| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.09 |
| Score | 0% | 62% |
How many 1\(\frac{1}{2}\) gallon cans worth of fuel would you need to pour into an empty 15 gallon tank to fill it exactly halfway?
| 4 | |
| 5 | |
| 9 | |
| 10 |
To fill a 15 gallon tank exactly halfway you'll need 7\(\frac{1}{2}\) gallons of fuel. Each fuel can holds 1\(\frac{1}{2}\) gallons so:
cans = \( \frac{7\frac{1}{2} \text{ gallons}}{1\frac{1}{2} \text{ gallons}} \) = 5
The __________ is the greatest factor that divides two integers.
least common multiple |
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greatest common factor |
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greatest common multiple |
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absolute value |
The greatest common factor (GCF) is the greatest factor that divides two integers.
Which of the following is a mixed number?
\({7 \over 5} \) |
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\(1 {2 \over 5} \) |
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\({5 \over 7} \) |
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\({a \over 5} \) |
A rational number (or fraction) is represented as a ratio between two integers, a and b, and has the form \({a \over b}\) where a is the numerator and b is the denominator. An improper fraction (\({5 \over 3} \)) has a numerator with a greater absolute value than the denominator and can be converted into a mixed number (\(1 {2 \over 3} \)) which has a whole number part and a fractional part.
What is \( 6 \)\( \sqrt{63} \) + \( 2 \)\( \sqrt{7} \)
| 12\( \sqrt{7} \) | |
| 20\( \sqrt{7} \) | |
| 8\( \sqrt{63} \) | |
| 8\( \sqrt{7} \) |
To add these radicals together their radicands must be the same:
6\( \sqrt{63} \) + 2\( \sqrt{7} \)
6\( \sqrt{9 \times 7} \) + 2\( \sqrt{7} \)
6\( \sqrt{3^2 \times 7} \) + 2\( \sqrt{7} \)
(6)(3)\( \sqrt{7} \) + 2\( \sqrt{7} \)
18\( \sqrt{7} \) + 2\( \sqrt{7} \)
Now that the radicands are identical, you can add them together:
18\( \sqrt{7} \) + 2\( \sqrt{7} \)A triathlon course includes a 400m swim, a 40.4km bike ride, and a 8.0km run. What is the total length of the race course?
| 57.7km | |
| 53.6km | |
| 48.8km | |
| 61km |
To add these distances, they must share the same unit so first you need to first convert the swim distance from meters (m) to kilometers (km) before adding it to the bike and run distances which are already in km. To convert 400 meters to kilometers, divide the distance by 1000 to get 0.4km then add the remaining distances:
total distance = swim + bike + run
total distance = 0.4km + 40.4km + 8.0km
total distance = 48.8km