| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.36 |
| Score | 0% | 67% |
Simplify \( \sqrt{175} \)
| 5\( \sqrt{7} \) | |
| 5\( \sqrt{14} \) | |
| 9\( \sqrt{7} \) | |
| 4\( \sqrt{14} \) |
To simplify a radical, factor out the perfect squares:
\( \sqrt{175} \)
\( \sqrt{25 \times 7} \)
\( \sqrt{5^2 \times 7} \)
5\( \sqrt{7} \)
This property states taht the order of addition or multiplication does not mater. For example, 2 + 5 and 5 + 2 are equivalent.
PEDMAS |
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commutative |
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distributive |
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associative |
The commutative property states that, when adding or multiplying numbers, the order in which they're added or multiplied does not matter. For example, 3 + 4 and 4 + 3 give the same result, as do 3 x 4 and 4 x 3.
What is the greatest common factor of 16 and 36?
| 12 | |
| 1 | |
| 6 | |
| 4 |
The factors of 16 are [1, 2, 4, 8, 16] and the factors of 36 are [1, 2, 3, 4, 6, 9, 12, 18, 36]. They share 3 factors [1, 2, 4] making 4 the greatest factor 16 and 36 have in common.
If a mayor is elected with 68% of the votes cast and 90% of a town's 46,000 voters cast a vote, how many votes did the mayor receive?
| 34,776 | |
| 27,324 | |
| 33,948 | |
| 28,152 |
If 90% of the town's 46,000 voters cast ballots the number of votes cast is:
(\( \frac{90}{100} \)) x 46,000 = \( \frac{4,140,000}{100} \) = 41,400
The mayor got 68% of the votes cast which is:
(\( \frac{68}{100} \)) x 41,400 = \( \frac{2,815,200}{100} \) = 28,152 votes.
How many hours does it take a car to travel 560 miles at an average speed of 70 miles per hour?
| 7 hours | |
| 2 hours | |
| 4 hours | |
| 8 hours |
Average speed in miles per hour is the number of miles traveled divided by the number of hours:
speed = \( \frac{\text{distance}}{\text{time}} \)Solving for time:
time = \( \frac{\text{distance}}{\text{speed}} \)
time = \( \frac{560mi}{70mph} \)
8 hours