| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.17 |
| Score | 0% | 63% |
Simplify \( \frac{28}{68} \).
| \( \frac{7}{17} \) | |
| \( \frac{4}{7} \) | |
| \( \frac{5}{16} \) | |
| \( \frac{7}{11} \) |
To simplify this fraction, first find the greatest common factor between them. The factors of 28 are [1, 2, 4, 7, 14, 28] and the factors of 68 are [1, 2, 4, 17, 34, 68]. They share 3 factors [1, 2, 4] making 4 their greatest common factor (GCF).
Next, divide both numerator and denominator by the GCF:
\( \frac{28}{68} \) = \( \frac{\frac{28}{4}}{\frac{68}{4}} \) = \( \frac{7}{17} \)
How many 15-passenger vans will it take to drive all 71 members of the football team to an away game?
| 4 vans | |
| 5 vans | |
| 11 vans | |
| 7 vans |
Calculate the number of vans needed by dividing the number of people that need transported by the capacity of one van:
vans = \( \frac{71}{15} \) = 4\(\frac{11}{15}\)
So, it will take 4 full vans and one partially full van to transport the entire team making a total of 5 vans.
Which of the following statements about exponents is false?
all of these are false |
|
b0 = 1 |
|
b1 = b |
|
b1 = 1 |
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).
How many 1\(\frac{1}{2}\) gallon cans worth of fuel would you need to pour into an empty 15 gallon tank to fill it exactly halfway?
| 5 | |
| 8 | |
| 10 | |
| 4 |
To fill a 15 gallon tank exactly halfway you'll need 7\(\frac{1}{2}\) gallons of fuel. Each fuel can holds 1\(\frac{1}{2}\) gallons so:
cans = \( \frac{7\frac{1}{2} \text{ gallons}}{1\frac{1}{2} \text{ gallons}} \) = 5
In a class of 19 students, 7 are taking German and 5 are taking Spanish. Of the students studying German or Spanish, 3 are taking both courses. How many students are not enrolled in either course?
| 10 | |
| 11 | |
| 13 | |
| 17 |
The number of students taking German or Spanish is 7 + 5 = 12. Of that group of 12, 3 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 12 - 3 = 9 who are taking at least one language. 19 - 9 = 10 students who are not taking either language.