| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.84 |
| Score | 0% | 57% |
In a class of 21 students, 8 are taking German and 8 are taking Spanish. Of the students studying German or Spanish, 5 are taking both courses. How many students are not enrolled in either course?
| 19 | |
| 17 | |
| 10 | |
| 14 |
The number of students taking German or Spanish is 8 + 8 = 16. Of that group of 16, 5 are taking both languages so they've been counted twice (once in the German group and once in the Spanish group). Subtracting them out leaves 16 - 5 = 11 who are taking at least one language. 21 - 11 = 10 students who are not taking either language.
Convert 631,000 to scientific notation.
| 63.1 x 104 | |
| 6.31 x 105 | |
| 6.31 x 106 | |
| 0.631 x 106 |
A number in scientific notation has the format 0.000 x 10exponent. To convert to scientific notation, move the decimal point to the right or the left until the number is a decimal between 1 and 10. The exponent of the 10 is the number of places you moved the decimal point and is positive if you moved the decimal point to the left and negative if you moved it to the right:
631,000 in scientific notation is 6.31 x 105
If a rectangle is twice as long as it is wide and has a perimeter of 54 meters, what is the area of the rectangle?
| 32 m2 | |
| 162 m2 | |
| 98 m2 | |
| 72 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 54 meters so the equation becomes: 2w + 2h = 54.
Putting these two equations together and solving for width (w):
2w + 2h = 54
w + h = \( \frac{54}{2} \)
w + h = 27
w = 27 - h
From the question we know that h = 2w so substituting 2w for h gives us:
w = 27 - 2w
3w = 27
w = \( \frac{27}{3} \)
w = 9
Since h = 2w that makes h = (2 x 9) = 18 and the area = h x w = 9 x 18 = 162 m2
What is \( \frac{8}{6} \) - \( \frac{6}{14} \)?
| 2 \( \frac{6}{10} \) | |
| 2 \( \frac{2}{42} \) | |
| \(\frac{19}{21}\) | |
| 1 \( \frac{2}{42} \) |
To subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 6 are [6, 12, 18, 24, 30, 36, 42, 48, 54, 60] and the first few multiples of 14 are [14, 28, 42, 56, 70, 84, 98]. The first few multiples they share are [42, 84] making 42 the smallest multiple 6 and 14 share.
Next, convert the fractions so each denominator equals the lowest common multiple:
\( \frac{8 x 7}{6 x 7} \) - \( \frac{6 x 3}{14 x 3} \)
\( \frac{56}{42} \) - \( \frac{18}{42} \)
Now, because the fractions share a common denominator, you can subtract them:
\( \frac{56 - 18}{42} \) = \( \frac{38}{42} \) = \(\frac{19}{21}\)
If a mayor is elected with 63% of the votes cast and 33% of a town's 22,000 voters cast a vote, how many votes did the mayor receive?
| 5,808 | |
| 4,574 | |
| 6,461 | |
| 4,937 |
If 33% of the town's 22,000 voters cast ballots the number of votes cast is:
(\( \frac{33}{100} \)) x 22,000 = \( \frac{726,000}{100} \) = 7,260
The mayor got 63% of the votes cast which is:
(\( \frac{63}{100} \)) x 7,260 = \( \frac{457,380}{100} \) = 4,574 votes.