You have 3 out of the total of 150 raffle tickets sold so you have a (\( \frac{3}{150} \)) x 100 = \( \frac{3 \times 100}{150} \) = \( \frac{300}{150} \) = 2% chance to win the raffle.

The factors of 56 are [1, 2, 4, 7, 8, 14, 28, 56] and the factors of 64 are [1, 2, 4, 8, 16, 32, 64]. They share 4 factors [1, 2, 4, 8] making 8 the greatest factor 56 and 64 have in common.

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 45% the radius (and, consequently, the total area) increases by \( \frac{45\text{%}}{2} \) = 22\(\frac{1}{2}\)%

A prime number is an integer greater than 1 that has no factors other than 1 and itself. Examples of prime numbers include 2, 3, 5, 7, and 11.

To add these fractions, first find the lowest common multiple of their denominators. The first few multiples of 3 are [3, 6, 9, 12, 15, 18, 21, 24, 27, 30] and the first few multiples of 9 are [9, 18, 27, 36, 45, 54, 63, 72, 81, 90]. The first few multiples they share are [9, 18, 27, 36, 45] making 9 the smallest multiple 3 and 9 share.

Next, convert the fractions so each denominator equals the lowest common multiple:

\( \frac{4 x 3}{3 x 3} \) + \( \frac{7 x 1}{9 x 1} \)

\( \frac{12}{9} \) + \( \frac{7}{9} \)

Now, because the fractions share a common denominator, you can add them:

\( \frac{12 + 7}{9} \) = \( \frac{19}{9} \) = 2\(\frac{1}{9}\)