| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.36 |
| Score | 0% | 67% |
Convert b-3 to remove the negative exponent.
| \( \frac{-3}{b} \) | |
| \( \frac{3}{b} \) | |
| \( \frac{-1}{b^{-3}} \) | |
| \( \frac{1}{b^3} \) |
To convert a negative exponent to a positive exponent, calculate the positive exponent then take the reciprocal.
What is the next number in this sequence: 1, 8, 15, 22, 29, __________ ?
| 34 | |
| 36 | |
| 28 | |
| 44 |
The equation for this sequence is:
an = an-1 + 7
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 + 7
a6 = 29 + 7
a6 = 36
If the ratio of home fans to visiting fans in a crowd is 4:1 and all 36,000 seats in a stadium are filled, how many home fans are in attendance?
| 24,667 | |
| 28,800 | |
| 39,167 | |
| 28,000 |
A ratio of 4:1 means that there are 4 home fans for every one visiting fan. So, of every 5 fans, 4 are home fans and \( \frac{4}{5} \) of every fan in the stadium is a home fan:
36,000 fans x \( \frac{4}{5} \) = \( \frac{144000}{5} \) = 28,800 fans.
This property states taht the order of addition or multiplication does not mater. For example, 2 + 5 and 5 + 2 are equivalent.
distributive |
|
PEDMAS |
|
commutative |
|
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.
Solve for \( \frac{5!}{2!} \)
| 60 | |
| \( \frac{1}{3024} \) | |
| \( \frac{1}{840} \) | |
| \( \frac{1}{20} \) |
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:
\( \frac{5!}{2!} \)
\( \frac{5 \times 4 \times 3 \times 2 \times 1}{2 \times 1} \)
\( \frac{5 \times 4 \times 3}{1} \)
\( 5 \times 4 \times 3 \)
60