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:

\( \frac{2!}{5!} \)
\( \frac{2 \times 1}{5 \times 4 \times 3 \times 2 \times 1} \)
\( \frac{1}{5 \times 4 \times 3} \)
\( \frac{1}{60} \)

First, solve for \( \left|y - 5\right| \):

\( \left|y - 5\right| \) + 9 = 5
\( \left|y - 5\right| \) = 5 - 9
\( \left|y - 5\right| \) = -4

The value inside the absolute value brackets can be either positive or negative so (y - 5) must equal - 4 or --4 for \( \left|y - 5\right| \) to equal -4:

So, y = 9 or y = 1.

By buying two shirts, Ezra will save $14 x \( \frac{45}{100} \) = \( \frac{$14 x 45}{100} \) = \( \frac{$630}{100} \) = $6.30 on the second shirt.

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

If the tiger has consumed 50 pounds of food in 5 days that's \( \frac{50}{5} \) = 10 pounds of food per day. The tiger needs to consume 90 - 50 = 40 more pounds of food to reach 90 pounds total. At 10 pounds of food per day that's \( \frac{40}{10} \) = 4 more days.