The equation for this sequence is:

a_n = a_n-1 + 8

where n is the term's order in the sequence, a_n is the value of the term, and a_n-1 is the value of the term before a_n. This makes the next number:

a₆ = a₅ + 8
a₆ = 33 + 8
a₆ = 41

Diane scored 77% on the test meaning she earned 77% of the possible points on the test. There were 60 possible points on the test so she earned 60 x 0.77 = 46 points. Each question is worth 2 points so she got \( \frac{46}{2} \) = 23 questions right.

The area of a circle is given by the formula A = πr² where r is the radius of the circle. The radius of a circle is its diameter divided by two so A = π(\( \frac{d}{2} \))². If the diameter of the logo increases by 70% the radius (and, consequently, the total area) increases by \( \frac{70\text{%}}{2} \) = 35%

67% of the water consumption is industrial use and 32% is personal use so (67% - 32%) = 35% more water is used for industrial purposes. 25,000 gallons are consumed daily so industry consumes \( \frac{35}{100} \) x 25,000 gallons = 8,750 gallons.

To multiply fractions, multiply the numerators together and then multiply the denominators together:

\( \frac{3}{9} \) x \( \frac{1}{6} \) = \( \frac{3 x 1}{9 x 6} \) = \( \frac{3}{54} \) = \(\frac{1}{18}\)