| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.12 |
| Score | 0% | 62% |
A circular logo is enlarged to fit the lid of a jar. The new diameter is 70% larger than the original. By what percentage has the area of the logo increased?
| 25% | |
| 35% | |
| 27\(\frac{1}{2}\)% | |
| 30% |
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 70% the radius (and, consequently, the total area) increases by \( \frac{70\text{%}}{2} \) = 35%
Solve 5 + (5 + 5) ÷ 5 x 4 - 32
| 1 | |
| \(\frac{1}{2}\) | |
| 3\(\frac{1}{2}\) | |
| 4 |
Use PEMDAS (Parentheses, Exponents, Multipy/Divide, Add/Subtract):
5 + (5 + 5) ÷ 5 x 4 - 32
P: 5 + (10) ÷ 5 x 4 - 32
E: 5 + 10 ÷ 5 x 4 - 9
MD: 5 + \( \frac{10}{5} \) x 4 - 9
MD: 5 + \( \frac{40}{5} \) - 9
AS: \( \frac{25}{5} \) + \( \frac{40}{5} \) - 9
AS: \( \frac{65}{5} \) - 9
AS: \( \frac{65 - 45}{5} \)
\( \frac{20}{5} \)
4
What is -3a2 x 9a5?
| -27a7 | |
| -27a10 | |
| -27a3 | |
| -27a2 |
To multiply terms with exponents, the base of both exponents must be the same. In this case they are so multiply the coefficients and add the exponents:
-3a2 x 9a5
(-3 x 9)a(2 + 5)
-27a7
How many hours does it take a car to travel 260 miles at an average speed of 65 miles per hour?
| 6 hours | |
| 3 hours | |
| 7 hours | |
| 4 hours |
Average speed in miles per hour is the number of miles traveled divided by the number of hours:
speed = \( \frac{\text{distance}}{\text{time}} \)Solving for time:
time = \( \frac{\text{distance}}{\text{speed}} \)
time = \( \frac{260mi}{65mph} \)
4 hours
If the ratio of home fans to visiting fans in a crowd is 2:1 and all 49,000 seats in a stadium are filled, how many home fans are in attendance?
| 20,000 | |
| 32,667 | |
| 34,500 | |
| 29,600 |
A ratio of 2:1 means that there are 2 home fans for every one visiting fan. So, of every 3 fans, 2 are home fans and \( \frac{2}{3} \) of every fan in the stadium is a home fan:
49,000 fans x \( \frac{2}{3} \) = \( \frac{98000}{3} \) = 32,667 fans.