A ratio of 5:1 means that there are 5 home fans for every one visiting fan. So, of every 6 fans, 5 are home fans and \( \frac{5}{6} \) of every fan in the stadium is a home fan:

40,000 fans x \( \frac{5}{6} \) = \( \frac{200000}{6} \) = 33,333 fans.

The equation for this sequence is:

a_n = a_n-1 + 2

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 + 2
a₆ = 9 + 2
a₆ = 11

A number with an exponent (b^e) consists of a base (b) raised to a power (e). The exponent indicates the number of times that the base is multiplied by itself. A base with an exponent of 1 equals the base (b¹ = b) and a base with an exponent of 0 equals 1 ( (b⁰ = 1).

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

2 + (3 + 4) ÷ 3 x 4 - 3²
P: 2 + (7) ÷ 3 x 4 - 3²
E: 2 + 7 ÷ 3 x 4 - 9
MD: 2 + \( \frac{7}{3} \) x 4 - 9
MD: 2 + \( \frac{28}{3} \) - 9
AS: \( \frac{6}{3} \) + \( \frac{28}{3} \) - 9
AS: \( \frac{34}{3} \) - 9
AS: \( \frac{34 - 27}{3} \)
\( \frac{7}{3} \)
2\(\frac{1}{3}\)

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.