| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.03 |
| Score | 0% | 61% |
On average, the center for a basketball team hits 25% of his shots while a guard on the same team hits 30% 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?
| 16 | |
| 10 | |
| 12 | |
| 24 |
guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 20 x \( \frac{30}{100} \) = \( \frac{30 x 20}{100} \) = \( \frac{600}{100} \) = 6 shots
The center makes 25% 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 = \( \frac{6}{\frac{25}{100}} \) = 6 x \( \frac{100}{25} \) = \( \frac{6 x 100}{25} \) = \( \frac{600}{25} \) = 24 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 25% off." If Frank buys two shirts, each with a regular price of $17, how much will he pay for both shirts?
| $4.25 | |
| $18.70 | |
| $29.75 | |
| $20.40 |
By buying two shirts, Frank will save $17 x \( \frac{25}{100} \) = \( \frac{$17 x 25}{100} \) = \( \frac{$425}{100} \) = $4.25 on the second shirt.
So, his total cost will be
$17.00 + ($17.00 - $4.25)
$17.00 + $12.75
$29.75
What is the distance in miles of a trip that takes 3 hours at an average speed of 25 miles per hour?
| 560 miles | |
| 60 miles | |
| 50 miles | |
| 75 miles |
Average speed in miles per hour is the number of miles traveled divided by the number of hours:
speed = \( \frac{\text{distance}}{\text{time}} \)Solving for distance:
distance = \( \text{speed} \times \text{time} \)
distance = \( 25mph \times 3h \)
75 miles
What is \( \frac{14\sqrt{18}}{2\sqrt{6}} \)?
| 3 \( \sqrt{7} \) | |
| 7 \( \sqrt{3} \) | |
| \(\frac{1}{3}\) \( \sqrt{\frac{1}{7}} \) | |
| \(\frac{1}{7}\) \( \sqrt{3} \) |
To divide terms with radicals, divide the coefficients and radicands separately:
\( \frac{14\sqrt{18}}{2\sqrt{6}} \)
\( \frac{14}{2} \) \( \sqrt{\frac{18}{6}} \)
7 \( \sqrt{3} \)
If a rectangle is twice as long as it is wide and has a perimeter of 24 meters, what is the area of the rectangle?
| 72 m2 | |
| 32 m2 | |
| 2 m2 | |
| 50 m2 |
The area of a rectangle is width (w) x height (h). In this problem we know that the rectangle is twice as long as it is wide so h = 2w. The perimeter of a rectangle is 2w + 2h and we know that the perimeter of this rectangle is 24 meters so the equation becomes: 2w + 2h = 24.
Putting these two equations together and solving for width (w):
2w + 2h = 24
w + h = \( \frac{24}{2} \)
w + h = 12
w = 12 - h
From the question we know that h = 2w so substituting 2w for h gives us:
w = 12 - 2w
3w = 12
w = \( \frac{12}{3} \)
w = 4
Since h = 2w that makes h = (2 x 4) = 8 and the area = h x w = 4 x 8 = 32 m2