An airline, believing that 5% of passengers fail to show up for flights, overbooks (sells more tickets than there are seats). Suppose a plane will hold 265 passengers, and the airline sells 275 tickets. What’s the probability the airline will not have enough seats, so someone gets bumped?

Calculate the molar solubility of $\mathrm{MnS}$ (pink) in a solution with a constant $\left[\mathrm{H}_3 \mathrm{O}^{+}\right]$of $*\left(\right.$ a) $3.00 \times 10^{-5}$ and (b) $3.00 \times 10^{-7}$

Write fractions in simplest form.

12.42 $\div$ (-4.8)

A newly hired telemarketer is told he will probably make a sale on about 12% of his phone calls. The first week he called 200 people, but only made 10 sales. Should he suspect he was misled about the true success rate? Explain.

An orchard owner knows that he'll have to use about 6% of the apples he harvests for cider because they will have bruises or blemishes. He expects a tree to produce about 300 apples. Describe an appropriate model for the number of cider apples that may come from that tree. Justify your model.

An airline finds that 5% of the persons making reservations on a certain flight will not show up for the flight. If the airline sells 160 tickets for a flight that has only 155 seats, what is the probability that a seat will be available for every person holding a reservation and planning to fly?

Show that the differential form in the integral is exact. Then evaluate the integral. \

$$\displaystyle\int_{(1.1 .2)}^{(3.5 .0)} y z d x+x z d y+x y d z$$

Evaluate the integral

$$\int_0^2\left(\tan ^{-1} \pi x-\tan ^{-1} x\right) d x .$$

(Hint: Write the integrand as an integral.)

Set up a definite integral that yields the area of the given region. (Do not evaluate the integral.)

f(x)=$x^2$, $0 \leq x \leq 2$

About 8% of males are colorblind. A researcher needs some colorblind subjects for an experiment and begins checking potential subjects. What's the probability that she finds someone who is colorblind before checking the 10th man?

An airline always overbooks if possible. A particular plane has 95 seats on a flight in which a ticket sells for $300. The airline sells 100 such tickets for this flight. a. If the probability of an individual not showing up is 0.05, assuming independence, what is the probability that the airline can accommodate all the passengers who do show up? b. If the airline must return the$300 price plus a penalty of $400 to each passenger that cannot get on the flight, what is the expected payout (penalty plus ticket refund) that the airline will pay?

Find the limit (if it exists). If the limit does not exist, explain why. Use a graphing utility to verify your result graphically.

$$\lim _{x \rightarrow \infty} \frac{3-7 x}{x+4}$$

Propane gas $\left(\mathrm{C}_3 \mathrm{H}_{\mathrm{s}}\right)$ is often used as a fuel in rural areas. How many liters of $\mathrm{CO}_2$ are formed at STP by the complete combustion of the propane in a container with a volume of $15.0 \mathrm{~L}$ and a pressure of $4.5 \mathrm{~atm}$ at $25^{\circ} \mathrm{C}$ ? The unbalanced equation is

$$\mathrm{C}_3 \mathrm{H}_8(\mathrm{~g})+\mathrm{O}_2(\mathrm{~g}) \longrightarrow \mathrm{CO}_2(\mathrm{~g})+\mathrm{H}_2 \mathrm{O}(\mathrm{l})$$

Find the equation of the tangent line to each curve when $x$ has the given value. Verify your answer by graphing both $f(x)$ and the tangent line with a calculator.

$$f(x)=x^2+2 x ; x=3$$