To add these radicals together their radicands must be the same:

8\( \sqrt{112} \) + 8\( \sqrt{7} \)
8\( \sqrt{16 \times 7} \) + 8\( \sqrt{7} \)
8\( \sqrt{4^2 \times 7} \) + 8\( \sqrt{7} \)
(8)(4)\( \sqrt{7} \) + 8\( \sqrt{7} \)
32\( \sqrt{7} \) + 8\( \sqrt{7} \)

Now that the radicands are identical, you can add them together:

The equation for this sequence is:

a_n = a_n-1 + 2(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 + 2(6 - 1)
a₆ = 21 + 2(5)
a₆ = 31

You have 22 out of the total of 250 raffle tickets sold so you have a (\( \frac{22}{250} \)) x 100 = \( \frac{22 \times 100}{250} \) = \( \frac{2200}{250} \) = 9% chance to win the raffle.

A number with an exponent (b^e) consists of a base (b) raised to a power (e). The exponent indicates the number of times that the base is multiplied by itself. A base with an exponent of 1 equals the base (b¹ = b) and a base with an exponent of 0 equals 1 ( (b⁰ = 1).

The area of a circle is given by the formula A = πr² where r is the radius of the circle. The radius of a circle is its diameter divided by two so A = π(\( \frac{d}{2} \))². If the diameter of the logo increases by 40% the radius (and, consequently, the total area) increases by \( \frac{40\text{%}}{2} \) = 20%