If a single cook can bake 2 large cakes per hour and the kitchen is available for 2 hours, a single cook can bake 2 x 2 = 4 large cakes during that time. 23 large cakes are needed for the party so \( \frac{23}{4} \) = 5\(\frac{3}{4}\) cooks are needed to bake the required number of large cakes.

If a single cook can bake 10 small cakes per hour and the kitchen is available for 2 hours, a single cook can bake 10 x 2 = 20 small cakes during that time. 400 small cakes are needed for the party so \( \frac{400}{20} \) = 20 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 6 + 20 = 26 cooks.

To add or subtract terms with exponents, both the base and the exponent must be the same. In this case they are so subtract the coefficients and retain the base and exponent:

5z⁵ - 2z⁵
(5 - 2)z⁵
3z⁵

The area of a rectangle is width (w) x height (h). In this problem we know that the rectangle is twice as long as it is wide so h = 2w. The perimeter of a rectangle is 2w + 2h and we know that the perimeter of this rectangle is 6 meters so the equation becomes: 2w + 2h = 6.

Putting these two equations together and solving for width (w):

2w + 2h = 6
w + h = \( \frac{6}{2} \)
w + h = 3
w = 3 - h

From the question we know that h = 2w so substituting 2w for h gives us:

w = 3 - 2w
3w = 3
w = \( \frac{3}{3} \)
w = 1

Since h = 2w that makes h = (2 x 1) = 2 and the area = h x w = 1 x 2 = 2 m²

There are 3 3-passenger taxis available so that's 3 x 3 = 9 total seats. There are 12 people needing transportation leaving 12 - 9 = 3 who will have to find other transportation.

To simplify a radical, factor out the perfect squares:

\( \sqrt{112} \)
\( \sqrt{16 \times 7} \)
\( \sqrt{4^2 \times 7} \)
4\( \sqrt{7} \)