In 1969, all field goal attempts in the National Football League and American Football League were analyzed. See Table A.15. (The data has been summarized: all attempts between 10 and 19 yards from the goal post are listed as 14.5 yards out, etc.)

$$\begin{matrix} \text{Successful fraction of field goal attempts}\\ \text{Distance from goal, x yards} & \text{14.5} & \text{24.5} & \text{34.5} & \text{44.5} & \text{52.0} & \text{50} & \text{58}\\ \text{Fraction successful, Y} & \text{0.90} & \text{0.75} & \text{0.54} & \text{0.29} & \text{0.15} & \text{6.1} & \text{6.7}\\ \end{matrix}$$

Find the exponential regression function; graph it with the data. What success rate does this function predict from a distance of 50 yards?

The table shows the approximate height and horizontal distance traveled by a football kicked at an angle of $30^{\circ}$ with an initial velocity of 30 yards per second.

$$\begin{array}{|c|c|c|}\hline \text { Time (s) } & {\text { Height }} & {\text { Length }} \\ \hline {} & \text{(yd)} & \text{(yd)} \\ \hline 0.0 & {0} & {0} \\ \hline 0.5 & {6.2} & {13} \\ \hline 1.0 & {9.7} & {26} \\ \hline 1.5 & {10.5} & {39} \\ \hline 2.0 & {8.7} & {52} \\ \hline 2.5 & {4.2} & {65} \\ \hline\end{array}$$

Did the football travel the same length each half-second? Justify your answer.

The acidity of a solution is measured by its pH, with lower pH values indicating more acidity. A study of acid rain was undertaken in Colorado between 1975 and 1978, in which the acidity of rain was measured for 150 consecutive weeks. The data followed a generally linear pattern. If P is the pH and t is the number of weeks into the study, the regression line was determined to be $P=5.43-0.0053 t$. According to the line , what was the pH at the begin of the study? At the end of the study (t=150)?

Researchers studying acid rain measured the acidity of precipitation in a Colorado wilderness area for 150 consecutive weeks. Acidity is measured by pH. Lower pH values show higher acidity. The researchers observed a linear pattern over time. They reported that the regression line

$$\widehat{pH} = 5.43 - 0.0053$$

(weeks) fit the data well. Identify the y intercept of the line and explain what it means in this setting.

Does it matter whether you remove x-tiles or 1-tiles first? Is one way more convenient? Explain.

Mailboxes Plus sends packages overnight for $5 plus$0.25 per ounce. United Packages charges $2 plus$0.35 per ounce. Mr. Molinari noticed that his package would cost the same to mail using either service. How much does his package weigh?

Find the missing properties of T, P, v, u, h, and x if applicable and plot the location of the three states as points in the T-v and the P-v diagrams. a. Water at 5000 kPa, u=800 kJ/kg. b. Water at 5000 kPa, v=0.06 $m^3$/kg. c. R-134a at $35^{\circ} \mathrm{C}$, v=0.01 $m^3$/kg

Define emissivity and absorptivity. What is Kirchhoff’s law of radiation?

Concept Vocabulary: reclusive, sinister, ethereal. How does the concept vocabulary help readers understand the elements of Gothic literature?

Global temperatures have been rising, on average, for more than a century, sparking concern that the polar ice will melt and sea levels will rise. With t in years since 1880, fitting functions to the data gives three models for the average global temperature in Celsius: $f(t)=13.625+0.006 t$, $g(t)=0.00006 t^{2}-0.0017 t+13.788$, $h(t)=13.63 e^{0.0004 t}$. Find the rate of change of temperature in 2010 in each of the three models. Give units.

Find the curvature $\kappa$ of the graph of each function at the indicated point. $y=\ln (x+1)$ at $(2, \ln 3)$

Find the value.

$$(\sqrt{\frac{25}{81}})^{2}=$$

Find the curvature $\kappa$ of each plane curve traced out by the vector function r=r(t). $\mathbf{r}(t)=\cos t \mathbf{i}+2 \sin t \mathbf{j}$

Evaluate the expression. Express the result in scientific notation.

$$\left(8.64 \times 10^{6}\right)+\left(1.334 \times 10^{10}\right)=$$