| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.09 |
| Score | 0% | 62% |
If \(\left|a\right| = 7\), which of the following best describes a?
a = 7 or a = -7 |
|
a = -7 |
|
none of these is correct |
|
a = 7 |
The absolute value is the positive magnitude of a particular number or variable and is indicated by two vertical lines: \(\left|-5\right| = 5\). In the case of a variable absolute value (\(\left|a\right| = 5\)) the value of a can be either positive or negative (a = -5 or a = 5).
A tiger in a zoo has consumed 49 pounds of food in 7 days. If the tiger continues to eat at the same rate, in how many more days will its total food consumtion be 91 pounds?
| 3 | |
| 13 | |
| 9 | |
| 6 |
If the tiger has consumed 49 pounds of food in 7 days that's \( \frac{49}{7} \) = 7 pounds of food per day. The tiger needs to consume 91 - 49 = 42 more pounds of food to reach 91 pounds total. At 7 pounds of food per day that's \( \frac{42}{7} \) = 6 more days.
Simplify \( \frac{24}{56} \).
| \( \frac{2}{3} \) | |
| \( \frac{5}{9} \) | |
| \( \frac{3}{7} \) | |
| \( \frac{6}{19} \) |
To simplify this fraction, first find the greatest common factor between them. The factors of 24 are [1, 2, 3, 4, 6, 8, 12, 24] and the factors of 56 are [1, 2, 4, 7, 8, 14, 28, 56]. They share 4 factors [1, 2, 4, 8] making 8 their greatest common factor (GCF).
Next, divide both numerator and denominator by the GCF:
\( \frac{24}{56} \) = \( \frac{\frac{24}{8}}{\frac{56}{8}} \) = \( \frac{3}{7} \)
A bread recipe calls for 2\(\frac{5}{8}\) cups of flour. If you only have \(\frac{3}{4}\) cup, how much more flour is needed?
| 1\(\frac{7}{8}\) cups | |
| 2\(\frac{1}{2}\) cups | |
| 2\(\frac{7}{8}\) cups | |
| \(\frac{7}{8}\) cups |
The amount of flour you need is (2\(\frac{5}{8}\) - \(\frac{3}{4}\)) cups. Rewrite the quantities so they share a common denominator and subtract:
(\( \frac{21}{8} \) - \( \frac{6}{8} \)) cups
\( \frac{15}{8} \) cups
1\(\frac{7}{8}\) cups
On average, the center for a basketball team hits 25% of his shots while a guard on the same team hits 30% of his shots. If the guard takes 15 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 | |
| 10 | |
| 9 | |
| 16 |
guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 15 x \( \frac{30}{100} \) = \( \frac{30 x 15}{100} \) = \( \frac{450}{100} \) = 4 shots
The center makes 25% 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 = \( \frac{4}{\frac{25}{100}} \) = 4 x \( \frac{100}{25} \) = \( \frac{4 x 100}{25} \) = \( \frac{400}{25} \) = 16 shots
to make the same number of shots as the guard and thus score the same number of points.