To divide terms with radicals, divide the coefficients and radicands separately:

\( \frac{35\sqrt{56}}{5\sqrt{8}} \)
\( \frac{35}{5} \) \( \sqrt{\frac{56}{8}} \)
7 \( \sqrt{7} \)

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

\( \frac{2}{100} \) x 9 = \( \frac{2 \times 9}{100} \) = \( \frac{18}{100} \) = 0.18 errors per hour

So, in an average hour, the machine will produce 9 - 0.18 = 8.82 error free parts.

The machine ran for 24 - 7 = 17 hours yesterday so you would expect that 17 x 8.82 = 149.9 error free parts were produced yesterday.

To fill a 15 gallon tank exactly halfway you'll need 7\(\frac{1}{2}\) gallons of fuel. Each fuel can holds 1\(\frac{1}{2}\) gallons so:

cans = \( \frac{7\frac{1}{2} \text{ gallons}}{1\frac{1}{2} \text{ gallons}} \) = 5

To multiply terms with radicals, multiply the coefficients and radicands separately:

7\( \sqrt{8} \) x 3\( \sqrt{6} \)
(7 x 3)\( \sqrt{8 \times 6} \)
21\( \sqrt{48} \)

Now we need to simplify the radical:

21\( \sqrt{48} \)
21\( \sqrt{3 \times 16} \)
21\( \sqrt{3 \times 4^2} \)
(21)(4)\( \sqrt{3} \)
84\( \sqrt{3} \)

If the tiger has consumed 54 pounds of food in 6 days that's \( \frac{54}{6} \) = 9 pounds of food per day. The tiger needs to consume 90 - 54 = 36 more pounds of food to reach 90 pounds total. At 9 pounds of food per day that's \( \frac{36}{9} \) = 4 more days.