To fill a 6 gallon tank exactly halfway you'll need 3 gallons of fuel. Each fuel can holds 1 gallons so:

cans = \( \frac{3 \text{ gallons}}{1 \text{ gallons}} \) = 3

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

2\( \sqrt{4} \) x 2\( \sqrt{3} \)
(2 x 2)\( \sqrt{4 \times 3} \)
4\( \sqrt{12} \)

Now we need to simplify the radical:

4\( \sqrt{12} \)
4\( \sqrt{3 \times 4} \)
4\( \sqrt{3 \times 2^2} \)
(4)(2)\( \sqrt{3} \)
8\( \sqrt{3} \)

Average speed in miles per hour is the number of miles traveled divided by the number of hours:

Solving for time:

time = \( \frac{\text{distance}}{\text{speed}} \)
time = \( \frac{30mi}{30mph} \)
1 hour

The equation for this sequence is:

a_n = a_n-1 + 4(n - 1)

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 + 4(6 - 1)
a₆ = 41 + 4(5)
a₆ = 61

If 36% of the town's 23,000 voters cast ballots the number of votes cast is:

(\( \frac{36}{100} \)) x 23,000 = \( \frac{828,000}{100} \) = 8,280

The mayor got 77% of the votes cast which is:

(\( \frac{77}{100} \)) x 8,280 = \( \frac{637,560}{100} \) = 6,376 votes.