| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.19 |
| Score | 0% | 64% |
In a class of 36 students, 14 are taking German and 11 are taking Spanish. Of the students studying German or Spanish, 4 are taking both courses. How many students are not enrolled in either course?
| 23 | |
| 15 | |
| 14 | |
| 10 |
The number of students taking German or Spanish is 14 + 11 = 25. Of that group of 25, 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 25 - 4 = 21 who are taking at least one language. 36 - 21 = 15 students who are not taking either language.
Betty scored 79% on her final exam. If each question was worth 2 points and there were 140 possible points on the exam, how many questions did Betty answer correctly?
| 55 | |
| 59 | |
| 57 | |
| 46 |
Betty scored 79% on the test meaning she earned 79% of the possible points on the test. There were 140 possible points on the test so she earned 140 x 0.79 = 110 points. Each question is worth 2 points so she got \( \frac{110}{2} \) = 55 questions right.
\({b + c \over a} = {b \over a} + {c \over a}\) defines which of the following?
commutative property for division |
|
distributive property for multiplication |
|
commutative property for multiplication |
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distributive property for division |
The distributive property for division helps in solving expressions like \({b + c \over a}\). It specifies that the result of dividing a fraction with multiple terms in the numerator and one term in the denominator can be obtained by dividing each term individually and then totaling the results: \({b + c \over a} = {b \over a} + {c \over a}\). For example, \({a^3 + 6a^2 \over a^2} = {a^3 \over a^2} + {6a^2 \over a^2} = a + 6\).
What is \( \frac{4}{5} \) x \( \frac{3}{7} \)?
| 2\(\frac{2}{5}\) | |
| \(\frac{4}{81}\) | |
| \(\frac{12}{35}\) | |
| \(\frac{1}{72}\) |
To multiply fractions, multiply the numerators together and then multiply the denominators together:
\( \frac{4}{5} \) x \( \frac{3}{7} \) = \( \frac{4 x 3}{5 x 7} \) = \( \frac{12}{35} \) = \(\frac{12}{35}\)
A triathlon course includes a 500m swim, a 50.5km bike ride, and a 8.3km run. What is the total length of the race course?
| 40.7km | |
| 43.5km | |
| 59.3km | |
| 38km |
To add these distances, they must share the same unit so first you need to first convert the swim distance from meters (m) to kilometers (km) before adding it to the bike and run distances which are already in km. To convert 500 meters to kilometers, divide the distance by 1000 to get 0.5km then add the remaining distances:
total distance = swim + bike + run
total distance = 0.5km + 50.5km + 8.3km
total distance = 59.3km