| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.07 |
| Score | 0% | 61% |
4! = ?
4 x 3 |
|
5 x 4 x 3 x 2 x 1 |
|
3 x 2 x 1 |
|
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.
If the ratio of home fans to visiting fans in a crowd is 2:1 and all 39,000 seats in a stadium are filled, how many home fans are in attendance?
| 33,333 | |
| 26,000 | |
| 27,500 | |
| 41,667 |
A ratio of 2:1 means that there are 2 home fans for every one visiting fan. So, of every 3 fans, 2 are home fans and \( \frac{2}{3} \) of every fan in the stadium is a home fan:
39,000 fans x \( \frac{2}{3} \) = \( \frac{78000}{3} \) = 26,000 fans.
What is 8y3 x y2?
| 9y2 | |
| 8y5 | |
| 9y3 | |
| 8y3 |
To multiply terms with exponents, the base of both exponents must be the same. In this case they are so multiply the coefficients and add the exponents:
8y3 x y2
(8 x 1)y(3 + 2)
8y5
A machine in a factory has an error rate of 5 parts per 100. The machine normally runs 24 hours a day and produces 5 parts per hour. Yesterday the machine was shut down for 2 hours for maintenance.
How many error-free parts did the machine produce yesterday?
| 186 | |
| 78.2 | |
| 102.9 | |
| 104.5 |
The hourly error rate for this machine is the error rate in parts per 100 multiplied by the number of parts produced per hour:
\( \frac{5}{100} \) x 5 = \( \frac{5 \times 5}{100} \) = \( \frac{25}{100} \) = 0.25 errors per hour
So, in an average hour, the machine will produce 5 - 0.25 = 4.75 error free parts.
The machine ran for 24 - 2 = 22 hours yesterday so you would expect that 22 x 4.75 = 104.5 error free parts were produced yesterday.
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?
| 50 m2 | |
| 72 m2 | |
| 162 m2 | |
| 18 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