| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.81 |
| Score | 0% | 56% |
What is 3\( \sqrt{3} \) x 9\( \sqrt{4} \)?
| 12\( \sqrt{12} \) | |
| 27\( \sqrt{7} \) | |
| 54\( \sqrt{3} \) | |
| 12\( \sqrt{3} \) |
To multiply terms with radicals, multiply the coefficients and radicands separately:
3\( \sqrt{3} \) x 9\( \sqrt{4} \)
(3 x 9)\( \sqrt{3 \times 4} \)
27\( \sqrt{12} \)
Now we need to simplify the radical:
27\( \sqrt{12} \)
27\( \sqrt{3 \times 4} \)
27\( \sqrt{3 \times 2^2} \)
(27)(2)\( \sqrt{3} \)
54\( \sqrt{3} \)
If \( \left|z + 5\right| \) - 6 = -4, which of these is a possible value for z?
| -3 | |
| 1 | |
| 8 | |
| -14 |
First, solve for \( \left|z + 5\right| \):
\( \left|z + 5\right| \) - 6 = -4
\( \left|z + 5\right| \) = -4 + 6
\( \left|z + 5\right| \) = 2
The value inside the absolute value brackets can be either positive or negative so (z + 5) must equal + 2 or -2 for \( \left|z + 5\right| \) to equal 2:
| z + 5 = 2 z = 2 - 5 z = -3 | z + 5 = -2 z = -2 - 5 z = -7 |
So, z = -7 or z = -3.
What is \( \frac{8}{2} \) - \( \frac{3}{10} \)?
| 2 \( \frac{3}{10} \) | |
| 2 \( \frac{9}{10} \) | |
| \( \frac{4}{10} \) | |
| 3\(\frac{7}{10}\) |
To subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 2 are [2, 4, 6, 8, 10, 12, 14, 16, 18, 20] and the first few multiples of 10 are [10, 20, 30, 40, 50, 60, 70, 80, 90]. The first few multiples they share are [10, 20, 30, 40, 50] making 10 the smallest multiple 2 and 10 share.
Next, convert the fractions so each denominator equals the lowest common multiple:
\( \frac{8 x 5}{2 x 5} \) - \( \frac{3 x 1}{10 x 1} \)
\( \frac{40}{10} \) - \( \frac{3}{10} \)
Now, because the fractions share a common denominator, you can subtract them:
\( \frac{40 - 3}{10} \) = \( \frac{37}{10} \) = 3\(\frac{7}{10}\)
On average, the center for a basketball team hits 50% of his shots while a guard on the same team hits 55% of his shots. If the guard takes 25 shots during a game, how many shots will the center have to take to score as many points as the guard assuming each shot is worth the same number of points?
| 26 | |
| 29 | |
| 35 | |
| 50 |
guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 25 x \( \frac{55}{100} \) = \( \frac{55 x 25}{100} \) = \( \frac{1375}{100} \) = 13 shots
The center makes 50% of his shots so he'll have to take:
shots made = shots taken x \( \frac{\text{% made}}{100} \)
shots taken = \( \frac{\text{shots taken}}{\frac{\text{% made}}{100}} \)
to make as many shots as the guard. Plugging in values for the center gives us:
center shots taken = \( \frac{13}{\frac{50}{100}} \) = 13 x \( \frac{100}{50} \) = \( \frac{13 x 100}{50} \) = \( \frac{1300}{50} \) = 26 shots
to make the same number of shots as the guard and thus score the same number of points.
Which of the following is an improper fraction?
\({7 \over 5} \) |
|
\(1 {2 \over 5} \) |
|
\({a \over 5} \) |
|
\({2 \over 5} \) |
A rational number (or fraction) is represented as a ratio between two integers, a and b, and has the form \({a \over b}\) where a is the numerator and b is the denominator. An improper fraction (\({5 \over 3} \)) has a numerator with a greater absolute value than the denominator and can be converted into a mixed number (\(1 {2 \over 3} \)) which has a whole number part and a fractional part.