Nitrogen and hydrogen gases react to form ammonia gas as follows:

N$_2$ (g) + 3 H$_2$ (g) $\rightarrow$ 2 NH$_3$ (g)

At a certain temperature and pressure, 1.5L of N$_2$ reacts with 4.5L of H$_2$.

If all the N$_2$ and H$_2$ are consumed, what volume of NH$_3$, at the same temperature and pressure, will be produced?

To complete each sentence, underline the correct pronoun from the pair in parentheses.

Garrison was a white person for (who, whom) Douglass had a great deal of respect.

A vessel of volume $22.4\ \mathrm{dm}^{3}$ contains $20\ \mathrm{mol}\ \mathrm{H}_{2}(\mathrm{g})$ and $1.0\ \mathrm{mol}\ \mathrm{N}_{2}(\mathrm{g})$ at 273.15 K initially. All the $\mathrm{H}_{2}$ then reacts with sufficient $\mathrm{N}_2$ to form $\mathrm{NH}_{3}.$ Calculate the partial pressures of the gases in the final mixture and the total pressure.

Which of the following gases has the highest root-mean-square speed? a) nttrogen at 1 atm and $30^{\circ} \mathrm{C}$ b) argon at 1 atm and $30^{\circ} \mathrm{C}$ c) argon at 2 atm and $30^{\circ} \mathrm{C}$ d) oxygen at 2 atm and $30^{\circ} \mathrm{C}$ e) nttrogen at 2 atm and $15^{\circ} \mathrm{C}$

Which of the following hardships did African Americans not typically face during the Great Depression?

A. lower farm wages in the South

B. the belief that white workers needed jobs more than their black counterparts

C. white workers taking historically "black" jobs, such as maids and janitors

D. widespread race riots in large urban centers

Although techniques are available for determining the sequences of amino acids in proteins, it is becoming more and more common to sequence proteins indirectly by determining the base sequence of the gene for the protein and then inferring the amino acid sequence from the genetic-code relationships. Suggest why the latter technique is being used for proteins.

For the following question, Consider this scenario: The number of people afflicted with the common cold in the winter months steadily decreased by $205$ each year from $2005$ until $2010$. In $$ 2005$, $12,025$ people were afflicted. If the function $C$ is graphed, find and interpret the $$

The value of $\Gamma(1 / 2)$ The gamma function.

$$\Gamma(x)=\int_0^{\infty} t^{x-1} e^{-t} d t,$$

extends the factorial function from the nonnegative integers to other real values. Of particular interest in the theory of differential equations is the number

$$\Gamma\left(\frac{1}{2}\right)=\int_0^{\infty} t^{(1 / 2)-1} e^{-t} d t=\int_0^{\infty} \frac{e^{-t}}{\sqrt{t}} d t .$$

Show that

$$I=\int_0^{\infty} e^{-y^2} d y=\frac{\sqrt{\pi}}{2} .$$

For the following exercises, consider this scenario: The number of people afflicted with the common cold in the winter months steadily decreased by 205 each year from 2005 until 2010. In 2005, 12,025 people were afflicted.
If the function $C$ is graphed, find and interpret the $x$-and $y$-intercepts.

Priceler manufactures sedans and wagons The number of vehicles that can be sold each of the next three months are listed in Table 83. Each sedan sells for $8,000, and each wagon sells for$9,000. It costs $6,000 to produce a sedan and$7,500 to produce a wagon. To hold a vehicle in inventory for one month costs $150 per sedan and$200 per wagon. During each month, at most 1,500 vehicles can be produced. Production line restrictions dictate that during month 1 at least two-thirds of all cars produced must be sedans. At the beginning of month 1, 200 sedans and 100 wagons are available. Formulate an LP that can be used to maximize Priceler’s profit during the next three months. Table 83:

$$\begin{matrix} \text{Month} & \text{Sedans} & \text{Wagons}\\ \text{1} & \text{1,100} & \text{600}\\ \text{2} & \text{1,500} & \text{700}\\ \text{3} & \text{1,200} & \text{50}\\ \end{matrix}$$

Fill in the blank with an appropriate word, phrase, or symbol(s). The symbol for the number of combinations when r items are selected from n distinct items is _.

The following table contains the scores of 25 students on a certain exam:

$$\begin{array}{rrrrr} 7 & 8 & 8 & 3 & 2 \\ 5 & 6 & 9 & 10 & 6 \\ 8 & 8 & 7 & 6 & 9 \\ 10 & 4 & 4 & 8 & 6 \\ 9 & 10 & 5 & 5 & 8 \end{array}$$

(a) Find the relative frequency distribution. (b) Compute the average value by (i) averaging the values in the table directly and (ii) using the relative frequency distribution obtained in (a).

Electrophoresis is a method of

(1) separating DNA fragments

(2) changing the genetic code of an organism

(3) indicating the presence of starch

(4) separating colored compounds on a strip of paper

The loss of flying ability by the beetle is most probably the result of

(1) predators eating the beetles' wings

(2) beetles not using their wings

(3) genetic changes in the beetles

(4) lack of vegetation for the beetle to feed on