| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.78 |
| Score | 0% | 56% |
If a rectangle is twice as long as it is wide and has a perimeter of 30 meters, what is the area of the rectangle?
| 8 m2 | |
| 50 m2 | |
| 128 m2 | |
| 162 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 30 meters so the equation becomes: 2w + 2h = 30.
Putting these two equations together and solving for width (w):
2w + 2h = 30
w + h = \( \frac{30}{2} \)
w + h = 15
w = 15 - h
From the question we know that h = 2w so substituting 2w for h gives us:
w = 15 - 2w
3w = 15
w = \( \frac{15}{3} \)
w = 5
Since h = 2w that makes h = (2 x 5) = 10 and the area = h x w = 5 x 10 = 50 m2
A circular logo is enlarged to fit the lid of a jar. The new diameter is 50% larger than the original. By what percentage has the area of the logo increased?
| 27\(\frac{1}{2}\)% | |
| 25% | |
| 15% | |
| 37\(\frac{1}{2}\)% |
The area of a circle is given by the formula A = πr2 where r is the radius of the circle. The radius of a circle is its diameter divided by two so A = π(\( \frac{d}{2} \))2. If the diameter of the logo increases by 50% the radius (and, consequently, the total area) increases by \( \frac{50\text{%}}{2} \) = 25%
A triathlon course includes a 200m swim, a 30.5km bike ride, and a 12.3km run. What is the total length of the race course?
| 44.6km | |
| 54.8km | |
| 38.5km | |
| 43km |
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 200 meters to kilometers, divide the distance by 1000 to get 0.2km then add the remaining distances:
total distance = swim + bike + run
total distance = 0.2km + 30.5km + 12.3km
total distance = 43km
If the ratio of home fans to visiting fans in a crowd is 3:1 and all 32,000 seats in a stadium are filled, how many home fans are in attendance?
| 24,000 | |
| 33,750 | |
| 24,667 | |
| 27,333 |
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:
32,000 fans x \( \frac{3}{4} \) = \( \frac{96000}{4} \) = 24,000 fans.
What is \( \frac{7}{3} \) - \( \frac{3}{9} \)?
| 2 | |
| 2 \( \frac{5}{12} \) | |
| \( \frac{2}{9} \) | |
| \( \frac{7}{16} \) |
To subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 3 are [3, 6, 9, 12, 15, 18, 21, 24, 27, 30] and the first few multiples of 9 are [9, 18, 27, 36, 45, 54, 63, 72, 81, 90]. The first few multiples they share are [9, 18, 27, 36, 45] making 9 the smallest multiple 3 and 9 share.
Next, convert the fractions so each denominator equals the lowest common multiple:
\( \frac{7 x 3}{3 x 3} \) - \( \frac{3 x 1}{9 x 1} \)
\( \frac{21}{9} \) - \( \frac{3}{9} \)
Now, because the fractions share a common denominator, you can subtract them:
\( \frac{21 - 3}{9} \) = \( \frac{18}{9} \) = 2