| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.50 |
| Score | 0% | 70% |
In a class of 16 students, 7 are taking German and 8 are taking Spanish. Of the students studying German or Spanish, 4 are taking both courses. How many students are not enrolled in either course?
| 11 | |
| 14 | |
| 5 | |
| 15 |
The number of students taking German or Spanish is 7 + 8 = 15. Of that group of 15, 4 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 15 - 4 = 11 who are taking at least one language. 16 - 11 = 5 students who are not taking either language.
What is \( \frac{4}{3} \) + \( \frac{9}{5} \)?
| 2 \( \frac{7}{14} \) | |
| 3\(\frac{2}{15}\) | |
| 2 \( \frac{5}{15} \) | |
| 2 \( \frac{7}{13} \) |
To add these fractions, first find the lowest common multiple of their denominators. The first few multiples of 3 are [3, 6, 9, 12, 15, 18, 21, 24, 27, 30] and the first few multiples of 5 are [5, 10, 15, 20, 25, 30, 35, 40, 45, 50]. The first few multiples they share are [15, 30, 45, 60, 75] making 15 the smallest multiple 3 and 5 share.
Next, convert the fractions so each denominator equals the lowest common multiple:
\( \frac{4 x 5}{3 x 5} \) + \( \frac{9 x 3}{5 x 3} \)
\( \frac{20}{15} \) + \( \frac{27}{15} \)
Now, because the fractions share a common denominator, you can add them:
\( \frac{20 + 27}{15} \) = \( \frac{47}{15} \) = 3\(\frac{2}{15}\)
9 members of a bridal party need transported to a wedding reception but there are only 2 4-passenger taxis available to take them. How many will need to find other transportation?
| 2 | |
| 50 | |
| 49 | |
| 1 |
There are 2 4-passenger taxis available so that's 2 x 4 = 8 total seats. There are 9 people needing transportation leaving 9 - 8 = 1 who will have to find other transportation.
If \(\left|a\right| = 7\), which of the following best describes a?
none of these is correct |
|
a = -7 |
|
a = 7 or a = -7 |
|
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).
What is the distance in miles of a trip that takes 1 hour at an average speed of 55 miles per hour?
| 280 miles | |
| 55 miles | |
| 160 miles | |
| 245 miles |
Average speed in miles per hour is the number of miles traveled divided by the number of hours:
speed = \( \frac{\text{distance}}{\text{time}} \)Solving for distance:
distance = \( \text{speed} \times \text{time} \)
distance = \( 55mph \times 1h \)
55 miles