| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.73 |
| Score | 0% | 75% |
What is the next number in this sequence: 1, 4, 10, 19, 31, __________ ?
| 44 | |
| 46 | |
| 37 | |
| 43 |
The equation for this sequence is:
an = an-1 + 3(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 + 3(6 - 1)
a6 = 31 + 3(5)
a6 = 46
Which of the following is an improper fraction?
\(1 {2 \over 5} \) |
|
\({7 \over 5} \) |
|
\({2 \over 5} \) |
|
\({a \over 5} \) |
A rational number (or fraction) is represented as a ratio between two integers, a and b, and has the form \({a \over b}\) where a is the numerator and b is the denominator. An improper fraction (\({5 \over 3} \)) has a numerator with a greater absolute value than the denominator and can be converted into a mixed number (\(1 {2 \over 3} \)) which has a whole number part and a fractional part.
Simplify \( \frac{36}{76} \).
| \( \frac{9}{19} \) | |
| \( \frac{2}{5} \) | |
| \( \frac{7}{15} \) | |
| \( \frac{7}{11} \) |
To simplify this fraction, first find the greatest common factor between them. The factors of 36 are [1, 2, 3, 4, 6, 9, 12, 18, 36] and the factors of 76 are [1, 2, 4, 19, 38, 76]. They share 3 factors [1, 2, 4] making 4 their greatest common factor (GCF).
Next, divide both numerator and denominator by the GCF:
\( \frac{36}{76} \) = \( \frac{\frac{36}{4}}{\frac{76}{4}} \) = \( \frac{9}{19} \)
If a car travels 385 miles in 7 hours, what is the average speed?
| 50 mph | |
| 35 mph | |
| 55 mph | |
| 40 mph |
Average speed in miles per hour is the number of miles traveled divided by the number of hours:
speed = \( \frac{\text{distance}}{\text{time}} \)What is 8y3 - 6y3?
| 2y3 | |
| 14y9 | |
| -2y3 | |
| 14y-6 |
To add or subtract terms with exponents, both the base and the exponent must be the same. In this case they are so subtract the coefficients and retain the base and exponent:
8y3 - 6y3
(8 - 6)y3
2y3