Diane scored 79% on the test meaning she earned 79% of the possible points on the test. There were 270 possible points on the test so she earned 270 x 0.79 = 213 points. Each question is worth 3 points so she got \( \frac{213}{3} \) = 71 questions right.

52% of the water consumption is industrial use and 35% is personal use so (52% - 35%) = 17% more water is used for industrial purposes. 40,000 gallons are consumed daily so industry consumes \( \frac{17}{100} \) x 40,000 gallons = 6,800 gallons.

You have 3 out of the total of 50 raffle tickets sold so you have a (\( \frac{3}{50} \)) x 100 = \( \frac{3 \times 100}{50} \) = \( \frac{300}{50} \) = 7% chance to win the raffle.

To take the square root of a fraction, break the fraction into two separate roots then calculate the square root of the numerator and denominator separately:

\( \sqrt{\frac{81}{16}} \)
\( \frac{\sqrt{81}}{\sqrt{16}} \)
\( \frac{\sqrt{9^2}}{\sqrt{4^2}} \)
\( \frac{9}{4} \)
2\(\frac{1}{4}\)

To multiply terms with radicals, multiply the coefficients and radicands separately:

6\( \sqrt{9} \) x 3\( \sqrt{7} \)
(6 x 3)\( \sqrt{9 \times 7} \)
18\( \sqrt{63} \)

Now we need to simplify the radical:

18\( \sqrt{63} \)
18\( \sqrt{7 \times 9} \)
18\( \sqrt{7 \times 3^2} \)
(18)(3)\( \sqrt{7} \)
54\( \sqrt{7} \)