| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.68 |
| Score | 0% | 54% |
What is \( 5 \)\( \sqrt{12} \) - \( 9 \)\( \sqrt{3} \)
| -4\( \sqrt{4} \) | |
| -4\( \sqrt{3} \) | |
| \( \sqrt{3} \) | |
| -4\( \sqrt{12} \) |
To subtract these radicals together their radicands must be the same:
5\( \sqrt{12} \) - 9\( \sqrt{3} \)
5\( \sqrt{4 \times 3} \) - 9\( \sqrt{3} \)
5\( \sqrt{2^2 \times 3} \) - 9\( \sqrt{3} \)
(5)(2)\( \sqrt{3} \) - 9\( \sqrt{3} \)
10\( \sqrt{3} \) - 9\( \sqrt{3} \)
Now that the radicands are identical, you can subtract them:
10\( \sqrt{3} \) - 9\( \sqrt{3} \)What is the greatest common factor of 52 and 72?
| 7 | |
| 28 | |
| 4 | |
| 20 |
The factors of 52 are [1, 2, 4, 13, 26, 52] and the factors of 72 are [1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72]. They share 3 factors [1, 2, 4] making 4 the greatest factor 52 and 72 have in common.
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| 4.2 | |
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| 2.4 |
1
A tiger in a zoo has consumed 72 pounds of food in 6 days. If the tiger continues to eat at the same rate, in how many more days will its total food consumtion be 156 pounds?
| 10 | |
| 7 | |
| 3 | |
| 6 |
If the tiger has consumed 72 pounds of food in 6 days that's \( \frac{72}{6} \) = 12 pounds of food per day. The tiger needs to consume 156 - 72 = 84 more pounds of food to reach 156 pounds total. At 12 pounds of food per day that's \( \frac{84}{12} \) = 7 more days.
Cooks are needed to prepare for a large party. Each cook can bake either 3 large cakes or 19 small cakes per hour. The kitchen is available for 3 hours and 22 large cakes and 410 small cakes need to be baked.
How many cooks are required to bake the required number of cakes during the time the kitchen is available?
| 6 | |
| 11 | |
| 5 | |
| 15 |
If a single cook can bake 3 large cakes per hour and the kitchen is available for 3 hours, a single cook can bake 3 x 3 = 9 large cakes during that time. 22 large cakes are needed for the party so \( \frac{22}{9} \) = 2\(\frac{4}{9}\) cooks are needed to bake the required number of large cakes.
If a single cook can bake 19 small cakes per hour and the kitchen is available for 3 hours, a single cook can bake 19 x 3 = 57 small cakes during that time. 410 small cakes are needed for the party so \( \frac{410}{57} \) = 7\(\frac{11}{57}\) cooks are needed to bake the required number of small cakes.
Because you can't employ a fractional cook, round the number of cooks needed for each type of cake up to the next whole number resulting in 3 + 8 = 11 cooks.