Determine values of
(b) $\beta_4$ for the formation of $\left[\mathrm{Ni}\left(\mathrm{H}_2 \mathrm{O}\right)_2\left(\mathrm{NH}_3\right)_4\right]^{2+}$.

The data show the most number of home runs hit by a batter in the American League over the last 30 seasons. Construct a frequency distribution using 5 classes. Sketch a histogram, a frequency polygon, and an ogive for the date, using relative frequencies. Describe the shape of the histogram.

$$\begin{array}{lll}40 & 43 & 40 \\ 53 & 47 & 46 \\ 44 & 57 & 43 \\ 43 & 52 & 44 \\ 54 & 47 & 51 \\ 39 & 48 & 36 \\ 37 & 56 & 42 \\ 54 & 56 & 49 \\ 54 & 52 & 40 \\ 48 & 50 & 40\end{array}$$

The following sentence may contain errors in capitalization and abbreviation. Cross out each error, and write the correct form above it. If the sentence is correct, write C above it.

Which planet, Jupiter or Saturn, has more Moons?

Underline the verb in each of the following sentences. If the subject and verb do not agree, write the correct verb form above the error. If the sentence is already correct, write C.

The children smile for the camera.

Find the point

$$\left( x _ { 0 } , y _ { 0 } \right)$$

on the line 4x + 9y = 12 that is closest to the origin.

Simplify the radical expression. Assume all variables are unrestricted.

$$\sqrt [ 4 ] { ( x - 7 ) ^ { 8 } }$$

Solve the given differential equation by separation of variables.

$$\frac { d y } { d x } = ( x + 1 ) ^ { 2 }$$

Find the point(s) on the graph of $y=\left(x^2+3 x-1\right) / x$ where the slope is 5.

Show that the point is on the unit circle.

$$\left( - \frac { 24 } { 25 } , - \frac { 7 } { 25 } \right)$$

The following sentence contains errors in capitalization and abbreviations. Cross out each error and write the correct form above it. If the sentence is correct, write C after it.

The bibliography entry ends with “$15$ Jan. $1998:10$.”

Using the following data that relate to the formation of Schottky defects in some oxide ceramic (having the chemical formula MO), determine the following:

(a) The energy for defect formation (in eV)

(b) The equilibrium number of Schottky defects per cubic meter at 1000 degree C

(c) The identity of the oxide (i.e., what is the metal M?)

Plot each point in polar coordinates. Then find another representation

$$( r , \theta )$$

of this point in which:

$$r > 0 , - 2 \pi < \theta < 0.$$

$$\left( 3.5 , \frac { \pi } { 2 } \right)$$

Plot each point in polar coordinates. Then find another representation

$$( r , \theta )$$

of this point in which:

$$r < 0,0 < \theta < 2 \pi.$$

$$\left( 2 , \frac { 2 \pi } { 3 } \right)$$

A meteor has a Pb-206:U-238 mass ratio of 0.855:1.00. What is the age of the meteor? (Assume that the meteor did not contain any Pb-206 at the time of its formation.)