| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.23 |
| Score | 0% | 65% |
What is the greatest common factor of 32 and 60?
| 13 | |
| 22 | |
| 26 | |
| 4 |
The factors of 32 are [1, 2, 4, 8, 16, 32] and the factors of 60 are [1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60]. They share 3 factors [1, 2, 4] making 4 the greatest factor 32 and 60 have in common.
The total water usage for a city is 45,000 gallons each day. Of that total, 14% is for personal use and 35% is for industrial use. How many more gallons of water each day is consumed for industrial use over personal use?
| 12,000 | |
| 9,450 | |
| 6,900 | |
| 3,200 |
35% of the water consumption is industrial use and 14% is personal use so (35% - 14%) = 21% more water is used for industrial purposes. 45,000 gallons are consumed daily so industry consumes \( \frac{21}{100} \) x 45,000 gallons = 9,450 gallons.
Convert a-5 to remove the negative exponent.
| \( \frac{-5}{a} \) | |
| \( \frac{-1}{-5a} \) | |
| \( \frac{1}{a^5} \) | |
| \( \frac{1}{a^{-5}} \) |
To convert a negative exponent to a positive exponent, calculate the positive exponent then take the reciprocal.
What is the next number in this sequence: 1, 3, 7, 13, 21, __________ ?
| 36 | |
| 37 | |
| 32 | |
| 31 |
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
If the ratio of home fans to visiting fans in a crowd is 5:1 and all 39,000 seats in a stadium are filled, how many home fans are in attendance?
| 41,667 | |
| 32,500 | |
| 30,667 | |
| 29,333 |
A ratio of 5:1 means that there are 5 home fans for every one visiting fan. So, of every 6 fans, 5 are home fans and \( \frac{5}{6} \) of every fan in the stadium is a home fan:
39,000 fans x \( \frac{5}{6} \) = \( \frac{195000}{6} \) = 32,500 fans.