Nitrogen $(N_2)$ initially at $40^{\circ} \mathrm{F} \text { and } 14.7 \mathrm{lbf} / \mathrm{in}^{2}$ fills a closed, rigid, $6.5-ft^3$ tank fitted with a paddle wheel. During a process, the paddle wheel provides 5 Btu of energy transfer by work to the gas. The gas temperature reaches $80^\circ F$ at the end of the process. Assuming ideal gas behavior, determine the mass of nitrogen, in lb, and the heat transfer, in Btu. Kinetic and potential energy effects can be ignored.

Solve each inequality and graph the solutions.

$$3 ( t - 1 ) \geq - 15$$

Create a generic connections web for proportional relationships. For each representation, explain how you know the relationship is proportional.

Use the data to make a box-and-whisker plot. 21, 31, 26, 24, 28, 26

If you have 49 data values randomly selected from a normally distributed population, and there is also a 50th value that is an outlier, will that outlier somehow stand out in the graph of the normal quantile plot, or will it seem to fit in because it is only one value among 50?

Jamal and Stephanie each have school loans issued from the same two banks. The amounts borrowed and the monthly interest rates are given next (interest is compounded monthly): $$ \begin{matrix} \text{ } & \text{Lender 1} & \text{Lender 2}\\ \text{Jamal} & \text{4000} & \text{3000}\\ \text{Stephanie} & \text{2500} & \text{3800}\\ \end{matrix} $$ $$ \begin{matrix} \text{ } & \text{Monthly Interest Rate}\\ \text{Lender 1} & \text{0.011 (1.1\\%)}\\ \text{Lender 2} & \text{0.006 (0.6\\%)}\\ \end{matrix} $$ Compute AB and interpret the results.

Find |u|, u + v, u - v, 2 u, and 3 u - 2 v. u = 2i + j, v = i - 2j

Sanderson is having trouble with his assignment. His work is as follows:

$$\frac{-\frac{3}{4}}{\frac{4}{3}}=-\frac{3}{4} \times \frac{4}{3}=-\frac{12}{12}=-1$$

However, his answer does not match the answer that his teacher gives him. What is Sanderson's mistake? Find the correct answer.

Classify the critical point (0, 0) of the plane autonomous system corresponding to the nonlinear second-order differential equation $x^{\prime \prime}+\mu\left(x^{2}-1\right) x^{\prime}+x=0$ where $\mu$ is a real constant.

Perform the operation and write the result in standard form. $−6(5 − 3i)$

Represent sampling distributions in the format of a table that lists the different values of the sample statistic along with their corresponding probabilities. Jupiter has 4 large moons and 12 small moons. The 4 large moons have these orbit times (in days): 1.8 (Io), 3.6 (Europa), 7.2 (Ganymede), and 16.7 (Callisto). Assume that two of these values are randomly selected with replacement. After identifying the 16 different possible samples, find the median in each of them, then use a table to describe the sampling distribution of the medians.

Simplify the product. (7 + 3√5)(7 - 3√5)

Solve the exponential equation algebraically. Round your result to three decimal places. Use a graphing utility to verify your answer. $6\left(8^{-2-x}\right)+15=2601$

Graph each function and its inverse on the same coordinate plane.

$$f(x) = 2x + 4$$

g(x) = -x - 2.