Remember to use the largest common factor and to check by multiplying. Factor out a negative factor if the first coefficient is negative.

$$5 x^4-x^2$$

Imagine that you are a scientist. You are studying an area that gets about 100 cm of rain each year. The average summer temperatures are near 30°C. What biome are you in? What plants and animals are likely to live in this area? If you stayed in this area for the winter, what kinds of preparations might you need to make?

Give the oxidation number of manganese in the following:
(a) $\mathrm{MnO}_4{ }^{2-}$

On the line provided, rewrite the following sentence to correct the misplaced or dangling modifier. Example 1. Ms. Nguyen will finish grading the projects that we turned in during spring break. $\underline{\text{\color{#c34632}During spring break, Ms. Nguyen will finish grading the projects that we turned in.}}$

While waiting for the bus in the rain, all the traffic lights went out at the intersection.

Contrast the compounds angiotensinogen and angiotensin in terms of enzyme activity.

Mr. Brown's present salary is $36,500. He is getting an increase of 7% in his salary next year. What will the new salary be?

Using the formula for the volume of a segment of a sphere, it can be shown that the depth x to which a floating sphere of radius sinks in water is a root of the equation $x^{3}-3 r x^{2}+4 r^{3} s=0$ where s is the specific gravity of the sphere. Suppose a wooden sphere of radius 0.5 m has specific gravity 0.75. Calculate, to four-decimal-place accuracy, the depth to which the sphere will sink.

For the following examples, tell whether there is positive association, negative association, or no association. a. The number of inches of rain per hour and the height of water in a reservoir. b. The amount of food a person eats and how many pets he or she has. c. The height of a tree and the amount of nutrients it gets. d. The number of hours spent hiking in the mountains and the amount of water left in your water bottle .

What is the least common multiple of $10$ and $16$?

You need to do a series of calculations involving the motion of an object. Another student hands you predefined parameters of the problem; you see that she has defined $x_i=-53.4 \mathrm{~m}$ and $x_f=71.6 \mathrm{~m}$. How might you redefine the problem so as to make it easier to solve?

Remember to use the largest common factor and to check by multiplying. Factor out a negative factor if the first coefficient is negative.

$$2 x^2+2 x-8$$

A deck of 52 cards is mixed well, and 5 cards are dealt. a. It can be shown that (disregarding the order in which the cards are dealt) there are 2,598,960 possible five-card hand s, of which only 1287 are hands consisting entirely of spades. What is the probability that a hand will consist entirely of spades? What is the probability that a hand will consist entirely of a single suit? b. It can be shown that exactly 63,206 hands contain only spades and clubs, with both suits represented. What is the probability that a hand consists entirely of spades and clubs with both suits represented? c. Using the result of Part (b), what is the probability that a hand contains cards from exactly two suits?

Remember to use the largest common factor and to check by multiplying. Factor out a negative factor if the first coefficient is negative.

$$x^3+6 x^2$$

Give the oxidation number of nitrogen in the following:
(d) $\mathrm{HNO}_2$