| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.97 |
| Score | 0% | 59% |
Bob loaned Ezra $500 at an annual interest rate of 9%. If no payments are made, what is the interest owed on this loan at the end of the first year?
| $90 | |
| $48 | |
| $45 | |
| $30 |
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 $500
i = 0.09 x $500
i = $45
The __________ is the smallest positive integer that is a multiple of two or more integers.
least common multiple |
|
least common factor |
|
absolute value |
|
greatest common factor |
The least common multiple (LCM) is the smallest positive integer that is a multiple of two or more integers.
What is 3\( \sqrt{6} \) x 7\( \sqrt{4} \)?
| 21\( \sqrt{4} \) | |
| 10\( \sqrt{24} \) | |
| 42\( \sqrt{6} \) | |
| 21\( \sqrt{10} \) |
To multiply terms with radicals, multiply the coefficients and radicands separately:
3\( \sqrt{6} \) x 7\( \sqrt{4} \)
(3 x 7)\( \sqrt{6 \times 4} \)
21\( \sqrt{24} \)
Now we need to simplify the radical:
21\( \sqrt{24} \)
21\( \sqrt{6 \times 4} \)
21\( \sqrt{6 \times 2^2} \)
(21)(2)\( \sqrt{6} \)
42\( \sqrt{6} \)
How many 16-passenger vans will it take to drive all 77 members of the football team to an away game?
| 5 vans | |
| 6 vans | |
| 7 vans | |
| 8 vans |
Calculate the number of vans needed by dividing the number of people that need transported by the capacity of one van:
vans = \( \frac{77}{16} \) = 4\(\frac{13}{16}\)
So, it will take 4 full vans and one partially full van to transport the entire team making a total of 5 vans.
If a rectangle is twice as long as it is wide and has a perimeter of 12 meters, what is the area of the rectangle?
| 32 m2 | |
| 72 m2 | |
| 8 m2 | |
| 98 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 12 meters so the equation becomes: 2w + 2h = 12.
Putting these two equations together and solving for width (w):
2w + 2h = 12
w + h = \( \frac{12}{2} \)
w + h = 6
w = 6 - h
From the question we know that h = 2w so substituting 2w for h gives us:
w = 6 - 2w
3w = 6
w = \( \frac{6}{3} \)
w = 2
Since h = 2w that makes h = (2 x 2) = 4 and the area = h x w = 2 x 4 = 8 m2