You have 10 out of the total of 150 raffle tickets sold so you have a (\( \frac{10}{150} \)) x 100 = \( \frac{10 \times 100}{150} \) = \( \frac{1000}{150} \) = 7% chance to win the raffle.

To simplify this fraction, first find the greatest common factor between them. The factors of 40 are [1, 2, 4, 5, 8, 10, 20, 40] and the factors of 52 are [1, 2, 4, 13, 26, 52]. They share 3 factors [1, 2, 4] making 4 their greatest common factor (GCF).

Next, divide both numerator and denominator by the GCF:

\( \frac{40}{52} \) = \( \frac{\frac{40}{4}}{\frac{52}{4}} \) = \( \frac{10}{13} \)

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

6\( \sqrt{50} \) + 5\( \sqrt{2} \)
6\( \sqrt{25 \times 2} \) + 5\( \sqrt{2} \)
6\( \sqrt{5^2 \times 2} \) + 5\( \sqrt{2} \)
(6)(5)\( \sqrt{2} \) + 5\( \sqrt{2} \)
30\( \sqrt{2} \) + 5\( \sqrt{2} \)

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

The distributive property for multiplication helps in solving expressions like a(b + c). It specifies that the result of multiplying one number by the sum or difference of two numbers can be obtained by multiplying each number individually and then totaling the results: a(b + c) = ab + ac. For example, 4(10-5) = (4 x 10) - (4 x 5) = 40 - 20 = 20.

If 63% of the town's 44,000 voters cast ballots the number of votes cast is:

(\( \frac{63}{100} \)) x 44,000 = \( \frac{2,772,000}{100} \) = 27,720

The mayor got 90% of the votes cast which is:

(\( \frac{90}{100} \)) x 27,720 = \( \frac{2,494,800}{100} \) = 24,948 votes.