To add or subtract terms with exponents, both the base and the exponent must be the same. In this case they are so subtract the coefficients and retain the base and exponent:

-8c⁶ - 8c⁶
(-8 - 8)c⁶
-16c⁶

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

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

So, in an average hour, the machine will produce 9 - 0.45 = 8.55 error free parts.

The machine ran for 24 - 8 = 16 hours yesterday so you would expect that 16 x 8.55 = 136.8 error free parts were produced yesterday.

51% of the water consumption is industrial use and 30% is personal use so (51% - 30%) = 21% more water is used for industrial purposes. 40,000 gallons are consumed daily so industry consumes \( \frac{21}{100} \) x 40,000 gallons = 8,400 gallons.

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 300 meters to kilometers, divide the distance by 1000 to get 0.3km then add the remaining distances:

total distance = swim + bike + run
total distance = 0.3km + 20.5km + 3.7km
total distance = 24.5km

To subtract these radicals together their radicands must be the same:

7\( \sqrt{125} \) - 8\( \sqrt{5} \)
7\( \sqrt{25 \times 5} \) - 8\( \sqrt{5} \)
7\( \sqrt{5^2 \times 5} \) - 8\( \sqrt{5} \)
(7)(5)\( \sqrt{5} \) - 8\( \sqrt{5} \)
35\( \sqrt{5} \) - 8\( \sqrt{5} \)

Now that the radicands are identical, you can subtract them: