The equation for this sequence is:

a_n = a_n-1 + 9

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 + 9
a₆ = 37 + 9
a₆ = 46

If a single cook can bake 3 large cakes per hour and the kitchen is available for 4 hours, a single cook can bake 3 x 4 = 12 large cakes during that time. 24 large cakes are needed for the party so \( \frac{24}{12} \) = 2 cooks are needed to bake the required number of large cakes.

If a single cook can bake 18 small cakes per hour and the kitchen is available for 4 hours, a single cook can bake 18 x 4 = 72 small cakes during that time. 320 small cakes are needed for the party so \( \frac{320}{72} \) = 4\(\frac{4}{9}\) 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 2 + 5 = 7 cooks.

Calculate the number of vans needed by dividing the number of people that need transported by the capacity of one van:

vans = \( \frac{90}{11} \) = 8\(\frac{2}{11}\)

So, it will take 8 full vans and one partially full van to transport the entire team making a total of 9 vans.

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

2 + (2 + 3) ÷ 3 x 4 - 4²
P: 2 + (5) ÷ 3 x 4 - 4²
E: 2 + 5 ÷ 3 x 4 - 16
MD: 2 + \( \frac{5}{3} \) x 4 - 16
MD: 2 + \( \frac{20}{3} \) - 16
AS: \( \frac{6}{3} \) + \( \frac{20}{3} \) - 16
AS: \( \frac{26}{3} \) - 16
AS: \( \frac{26 - 48}{3} \)
\( \frac{-22}{3} \)
-7\(\frac{1}{3}\)

A rational number (or fraction) is represented as a ratio between two integers, a and b, and has the form \({a \over b}\) where a is the numerator and b is the denominator. An improper fraction (\({5 \over 3} \)) has a numerator with a greater absolute value than the denominator and can be converted into a mixed number (\(1 {2 \over 3} \)) which has a whole number part and a fractional part.