The first few multiples of 3 are [3, 6, 9, 12, 15, 18, 21, 24, 27, 30] and the first few multiples of 5 are [5, 10, 15, 20, 25, 30, 35, 40, 45, 50]. The first few multiples they share are [15, 30, 45, 60, 75] making 15 the smallest multiple 3 and 5 have in common.

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

vans = \( \frac{79}{12} \) = 6\(\frac{7}{12}\)

So, it will take 6 full vans and one partially full van to transport the entire team making a total of 7 vans.

To add or subtract terms with exponents, both the base and the exponent must be the same. In this case they are so add the coefficients and retain the base and exponent:

-3c⁶ + 8c⁶
(-3 + 8)c⁶
5c⁶

A ratio of 2:1 means that there are 2 home fans for every one visiting fan. So, of every 3 fans, 2 are home fans and \( \frac{2}{3} \) of every fan in the stadium is a home fan:

44,000 fans x \( \frac{2}{3} \) = \( \frac{88000}{3} \) = 29,333 fans.

The equation for this sequence is:

a_n = a_n-1 + 3(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 + 3(6 - 1)
a₆ = 31 + 3(5)
a₆ = 46