Write the common name for O$_3$.

Suppose that trees are distributed in a forest according to a two-dimensional Poisson process with parameter $\alpha$, the expected number of trees per acre, equal to 80. a. What is the probability that in a certain quarter-acre plot, there will be at most 16 trees? b. If the forest covers 85,000 acres, what is the expected number of trees in the forest? c. Suppose you select a point in the forest and construct a circle of radius .1 mile. Let X=the number of trees within that circular region. What is the pmf of X? [Hint: 1 sq mile=640 acres.]

Write the common name for calcium carbonate.

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.

Describe the trend in temperate and tropical deforestation over the last 300 years.

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

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.

Determine whether the given event is 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 getting a sum of either 6 or 10.

Portland cement acts as the binding agent in concrete. A typical Portland cement has the following composition:

$$\begin{matrix} \text{Formula} &&&&&&& \text{Name} &&&&&&& \text{Mass }\\ &&&&&& {} &&&&&&&& \text{Percent}\\ \hline \end{matrix}$$

$$\begin{array} { l } { \mathrm { Ca } _ { 3 } \mathrm { SiO } _ { 5 } } \\ { \mathrm { Ca } _ { 2 } \mathrm { SiO } _ { 4 } } \\ { \mathrm { Ca } _ { 3 } \mathrm { Al } _ { 2 } \mathrm { O } _ { 6 } } \\ { \mathrm { Ca } _ { 2 } \mathrm { AlFeO } _ { 5 } } \\ { \mathrm { CaSO } _ { 4 } \cdot 2 \mathrm { H } _ { 2 } \mathrm { O } } \\ { \text { Other substances, } } \\ { \text { mostly MgO } } \end{array} \quad \begin{array} { l } { \text { Tricalcium silicate } } \\ { \text { Dicalcium silicate } } \\ { \text { Tricalcium aluminate } } \\ { \text { Calcium aluminoferrite } } \\ { \text { Calcium sulfate dihydrate } \\ {\ } \\ {\ } } \end{array} \quad \begin{array} { l } { 50. } \\ { 25 } \\ { 12 } \\ { 8.0 } \\ { 3.5 } \\ { 1.5 } \\ {} \end{array}$$

For each of the following sentences, choose the correct word or words in parentheses. Base your answers on the rules of standard, formal usage.

Do you remember borrowing a dollar (off, off of, from) me?

A forest contains about 500 trees. You randomly pick 67 trees and find that 27 of them are oaks. b. Predict how many oak trees there are in the forest.

Mutually exclusive means that two sets of numbers have no numbers in common. Name two subsets of real numbers that are mutually exclusive. Explain.

Determine whether the events are mutually exclusive or not mutually exclusive. Then find the probability. Round to the nearest hundredth.

selecting a number from a list of integers 1 to 20 and getting a prime or even number

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