| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.10 |
| Score | 0% | 62% |
What is the next number in this sequence: 1, 3, 7, 13, 21, __________ ?
| 40 | |
| 38 | |
| 31 | |
| 32 |
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
Convert b-5 to remove the negative exponent.
| \( \frac{1}{b^5} \) | |
| \( \frac{-1}{-5b^{5}} \) | |
| \( \frac{-5}{b} \) | |
| \( \frac{-1}{-5b} \) |
To convert a negative exponent to a positive exponent, calculate the positive exponent then take the reciprocal.
The total water usage for a city is 25,000 gallons each day. Of that total, 10% is for personal use and 36% is for industrial use. How many more gallons of water each day is consumed for industrial use over personal use?
| 11,250 | |
| 6,500 | |
| 3,000 | |
| 900 |
36% of the water consumption is industrial use and 10% is personal use so (36% - 10%) = 26% more water is used for industrial purposes. 25,000 gallons are consumed daily so industry consumes \( \frac{26}{100} \) x 25,000 gallons = 6,500 gallons.
Simplify \( \sqrt{28} \)
| 3\( \sqrt{7} \) | |
| 2\( \sqrt{7} \) | |
| 9\( \sqrt{7} \) | |
| 3\( \sqrt{14} \) |
To simplify a radical, factor out the perfect squares:
\( \sqrt{28} \)
\( \sqrt{4 \times 7} \)
\( \sqrt{2^2 \times 7} \)
2\( \sqrt{7} \)
A sports card collection contains football, baseball, and basketball cards. If the ratio of football to baseball cards is 5 to 2 and the ratio of baseball to basketball cards is 5 to 1, what is the ratio of football to basketball cards?
| 25:2 | |
| 5:8 | |
| 1:4 | |
| 5:6 |
The ratio of football cards to baseball cards is 5:2 and the ratio of baseball cards to basketball cards is 5:1. To solve this problem, we need the baseball card side of each ratio to be equal so we need to rewrite the ratios in terms of a common number of baseball cards. (Think of this like finding the common denominator when adding fractions.) The ratio of football to baseball cards can also be written as 25:10 and the ratio of baseball cards to basketball cards as 10:2. So, the ratio of football cards to basketball cards is football:baseball, baseball:basketball or 25:10, 10:2 which reduces to 25:2.