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 7 = \( \frac{2 \times 7}{100} \) = \( \frac{14}{100} \) = 0.14 errors per hour

So, in an average hour, the machine will produce 7 - 0.14 = 6.86 error free parts.

The machine ran for 24 - 9 = 15 hours yesterday so you would expect that 15 x 6.86 = 102.9 error free parts were produced yesterday.

The area of a rectangle is width (w) x height (h). In this problem we know that the rectangle is twice as long as it is wide so h = 2w. The perimeter of a rectangle is 2w + 2h and we know that the perimeter of this rectangle is 18 meters so the equation becomes: 2w + 2h = 18.

Putting these two equations together and solving for width (w):

2w + 2h = 18
w + h = \( \frac{18}{2} \)
w + h = 9
w = 9 - h

From the question we know that h = 2w so substituting 2w for h gives us:

w = 9 - 2w
3w = 9
w = \( \frac{9}{3} \)
w = 3

Since h = 2w that makes h = (2 x 3) = 6 and the area = h x w = 3 x 6 = 18 m²

The amount of flour you need is (2\(\frac{1}{2}\) - 1\(\frac{1}{4}\)) cups. Rewrite the quantities so they share a common denominator and subtract:

(\( \frac{20}{8} \) - \( \frac{10}{8} \)) cups
\( \frac{10}{8} \) cups
1\(\frac{1}{4}\) cups

The equation for this sequence is:

a_n = a_n-1 + 4

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
a₆ = 17 + 4
a₆ = 21

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:

\( \frac{-9z^8}{5z^4} \)
\( \frac{-9}{5} \) z^{(8 - 4)}
-1\(\frac{4}{5}\)z⁴