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:

\( \frac{-5y^9}{7y^3} \)
\( \frac{-5}{7} \) y^{(9 - 3)}
-\(\frac{5}{7}\)y⁶

There are 4 4-passenger taxis available so that's 4 x 4 = 16 total seats. There are 21 people needing transportation leaving 21 - 16 = 5 who will have to find other transportation.

The ratio of football cards to baseball cards is 5:2 and the ratio of baseball cards to basketball cards is 5:1. To solve this problem, we need the baseball card side of each ratio to be equal so we need to rewrite the ratios in terms of a common number of baseball cards. (Think of this like finding the common denominator when adding fractions.) The ratio of football to baseball cards can also be written as 25:10 and the ratio of baseball cards to basketball cards as 10:2. So, the ratio of football cards to basketball cards is football:baseball, baseball:basketball or 25:10, 10:2 which reduces to 25:2.

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 5 = \( \frac{5 \times 5}{100} \) = \( \frac{25}{100} \) = 0.25 errors per hour

So, in an average hour, the machine will produce 5 - 0.25 = 4.75 error free parts.

The machine ran for 24 - 2 = 22 hours yesterday so you would expect that 22 x 4.75 = 104.5 error free parts were produced yesterday.

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

7\( \sqrt{48} \) + 6\( \sqrt{3} \)
7\( \sqrt{16 \times 3} \) + 6\( \sqrt{3} \)
7\( \sqrt{4^2 \times 3} \) + 6\( \sqrt{3} \)
(7)(4)\( \sqrt{3} \) + 6\( \sqrt{3} \)
28\( \sqrt{3} \) + 6\( \sqrt{3} \)

Now that the radicands are identical, you can add them together: