To fill a 20 gallon tank exactly halfway you'll need 10 gallons of fuel. Each fuel can holds 2\(\frac{1}{2}\) gallons so:

cans = \( \frac{10 \text{ gallons}}{2\frac{1}{2} \text{ gallons}} \) = 4

You have 4 out of the total of 50 raffle tickets sold so you have a (\( \frac{4}{50} \)) x 100 = \( \frac{4 \times 100}{50} \) = \( \frac{400}{50} \) = 9% chance to win the raffle.

1

The equation for this sequence is:

a_n = a_n-1 + 6

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 + 6
a₆ = 25 + 6
a₆ = 31

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

7\( \sqrt{2} \) x 6\( \sqrt{9} \)
(7 x 6)\( \sqrt{2 \times 9} \)
42\( \sqrt{18} \)

Now we need to simplify the radical:

42\( \sqrt{18} \)
42\( \sqrt{2 \times 9} \)
42\( \sqrt{2 \times 3^2} \)
(42)(3)\( \sqrt{2} \)
126\( \sqrt{2} \)