To add these fractions, first find the lowest common multiple of their denominators. The first few multiples of 4 are [4, 8, 12, 16, 20, 24, 28, 32, 36, 40] and the first few multiples of 6 are [6, 12, 18, 24, 30, 36, 42, 48, 54, 60]. The first few multiples they share are [12, 24, 36, 48, 60] making 12 the smallest multiple 4 and 6 share.

Next, convert the fractions so each denominator equals the lowest common multiple:

\( \frac{2 x 3}{4 x 3} \) + \( \frac{4 x 2}{6 x 2} \)

\( \frac{6}{12} \) + \( \frac{8}{12} \)

Now, because the fractions share a common denominator, you can add them:

\( \frac{6 + 8}{12} \) = \( \frac{14}{12} \) = 1\(\frac{1}{6}\)

To divide terms with radicals, divide the coefficients and radicands separately:

\( \frac{20\sqrt{15}}{4\sqrt{3}} \)
\( \frac{20}{4} \) \( \sqrt{\frac{15}{3}} \)
5 \( \sqrt{5} \)

By buying two shirts, Roger will save $36 x \( \frac{50}{100} \) = \( \frac{$36 x 50}{100} \) = \( \frac{$1800}{100} \) = $18.00 on the second shirt.

So, his total cost will be
$36.00 + ($36.00 - $18.00)
$36.00 + $18.00
$54.00

The factors of 16 are [1, 2, 4, 8, 16] and the factors of 52 are [1, 2, 4, 13, 26, 52]. They share 3 factors [1, 2, 4] making 4 the greatest factor 16 and 52 have in common.

Diane scored 86% on the test meaning she earned 86% of the possible points on the test. There were 150 possible points on the test so she earned 150 x 0.86 = 129 points. Each question is worth 3 points so she got \( \frac{129}{3} \) = 43 questions right.