} \hline \text { Period } & \text { Demand } & \text { Period } & \text { Demand } \\ \hline 1 & 138 & 8 & 103 \\ 2 & 131 & 9 & 142 \\ 3 & 149 & 10 & 122 \\ 4 & 110 & 11 & 121 \\ 5 & 175 & 12 & 130 \\ 6 & 194 & 13 & 126 \\ 7 & 166 & 14 & 140 \\ \hline \end{array}$$

a. Graph the time series data. What do you observe? b. Compute all possible forecasts using exponential smoothing with a smoothing coefficient $(\alpha)$ of $0.4$ c. Compute all possible forecasts using exponential smoothing with a smoothing coefficient $(\alpha)$ of $0.9$. d. Compute the MADs for each forecast model. e. Which forecast model would you choose? Why?

Suppose B lies on $f(x)=x^{2}$ and B has coordinates $\left(x, x^{2}\right)$. Copy and complete the table below:

$$\begin{matrix} \text{x} & \text{Point B} & \text{gradient of [AB]}\\ \text{5} & \text{(5, 25)} & \text{6}\\ \text{3}\\ \text{2}\\ \text{1.5}\\ \text{1.1}\\ \text{1.01}\\ \text{1.001}\\ \end{matrix}$$

Pick the stronger base from each pair. a. $\mathrm{ClO}_{4}^{-} \text { or } \mathrm{ClO}_{2}^{-}$ b. $\mathrm{Cl}^{-} \text { or } \mathrm{H}_{2} \mathrm{O}$ c. $\mathrm{CN}^{-} \text { or } \mathrm{ClO}^{-}$

Which of the following would not be a valid reason for a statement in a flowchart proof? A. Vertical angles are congruent. B. Definition of segment bisector C. Given D. Prove

For each function f, find the limit as x approaches c of the average rate of change of f from c to x. That is, find $\lim _{x \rightarrow c} \frac{f(x)-f(c)}{x-c}$. $f(x)=\sqrt{2 x}, c=5$

The table shows the sales $S$ (in millions of dollars) for Timberland from 1995 to 2002.

Use a graphing utility to plot the data and graph the model in the same viewing window.

Find each exact function value. $\cot \frac{5 \pi}{6}$

In the following exercise, use a graphing utility to graph the polar equation.

$$r=4(\sec \theta-\cos \theta)$$

Approximate the expression to four decimal places:

$$\operatorname{coth}^{-1} 3$$

Solve the puzzle by figuring out the missing month.

SUDOKU des mois fran$\c{c}$ais

If g is the inverse function of f and $f(x)=x^3+3 x-1$, what is the value of g'(35)?

Use a calculator to find the value of x to four decimal places.

$$\log x = 1.43$$