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

5\( \sqrt{8} \) + 3\( \sqrt{2} \)
5\( \sqrt{4 \times 2} \) + 3\( \sqrt{2} \)
5\( \sqrt{2^2 \times 2} \) + 3\( \sqrt{2} \)
(5)(2)\( \sqrt{2} \) + 3\( \sqrt{2} \)
10\( \sqrt{2} \) + 3\( \sqrt{2} \)

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

If the tiger has consumed 70 pounds of food in 5 days that's \( \frac{70}{5} \) = 14 pounds of food per day. The tiger needs to consume 140 - 70 = 70 more pounds of food to reach 140 pounds total. At 14 pounds of food per day that's \( \frac{70}{14} \) = 5 more days.

The area of a circle is given by the formula A = πr² where r is the radius of the circle. The radius of a circle is its diameter divided by two so A = π(\( \frac{d}{2} \))². If the diameter of the logo increases by 55% the radius (and, consequently, the total area) increases by \( \frac{55\text{%}}{2} \) = 27\(\frac{1}{2}\)%

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 - 6 = 18 hours yesterday so you would expect that 18 x 4.75 = 85.5 error free parts were produced yesterday.

To find the average of these 4 numbers add them together then divide by 4:

\( \frac{7 + 5 + 8 + 4}{4} \) = \( \frac{24}{4} \) = 6