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:

\( \frac{8x^9}{6x^3} \)
\( \frac{8}{6} \) x^{(9 - 3)}
1\(\frac{1}{3}\)x⁶

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

\( \frac{2}{100} \) x 6 = \( \frac{2 \times 6}{100} \) = \( \frac{12}{100} \) = 0.12 errors per hour

So, in an average hour, the machine will produce 6 - 0.12 = 5.88 error free parts.

The machine ran for 24 - 2 = 22 hours yesterday so you would expect that 22 x 5.88 = 129.4 error free parts were produced yesterday.

A number with an exponent (b^e) consists of a base (b) raised to a power (e). The exponent indicates the number of times that the base is multiplied by itself. A base with an exponent of 1 equals the base (b¹ = b) and a base with an exponent of 0 equals 1 ( (b⁰ = 1).

You have 12 out of the total of 250 raffle tickets sold so you have a (\( \frac{12}{250} \)) x 100 = \( \frac{12 \times 100}{250} \) = \( \frac{1200}{250} \) = 5% chance to win the raffle.

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