If a single cook can bake 4 large cakes per hour and the kitchen is available for 4 hours, a single cook can bake 4 x 4 = 16 large cakes during that time. 28 large cakes are needed for the party so \( \frac{28}{16} \) = 1\(\frac{3}{4}\) cooks are needed to bake the required number of large cakes.

If a single cook can bake 11 small cakes per hour and the kitchen is available for 4 hours, a single cook can bake 11 x 4 = 44 small cakes during that time. 110 small cakes are needed for the party so \( \frac{110}{44} \) = 2\(\frac{1}{2}\) 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 2 + 3 = 5 cooks.

If the tiger has consumed 30 pounds of food in 6 days that's \( \frac{30}{6} \) = 5 pounds of food per day. The tiger needs to consume 55 - 30 = 25 more pounds of food to reach 55 pounds total. At 5 pounds of food per day that's \( \frac{25}{5} \) = 5 more days.

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 48 meters so the equation becomes: 2w + 2h = 48.

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

2w + 2h = 48
w + h = \( \frac{48}{2} \)
w + h = 24
w = 24 - h

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

w = 24 - 2w
3w = 24
w = \( \frac{24}{3} \)
w = 8

Since h = 2w that makes h = (2 x 8) = 16 and the area = h x w = 8 x 16 = 128 m²

To simplify a radical, factor out the perfect squares:

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

The factors of a number are all positive integers that divide evenly into the number. The factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24.