| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.52 |
| Score | 0% | 70% |
What is (y2)5?
| y-3 | |
| y10 | |
| 2y5 | |
| y7 |
To raise a term with an exponent to another exponent, retain the base and multiply the exponents:
(y2)5Bob loaned Monica $700 at an annual interest rate of 1%. If no payments are made, what is the total amount owed at the end of the first year?
| $763 | |
| $735 | |
| $707 | |
| $756 |
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 $700
i = 0.01 x $700
No payments were made so the total amount due is the original amount + the accumulated interest:
total = $700 + $7What is the next number in this sequence: 1, 9, 17, 25, 33, __________ ?
| 41 | |
| 32 | |
| 36 | |
| 34 |
The equation for this sequence is:
an = an-1 + 8
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 + 8
a6 = 33 + 8
a6 = 41
A machine in a factory has an error rate of 3 parts per 100. The machine normally runs 24 hours a day and produces 10 parts per hour. Yesterday the machine was shut down for 5 hours for maintenance.
How many error-free parts did the machine produce yesterday?
| 184.3 | |
| 117.2 | |
| 89.3 | |
| 117.6 |
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 10 = \( \frac{3 \times 10}{100} \) = \( \frac{30}{100} \) = 0.3 errors per hour
So, in an average hour, the machine will produce 10 - 0.3 = 9.7 error free parts.
The machine ran for 24 - 5 = 19 hours yesterday so you would expect that 19 x 9.7 = 184.3 error free parts were produced yesterday.
What is \( \frac{5}{2} \) - \( \frac{8}{4} \)?
| 1 \( \frac{6}{14} \) | |
| \(\frac{1}{2}\) | |
| \( \frac{3}{7} \) | |
| \( \frac{7}{15} \) |
To subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 2 are [2, 4, 6, 8, 10, 12, 14, 16, 18, 20] and the first few multiples of 4 are [4, 8, 12, 16, 20, 24, 28, 32, 36, 40]. The first few multiples they share are [4, 8, 12, 16, 20] making 4 the smallest multiple 2 and 4 share.
Next, convert the fractions so each denominator equals the lowest common multiple:
\( \frac{5 x 2}{2 x 2} \) - \( \frac{8 x 1}{4 x 1} \)
\( \frac{10}{4} \) - \( \frac{8}{4} \)
Now, because the fractions share a common denominator, you can subtract them:
\( \frac{10 - 8}{4} \) = \( \frac{2}{4} \) = \(\frac{1}{2}\)