When commercial aircraft are inspected, wing cracks are reported as nonexistent, detectable, or critical. The history of a particular fleet indicates that 70% of the planes inspected have no wing cracks, 25% have detectable wing cracks, and 5% have critical wing cracks. Five planes are randomly selected. Find the probability that one has a critical crack, two have detectable cracks, and two have no cracks.

Express the integrand as a sum of partial fractions and evaluate the integrals.

$$\int \frac { d x } { x ^ { 2 } + 2 x }$$

Let $\mathcal{B}$ be a basis for $R^n$ and $T$ be an invertible linear operator on $R^n$. Prove that $[T^{-1}]_B=([T]_B)^{-1}$.

Complete each statement.

$$2 \frac { 2 } { 3 } \mathrm { ft } = 32 \ ?$$

Is the sequence geometric? If so, find the common ratio and the next two terms. $1,-2,4,-8, \dots$

The National Fire Incident Reporting Service stated that, among residential fires, 73% are in family homes, 20% are in apartments, and 7% are in other types of dwellings. If four residential fires are independently reported on a single day, what is the probability that two are in family homes, one is in an apartment, and one is in another type of dwelling?

Suppose you roll two fair, six-sided dice - one red and one green. Are the events "sum is 7" and "green die shows a 4" independent? Justify your answer.

An investor bought 100 shares of Omega common stock for $14,000. He held the stock for 9 years. For the first 4 years he received annual end-of-year dividends of$800. For the next 4 years he received annual dividends of $400. He received no dividend for the ninth year. At the end of the ninth year he sold his stock for$6000. What rate of return did he receive on his investment?

$$\begin{array} { l } { \text { Suppose a certain economy's consumption function is } } \\ \qquad { C ( x ) = 0.873 x ^ { 1.1 } + 20.34 } \\ { \text { where } C ( x ) \text { are measured in billions of dollars. Find } } \\ { \text { the marginal propensity to consume when } x = 10. } \end{array}$$

Your friend wants to prove indirectly that $\triangle A B C$ is equilateral. For a first step, he writes, "Assume temporarily that $\triangle A B C$ is scalene." What is wrong with your friend's statement? How can he correct himself?

List all possible rational roots or rational zeros.

$$8 x ^ { 3 } - 36 x ^ { 2 } + 46 x - 15 = 0$$

Z is the standard normal distribution. Find the indicated probabilities. $P(0 \leq Z \leq 1.5)$

Write each measure in radians. Express your answer in terms of π and as a decimal rounded to the nearest hundredth. 270°

Find the inverse of each function. Is the inverse a function? y = 5 - 2x