| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.02 |
| Score | 0% | 60% |
How many 2 gallon cans worth of fuel would you need to pour into an empty 16 gallon tank to fill it exactly halfway?
| 9 | |
| 4 | |
| 8 | |
| 2 |
To fill a 16 gallon tank exactly halfway you'll need 8 gallons of fuel. Each fuel can holds 2 gallons so:
cans = \( \frac{8 \text{ gallons}}{2 \text{ gallons}} \) = 4
The __________ is the greatest factor that divides two integers.
greatest common multiple |
|
least common multiple |
|
absolute value |
|
greatest common factor |
The greatest common factor (GCF) is the greatest factor that divides two integers.
What is the next number in this sequence: 1, 5, 13, 25, 41, __________ ?
| 53 | |
| 57 | |
| 62 | |
| 61 |
The equation for this sequence is:
an = an-1 + 4(n - 1)
where n is the term's order in the sequence, an is the value of the term, and an-1 is the value of the term before an. This makes the next number:
a6 = a5 + 4(6 - 1)
a6 = 41 + 4(5)
a6 = 61
What is 9\( \sqrt{7} \) x 5\( \sqrt{4} \)?
| 45\( \sqrt{7} \) | |
| 90\( \sqrt{7} \) | |
| 14\( \sqrt{28} \) | |
| 45\( \sqrt{4} \) |
To multiply terms with radicals, multiply the coefficients and radicands separately:
9\( \sqrt{7} \) x 5\( \sqrt{4} \)
(9 x 5)\( \sqrt{7 \times 4} \)
45\( \sqrt{28} \)
Now we need to simplify the radical:
45\( \sqrt{28} \)
45\( \sqrt{7 \times 4} \)
45\( \sqrt{7 \times 2^2} \)
(45)(2)\( \sqrt{7} \)
90\( \sqrt{7} \)
What is the least common multiple of 6 and 12?
| 5 | |
| 17 | |
| 6 | |
| 12 |
The first few multiples of 6 are [6, 12, 18, 24, 30, 36, 42, 48, 54, 60] and the first few multiples of 12 are [12, 24, 36, 48, 60, 72, 84, 96]. The first few multiples they share are [12, 24, 36, 48, 60] making 12 the smallest multiple 6 and 12 have in common.