To add these fractions, first find the lowest common multiple of their denominators. The first few multiples of 6 are [6, 12, 18, 24, 30, 36, 42, 48, 54, 60] and the first few multiples of 12 are [12, 24, 36, 48, 60, 72, 84, 96]. The first few multiples they share are [12, 24, 36, 48, 60] making 12 the smallest multiple 6 and 12 share.

Next, convert the fractions so each denominator equals the lowest common multiple:

\( \frac{7 x 2}{6 x 2} \) + \( \frac{3 x 1}{12 x 1} \)

\( \frac{14}{12} \) + \( \frac{3}{12} \)

Now, because the fractions share a common denominator, you can add them:

\( \frac{14 + 3}{12} \) = \( \frac{17}{12} \) = 1\(\frac{5}{12}\)

47% of the water consumption is industrial use and 16% is personal use so (47% - 16%) = 31% more water is used for industrial purposes. 25,000 gallons are consumed daily so industry consumes \( \frac{31}{100} \) x 25,000 gallons = 7,750 gallons.

To divide terms with exponents, the base of both exponents must be the same. In this case they are so divide the coefficients and subtract the exponents:

\( \frac{-7y^5}{3y^2} \)
\( \frac{-7}{3} \) y^{(5 - 2)}
-2\(\frac{1}{3}\)y³

The equation for this sequence is:

a_n = a_n-1 + 2(n - 1)

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 + 2(6 - 1)
a₆ = 21 + 2(5)
a₆ = 31

To add these distances, they must share the same unit so first you need to first convert the swim distance from meters (m) to kilometers (km) before adding it to the bike and run distances which are already in km. To convert 500 meters to kilometers, divide the distance by 1000 to get 0.5km then add the remaining distances:

total distance = swim + bike + run
total distance = 0.5km + 50.8km + 5.1km
total distance = 56.4km