The factors of 20 are [1, 2, 4, 5, 10, 20] and the factors of 64 are [1, 2, 4, 8, 16, 32, 64]. They share 3 factors [1, 2, 4] making 4 the greatest factor 20 and 64 have in common.

The hourly error rate for this machine is the error rate in parts per 100 multiplied by the number of parts produced per hour:

\( \frac{9}{100} \) x 5 = \( \frac{9 \times 5}{100} \) = \( \frac{45}{100} \) = 0.45 errors per hour

So, in an average hour, the machine will produce 5 - 0.45 = 4.55 error free parts.

The machine ran for 24 - 2 = 22 hours yesterday so you would expect that 22 x 4.55 = 100.1 error free parts were produced yesterday.

38% of the water consumption is industrial use and 21% is personal use so (38% - 21%) = 17% more water is used for industrial purposes. 10,000 gallons are consumed daily so industry consumes \( \frac{17}{100} \) x 10,000 gallons = 1,700 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:

\( \frac{5y^5}{6y^4} \)
\( \frac{5}{6} \) y^{(5 - 4)}
\(\frac{5}{6}\)y

First, solve for \( \left|x + 5\right| \):

\( \left|x + 5\right| \) + 3 = 4
\( \left|x + 5\right| \) = 4 - 3
\( \left|x + 5\right| \) = 1

The value inside the absolute value brackets can be either positive or negative so (x + 5) must equal + 1 or -1 for \( \left|x + 5\right| \) to equal 1:

So, x = -6 or x = -4.