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 100 meters to kilometers, divide the distance by 1000 to get 0.1km then add the remaining distances:

total distance = swim + bike + run
total distance = 0.1km + 30.6km + 8.0km
total distance = 38.7km

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

4\( \sqrt{7} \) x 3\( \sqrt{7} \)
(4 x 3)\( \sqrt{7 \times 7} \)
12\( \sqrt{49} \)

Now we need to simplify the radical:

12\( \sqrt{49} \)
12\( \sqrt{7^2} \)
(12)(7)
84

If a single cook can bake 5 large cakes per hour and the kitchen is available for 2 hours, a single cook can bake 5 x 2 = 10 large cakes during that time. 28 large cakes are needed for the party so \( \frac{28}{10} \) = 2\(\frac{4}{5}\) cooks are needed to bake the required number of large cakes.

If a single cook can bake 14 small cakes per hour and the kitchen is available for 2 hours, a single cook can bake 14 x 2 = 28 small cakes during that time. 440 small cakes are needed for the party so \( \frac{440}{28} \) = 15\(\frac{5}{7}\) cooks are needed to bake the required number of small cakes.

Because you can't employ a fractional cook, round the number of cooks needed for each type of cake up to the next whole number resulting in 3 + 16 = 19 cooks.

Use PEMDAS (Parentheses, Exponents, Multipy/Divide, Add/Subtract):

4 + (5 + 5) ÷ 2 x 4 - 3²
P: 4 + (10) ÷ 2 x 4 - 3²
E: 4 + 10 ÷ 2 x 4 - 9
MD: 4 + \( \frac{10}{2} \) x 4 - 9
MD: 4 + \( \frac{40}{2} \) - 9
AS: \( \frac{8}{2} \) + \( \frac{40}{2} \) - 9
AS: \( \frac{48}{2} \) - 9
AS: \( \frac{48 - 18}{2} \)
\( \frac{30}{2} \)
15

To simplify a radical, factor out the perfect squares:

\( \sqrt{63} \)
\( \sqrt{9 \times 7} \)
\( \sqrt{3^2 \times 7} \)
3\( \sqrt{7} \)