| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.87 |
| Score | 0% | 57% |
The total water usage for a city is 30,000 gallons each day. Of that total, 20% is for personal use and 42% is for industrial use. How many more gallons of water each day is consumed for industrial use over personal use?
| 6,650 | |
| 6,600 | |
| 900 | |
| 5,250 |
42% of the water consumption is industrial use and 20% is personal use so (42% - 20%) = 22% more water is used for industrial purposes. 30,000 gallons are consumed daily so industry consumes \( \frac{22}{100} \) x 30,000 gallons = 6,600 gallons.
What is the next number in this sequence: 1, 4, 10, 19, 31, __________ ?
| 46 | |
| 50 | |
| 48 | |
| 53 |
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
A circular logo is enlarged to fit the lid of a jar. The new diameter is 45% larger than the original. By what percentage has the area of the logo increased?
| 25% | |
| 22\(\frac{1}{2}\)% | |
| 35% | |
| 15% |
The area of a circle is given by the formula A = πr2 where r is the radius of the circle. The radius of a circle is its diameter divided by two so A = π(\( \frac{d}{2} \))2. If the diameter of the logo increases by 45% the radius (and, consequently, the total area) increases by \( \frac{45\text{%}}{2} \) = 22\(\frac{1}{2}\)%
What is \( \frac{-4y^8}{4y^3} \)?
| -y5 | |
| -y2\(\frac{2}{3}\) | |
| -y11 | |
| -y24 |
To divide terms with exponents, the base of both exponents must be the same. In this case they are so divide the coefficients and subtract the exponents:
\( \frac{-4y^8}{4y^3} \)
\( \frac{-4}{4} \) y(8 - 3)
-y5
If the ratio of home fans to visiting fans in a crowd is 3:1 and all 31,000 seats in a stadium are filled, how many home fans are in attendance?
| 40,000 | |
| 32,250 | |
| 23,250 | |
| 35,000 |
A ratio of 3:1 means that there are 3 home fans for every one visiting fan. So, of every 4 fans, 3 are home fans and \( \frac{3}{4} \) of every fan in the stadium is a home fan:
31,000 fans x \( \frac{3}{4} \) = \( \frac{93000}{4} \) = 23,250 fans.