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

4\( \sqrt{75} \) + 4\( \sqrt{3} \)
4\( \sqrt{25 \times 3} \) + 4\( \sqrt{3} \)
4\( \sqrt{5^2 \times 3} \) + 4\( \sqrt{3} \)
(4)(5)\( \sqrt{3} \) + 4\( \sqrt{3} \)
20\( \sqrt{3} \) + 4\( \sqrt{3} \)

Now that the radicands are identical, you can add them together:

The ratio of football cards to baseball cards is 5:2 and the ratio of baseball cards to basketball cards is 5:1. To solve this problem, we need the baseball card side of each ratio to be equal so we need to rewrite the ratios in terms of a common number of baseball cards. (Think of this like finding the common denominator when adding fractions.) The ratio of football to baseball cards can also be written as 25:10 and the ratio of baseball cards to basketball cards as 10:2. So, the ratio of football cards to basketball cards is football:baseball, baseball:basketball or 25:10, 10:2 which reduces to 25:2.

A factorial is the product of an integer and all the positive integers below it. To solve a fraction featuring factorials, expand the factorials and cancel out like numbers:

\( \frac{4!}{6!} \)
\( \frac{4 \times 3 \times 2 \times 1}{6 \times 5 \times 4 \times 3 \times 2 \times 1} \)
\( \frac{1}{6 \times 5} \)
\( \frac{1}{30} \)

To fill a 12 gallon tank exactly halfway you'll need 6 gallons of fuel. Each fuel can holds 2 gallons so:

cans = \( \frac{6 \text{ gallons}}{2 \text{ gallons}} \) = 3

Christine scored 90% on the test meaning she earned 90% of the possible points on the test. There were 150 possible points on the test so she earned 150 x 0.9 = 135 points. Each question is worth 3 points so she got \( \frac{135}{3} \) = 45 questions right.