| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.64 |
| Score | 0% | 53% |
If a rectangle is twice as long as it is wide and has a perimeter of 42 meters, what is the area of the rectangle?
| 162 m2 | |
| 98 m2 | |
| 50 m2 | |
| 128 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 42 meters so the equation becomes: 2w + 2h = 42.
Putting these two equations together and solving for width (w):
2w + 2h = 42
w + h = \( \frac{42}{2} \)
w + h = 21
w = 21 - h
From the question we know that h = 2w so substituting 2w for h gives us:
w = 21 - 2w
3w = 21
w = \( \frac{21}{3} \)
w = 7
Since h = 2w that makes h = (2 x 7) = 14 and the area = h x w = 7 x 14 = 98 m2
On average, the center for a basketball team hits 25% of his shots while a guard on the same team hits 45% 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?
| 7 | |
| 9 | |
| 16 | |
| 8 |
guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 10 x \( \frac{45}{100} \) = \( \frac{45 x 10}{100} \) = \( \frac{450}{100} \) = 4 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 = \( \frac{4}{\frac{25}{100}} \) = 4 x \( \frac{100}{25} \) = \( \frac{4 x 100}{25} \) = \( \frac{400}{25} \) = 16 shots
to make the same number of shots as the guard and thus score the same number of points.
Which of the following is an improper fraction?
\(1 {2 \over 5} \) |
|
\({7 \over 5} \) |
|
\({a \over 5} \) |
|
\({2 \over 5} \) |
A rational number (or fraction) is represented as a ratio between two integers, a and b, and has the form \({a \over b}\) where a is the numerator and b is the denominator. An improper fraction (\({5 \over 3} \)) has a numerator with a greater absolute value than the denominator and can be converted into a mixed number (\(1 {2 \over 3} \)) which has a whole number part and a fractional part.
How many 2 gallon cans worth of fuel would you need to pour into an empty 12 gallon tank to fill it exactly halfway?
| 3 | |
| 9 | |
| 7 | |
| 6 |
To fill a 12 gallon tank exactly halfway you'll need 6 gallons of fuel. Each fuel can holds 2 gallons so:
cans = \( \frac{6 \text{ gallons}}{2 \text{ gallons}} \) = 3
If a mayor is elected with 87% of the votes cast and 31% of a town's 48,000 voters cast a vote, how many votes did the mayor receive?
| 7,589 | |
| 12,202 | |
| 12,946 | |
| 12,648 |
If 31% of the town's 48,000 voters cast ballots the number of votes cast is:
(\( \frac{31}{100} \)) x 48,000 = \( \frac{1,488,000}{100} \) = 14,880
The mayor got 87% of the votes cast which is:
(\( \frac{87}{100} \)) x 14,880 = \( \frac{1,294,560}{100} \) = 12,946 votes.