| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.90 |
| Score | 0% | 58% |
If the ratio of home fans to visiting fans in a crowd is 3:1 and all 35,000 seats in a stadium are filled, how many home fans are in attendance?
| 22,000 | |
| 31,667 | |
| 39,167 | |
| 26,250 |
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:
35,000 fans x \( \frac{3}{4} \) = \( \frac{105000}{4} \) = 26,250 fans.
A circular logo is enlarged to fit the lid of a jar. The new diameter is 50% larger than the original. By what percentage has the area of the logo increased?
| 35% | |
| 15% | |
| 17\(\frac{1}{2}\)% | |
| 25% |
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 50% the radius (and, consequently, the total area) increases by \( \frac{50\text{%}}{2} \) = 25%
What is \( 8 \)\( \sqrt{27} \) - \( 7 \)\( \sqrt{3} \)
| 17\( \sqrt{3} \) | |
| 56\( \sqrt{3} \) | |
| \( \sqrt{81} \) | |
| 56\( \sqrt{9} \) |
To subtract these radicals together their radicands must be the same:
8\( \sqrt{27} \) - 7\( \sqrt{3} \)
8\( \sqrt{9 \times 3} \) - 7\( \sqrt{3} \)
8\( \sqrt{3^2 \times 3} \) - 7\( \sqrt{3} \)
(8)(3)\( \sqrt{3} \) - 7\( \sqrt{3} \)
24\( \sqrt{3} \) - 7\( \sqrt{3} \)
Now that the radicands are identical, you can subtract them:
24\( \sqrt{3} \) - 7\( \sqrt{3} \)The __________ is the greatest factor that divides two integers.
absolute value |
|
greatest common factor |
|
least common multiple |
|
greatest common multiple |
The greatest common factor (GCF) is the greatest factor that divides two integers.
How many 9-passenger vans will it take to drive all 49 members of the football team to an away game?
| 4 vans | |
| 6 vans | |
| 8 vans | |
| 11 vans |
Calculate the number of vans needed by dividing the number of people that need transported by the capacity of one van:
vans = \( \frac{49}{9} \) = 5\(\frac{4}{9}\)
So, it will take 5 full vans and one partially full van to transport the entire team making a total of 6 vans.