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:

32,000 fans x \( \frac{3}{4} \) = \( \frac{96000}{4} \) = 24,000 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

guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 30 x \( \frac{60}{100} \) = \( \frac{60 x 30}{100} \) = \( \frac{1800}{100} \) = 18 shots

The center makes 40% of his shots so he'll have to take:

shots made = shots taken x \( \frac{\text{% made}}{100} \)
shots taken = \( \frac{\text{shots taken}}{\frac{\text{% made}}{100}} \)

to make as many shots as the guard. Plugging in values for the center gives us:

center shots taken = \( \frac{18}{\frac{40}{100}} \) = 18 x \( \frac{100}{40} \) = \( \frac{18 x 100}{40} \) = \( \frac{1800}{40} \) = 45 shots

to make the same number of shots as the guard and thus score the same number of points.

If the tiger has consumed 121 pounds of food in 11 days that's \( \frac{121}{11} \) = 11 pounds of food per day. The tiger needs to consume 165 - 121 = 44 more pounds of food to reach 165 pounds total. At 11 pounds of food per day that's \( \frac{44}{11} \) = 4 more days.

To find the average of these 4 numbers add them together then divide by 4:

\( \frac{10 + 8 + 11 + 7}{4} \) = \( \frac{36}{4} \) = 9