The commutative property states that, when adding or multiplying numbers, the order in which they're added or multiplied does not matter. For example, 3 + 4 and 4 + 3 give the same result, as do 3 x 4 and 4 x 3.

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 400 meters to kilometers, divide the distance by 1000 to get 0.4km then add the remaining distances:

total distance = swim + bike + run
total distance = 0.4km + 40.5km + 5.9km
total distance = 46.8km

April scored 87% on the test meaning she earned 87% of the possible points on the test. There were 240 possible points on the test so she earned 240 x 0.87 = 208 points. Each question is worth 4 points so she got \( \frac{208}{4} \) = 52 questions right.

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

4\( \sqrt{6} \) x 4\( \sqrt{8} \)
(4 x 4)\( \sqrt{6 \times 8} \)
16\( \sqrt{48} \)

Now we need to simplify the radical:

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

If a single cook can bake 3 large cakes per hour and the kitchen is available for 3 hours, a single cook can bake 3 x 3 = 9 large cakes during that time. 33 large cakes are needed for the party so \( \frac{33}{9} \) = 3\(\frac{2}{3}\) cooks are needed to bake the required number of large cakes.

If a single cook can bake 12 small cakes per hour and the kitchen is available for 3 hours, a single cook can bake 12 x 3 = 36 small cakes during that time. 500 small cakes are needed for the party so \( \frac{500}{36} \) = 13\(\frac{8}{9}\) 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 4 + 14 = 18 cooks.