You have 24 out of the total of 300 raffle tickets sold so you have a (\( \frac{24}{300} \)) x 100 = \( \frac{24 \times 100}{300} \) = \( \frac{2400}{300} \) = 8% chance to win the raffle.

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

vans = \( \frac{31}{10} \) = 3\(\frac{1}{10}\)

So, it will take 3 full vans and one partially full van to transport the entire team making a total of 4 vans.

To simplify this fraction, first find the greatest common factor between them. The factors of 28 are [1, 2, 4, 7, 14, 28] and the factors of 44 are [1, 2, 4, 11, 22, 44]. They share 3 factors [1, 2, 4] making 4 their greatest common factor (GCF).

Next, divide both numerator and denominator by the GCF:

\( \frac{28}{44} \) = \( \frac{\frac{28}{4}}{\frac{44}{4}} \) = \( \frac{7}{11} \)

The hourly error rate for this machine is the error rate in parts per 100 multiplied by the number of parts produced per hour:

\( \frac{8}{100} \) x 6 = \( \frac{8 \times 6}{100} \) = \( \frac{48}{100} \) = 0.48 errors per hour

So, in an average hour, the machine will produce 6 - 0.48 = 5.52 error free parts.

The machine ran for 24 - 3 = 21 hours yesterday so you would expect that 21 x 5.52 = 115.9 error free parts were produced yesterday.

To divide terms with exponents, the base of both exponents must be the same. In this case they are so divide the coefficients and subtract the exponents:

\( \frac{-5a^6}{2a^2} \)
\( \frac{-5}{2} \) a^{(6 - 2)}
-2\(\frac{1}{2}\)a⁴