| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.17 |
| Score | 0% | 63% |
What is the least common multiple of 3 and 7?
| 21 | |
| 14 | |
| 16 | |
| 10 |
The first few multiples of 3 are [3, 6, 9, 12, 15, 18, 21, 24, 27, 30] and the first few multiples of 7 are [7, 14, 21, 28, 35, 42, 49, 56, 63, 70]. The first few multiples they share are [21, 42, 63, 84] making 21 the smallest multiple 3 and 7 have in common.
What is \( \sqrt{\frac{25}{25}} \)?
| 1 | |
| 1\(\frac{1}{2}\) | |
| 3 | |
| \(\frac{3}{7}\) |
To take the square root of a fraction, break the fraction into two separate roots then calculate the square root of the numerator and denominator separately:
\( \sqrt{\frac{25}{25}} \)
\( \frac{\sqrt{25}}{\sqrt{25}} \)
\( \frac{\sqrt{5^2}}{\sqrt{5^2}} \)
1
23 members of a bridal party need transported to a wedding reception but there are only 4 5-passenger taxis available to take them. How many will need to find other transportation?
| 3 | |
| 5 | |
| 8 | |
| 6 |
There are 4 5-passenger taxis available so that's 4 x 5 = 20 total seats. There are 23 people needing transportation leaving 23 - 20 = 3 who will have to find other transportation.
The __________ is the smallest positive integer that is a multiple of two or more integers.
least common factor |
|
least common multiple |
|
greatest common factor |
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absolute value |
The least common multiple (LCM) is the smallest positive integer that is a multiple of two or more integers.
On average, the center for a basketball team hits 30% of his shots while a guard on the same team hits 45% 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?
| 42 | |
| 27 | |
| 37 | |
| 31 |
guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 25 x \( \frac{45}{100} \) = \( \frac{45 x 25}{100} \) = \( \frac{1125}{100} \) = 11 shots
The center makes 30% 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 = \( \frac{11}{\frac{30}{100}} \) = 11 x \( \frac{100}{30} \) = \( \frac{11 x 100}{30} \) = \( \frac{1100}{30} \) = 37 shots
to make the same number of shots as the guard and thus score the same number of points.