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 100 meters to kilometers, divide the distance by 1000 to get 0.1km then add the remaining distances:

total distance = swim + bike + run
total distance = 0.1km + 40.6km + 14.4km
total distance = 55.1km

The distributive property for multiplication helps in solving expressions like a(b + c). It specifies that the result of multiplying one number by the sum or difference of two numbers can be obtained by multiplying each number individually and then totaling the results: a(b + c) = ab + ac. For example, 4(10-5) = (4 x 10) - (4 x 5) = 40 - 20 = 20.

31% of the water consumption is industrial use and 19% is personal use so (31% - 19%) = 12% more water is used for industrial purposes. 45,000 gallons are consumed daily so industry consumes \( \frac{12}{100} \) x 45,000 gallons = 5,400 gallons.

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:

\( \sqrt{\frac{25}{16}} \)
\( \frac{\sqrt{25}}{\sqrt{16}} \)
\( \frac{\sqrt{5^2}}{\sqrt{4^2}} \)
\( \frac{5}{4} \)
1\(\frac{1}{4}\)

A prime number is an integer greater than 1 that has no factors other than 1 and itself. Examples of prime numbers include 2, 3, 5, 7, and 11.