| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.98 |
| Score | 0% | 60% |
Convert b-2 to remove the negative exponent.
| \( \frac{-2}{-b} \) | |
| \( \frac{1}{b^2} \) | |
| \( \frac{-1}{b^{-2}} \) | |
| \( \frac{2}{b} \) |
To convert a negative exponent to a positive exponent, calculate the positive exponent then take the reciprocal.
Solve for \( \frac{4!}{3!} \)
| 9 | |
| \( \frac{1}{20} \) | |
| 4 | |
| 6720 |
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:
\( \frac{4!}{3!} \)
\( \frac{4 \times 3 \times 2 \times 1}{3 \times 2 \times 1} \)
\( \frac{4}{1} \)
4
On average, the center for a basketball team hits 30% of his shots while a guard on the same team hits 50% of his shots. If the guard takes 20 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?
| 33 | |
| 19 | |
| 18 | |
| 17 |
guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 20 x \( \frac{50}{100} \) = \( \frac{50 x 20}{100} \) = \( \frac{1000}{100} \) = 10 shots
The center makes 30% 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 = \( \frac{10}{\frac{30}{100}} \) = 10 x \( \frac{100}{30} \) = \( \frac{10 x 100}{30} \) = \( \frac{1000}{30} \) = 33 shots
to make the same number of shots as the guard and thus score the same number of points.
A menswear store is having a sale: "Buy one shirt at full price and get another shirt for 5% off." If Alex buys two shirts, each with a regular price of $46, how much money will he save?
| $4.60 | |
| $23.00 | |
| $18.40 | |
| $2.30 |
By buying two shirts, Alex will save $46 x \( \frac{5}{100} \) = \( \frac{$46 x 5}{100} \) = \( \frac{$230}{100} \) = $2.30 on the second shirt.
If the ratio of home fans to visiting fans in a crowd is 3:1 and all 46,000 seats in a stadium are filled, how many home fans are in attendance?
| 34,500 | |
| 25,600 | |
| 30,000 | |
| 20,667 |
A ratio of 3:1 means that there are 3 home fans for every one visiting fan. So, of every 4 fans, 3 are home fans and \( \frac{3}{4} \) of every fan in the stadium is a home fan:
46,000 fans x \( \frac{3}{4} \) = \( \frac{138000}{4} \) = 34,500 fans.