You have 9 out of the total of 450 raffle tickets sold so you have a (\( \frac{9}{450} \)) x 100 = \( \frac{9 \times 100}{450} \) = \( \frac{900}{450} \) = 2% chance to win the raffle.

To multiply terms with exponents, the base of both exponents must be the same. In this case they are so multiply the coefficients and add the exponents:

8a⁷ x 4a⁴
(8 x 4)a^{(7 + 4)}
32a¹¹

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

The distributive property for division helps in solving expressions like \({b + c \over a}\). It specifies that the result of dividing a fraction with multiple terms in the numerator and one term in the denominator can be obtained by dividing each term individually and then totaling the results: \({b + c \over a} = {b \over a} + {c \over a}\). For example, \({a^3 + 6a^2 \over a^2} = {a^3 \over a^2} + {6a^2 \over a^2} = a + 6\).

If the tiger has consumed 100 pounds of food in 10 days that's \( \frac{100}{10} \) = 10 pounds of food per day. The tiger needs to consume 130 - 100 = 30 more pounds of food to reach 130 pounds total. At 10 pounds of food per day that's \( \frac{30}{10} \) = 3 more days.