| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.90 |
| Score | 0% | 58% |
If the ratio of home fans to visiting fans in a crowd is 4:1 and all 37,000 seats in a stadium are filled, how many home fans are in attendance?
| 28,333 | |
| 29,600 | |
| 23,250 | |
| 36,750 |
A ratio of 4:1 means that there are 4 home fans for every one visiting fan. So, of every 5 fans, 4 are home fans and \( \frac{4}{5} \) of every fan in the stadium is a home fan:
37,000 fans x \( \frac{4}{5} \) = \( \frac{148000}{5} \) = 29,600 fans.
The __________ is the smallest positive integer that is a multiple of two or more integers.
absolute value |
|
least common multiple |
|
least common factor |
|
greatest common factor |
The least common multiple (LCM) is the smallest positive integer that is a multiple of two or more integers.
What is \( 4 \)\( \sqrt{75} \) + \( 9 \)\( \sqrt{3} \)
| 13\( \sqrt{3} \) | |
| 13\( \sqrt{75} \) | |
| 29\( \sqrt{3} \) | |
| 36\( \sqrt{75} \) |
To add these radicals together their radicands must be the same:
4\( \sqrt{75} \) + 9\( \sqrt{3} \)
4\( \sqrt{25 \times 3} \) + 9\( \sqrt{3} \)
4\( \sqrt{5^2 \times 3} \) + 9\( \sqrt{3} \)
(4)(5)\( \sqrt{3} \) + 9\( \sqrt{3} \)
20\( \sqrt{3} \) + 9\( \sqrt{3} \)
Now that the radicands are identical, you can add them together:
20\( \sqrt{3} \) + 9\( \sqrt{3} \)21 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?
| 4 | |
| 6 | |
| 5 | |
| 1 |
There are 4 5-passenger taxis available so that's 4 x 5 = 20 total seats. There are 21 people needing transportation leaving 21 - 20 = 1 who will have to find other transportation.
What is the least common multiple of 8 and 12?
| 24 | |
| 83 | |
| 70 | |
| 84 |
The first few multiples of 8 are [8, 16, 24, 32, 40, 48, 56, 64, 72, 80] and the first few multiples of 12 are [12, 24, 36, 48, 60, 72, 84, 96]. The first few multiples they share are [24, 48, 72, 96] making 24 the smallest multiple 8 and 12 have in common.