You have 3 out of the total of 50 raffle tickets sold so you have a (\( \frac{3}{50} \)) x 100 = \( \frac{3 \times 100}{50} \) = \( \frac{300}{50} \) = 7% chance to win the raffle.

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

5\( \sqrt{175} \) - 4\( \sqrt{7} \)
5\( \sqrt{25 \times 7} \) - 4\( \sqrt{7} \)
5\( \sqrt{5^2 \times 7} \) - 4\( \sqrt{7} \)
(5)(5)\( \sqrt{7} \) - 4\( \sqrt{7} \)
25\( \sqrt{7} \) - 4\( \sqrt{7} \)

Now that the radicands are identical, you can subtract them:

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:

\( \frac{2!}{3!} \)
\( \frac{2 \times 1}{3 \times 2 \times 1} \)
\( \frac{1}{3} \)
\( \frac{1}{3} \)

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.

A ratio of 3:1 means that there are 3 home fans for every one visiting fan. So, of every 4 fans, 3 are home fans and \( \frac{3}{4} \) of every fan in the stadium is a home fan:

47,000 fans x \( \frac{3}{4} \) = \( \frac{141000}{4} \) = 35,250 fans.