guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 30 x \( \frac{55}{100} \) = \( \frac{55 x 30}{100} \) = \( \frac{1650}{100} \) = 16 shots

The center makes 45% of his shots so he'll have to take:

shots made = shots taken x \( \frac{\text{% made}}{100} \)
shots taken = \( \frac{\text{shots taken}}{\frac{\text{% made}}{100}} \)

to make as many shots as the guard. Plugging in values for the center gives us:

center shots taken = \( \frac{16}{\frac{45}{100}} \) = 16 x \( \frac{100}{45} \) = \( \frac{16 x 100}{45} \) = \( \frac{1600}{45} \) = 36 shots

to make the same number of shots as the guard and thus score the same number of points.

To subtract these radicals together their radicands must be the same:

2\( \sqrt{18} \) - 6\( \sqrt{2} \)
2\( \sqrt{9 \times 2} \) - 6\( \sqrt{2} \)
2\( \sqrt{3^2 \times 2} \) - 6\( \sqrt{2} \)
(2)(3)\( \sqrt{2} \) - 6\( \sqrt{2} \)
6\( \sqrt{2} \) - 6\( \sqrt{2} \)

Now that the radicands are identical, you can subtract them:

Jennifer scored 76% on the test meaning she earned 76% of the possible points on the test. There were 400 possible points on the test so she earned 400 x 0.76 = 304 points. Each question is worth 4 points so she got \( \frac{304}{4} \) = 76 questions right.

First, solve for \( \left|x + 8\right| \):

\( \left|x + 8\right| \) - 9 = -6
\( \left|x + 8\right| \) = -6 + 9
\( \left|x + 8\right| \) = 3

The value inside the absolute value brackets can be either positive or negative so (x + 8) must equal + 3 or -3 for \( \left|x + 8\right| \) to equal 3:

So, x = -11 or x = -5.

33% of the water consumption is industrial use and 11% is personal use so (33% - 11%) = 22% more water is used for industrial purposes. 5,000 gallons are consumed daily so industry consumes \( \frac{22}{100} \) x 5,000 gallons = 1,100 gallons.