| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.19 |
| Score | 0% | 64% |
A machine in a factory has an error rate of 3 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?
| 72.8 | |
| 124.2 | |
| 139.7 | |
| 200.2 |
The hourly error rate for this machine is the error rate in parts per 100 multiplied by the number of parts produced per hour:
\( \frac{3}{100} \) x 8 = \( \frac{3 \times 8}{100} \) = \( \frac{24}{100} \) = 0.24 errors per hour
So, in an average hour, the machine will produce 8 - 0.24 = 7.76 error free parts.
The machine ran for 24 - 8 = 16 hours yesterday so you would expect that 16 x 7.76 = 124.2 error free parts were produced yesterday.
What is the next number in this sequence: 1, 5, 9, 13, 17, __________ ?
| 20 | |
| 15 | |
| 21 | |
| 18 |
The equation for this sequence is:
an = an-1 + 4
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 + 4
a6 = 17 + 4
a6 = 21
Bob loaned Ezra $1,400 at an annual interest rate of 1%. If no payments are made, what is the interest owed on this loan at the end of the first year?
| $5 | |
| $14 | |
| $12 | |
| $6 |
The yearly interest charged on this loan is the annual interest rate multiplied by the amount borrowed:
interest = annual interest rate x loan amount
i = (\( \frac{6}{100} \)) x $1,400
i = 0.01 x $1,400
i = $14
What is 9\( \sqrt{9} \) x 8\( \sqrt{7} \)?
| 216\( \sqrt{7} \) | |
| 17\( \sqrt{9} \) | |
| 72\( \sqrt{7} \) | |
| 17\( \sqrt{63} \) |
To multiply terms with radicals, multiply the coefficients and radicands separately:
9\( \sqrt{9} \) x 8\( \sqrt{7} \)
(9 x 8)\( \sqrt{9 \times 7} \)
72\( \sqrt{63} \)
Now we need to simplify the radical:
72\( \sqrt{63} \)
72\( \sqrt{7 \times 9} \)
72\( \sqrt{7 \times 3^2} \)
(72)(3)\( \sqrt{7} \)
216\( \sqrt{7} \)
In a class of 38 students, 15 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?
| 21 | |
| 14 | |
| 30 | |
| 23 |
The number of students taking German or Spanish is 15 + 11 = 26. Of that group of 26, 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 26 - 2 = 24 who are taking at least one language. 38 - 24 = 14 students who are not taking either language.