(a) For ${ }^{16} \mathrm{O}_2, \Delta G$ values for the transitions $v=1 \leftarrow 0,2 \leftarrow 0$, and $3 \leftarrow 0$ are, respectively, 1556.22, 3088.28, and $4596.21 \mathrm{~cm}^{-1}$. Calculate $\tilde{v}$ and $x_{e^*}$. Assume $y_e$ to be zero.

(b) For ${ }^{14} \mathrm{~N}_2, \Delta G$ values for the transitions $v=1 \leftarrow 0,2 \leftarrow 0$, and $3 \leftarrow 0$ are, respectively, 2345.15, 4661.40, and $6983.73 \mathrm{~cm}^{-1}$. Calculate $\tilde{v}$ and $x_{e^*}$. Assume $y_e$ to be zero.

Choose the correct answer.

A Kickstarter campaign raised enough money to fund (a) a, (b) an extraordinary documentary about the Kronos Quartet.

According to the law of effect, how are desired behaviors strengthened?

Explain why the slope of the line tangent to the polar graph of r=$f ( \theta )$ is not $\frac { d r } { d \theta }$.

Bismuth-209 was bombarded with iron-58 for several days. Meitnerium ($_{266}^{109}$Mt) was produced. How many neutrons were released per atom?

$^{209}_{83}$Bi + $^{58}_{26}$Fe $\longrightarrow$ $_{266}^{109}$Mt + ?$^1_0$n

Suppose a word is picked at random from this sentence.

a) What is the distribution of the length of the word picked?

b) What is the distribution of the number of vowels in the word?

In this exercise, solve the given problems.

Using the fact that $\tan \frac{\pi}{6}=0.5774$, find the value of $\cot \frac{5 \pi}{3}$. (A calculator should be used only to check the result.)

Find the real solutions of each equation by factoring. $x^{3}+4 x^{2}-x-4=0$

Determine which numbers in the set are whole numbers.

$-9,-\frac{7}{2}, 5, \frac{2}{3}, \sqrt{2}, 0,1,-4,2,-11$

(Continuation of the previous exericse.) For each vertex x, let C(x)={z:x~x}.

Prove the following:

(i) For all vertices x and y, either C(x)=C(y) or else $C(x) \cap C(y)=\emptyset$. In other words two of the sets C(x) and C(y) cannot intersect unless they are equal.

(ii) If $C(x) \cap C(y)=\emptyset$, then there does not exist an edge joining a vertex in C(x) to a vertex in C(y).

Which of the following statements about the tundra is not true?

• a. Tundra means “treeless land.”
• b. Plants and animals in the tundra have adapted to the extreme climate.
• c. Temperatures in the tundra range from extreme highs to extreme lows.
• d. The alpine tundra can be found on mountaintops.

Multiply or divide.

$$\frac{8}{3} \times\left(-2 \frac{1}{2}\right)$$

Determine whether the following pairs are equal by changing both to have the same denominator.
a. $\frac{10} {16}$ and $\frac{12} {18}$
b.$\frac{-_{21}} {86}$ and $\frac{-51}{ 215}$

Establish the identity $\tan^{-1} x+\cot ^{-1} x=\frac{\pi}{2}$ by showing that the derivative of $y=\tan ^{-1} x+\cot ^{-1} x$ is 0. Then use the fact that when x=1, then $y=\frac{\pi}{2}$.