Average speed in miles per hour is the number of miles traveled divided by the number of hours:

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

2 + (3 + 4) ÷ 4 x 3 - 2²
P: 2 + (7) ÷ 4 x 3 - 2²
E: 2 + 7 ÷ 4 x 3 - 4
MD: 2 + \( \frac{7}{4} \) x 3 - 4
MD: 2 + \( \frac{21}{4} \) - 4
AS: \( \frac{8}{4} \) + \( \frac{21}{4} \) - 4
AS: \( \frac{29}{4} \) - 4
AS: \( \frac{29 - 16}{4} \)
\( \frac{13}{4} \)
3\(\frac{1}{4}\)

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

vans = \( \frac{65}{15} \) = 4\(\frac{1}{3}\)

So, it will take 4 full vans and one partially full van to transport the entire team making a total of 5 vans.

The distributive property for division helps in solving expressions like \({b + c \over a}\). It specifies that the result of dividing a fraction with multiple terms in the numerator and one term in the denominator can be obtained by dividing each term individually and then totaling the results: \({b + c \over a} = {b \over a} + {c \over a}\). For example, \({a^3 + 6a^2 \over a^2} = {a^3 \over a^2} + {6a^2 \over a^2} = a + 6\).

The ratio of football cards to baseball cards is 9:2 and the ratio of baseball cards to basketball cards is 9:1. To solve this problem, we need the baseball card side of each ratio to be equal so we need to rewrite the ratios in terms of a common number of baseball cards. (Think of this like finding the common denominator when adding fractions.) The ratio of football to baseball cards can also be written as 81:18 and the ratio of baseball cards to basketball cards as 18:2. So, the ratio of football cards to basketball cards is football:baseball, baseball:basketball or 81:18, 18:2 which reduces to 81:2.