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

vans = \( \frac{60}{16} \) = 3\(\frac{3}{4}\)

So, it will take 3 full vans and one partially full van to transport the entire team making a total of 4 vans.

First, solve for \( \left|a + 0\right| \):

\( \left|a + 0\right| \) - 9 = 0
\( \left|a + 0\right| \) = 0 + 9
\( \left|a + 0\right| \) = 9

The value inside the absolute value brackets can be either positive or negative so (a + 0) must equal + 9 or -9 for \( \left|a + 0\right| \) to equal 9:

So, a = -9 or a = 9.

The ratio of football cards to baseball cards is 7:2 and the ratio of baseball cards to basketball cards is 7:1. 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 49:14 and the ratio of baseball cards to basketball cards as 14:2. So, the ratio of football cards to basketball cards is football:baseball, baseball:basketball or 49:14, 14:2 which reduces to 49:2.

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

Solving for distance:

distance = \( \text{speed} \times \text{time} \)
distance = \( 20mph \times 5h \)
100 miles

A factorial is the product of an integer and all the positive integers below it. To solve a fraction featuring factorials, expand the factorials and cancel out like numbers:

\( \frac{5!}{6!} \)
\( \frac{5 \times 4 \times 3 \times 2 \times 1}{6 \times 5 \times 4 \times 3 \times 2 \times 1} \)
\( \frac{1}{6} \)
\( \frac{1}{6} \)