To multiply terms with radicals, multiply the coefficients and radicands separately:

5\( \sqrt{9} \) x 3\( \sqrt{3} \)
(5 x 3)\( \sqrt{9 \times 3} \)
15\( \sqrt{27} \)

Now we need to simplify the radical:

15\( \sqrt{27} \)
15\( \sqrt{3 \times 9} \)
15\( \sqrt{3 \times 3^2} \)
(15)(3)\( \sqrt{3} \)
45\( \sqrt{3} \)

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

3\( \sqrt{48} \) + 7\( \sqrt{3} \)
3\( \sqrt{16 \times 3} \) + 7\( \sqrt{3} \)
3\( \sqrt{4^2 \times 3} \) + 7\( \sqrt{3} \)
(3)(4)\( \sqrt{3} \) + 7\( \sqrt{3} \)
12\( \sqrt{3} \) + 7\( \sqrt{3} \)

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

Calculate the number of vans needed by dividing the number of people that need transported by the capacity of one van:

vans = \( \frac{76}{10} \) = 7\(\frac{3}{5}\)

So, it will take 7 full vans and one partially full van to transport the entire team making a total of 8 vans.

You have 24 out of the total of 350 raffle tickets sold so you have a (\( \frac{24}{350} \)) x 100 = \( \frac{24 \times 100}{350} \) = \( \frac{2400}{350} \) = 7% chance to win the raffle.

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.