| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.52 |
| Score | 0% | 70% |
In a class of 22 students, 6 are taking German and 15 are taking Spanish. Of the students studying German or Spanish, 5 are taking both courses. How many students are not enrolled in either course?
| 6 | |
| 21 | |
| 17 | |
| 11 |
The number of students taking German or Spanish is 6 + 15 = 21. Of that group of 21, 5 are taking both languages so they've been counted twice (once in the German group and once in the Spanish group). Subtracting them out leaves 21 - 5 = 16 who are taking at least one language. 22 - 16 = 6 students who are not taking either language.
4! = ?
4 x 3 x 2 x 1 |
|
3 x 2 x 1 |
|
4 x 3 |
|
5 x 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.
What is the next number in this sequence: 1, 4, 10, 19, 31, __________ ?
| 55 | |
| 46 | |
| 54 | |
| 37 |
The equation for this sequence is:
an = an-1 + 3(n - 1)
where n is the term's order in the sequence, an is the value of the term, and an-1 is the value of the term before an. This makes the next number:
a6 = a5 + 3(6 - 1)
a6 = 31 + 3(5)
a6 = 46
How many hours does it take a car to travel 110 miles at an average speed of 55 miles per hour?
| 5 hours | |
| 2 hours | |
| 9 hours | |
| 3 hours |
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 time:
time = \( \frac{\text{distance}}{\text{speed}} \)
time = \( \frac{110mi}{55mph} \)
2 hours
A machine in a factory has an error rate of 6 parts per 100. The machine normally runs 24 hours a day and produces 8 parts per hour. Yesterday the machine was shut down for 8 hours for maintenance.
How many error-free parts did the machine produce yesterday?
| 120.3 | |
| 176.7 | |
| 135.2 | |
| 96.9 |
The hourly error rate for this machine is the error rate in parts per 100 multiplied by the number of parts produced per hour:
\( \frac{6}{100} \) x 8 = \( \frac{6 \times 8}{100} \) = \( \frac{48}{100} \) = 0.48 errors per hour
So, in an average hour, the machine will produce 8 - 0.48 = 7.52 error free parts.
The machine ran for 24 - 8 = 16 hours yesterday so you would expect that 16 x 7.52 = 120.3 error free parts were produced yesterday.