To fill a 20 gallon tank exactly halfway you'll need 10 gallons of fuel. Each fuel can holds 2 gallons so:

cans = \( \frac{10 \text{ gallons}}{2 \text{ gallons}} \) = 5

guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 30 x \( \frac{35}{100} \) = \( \frac{35 x 30}{100} \) = \( \frac{1050}{100} \) = 10 shots

The center makes 30% of his shots so he'll have to take:

shots made = shots taken x \( \frac{\text{% made}}{100} \)
shots taken = \( \frac{\text{shots taken}}{\frac{\text{% made}}{100}} \)

to make as many shots as the guard. Plugging in values for the center gives us:

center shots taken = \( \frac{10}{\frac{30}{100}} \) = 10 x \( \frac{100}{30} \) = \( \frac{10 x 100}{30} \) = \( \frac{1000}{30} \) = 33 shots

to make the same number of shots as the guard and thus score the same number of points.

By buying two shirts, Alex will save $40 x \( \frac{20}{100} \) = \( \frac{$40 x 20}{100} \) = \( \frac{$800}{100} \) = $8.00 on the second shirt.

So, his total cost will be
$40.00 + ($40.00 - $8.00)
$40.00 + $32.00
$72.00

To subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 8 are [8, 16, 24, 32, 40, 48, 56, 64, 72, 80] and the first few multiples of 12 are [12, 24, 36, 48, 60, 72, 84, 96]. The first few multiples they share are [24, 48, 72, 96] making 24 the smallest multiple 8 and 12 share.

Next, convert the fractions so each denominator equals the lowest common multiple:

\( \frac{5 x 3}{8 x 3} \) - \( \frac{7 x 2}{12 x 2} \)

\( \frac{15}{24} \) - \( \frac{14}{24} \)

Now, because the fractions share a common denominator, you can subtract them:

\( \frac{15 - 14}{24} \) = \( \frac{1}{24} \) = \(\frac{1}{24}\)

The equation for this sequence is:

a_n = a_n-1 + 3(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 + 3(6 - 1)
a₆ = 31 + 3(5)
a₆ = 46