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

2\( \sqrt{28} \) - 9\( \sqrt{7} \)
2\( \sqrt{4 \times 7} \) - 9\( \sqrt{7} \)
2\( \sqrt{2^2 \times 7} \) - 9\( \sqrt{7} \)
(2)(2)\( \sqrt{7} \) - 9\( \sqrt{7} \)
4\( \sqrt{7} \) - 9\( \sqrt{7} \)

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

Betty scored 83% on the test meaning she earned 83% of the possible points on the test. There were 180 possible points on the test so she earned 180 x 0.83 = 150 points. Each question is worth 2 points so she got \( \frac{150}{2} \) = 75 questions right.

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 45% the radius (and, consequently, the total area) increases by \( \frac{45\text{%}}{2} \) = 22\(\frac{1}{2}\)%

The equation for this sequence is:

a_n = a_n-1 + 3(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 + 3(6 - 1)
a₆ = 31 + 3(5)
a₆ = 46

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 - 5 = 19 hours yesterday so you would expect that 19 x 6.51 = 123.7 error free parts were produced yesterday.