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

\( \frac{7}{100} \) x 7 = \( \frac{7 \times 7}{100} \) = \( \frac{49}{100} \) = 0.49 errors per hour

So, in an average hour, the machine will produce 7 - 0.49 = 6.51 error free parts.

The machine ran for 24 - 3 = 21 hours yesterday so you would expect that 21 x 6.51 = 136.7 error free parts were produced yesterday.

A ratio of 2:1 means that there are 2 home fans for every one visiting fan. So, of every 3 fans, 2 are home fans and \( \frac{2}{3} \) of every fan in the stadium is a home fan:

37,000 fans x \( \frac{2}{3} \) = \( \frac{74000}{3} \) = 24,667 fans.

The area of a circle is given by the formula A = πr² where r is the radius of the circle. The radius of a circle is its diameter divided by two so A = π(\( \frac{d}{2} \))². If the diameter of the logo increases by 30% the radius (and, consequently, the total area) increases by \( \frac{30\text{%}}{2} \) = 15%

To subtract these radicals together their radicands must be the same:

2\( \sqrt{125} \) - 8\( \sqrt{5} \)
2\( \sqrt{25 \times 5} \) - 8\( \sqrt{5} \)
2\( \sqrt{5^2 \times 5} \) - 8\( \sqrt{5} \)
(2)(5)\( \sqrt{5} \) - 8\( \sqrt{5} \)
10\( \sqrt{5} \) - 8\( \sqrt{5} \)

Now that the radicands are identical, you can subtract them:

The distributive property for division helps in solving expressions like \({b + c \over a}\). It specifies that the result of dividing a fraction with multiple terms in the numerator and one term in the denominator can be obtained by dividing each term individually and then totaling the results: \({b + c \over a} = {b \over a} + {c \over a}\). For example, \({a^3 + 6a^2 \over a^2} = {a^3 \over a^2} + {6a^2 \over a^2} = a + 6\).