You have 1 out of the total of 50 raffle tickets sold so you have a (\( \frac{1}{50} \)) x 100 = \( \frac{1 \times 100}{50} \) = \( \frac{100}{50} \) = 2% chance to win the raffle.

By buying two shirts, Roger will save $48 x \( \frac{25}{100} \) = \( \frac{$48 x 25}{100} \) = \( \frac{$1200}{100} \) = $12.00 on the second shirt.

So, his total cost will be
$48.00 + ($48.00 - $12.00)
$48.00 + $36.00
$84.00

There are 4 2-passenger taxis available so that's 4 x 2 = 8 total seats. There are 13 people needing transportation leaving 13 - 8 = 5 who will have to find other transportation.

To add these fractions, first find the lowest common multiple of their denominators. The first few multiples of 6 are [6, 12, 18, 24, 30, 36, 42, 48, 54, 60] and the first few multiples of 10 are [10, 20, 30, 40, 50, 60, 70, 80, 90]. The first few multiples they share are [30, 60, 90] making 30 the smallest multiple 6 and 10 share.

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

\( \frac{2 x 5}{6 x 5} \) + \( \frac{8 x 3}{10 x 3} \)

\( \frac{10}{30} \) + \( \frac{24}{30} \)

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

\( \frac{10 + 24}{30} \) = \( \frac{34}{30} \) = 1\(\frac{2}{15}\)

To add or subtract terms with exponents, both the base and the exponent must be the same. In this case they are so subtract the coefficients and retain the base and exponent:

7z⁶ - 8z⁶
(7 - 8)z⁶
-z⁶