Find out if the sentence below is incomplete. Then, rewrite the sentence fragment as a complete sentence.

Hasten to the hotel---find it very much crowded.

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.

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

Choose the word or phrase that is closest in meaning to the word in capital letters.

DEHYDRATE
(A) dry out
(B) forget
(C) spoil
(D) care for

Write an equivalent expression by factoring out the greatest common factor.

$$15 m^4 n+30 m^5 n^2+25 m^3 n^3$$

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.

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

$$9 x^2-12 x+4$$

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

$$9 x^2-12 x+4$$

Write out the form of the partial fraction decomposition of :

$$\frac{3 x-1}{(x-3)(x+4)}$$

(Do not find the numerical values of the coefficients.)

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

$$16 x^2-40 x+25$$

The volume of water in a tank t min after it starts draining is $V(t)=350(20-t)^{2} \mathrm{L}$.

How fast is the water draining out after 5 min? after 15 min?

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 $2010$, 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.

The speed, s, in metres per second, of water flowing out of a hole near the bottom of a tank relates to the height, h, in metres, of the water above the hole by the formula $s=\sqrt{2gh}$ . In the formula, g represents the acceleration due to gravity, 9.8 m/$s^2$. At what height is the water flowing out a speed of 9 m/s?