| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.45 |
| Score | 0% | 69% |
How many 14-passenger vans will it take to drive all 69 members of the football team to an away game?
| 9 vans | |
| 5 vans | |
| 12 vans | |
| 11 vans |
Calculate the number of vans needed by dividing the number of people that need transported by the capacity of one van:
vans = \( \frac{69}{14} \) = 4\(\frac{13}{14}\)
So, it will take 4 full vans and one partially full van to transport the entire team making a total of 5 vans.
What is the next number in this sequence: 1, 3, 5, 7, 9, __________ ?
| 20 | |
| 4 | |
| 15 | |
| 11 |
The equation for this sequence is:
an = an-1 + 2
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 + 2
a6 = 9 + 2
a6 = 11
Solve for \( \frac{2!}{6!} \)
| \( \frac{1}{120} \) | |
| \( \frac{1}{15120} \) | |
| \( \frac{1}{72} \) | |
| \( \frac{1}{360} \) |
A factorial is the product of an integer and all the positive integers below it. To solve a fraction featuring factorials, expand the factorials and cancel out like numbers:
\( \frac{2!}{6!} \)
\( \frac{2 \times 1}{6 \times 5 \times 4 \times 3 \times 2 \times 1} \)
\( \frac{1}{6 \times 5 \times 4 \times 3} \)
\( \frac{1}{360} \)
On average, the center for a basketball team hits 50% of his shots while a guard on the same team hits 60% of his shots. If the guard takes 25 shots during a game, how many shots will the center have to take to score as many points as the guard assuming each shot is worth the same number of points?
| 30 | |
| 52 | |
| 31 | |
| 36 |
guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 25 x \( \frac{60}{100} \) = \( \frac{60 x 25}{100} \) = \( \frac{1500}{100} \) = 15 shots
The center makes 50% of his shots so he'll have to take:
shots made = shots taken x \( \frac{\text{% made}}{100} \)
shots taken = \( \frac{\text{shots taken}}{\frac{\text{% made}}{100}} \)
to make as many shots as the guard. Plugging in values for the center gives us:
center shots taken = \( \frac{15}{\frac{50}{100}} \) = 15 x \( \frac{100}{50} \) = \( \frac{15 x 100}{50} \) = \( \frac{1500}{50} \) = 30 shots
to make the same number of shots as the guard and thus score the same number of points.
What is \( \frac{5}{6} \) - \( \frac{5}{12} \)?
| 2 \( \frac{6}{14} \) | |
| \( \frac{1}{7} \) | |
| 1 \( \frac{1}{12} \) | |
| \(\frac{5}{12}\) |
To subtract these fractions, first find the lowest common multiple of their denominators. 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 share.
Next, convert the fractions so each denominator equals the lowest common multiple:
\( \frac{5 x 2}{6 x 2} \) - \( \frac{5 x 1}{12 x 1} \)
\( \frac{10}{12} \) - \( \frac{5}{12} \)
Now, because the fractions share a common denominator, you can subtract them:
\( \frac{10 - 5}{12} \) = \( \frac{5}{12} \) = \(\frac{5}{12}\)