The equilibrium constant $K_P$ for the reaction

$$2 \mathrm{NO}_2(g) \rightleftharpoons 2 \mathrm{NO}(g)+\mathrm{O}_2(g)$$

is 158 at $1000 \mathrm{~K}$. Calculate $P_{\mathrm{O}_2}$ if $P_{\mathrm{NO}_2}=0.400 \mathrm{~atm}$ and $P_{\mathrm{NO}}=0.270 \mathrm{~atm}$.

The SD of a bounded random variable.

a) Let X be a random variable with $0 \leq X \leq 1$ and $E(X)=\mu$. Show that:

(i) $0 \leq \mu \leq 1$ (ii) $0 \leq \operatorname{Var}(X) \leq \mu(1-\mu) \leq \frac{1}{4}$

b) Let $X$ be a random variable with $a \leq X \leq b$ and $E(X)=\mu$. Show that:

(i) $a \leq \mu \leq b$; (ii) $0 \leq \operatorname{Var}(X) \leq(\mu-a)(b-\mu) \leq \frac{1}{4}(b-a)^2$; (iii) $0 \leq S D(X) \leq(b-a) / 2$.

c) The standard deviation of a list of a million digits $0,1,2, \ldots, 9$ is exactly $4 \frac{1}{2}$. How many nines are there in the list? Or is it impossible to answer this question without more information?

Convert $634\mathrm{~mmHg}$ to $\mathrm{atm}$, $\mathrm{torr}$, and $\mathrm{kPa}$.

Consider the following convergent series.

$$\sum _ { k = 1 } ^ { \infty } \frac { 1 } { k ^ { 3 / 2 } }$$

Find how many terms are needed to ensure that the remainder less than $10^{-3}$.

Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement.

$$fxy=∂^2f/∂x∂y$$

How does chapter 16 of Of Mice and Men, by John Steinbeck, aid in the character development of Lennie and George?

Simplify each expression. Justify each step.

$$2 g + 3 ( g + 5 )$$

On the line in each sentence below, write the form of rise or raise that correctly and sensibly completes the sentence. The cost of concert tickets has --- until it is more than I want to pay.

Differentiate: $y=\tan x \cot x$

Calculate the mass, in grams, for each of the following using Table 3.8: a. a sample of water, $\mathrm{H}_2 \mathrm{O}$, that absorbs $8250 \mathrm{~J}$ when its temperature increases from $18.4^{\circ} \mathrm{C}$ to $92.6^{\circ} \mathrm{C}$ b. a sample of silver $(\mathrm{Ag})$ that loses $3.22 \mathrm{~kJ}$ when its temperature decreases from $145{ }^{\circ} \mathrm{C}$ to $24^{\circ} \mathrm{C}$

Would a precipitate of silver acetate form if $22.0 \mathrm{~mL}$ of $0.100 \mathrm{M} \mathrm{AgNO}_3$ were added to $45.0 \mathrm{~mL}$ of $0.0260 \mathrm{M}$ $\mathrm{NaC}_2 \mathrm{H}_3 \mathrm{O}_2$ ? For $\mathrm{AgC}_2 \mathrm{H}_3 \mathrm{O}_2, K_{\text {sp }}=2.3 \times 10^{-3}$.

Choose the letter of the best antonym of the word "doleful" from the phrase "a doleful report".

a. generous

b. exclusive

c. prodigal

d. brief

e. joyful

The following sentence contains misplaced verbal modifier. Rewrite the sentence so that the verbal phrase is close to the word it can logically modify.

Coming in fast across the Atlantic Ocean, we hunkered down to await the hurricane.

Write the following logarithmic equation in exponential form.

log$_{10}$ 100,000 = 5