| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.89 |
| Score | 0% | 58% |
What is \( \frac{-4y^6}{4y^3} \)?
| -y3 | |
| -y\(\frac{1}{2}\) | |
| -y-3 | |
| -y18 |
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:
\( \frac{-4y^6}{4y^3} \)
\( \frac{-4}{4} \) y(6 - 3)
-y3
Which of the following is not a prime number?
9 |
|
7 |
|
5 |
|
2 |
A prime number is an integer greater than 1 that has no factors other than 1 and itself. Examples of prime numbers include 2, 3, 5, 7, and 11.
A machine in a factory has an error rate of 7 parts per 100. The machine normally runs 24 hours a day and produces 8 parts per hour. Yesterday the machine was shut down for 3 hours for maintenance.
How many error-free parts did the machine produce yesterday?
| 156.2 | |
| 152.3 | |
| 132.5 | |
| 133 |
The hourly error rate for this machine is the error rate in parts per 100 multiplied by the number of parts produced per hour:
\( \frac{7}{100} \) x 8 = \( \frac{7 \times 8}{100} \) = \( \frac{56}{100} \) = 0.56 errors per hour
So, in an average hour, the machine will produce 8 - 0.56 = 7.4399999999999995 error free parts.
The machine ran for 24 - 3 = 21 hours yesterday so you would expect that 21 x 7.4399999999999995 = 156.2 error free parts were produced yesterday.
A menswear store is having a sale: "Buy one shirt at full price and get another shirt for 40% off." If Damon buys two shirts, each with a regular price of $40, how much will he pay for both shirts?
| $24.00 | |
| $16.00 | |
| $60.00 | |
| $64.00 |
By buying two shirts, Damon will save $40 x \( \frac{40}{100} \) = \( \frac{$40 x 40}{100} \) = \( \frac{$1600}{100} \) = $16.00 on the second shirt.
So, his total cost will be
$40.00 + ($40.00 - $16.00)
$40.00 + $24.00
$64.00
The total water usage for a city is 10,000 gallons each day. Of that total, 30% is for personal use and 65% is for industrial use. How many more gallons of water each day is consumed for industrial use over personal use?
| 3,500 | |
| 650 | |
| 11,200 | |
| 4,000 |
65% of the water consumption is industrial use and 30% is personal use so (65% - 30%) = 35% more water is used for industrial purposes. 10,000 gallons are consumed daily so industry consumes \( \frac{35}{100} \) x 10,000 gallons = 3,500 gallons.