| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.17 |
| Score | 0% | 63% |
Solve 5 + (5 + 3) ÷ 3 x 2 - 42
| 1\(\frac{1}{7}\) | |
| 1 | |
| \(\frac{4}{7}\) | |
| -5\(\frac{2}{3}\) |
Use PEMDAS (Parentheses, Exponents, Multipy/Divide, Add/Subtract):
5 + (5 + 3) ÷ 3 x 2 - 42
P: 5 + (8) ÷ 3 x 2 - 42
E: 5 + 8 ÷ 3 x 2 - 16
MD: 5 + \( \frac{8}{3} \) x 2 - 16
MD: 5 + \( \frac{16}{3} \) - 16
AS: \( \frac{15}{3} \) + \( \frac{16}{3} \) - 16
AS: \( \frac{31}{3} \) - 16
AS: \( \frac{31 - 48}{3} \)
\( \frac{-17}{3} \)
-5\(\frac{2}{3}\)
What is -9y3 + 4y3?
| -5y6 | |
| -13y-3 | |
| 13y3 | |
| -5y3 |
To add or subtract terms with exponents, both the base and the exponent must be the same. In this case they are so add the coefficients and retain the base and exponent:
-9y3 + 4y3
(-9 + 4)y3
-5y3
Monty loaned Diane $500 at an annual interest rate of 3%. If no payments are made, what is the total amount owed at the end of the first year?
| $535 | |
| $515 | |
| $520 | |
| $505 |
The yearly interest charged on this loan is the annual interest rate multiplied by the amount borrowed:
interest = annual interest rate x loan amount
i = (\( \frac{6}{100} \)) x $500
i = 0.03 x $500
No payments were made so the total amount due is the original amount + the accumulated interest:
total = $500 + $154! = ?
4 x 3 |
|
4 x 3 x 2 x 1 |
|
3 x 2 x 1 |
|
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.
On average, the center for a basketball team hits 50% of his shots while a guard on the same team hits 55% of his shots. If the guard takes 30 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?
| 53 | |
| 40 | |
| 27 | |
| 32 |
guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 30 x \( \frac{55}{100} \) = \( \frac{55 x 30}{100} \) = \( \frac{1650}{100} \) = 16 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 = \( \frac{16}{\frac{50}{100}} \) = 16 x \( \frac{100}{50} \) = \( \frac{16 x 100}{50} \) = \( \frac{1600}{50} \) = 32 shots
to make the same number of shots as the guard and thus score the same number of points.