On May 1, Jennings, a car dealer, e-mails Wheeler and says, “I have a 1955 Thunderbird convertible in mint condition that I will sell you for $13,500 at any time before June 9. [Signed] Peter Jennings.” By May 15, having heard nothing from Wheeler, Jennings sells the car to another. On May 29, Wheeler accepts Jennings’s offer and tenders$13,500. When told Jennings has sold the car to another, Wheeler claims Jennings has breached their contract. Is Jennings in breach? Explain.

Let f(t) = t for $0 \leq t \leq 2$ and f(t) = 3 for $2<t \leq 4$. (a) Find an explicit expression for $F(x)=\int_{0}^{x} f(t) d t$ as a function of x. (b) Sketch F and determine where F is differentiable. (c) Find a formula for $F^{\prime}(x)$ wherever F is differentiable.

Additional Terms. B.S. International, Ltd. (BSI), makes costume jewelry. JMAM, LLC, is a wholesaler of costume jewelry. JMAM sent BSI a letter with the terms for orders, including the necessary procedure for obtaining credit for items that customers rejected. The letter stated, "By signing below, you agree to the terms." Steven Baracsi, BSI's owner, signed the letter and returned it. For six years, BSI made jewelry for JMAM, which resold it. Items rejected by customers were sent back to JMAM, but were never returned to BSI. BSI filed a suit against JMAM, claiming $\$ 41,294.21$ for the unreturned items. BSI showed the court a copy of JMAM's terms. Across the bottom had been typed a "PS" requiring the return of rejected merchandise. Was this "PS" part of the contract? Discuss.

New techniques have changed the cost function. For the new function $g(p)=\frac{3.2 p+1}{100-p},$ what percent of the pollutant can be removed for $\$ 50$ million?

The file New Home Sales contains the number of new homes sold (in thousands) and the median sales price of new single-family houses sold in the United States recorded at the end of each month from January 2000 through December 2017. What pattern, if any, is present in the data?

Consider a semi cylindrical trough of radius R and length L. Develop general expressions for the magnitude and line of action of the hydrostatic force on one end, if the trough is partially filled with water and open to atmosphere. Plot the results (in non dimensional form) over the range of water depth $0 \leq \mathrm{d} / \mathrm{R} \leq 1$.

Chloroform, $\mathrm{CHCl}_3$, is a solvent and has been used as an anesthetic. The heat of vaporization of chloroform at its boiling point $\left(61.2^{\circ} \mathrm{C}\right)$ is $29.6 \mathrm{~kJ} / \mathrm{mol}$. What is the entropy change when $1.20 \mathrm{~mol} \mathrm{CHCl}_3$ vaporizes at its boiling point?

For the following problem, write an equation for the inverse relation by interchanging the variables and solving for y in terms of x. Then plot the function and its inverse on the same screen, using function mode. Sketch the result, showing that the function and its inverse are reflections across the line y = x. Tell whether or not the inverse relation is a function.

$$y=-0.5 x^2-2$$

Verify that the indicated function is an explicit solution of the given differential equation. Give an interval of definition I for each solution.

$$\begin{array}{l} x^{2} y^{\prime \prime}+x y^{\prime}+y=\sec (\ln x) \\ y=\cos (\ln x) \ln (\cos (\ln x))+(\ln x) \sin (\ln x) \end{array}$$

At higher altitudes, water boils at lower temperatures. This relationship between altitude and boiling point is linear. At an altitude of 1000 feet, water boils at

$$210 ^ { \circ } \mathrm { F }$$

. At an altitude of 3000 feet, water boils at

$$206 ^ { \circ } \mathrm { F }$$

. Write an equation in slope-intercept form that represents this linear function. Then find the boiling point at 6000 feet.

Perform the indicated operation and, if possible, simplify.

$$\frac{a}{6 a-9 b}-\frac{b}{4 a-6 b}$$

Calculate the dealer's cost.

$$\scriptscriptstyle\begin{array}{|c|c|c|c|c|c|c|c|c|c|c|c|} \hline\text{ Base} & \times & \text{ Dealer's } & + & \text{ Option } & \times & \text{ Dealer's } & + & \text{ Destination } & = & \text{ Dealer's }\\ \text{ Price} & \text{ } & \text{ Percent} & \text{ } & \text{ Price } & \text{ } & \text{ Percent } & \text{ } & \text{ Charge} & & \text{ Cost} \\ \hline \$36,890 & \times & 87.0 \% & + & \$ 5,680 & \times & 91.0 \% & + & \$980 & &\\ \hline \end{array}$$

To encourage telephone efficiency, a catalog call center issues a guideline that at least half of all telephone orders should be completed within 2 minutes. Subsequently, a random sample of 64 telephone calls showed that only 24 calls lasted 2 minutes or less. (a) At $\alpha=.05$ is this a significant departure from the guideline in a left-tailed test? State your hypotheses and decision rule. (b) Find the $p$-value. (c) Is the difference important (as opposed to significant)?

Perform the indicated operation and write the result in standard form.

$$\sqrt { - 81 } - \sqrt { - 144 }$$