| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.78 |
| Score | 0% | 56% |
A machine in a factory has an error rate of 4 parts per 100. The machine normally runs 24 hours a day and produces 5 parts per hour. Yesterday the machine was shut down for 5 hours for maintenance.
How many error-free parts did the machine produce yesterday?
| 84.6 | |
| 174.6 | |
| 91.2 | |
| 119.7 |
The hourly error rate for this machine is the error rate in parts per 100 multiplied by the number of parts produced per hour:
\( \frac{4}{100} \) x 5 = \( \frac{4 \times 5}{100} \) = \( \frac{20}{100} \) = 0.2 errors per hour
So, in an average hour, the machine will produce 5 - 0.2 = 4.8 error free parts.
The machine ran for 24 - 5 = 19 hours yesterday so you would expect that 19 x 4.8 = 91.2 error free parts were produced yesterday.
If the ratio of home fans to visiting fans in a crowd is 3:1 and all 43,000 seats in a stadium are filled, how many home fans are in attendance?
| 32,250 | |
| 31,200 | |
| 27,000 | |
| 20,667 |
A ratio of 3:1 means that there are 3 home fans for every one visiting fan. So, of every 4 fans, 3 are home fans and \( \frac{3}{4} \) of every fan in the stadium is a home fan:
43,000 fans x \( \frac{3}{4} \) = \( \frac{129000}{4} \) = 32,250 fans.
A menswear store is having a sale: "Buy one shirt at full price and get another shirt for 5% off." If Ezra buys two shirts, each with a regular price of $17, how much will he pay for both shirts?
| $16.15 | |
| $21.25 | |
| $33.15 | |
| $0.85 |
By buying two shirts, Ezra will save $17 x \( \frac{5}{100} \) = \( \frac{$17 x 5}{100} \) = \( \frac{$85}{100} \) = $0.85 on the second shirt.
So, his total cost will be
$17.00 + ($17.00 - $0.85)
$17.00 + $16.15
$33.15
The __________ is the smallest positive integer that is a multiple of two or more integers.
absolute value |
|
greatest common factor |
|
least common multiple |
|
least common factor |
The least common multiple (LCM) is the smallest positive integer that is a multiple of two or more integers.
Solve for \( \frac{4!}{2!} \)
| 12 | |
| \( \frac{1}{6} \) | |
| \( \frac{1}{3024} \) | |
| 8 |
A factorial is the product of an integer and all the positive integers below it. To solve a fraction featuring factorials, expand the factorials and cancel out like numbers:
\( \frac{4!}{2!} \)
\( \frac{4 \times 3 \times 2 \times 1}{2 \times 1} \)
\( \frac{4 \times 3}{1} \)
\( 4 \times 3 \)
12