| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.72 |
| Score | 0% | 54% |
A machine in a factory has an error rate of 8 parts per 100. The machine normally runs 24 hours a day and produces 8 parts per hour. Yesterday the machine was shut down for 4 hours for maintenance.
How many error-free parts did the machine produce yesterday?
| 118.4 | |
| 98 | |
| 156.2 | |
| 147.2 |
The hourly error rate for this machine is the error rate in parts per 100 multiplied by the number of parts produced per hour:
\( \frac{8}{100} \) x 8 = \( \frac{8 \times 8}{100} \) = \( \frac{64}{100} \) = 0.64 errors per hour
So, in an average hour, the machine will produce 8 - 0.64 = 7.36 error free parts.
The machine ran for 24 - 4 = 20 hours yesterday so you would expect that 20 x 7.36 = 147.2 error free parts were produced yesterday.
In a class of 36 students, 12 are taking German and 11 are taking Spanish. Of the students studying German or Spanish, 2 are taking both courses. How many students are not enrolled in either course?
| 20 | |
| 15 | |
| 30 | |
| 24 |
The number of students taking German or Spanish is 12 + 11 = 23. Of that group of 23, 2 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 23 - 2 = 21 who are taking at least one language. 36 - 21 = 15 students who are not taking either language.
What is \( \frac{-2z^7}{4z^3} \)?
| -\(\frac{1}{2}\)z\(\frac{3}{7}\) | |
| -\(\frac{1}{2}\)z-4 | |
| -\(\frac{1}{2}\)z4 | |
| -2z-4 |
To divide terms with exponents, the base of both exponents must be the same. In this case they are so divide the coefficients and subtract the exponents:
\( \frac{-2z^7}{4z^3} \)
\( \frac{-2}{4} \) z(7 - 3)
-\(\frac{1}{2}\)z4
A circular logo is enlarged to fit the lid of a jar. The new diameter is 65% larger than the original. By what percentage has the area of the logo increased?
| 32\(\frac{1}{2}\)% | |
| 22\(\frac{1}{2}\)% | |
| 27\(\frac{1}{2}\)% | |
| 30% |
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 65% the radius (and, consequently, the total area) increases by \( \frac{65\text{%}}{2} \) = 32\(\frac{1}{2}\)%
If the ratio of home fans to visiting fans in a crowd is 4:1 and all 38,000 seats in a stadium are filled, how many home fans are in attendance?
| 34,400 | |
| 33,000 | |
| 30,400 | |
| 22,000 |
A ratio of 4:1 means that there are 4 home fans for every one visiting fan. So, of every 5 fans, 4 are home fans and \( \frac{4}{5} \) of every fan in the stadium is a home fan:
38,000 fans x \( \frac{4}{5} \) = \( \frac{152000}{5} \) = 30,400 fans.