A ratio of 3:1 means that there are 3 home fans for every one visiting fan. So, of every 4 fans, 3 are home fans and \( \frac{3}{4} \) of every fan in the stadium is a home fan:

44,000 fans x \( \frac{3}{4} \) = \( \frac{132000}{4} \) = 33,000 fans.

To multiply terms with radicals, multiply the coefficients and radicands separately:

5\( \sqrt{3} \) x 4\( \sqrt{7} \)
(5 x 4)\( \sqrt{3 \times 7} \)
20\( \sqrt{21} \)

To fill a 9 gallon tank exactly halfway you'll need 4\(\frac{1}{2}\) gallons of fuel. Each fuel can holds 1\(\frac{1}{2}\) gallons so:

cans = \( \frac{4\frac{1}{2} \text{ gallons}}{1\frac{1}{2} \text{ gallons}} \) = 3

The equation for this sequence is:

a_n = a_n-1 + 4(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 + 4(6 - 1)
a₆ = 41 + 4(5)
a₆ = 61

First, solve for \( \left|a - 6\right| \):

\( \left|a - 6\right| \) + 9 = -5
\( \left|a - 6\right| \) = -5 - 9
\( \left|a - 6\right| \) = -14

The value inside the absolute value brackets can be either positive or negative so (a - 6) must equal - 14 or --14 for \( \left|a - 6\right| \) to equal -14:

So, a = 20 or a = -8.