| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.40 |
| Score | 0% | 68% |
If \( \left|y + 1\right| \) - 9 = -5, which of these is a possible value for y?
| 2 | |
| -4 | |
| -5 | |
| -8 |
First, solve for \( \left|y + 1\right| \):
\( \left|y + 1\right| \) - 9 = -5
\( \left|y + 1\right| \) = -5 + 9
\( \left|y + 1\right| \) = 4
The value inside the absolute value brackets can be either positive or negative so (y + 1) must equal + 4 or -4 for \( \left|y + 1\right| \) to equal 4:
| y + 1 = 4 y = 4 - 1 y = 3 | y + 1 = -4 y = -4 - 1 y = -5 |
So, y = -5 or y = 3.
How many 1 gallon cans worth of fuel would you need to pour into an empty 10 gallon tank to fill it exactly halfway?
| 9 | |
| 2 | |
| 10 | |
| 5 |
To fill a 10 gallon tank exactly halfway you'll need 5 gallons of fuel. Each fuel can holds 1 gallons so:
cans = \( \frac{5 \text{ gallons}}{1 \text{ gallons}} \) = 5
9 members of a bridal party need transported to a wedding reception but there are only 2 3-passenger taxis available to take them. How many will need to find other transportation?
| 2 | |
| 3 | |
| 1 | |
| 7 |
There are 2 3-passenger taxis available so that's 2 x 3 = 6 total seats. There are 9 people needing transportation leaving 9 - 6 = 3 who will have to find other transportation.
What is the distance in miles of a trip that takes 9 hours at an average speed of 45 miles per hour?
| 195 miles | |
| 405 miles | |
| 420 miles | |
| 135 miles |
Average speed in miles per hour is the number of miles traveled divided by the number of hours:
speed = \( \frac{\text{distance}}{\text{time}} \)Solving for distance:
distance = \( \text{speed} \times \text{time} \)
distance = \( 45mph \times 9h \)
405 miles
Solve for \( \frac{5!}{6!} \)
| \( \frac{1}{15120} \) | |
| \( \frac{1}{42} \) | |
| 56 | |
| \( \frac{1}{6} \) |
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:
\( \frac{5!}{6!} \)
\( \frac{5 \times 4 \times 3 \times 2 \times 1}{6 \times 5 \times 4 \times 3 \times 2 \times 1} \)
\( \frac{1}{6} \)
\( \frac{1}{6} \)