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:

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

Jennifer scored 84% on the test meaning she earned 84% of the possible points on the test. There were 270 possible points on the test so she earned 270 x 0.84 = 228 points. Each question is worth 3 points so she got \( \frac{228}{3} \) = 76 questions right.

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

4 + (3 + 4) ÷ 3 x 3 - 5²
P: 4 + (7) ÷ 3 x 3 - 5²
E: 4 + 7 ÷ 3 x 3 - 25
MD: 4 + \( \frac{7}{3} \) x 3 - 25
MD: 4 + \( \frac{21}{3} \) - 25
AS: \( \frac{12}{3} \) + \( \frac{21}{3} \) - 25
AS: \( \frac{33}{3} \) - 25
AS: \( \frac{33 - 75}{3} \)
\( \frac{-42}{3} \)
-14

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

You have 24 out of the total of 350 raffle tickets sold so you have a (\( \frac{24}{350} \)) x 100 = \( \frac{24 \times 100}{350} \) = \( \frac{2400}{350} \) = 7% chance to win the raffle.