If a single cook can bake 2 large cakes per hour and the kitchen is available for 4 hours, a single cook can bake 2 x 4 = 8 large cakes during that time. 20 large cakes are needed for the party so \( \frac{20}{8} \) = 2\(\frac{1}{2}\) cooks are needed to bake the required number of large cakes.

If a single cook can bake 19 small cakes per hour and the kitchen is available for 4 hours, a single cook can bake 19 x 4 = 76 small cakes during that time. 340 small cakes are needed for the party so \( \frac{340}{76} \) = 4\(\frac{9}{19}\) 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 + 5 = 8 cooks.

1

The equation for this sequence is:

a_n = a_n-1 + 4(n - 1)

where n is the term's order in the sequence, a_n is the value of the term, and a_n-1 is the value of the term before a_n. This makes the next number:

a₆ = a₅ + 4(6 - 1)
a₆ = 41 + 4(5)
a₆ = 61

To take the square root of a fraction, break the fraction into two separate roots then calculate the square root of the numerator and denominator separately:

\( \sqrt{\frac{9}{36}} \)
\( \frac{\sqrt{9}}{\sqrt{36}} \)
\( \frac{\sqrt{3^2}}{\sqrt{6^2}} \)
\(\frac{1}{2}\)

To add these fractions, first find the lowest common multiple of their denominators. The first few multiples of 6 are [6, 12, 18, 24, 30, 36, 42, 48, 54, 60] and the first few multiples of 12 are [12, 24, 36, 48, 60, 72, 84, 96]. The first few multiples they share are [12, 24, 36, 48, 60] making 12 the smallest multiple 6 and 12 share.

Next, convert the fractions so each denominator equals the lowest common multiple:

\( \frac{9 x 2}{6 x 2} \) + \( \frac{2 x 1}{12 x 1} \)

\( \frac{18}{12} \) + \( \frac{2}{12} \)

Now, because the fractions share a common denominator, you can add them:

\( \frac{18 + 2}{12} \) = \( \frac{20}{12} \) = 1\(\frac{2}{3}\)