The data is below:

$$\begin{array}{r|rrrrr} x_i & 2 & 6 & 9 & 13 & 20 \\ \hline y_i & 7 & 18 & 9 & 26 & 23 \end{array}$$

The estimated regression equation for these data is $\hat{y}=7.6+.9 x$. What percentage of the total sum of squares can be accounted for by the estimated regression equation? What is the value of the sample correlation coefficient?

A large city hospital conducted a study to investigate the relationship between the number of unauthorized days that employees are absent per year and the distance (miles) between home and work for the employees. A sample of 10 employees was selected and the following data were collected.

$$\begin{array}{cc}\text{Distance to Work} & \text{Number of Days}\\\text { (miles) } & \text { Absent } \\ 1 & 8 \\ 3 & 5 \\ 4 & 8 \\ 6 & 7 \\ 8 & 6 \\ 10 & 3 \\ 12 & 5 \\ 14 & 2 \\ 14 & 4 \\ 18 & 2\end{array}$$

a. Develop a scatter diagram for these data. Does a linear relationship appear reasonable? Explain.

b. Develop the least squares estimated regression equation that relates the distance to work to the number of days absent.

c. Predict the number of days absent for an employee that lives 5 miles from the hospital.

Use the following data:

$$\begin{matrix} x_i& \text{2} & \text{6} & \text{9} & \text{13} & \text{20}\\ y_i & \text{7} & \text{18} & \text{9} & \text{26} & \text{23}\\ \end{matrix}$$

What is the value of the standard error of the estimate?

An element has two naturally occurring isotopes. The isotope has a mass of 62.9396 amu and a relative abundance of 69.17 %, and isotope 2 has a mass of 64.9278 amu.

Find the atomic mass of this element.

Express each quadratic function in the form $f(x)=a(x-h)^2+k$. Then use transformations of the graph of $f(x)=x^2$ to graph each function.

$$f(x)=-\frac{1}{2} x^2+4 x-2$$

What evidence indicates that some asteroids once had geologically active surfaces?

Graph each function on the interval $[-2 \pi, 2 \pi]$. For the trigonometric functions, explain how the graphs are transformations of $y=\sin x$ or $y=\cos x$.

$$H(x)=-\frac{1}{3} \sin x$$

Prove that each identity holds for all permissible values of x.

$$\begin{array}{l}{\text { a) } 1+\cot ^{2} x=\csc ^{2} x} \\ {\text { b) } \tan x=\csc 2 x-\cot 2 x} \\ {\text { c) } \sec x+\tan x=\frac{\cos x}{1-\sin x}} \\ {\text { d) } \frac{1}{1+\cos x}+\frac{1}{1-\cos x}=2 \csc ^{2} x}\end{array}$$

Indicate whether the following statement is true (T) or false (F).

Semicolons and colons are always placed before closing quotation marks.

Find the sum. 9.6 + 5.49

Five observations taken for two variables follow.

$$\begin{matrix} x_i & \text{4} & \text{6} & \text{11} & \text{3} & \text{16}\\ y_i & \text{50} & \text{50} & \text{40} & \text{60} & \text{30}\\ \end{matrix}$$

Develop a scatter diagram with x on the horizontal axis.

A baseball is thrown from the outfield toward the catcher. When the ball reaches its highest point, which statement is true?

Find the derivatives of the functions in the ff exercise

$$k(x)=x^2 \sec (\frac{1}{x})$$

Using what you have learned about transformations of the graph $y=\frac{1}{x}$, can you find the equations of the asymptotes of the function $f(x)=\frac{p}{c x+d}+q$, and hence state the domain and range?