| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.08 |
| Score | 0% | 62% |
On average, the center for a basketball team hits 45% of his shots while a guard on the same team hits 55% of his shots. If the guard takes 10 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?
| 14 | |
| 19 | |
| 9 | |
| 11 |
guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 10 x \( \frac{55}{100} \) = \( \frac{55 x 10}{100} \) = \( \frac{550}{100} \) = 5 shots
The center makes 45% 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 = \( \frac{5}{\frac{45}{100}} \) = 5 x \( \frac{100}{45} \) = \( \frac{5 x 100}{45} \) = \( \frac{500}{45} \) = 11 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 50% off." If Charlie buys two shirts, each with a regular price of $49, how much money will he save?
| $9.80 | |
| $24.50 | |
| 78 | |
| $2.45 |
By buying two shirts, Charlie will save $49 x \( \frac{50}{100} \) = \( \frac{$49 x 50}{100} \) = \( \frac{$2450}{100} \) = $24.50 on the second shirt.
If \( \left|x + 6\right| \) + 0 = -4, which of these is a possible value for x?
| -2 | |
| -6 | |
| 9 | |
| 4 |
First, solve for \( \left|x + 6\right| \):
\( \left|x + 6\right| \) + 0 = -4
\( \left|x + 6\right| \) = -4 + 0
\( \left|x + 6\right| \) = -4
The value inside the absolute value brackets can be either positive or negative so (x + 6) must equal - 4 or --4 for \( \left|x + 6\right| \) to equal -4:
| x + 6 = -4 x = -4 - 6 x = -10 | x + 6 = 4 x = 4 - 6 x = -2 |
So, x = -2 or x = -10.
Convert 0.0008253 to scientific notation.
| 8.253 x 10-3 | |
| 8.253 x 10-4 | |
| 8.253 x 104 | |
| 8.253 x 10-5 |
A number in scientific notation has the format 0.000 x 10exponent. To convert to scientific notation, move the decimal point to the right or the left until the number is a decimal between 1 and 10. The exponent of the 10 is the number of places you moved the decimal point and is positive if you moved the decimal point to the left and negative if you moved it to the right:
0.0008253 in scientific notation is 8.253 x 10-4
A triathlon course includes a 400m swim, a 30.8km bike ride, and a 13.9km run. What is the total length of the race course?
| 36km | |
| 35.2km | |
| 61.7km | |
| 45.1km |
To add these distances, they must share the same unit so first you need to first convert the swim distance from meters (m) to kilometers (km) before adding it to the bike and run distances which are already in km. To convert 400 meters to kilometers, divide the distance by 1000 to get 0.4km then add the remaining distances:
total distance = swim + bike + run
total distance = 0.4km + 30.8km + 13.9km
total distance = 45.1km