| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.84 |
| Score | 0% | 57% |
A factor is a positive __________ that divides evenly into a given number.
fraction |
|
integer |
|
improper fraction |
|
mixed number |
A factor is a positive integer that divides evenly into a given number. For example, the factors of 8 are 1, 2, 4, and 8.
On average, the center for a basketball team hits 50% of his shots while a guard on the same team hits 65% 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?
| 32 | |
| 46 | |
| 39 | |
| 33 |
guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 25 x \( \frac{65}{100} \) = \( \frac{65 x 25}{100} \) = \( \frac{1625}{100} \) = 16 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 = \( \frac{16}{\frac{50}{100}} \) = 16 x \( \frac{100}{50} \) = \( \frac{16 x 100}{50} \) = \( \frac{1600}{50} \) = 32 shots
to make the same number of shots as the guard and thus score the same number of points.
Convert 2,240,000 to scientific notation.
| 2.24 x 105 | |
| 2.24 x 106 | |
| 2.24 x 107 | |
| 0.224 x 107 |
A number in scientific notation has the format 0.000 x 10exponent. To convert to scientific notation, move the decimal point to the right or the left until the number is a decimal between 1 and 10. The exponent of the 10 is the number of places you moved the decimal point and is positive if you moved the decimal point to the left and negative if you moved it to the right:
2,240,000 in scientific notation is 2.24 x 106
What is \( 2 \)\( \sqrt{27} \) + \( 9 \)\( \sqrt{3} \)
| 18\( \sqrt{81} \) | |
| 11\( \sqrt{9} \) | |
| 15\( \sqrt{3} \) | |
| 11\( \sqrt{27} \) |
To add these radicals together their radicands must be the same:
2\( \sqrt{27} \) + 9\( \sqrt{3} \)
2\( \sqrt{9 \times 3} \) + 9\( \sqrt{3} \)
2\( \sqrt{3^2 \times 3} \) + 9\( \sqrt{3} \)
(2)(3)\( \sqrt{3} \) + 9\( \sqrt{3} \)
6\( \sqrt{3} \) + 9\( \sqrt{3} \)
Now that the radicands are identical, you can add them together:
6\( \sqrt{3} \) + 9\( \sqrt{3} \)What is \( \frac{9}{2} \) + \( \frac{3}{8} \)?
| \( \frac{3}{8} \) | |
| 2 \( \frac{2}{8} \) | |
| 4\(\frac{7}{8}\) | |
| 1 \( \frac{4}{10} \) |
To add 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 8 are [8, 16, 24, 32, 40, 48, 56, 64, 72, 80]. The first few multiples they share are [8, 16, 24, 32, 40] making 8 the smallest multiple 2 and 8 share.
Next, convert the fractions so each denominator equals the lowest common multiple:
\( \frac{9 x 4}{2 x 4} \) + \( \frac{3 x 1}{8 x 1} \)
\( \frac{36}{8} \) + \( \frac{3}{8} \)
Now, because the fractions share a common denominator, you can add them:
\( \frac{36 + 3}{8} \) = \( \frac{39}{8} \) = 4\(\frac{7}{8}\)