If $P (A) = 0.3$, $P (B) = 0.4$, and $P (A\ \text{or}\ B) = 0.7$, are $A$ and $B$ mutually exclusive?

What happens to the probability of becoming a hurricane when a tropical storm passes over a landmass such as Cuba?

(a) In Gaussian units, show that the square of a potential difference $\left(\phi_{2}-\phi_{1}\right)^{2}$ has the same dimensions as force. (In SI units, $\epsilon_{0}\left(\phi_{2}-\phi_{1}\right)^{2}$ has the same units as force.) This tells us that the electrostatic forces between bodies will largely be determined, as to order of magnitude, by the potential differences involved. Dimensions will enter only in ratios, and there may be some constants like $4 \pi$. What is the order of magnitude of force you expect with 1 statvolt potential difference between something and something else? (b) Practically achievable potential differences are rather severely limited, for reasons having to do with the structure of matter. The highest man-made difference of electric potential is about $10^{7}$ volts, achieved by a Van de Graaff electrostatic generator operating under high pressure. (Billion-volt accelerators do not involve potential differences that large.) How many pounds force are you likely to find associated with a “square megavolt”? These considerationsmay suggestwhy electrostatic motors have not found much application.

Name six common sources of light.

Which of the following is not a density independent factor for a population of deer in a forest? (a) a period of freezing weather (b) the number of cougars in the forest $(c)$ a drought (d) a landslide

Automobile unit sales at B. J. Scott Motors, Inc., provided the following 10-year time series.

a. Construct a time series plot. Comment on the appropriateness of a linear trend.

b. Using Minitab or Excel, develop a quadratic trend equation that can be used to forecast sales.

c. Using the trend equation developed in part (b), forecast sales in year 11.

d. Suggest an alternative to using a quadratic trend equation to forecast sales. Explain.

Production Line Speed and Quality Control. Brawdy Plastics, Inc., produces plastic seat belt retainers for General Motors at their plant in Buffalo, New York. After final assembly and painting, the parts are placed on a conveyor belt that moves the parts past a final inspection station. How fast the parts move past the final inspection station depends upon the line speed of the conveyor belt (feet per minute). Although faster line speeds are desirable, management is concerned that increasing the line speed too much may not provide enough time for inspectors to identify which parts are actually defective. To test this theory, Brawdy Plastics conducted an experiment in which the same batch of parts, with a known number of defective parts, was inspected using a variety of line speeds. The following data were collected.

Number of Defective

$$\begin{array}{cr}\begin{array}{lr}\text { Line } \\ \text { Speed }\end{array} & \begin{array}{r}\text { Defective } \\ \text { Parts Four }\end{array} \\ 20 & 23 \\ 20 & 21 \\ 30 & 19 \\ 30 & 16 \\ 40 & 15 \\ 40 & 17 \\ 50 & 14 \\ 50 & 11\end{array}$$

Develop a scatter diagram with the line speed as the independent variable.

What bargain does Tom make with the stranger in the forest?

Are the events $A$ and $A^{\prime}$ mutually exclusive? Explain.

Give an answer for the follwoing exercise.

(a) Trouton's rule states that the ratio of the molar heat of vaporization of a liquid $\left(\Delta H_{\text {vap }}\right)$ to its boiling point in kelvins is approximately $90 \mathrm{~J} / \mathrm{K} \cdot \mathrm{mol}$. Use the following data to show that this is the case and explain why Trouton's rule holds true.

$$\begin{array}{lcc} & \boldsymbol{T}_{\mathbf{b p}}\left({ }^{\circ} \mathbf{C}\right) & \boldsymbol{\Delta} \boldsymbol{H}_{\text {vap }}(\mathbf{k} \mathbf{J} / \mathbf{m o l}) \\ \hline \text { Benzene } & 80.1 & 31.0 \\ \text { Hexane } & 68.7 & 30.8 \\ \text { Mercury } & 357 & 59.0 \\ \text { Toluene } & 110.6 & 35.2 \end{array}$$

(b) Use the values in the table to calculate the same ratio for ethanol and water. Explain why Trouton's rule does not apply to these two substances as well as it does to other liquids.

$$\begin{array}{ccc} \text { Substance } & \text { Boiling point }\left({ }^{\circ} \mathrm{C}\right) & \Delta H_{\text {vap }}(\mathrm{kJ} / \mathrm{mol}) \\ \text { Argon }(\mathrm{Ar}) & -186 & 6.3 \\ \text { Benzene }\left(\mathrm{C}_6 \mathrm{H}_6\right) & 80.1 & 31.0 \\ \text { Ethanol }\left(\mathrm{C}_2 \mathrm{H}_5 \mathrm{OH}\right) & 78.3 & 39.3 \\ \text { Diethyl ether }\left(\mathrm{C}_2 \mathrm{H}_5 \mathrm{OC}_2 \mathrm{H}_5\right) & 34.6 & 26.0 \\ \text { Mercury }\left(\mathrm{Hg}^2\right) & 357 & 59.0 \\ \text { Methane }\left(\mathrm{CH}_4\right) & -164 & 9.2 \\ \text { Water }\left(\mathrm{H}_2 \mathrm{O}\right) & 100 & 40.79 \end{array}$$

Explain why the ratio is considerably smaller than $90 \mathrm{~J} / \mathrm{K} \cdot \mathrm{mol}$ for liquid $\mathrm{HF}$.

Pine trees grow throughout a large tract of forest. Suppose a highway is built through the forest, effectively dividing it in half. Is it likely that the two groups of pine trees will evolve separately? Explain your prediction.

Determine whether the events are mutually exclusive or not mutually exclusive. Then find the probability. Round to the nearest tenth of a percent if necessary.

Rolling a pair of dice and doubles or a sum of 6 is rolled

An annual report issued by General Motors Corporation included the following information:

$$\begin{array}{|cc} \text{Inventories are valued using various cost methods. The percentage of year-end}\\ \text{inventories valued using each of these methods is:}\\ \text {LIFO} & \cdots\cdots\cdots\cdots\cdots\cdots\cdots\cdots & 50\%& \\ \text { FIFO and Average Cost} & \cdots\cdots\cdots\cdots\cdots\cdots\cdots\cdots & 50 \% & \\ \text {If the LIFO method of valuation had not been used, total inventories would have } \\ \text {been \$1.4 billion more than reported.} \\ \end{array}$$

c. On the basis of the information from the company's annual report, do its inventory replacement costs appear to be rising or falling? Explain.

Which forest biome has the richest soil type?