Add parentheses and brackets where they are needed in the following sentences.

Afterward Nigel said, "He Newfie seemed to come out of nowhere!"

Carry out the differentiation.
$\displaystyle \frac{d}{dx}\left( \int_0^{x^2} \frac{dt}{1+t^2}\right)$.

For each of the following sentences, write the correct form of the italicized verb in parentheses.

She (fing) open the door and raced out of the house.

A manufacturer of lightbulbs wants to produce bulbs that last about 700 hours but, of course, some bulbs burn out faster than others. Let $F ( t )$ be the fraction of the company's bulbs that burn out before t hours, so $F ( t )$ always lies between 0 and 1. What is the meaning of the derivative $r ( t ) = F' ( t )$ ?

Carry out the differentiation.
$\displaystyle \frac{d}{dx}\left(\int_x^{x^2} \frac{dt}{1+t^2}\right)$.

Factor each perfect square trinomial. It may be necessary to factor out a common factor first.

$$32 x^2-48 x+18$$

Mark each of the following events as independent or dependent. A woman accidentally throw 4 used batteries in with her 12 new batteries. She pulls out a battery, plugs it into her remote, and realizes it was one of the used ones. She throws it away and pulls out another battery. What is the probability this one will also be a used one?

Write out and evaluate each sum.

$$\sum_{k=0}^5\left(k^2-2 k+3\right)$$

Complete the sentence in a way that shows you understand the meaning of the italicized vocabulary word.

I will not go out to dinner with you; ergo,...

In $2010$, there were $40$ million people over $65$ years of age out of a U.S. population of $310$ million. By $2050$, it is estimated that there will be $82$ million people over $65$ years of age out of a U.S. population of $439$ million. Would your chances of meeting a person over $65$ at random be greater in $2010$ or $2050$? Explain.

How would the income effect of a price change be demonstrated by a $10 reduction in the price of tickets to a concert that resulted in a sell-out crowd?

Show that a directed multigraph having no isolated vertices has an Euler path but not an Euler circuit if and only if the graph is weakly connected and the in-degree and out-degree of each vertex are equal for all but two vertices, one that has in-degree one larger than its outdegree and the other that has out-degree one larger than its in-degree.

In $\text{Fig. 29–20}a$, what are the new values for $A_\text{V}$ and $V_\text{out}$ if $R_\text{L}$ is removed?

After a collision with a power pole, you are trapped in your car, with a high-voltage line (with frayed insulation) in contact with the hood of the car. If you must get out before help arrives, is it safer to step out of the car one foot at a time or to jump with both feet leaving the car at the same time? Explain your reasoning.