Which, if any, of the integrals listed below can be found using the 20 basic integration rules? For any that can be found, do so. For any that cannot, explain why not.

$$\int \frac{3 x^2}{\sqrt{1-x^2}} d x$$

Divide. $50 \div(-5)=$

A $2-f t^{3}$ rigid tank contains saturated refrigerant- 134a at 160 psia. Initially, 5 percent of the volume is occupied by liquid and the rest by vapor. A valve at the top of the tank is now opened, and vapor is allowed to escape slowly from the tank. Heat is transferred to the refrigerant such that the pressure inside the tank remains constant. The valve is closed when the last drop of liquid in the tank is vaporized. Determine the total heat transfer for this process.

The volume of a sample of ideal gas is___ proportional to its temperature $(\mathrm{K})$ at constant pressure.

Trace your cutout triangle onto a blank sheet of paper. This time you will make a pattern by reflecting the triangle. Draw $x$-and $y$-axes and orient the triangle so its base lies on the $x$-axis and one of its acute angles lies on the origin.
Reflect the pattern from step 3 over the $x$-axis and draw the resulting pattern.

In the California Health Interview Survey, randomly selected adults are interviewed. One of the questions asks how many cigarettes are smoked per day, and results are listed below for 50 randomly selected respondents. How well do the results reflect the smoking behavior of California adults?

$$\begin{matrix} \text{9} & \text{10} & \text{10} & \text{20} & \text{40} & \text{50} & \text{0} & \text{0} & \text{0} & \text{0} & \text{0} & \text{0} & \text{0} & \text{0} & \text{0}\\ \text{0} & \text{0} & \text{0} & \text{0} & \text{0} & \text{0} & \text{0} & \text{0} & \text{0} & \text{0} & \text{0} & \text{0} & \text{0} & \text{0} & \text{0}\\ \text{0} & \text{0} & \text{0} & \text{0} & \text{0} & \text{0} & \text{0} & \text{0} & \text{0} & \text{0} & \text{0} & \text{0} & \text{0} & \text{0} & \text{0}\\ \text{0} & \text{0} & \text{0} & \text{0} & \text{0}\\ \end{matrix}$$

					Find the median.

Describe how the following changes affect the positional entropy of a substance.

increase in pressure of a gas at constant T

A stack of quarters is worth $2.25 . Use the equation$0.25 q=2.25$and the replacement set$\{7,8,9\} .$Find$q,$ the number of quarters in the stack.

What is a stack? What is the stack pointer used for?

In Problems 50 through 53 , the initial state of $1.00 \text{~mol}$ of a dilute gas is $P_1=3.00 \text{~atm}, V_1=1.00 \text{~L}$, and $E_{\text {int } 1}=456 \text{~J}$, and its final state is $P_2=2.00 \text{~atm}, V_2=3.00 \text{~L}$, and $E_{\text {int } 2}=912 \text{~J}$.

The gas is allowed to expand at constant pressure until it reaches its final volume. It is then cooled at constant volume until it reaches its final pressure. $(b)$ Find the heat absorbed by the gas during this process.

A double-slit diffraction pattern is formed using mercury green light at $546.1$ nm. Each slit has a width of $0.100$ mm. The pattern reveals that the fourth-order interference maxima are missing from the pattern.

$\textbf{a}$. What is the slit separation?

$\textbf{b}$. What is the irradiance of the first three orders of interference fringes, relative to the zeroth-order maximum?

A constant pressure container of 1.2 kg steel contains 1.5 kg of R134a at 40C, 500 kPa. The container is placed in a refrigerator that brings it to −20$^{\circ} \mathrm{C}$. Find the process heat transfer and the combined steel and R134a change in entropy.

Weights of respondents were recorded as part of the California Health Interview Survey. The last digits of weights from 50 randomly selected respondents are listed below.

$$\begin{matrix} \text{5} & \text{0} & \text{1} & \text{0} & \text{2} & \text{0} & \text{5} & \text{0} & \text{5} & \text{0} & \text{3} & \text{8} & \text{5} & \text{0} & \text{5} & \text{0} & \text{5} & \text{6} & \text{0} & \text{0} & \text{0} & \text{0}\\ \text{5} & \text{5} & \text{0} & \text{4} & \text{5} & \text{0} & \text{0} & \text{4} & \text{0} & \text{0} & \text{0} & \text{0} & \text{0} & \text{8} & \text{0} & \text{9} & \text{5} & \text{3} & \text{0} & \text{5} & \text{0} & \text{0}\\ \end{matrix}$$

	 Find the 95% confidence interval estimate of $\sigma$.

A piston–cylinder device contains steam initially at 1 MPa, $450^{\circ} \mathrm{C}$, and $2.5 \mathrm{m}^{3}$. Steam is allowed to cool at constant pressure until it first starts condensing. Show the process on a T-v diagram with respect to saturation lines and determine (a) the mass of the steam, (b) the final temperature, and (c) the amount of heat transfer.