| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.61 |
| Score | 0% | 52% |
In a class of 26 students, 12 are taking German and 8 are taking Spanish. Of the students studying German or Spanish, 2 are taking both courses. How many students are not enrolled in either course?
| 20 | |
| 14 | |
| 8 | |
| 16 |
The number of students taking German or Spanish is 12 + 8 = 20. Of that group of 20, 2 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 20 - 2 = 18 who are taking at least one language. 26 - 18 = 8 students who are not taking either language.
On average, the center for a basketball team hits 35% of his shots while a guard on the same team hits 50% of his shots. If the guard takes 10 shots during a game, how many shots will the center have to take to score as many points as the guard assuming each shot is worth the same number of points?
| 14 | |
| 9 | |
| 15 | |
| 17 |
guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 10 x \( \frac{50}{100} \) = \( \frac{50 x 10}{100} \) = \( \frac{500}{100} \) = 5 shots
The center makes 35% of his shots so he'll have to take:
shots made = shots taken x \( \frac{\text{% made}}{100} \)
shots taken = \( \frac{\text{shots taken}}{\frac{\text{% made}}{100}} \)
to make as many shots as the guard. Plugging in values for the center gives us:
center shots taken = \( \frac{5}{\frac{35}{100}} \) = 5 x \( \frac{100}{35} \) = \( \frac{5 x 100}{35} \) = \( \frac{500}{35} \) = 14 shots
to make the same number of shots as the guard and thus score the same number of points.
Which of the following statements about exponents is false?
b1 = b |
|
b1 = 1 |
|
b0 = 1 |
|
all of these are false |
A number with an exponent (be) consists of a base (b) raised to a power (e). The exponent indicates the number of times that the base is multiplied by itself. A base with an exponent of 1 equals the base (b1 = b) and a base with an exponent of 0 equals 1 ( (b0 = 1).
A bread recipe calls for 2\(\frac{3}{4}\) cups of flour. If you only have \(\frac{7}{8}\) cup, how much more flour is needed?
| 3\(\frac{1}{4}\) cups | |
| 1\(\frac{1}{2}\) cups | |
| 3\(\frac{1}{8}\) cups | |
| 1\(\frac{7}{8}\) cups |
The amount of flour you need is (2\(\frac{3}{4}\) - \(\frac{7}{8}\)) cups. Rewrite the quantities so they share a common denominator and subtract:
(\( \frac{22}{8} \) - \( \frac{7}{8} \)) cups
\( \frac{15}{8} \) cups
1\(\frac{7}{8}\) cups
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?
| 72 m2 | |
| 8 m2 | |
| 2 m2 | |
| 18 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