| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.31 |
| Score | 0% | 66% |
What is the next number in this sequence: 1, 3, 7, 13, 21, __________ ?
| 25 | |
| 31 | |
| 26 | |
| 38 |
The equation for this sequence is:
an = an-1 + 2(n - 1)
where n is the term's order in the sequence, an is the value of the term, and an-1 is the value of the term before an. This makes the next number:
a6 = a5 + 2(6 - 1)
a6 = 21 + 2(5)
a6 = 31
Simplify \( \frac{32}{72} \).
| \( \frac{4}{9} \) | |
| \( \frac{1}{2} \) | |
| \( \frac{2}{9} \) | |
| \( \frac{10}{11} \) |
To simplify this fraction, first find the greatest common factor between them. The factors of 32 are [1, 2, 4, 8, 16, 32] and the factors of 72 are [1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72]. They share 4 factors [1, 2, 4, 8] making 8 their greatest common factor (GCF).
Next, divide both numerator and denominator by the GCF:
\( \frac{32}{72} \) = \( \frac{\frac{32}{8}}{\frac{72}{8}} \) = \( \frac{4}{9} \)
Which of the following statements about exponents is false?
all of these are false |
|
b1 = 1 |
|
b0 = 1 |
|
b1 = b |
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).
In a class of 28 students, 11 are taking German and 14 are taking Spanish. Of the students studying German or Spanish, 7 are taking both courses. How many students are not enrolled in either course?
| 19 | |
| 21 | |
| 17 | |
| 10 |
The number of students taking German or Spanish is 11 + 14 = 25. Of that group of 25, 7 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 - 7 = 18 who are taking at least one language. 28 - 18 = 10 students who are not taking either language.
What is the greatest common factor of 40 and 36?
| 4 | |
| 9 | |
| 5 | |
| 8 |
The factors of 40 are [1, 2, 4, 5, 8, 10, 20, 40] and the factors of 36 are [1, 2, 3, 4, 6, 9, 12, 18, 36]. They share 3 factors [1, 2, 4] making 4 the greatest factor 40 and 36 have in common.