| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.63 |
| Score | 0% | 73% |
What is the next number in this sequence: 1, 3, 7, 13, 21, __________ ?
| 37 | |
| 26 | |
| 35 | |
| 31 |
The equation for this sequence is:
an = an-1 + 2(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 + 2(6 - 1)
a6 = 21 + 2(5)
a6 = 31
How many 15-passenger vans will it take to drive all 63 members of the football team to an away game?
| 15 vans | |
| 3 vans | |
| 4 vans | |
| 5 vans |
Calculate the number of vans needed by dividing the number of people that need transported by the capacity of one van:
vans = \( \frac{63}{15} \) = 4\(\frac{1}{5}\)
So, it will take 4 full vans and one partially full van to transport the entire team making a total of 5 vans.
If \( \left|a - 7\right| \) - 7 = 7, which of these is a possible value for a?
| -3 | |
| -4 | |
| -21 | |
| -7 |
First, solve for \( \left|a - 7\right| \):
\( \left|a - 7\right| \) - 7 = 7
\( \left|a - 7\right| \) = 7 + 7
\( \left|a - 7\right| \) = 14
The value inside the absolute value brackets can be either positive or negative so (a - 7) must equal + 14 or -14 for \( \left|a - 7\right| \) to equal 14:
| a - 7 = 14 a = 14 + 7 a = 21 | a - 7 = -14 a = -14 + 7 a = -7 |
So, a = -7 or a = 21.
Convert y-4 to remove the negative exponent.
| \( \frac{-1}{-4y^{4}} \) | |
| \( \frac{4}{y} \) | |
| \( \frac{-4}{-y} \) | |
| \( \frac{1}{y^4} \) |
To convert a negative exponent to a positive exponent, calculate the positive exponent then take the reciprocal.
4! = ?
4 x 3 x 2 x 1 |
|
3 x 2 x 1 |
|
4 x 3 |
|
5 x 4 x 3 x 2 x 1 |
A factorial has the form n! and is the product of the integer (n) and all the positive integers below it. For example, 5! = 5 x 4 x 3 x 2 x 1 = 120.