| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.94 |
| Score | 0% | 59% |
The __________ is the greatest factor that divides two integers.
absolute value |
|
least common multiple |
|
greatest common factor |
|
greatest common multiple |
The greatest common factor (GCF) is the greatest factor that divides two integers.
A machine in a factory has an error rate of 9 parts per 100. The machine normally runs 24 hours a day and produces 5 parts per hour. Yesterday the machine was shut down for 8 hours for maintenance.
How many error-free parts did the machine produce yesterday?
| 81.9 | |
| 97.7 | |
| 72.8 | |
| 98.7 |
The hourly error rate for this machine is the error rate in parts per 100 multiplied by the number of parts produced per hour:
\( \frac{9}{100} \) x 5 = \( \frac{9 \times 5}{100} \) = \( \frac{45}{100} \) = 0.45 errors per hour
So, in an average hour, the machine will produce 5 - 0.45 = 4.55 error free parts.
The machine ran for 24 - 8 = 16 hours yesterday so you would expect that 16 x 4.55 = 72.8 error free parts were produced yesterday.
A tiger in a zoo has consumed 18 pounds of food in 3 days. If the tiger continues to eat at the same rate, in how many more days will its total food consumtion be 60 pounds?
| 6 | |
| 2 | |
| 10 | |
| 7 |
If the tiger has consumed 18 pounds of food in 3 days that's \( \frac{18}{3} \) = 6 pounds of food per day. The tiger needs to consume 60 - 18 = 42 more pounds of food to reach 60 pounds total. At 6 pounds of food per day that's \( \frac{42}{6} \) = 7 more days.
If a rectangle is twice as long as it is wide and has a perimeter of 36 meters, what is the area of the rectangle?
| 128 m2 | |
| 72 m2 | |
| 162 m2 | |
| 32 m2 |
The area of a rectangle is width (w) x height (h). In this problem we know that the rectangle is twice as long as it is wide so h = 2w. The perimeter of a rectangle is 2w + 2h and we know that the perimeter of this rectangle is 36 meters so the equation becomes: 2w + 2h = 36.
Putting these two equations together and solving for width (w):
2w + 2h = 36
w + h = \( \frac{36}{2} \)
w + h = 18
w = 18 - h
From the question we know that h = 2w so substituting 2w for h gives us:
w = 18 - 2w
3w = 18
w = \( \frac{18}{3} \)
w = 6
Since h = 2w that makes h = (2 x 6) = 12 and the area = h x w = 6 x 12 = 72 m2
Monty loaned Frank $1,100 at an annual interest rate of 3%. If no payments are made, what is the interest owed on this loan at the end of the first year?
| $91 | |
| $56 | |
| $28 | |
| $33 |
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 $1,100
i = 0.03 x $1,100
i = $33