| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.12 |
| Score | 0% | 62% |
What is \( 5 \)\( \sqrt{50} \) - \( 5 \)\( \sqrt{2} \)
| 25\( \sqrt{2} \) | |
| 0\( \sqrt{50} \) | |
| 25\( \sqrt{100} \) | |
| 20\( \sqrt{2} \) |
To subtract these radicals together their radicands must be the same:
5\( \sqrt{50} \) - 5\( \sqrt{2} \)
5\( \sqrt{25 \times 2} \) - 5\( \sqrt{2} \)
5\( \sqrt{5^2 \times 2} \) - 5\( \sqrt{2} \)
(5)(5)\( \sqrt{2} \) - 5\( \sqrt{2} \)
25\( \sqrt{2} \) - 5\( \sqrt{2} \)
Now that the radicands are identical, you can subtract them:
25\( \sqrt{2} \) - 5\( \sqrt{2} \)11 members of a bridal party need transported to a wedding reception but there are only 4 2-passenger taxis available to take them. How many will need to find other transportation?
| 2 | |
| 4 | |
| 3 | |
| 8 |
There are 4 2-passenger taxis available so that's 4 x 2 = 8 total seats. There are 11 people needing transportation leaving 11 - 8 = 3 who will have to find other transportation.
Alex loaned Jennifer $900 at an annual interest rate of 8%. If no payments are made, what is the total amount owed at the end of the first year?
| $963 | |
| $918 | |
| $981 | |
| $972 |
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 $900
i = 0.08 x $900
No payments were made so the total amount due is the original amount + the accumulated interest:
total = $900 + $72A triathlon course includes a 200m swim, a 40.6km bike ride, and a 7.0km run. What is the total length of the race course?
| 66.7km | |
| 35.2km | |
| 42.9km | |
| 47.8km |
To add these distances, they must share the same unit so first you need to first convert the swim distance from meters (m) to kilometers (km) before adding it to the bike and run distances which are already in km. To convert 200 meters to kilometers, divide the distance by 1000 to get 0.2km then add the remaining distances:
total distance = swim + bike + run
total distance = 0.2km + 40.6km + 7.0km
total distance = 47.8km
The total water usage for a city is 50,000 gallons each day. Of that total, 27% is for personal use and 54% is for industrial use. How many more gallons of water each day is consumed for industrial use over personal use?
| 5,500 | |
| 13,500 | |
| 7,500 | |
| 9,450 |
54% of the water consumption is industrial use and 27% is personal use so (54% - 27%) = 27% more water is used for industrial purposes. 50,000 gallons are consumed daily so industry consumes \( \frac{27}{100} \) x 50,000 gallons = 13,500 gallons.