| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.57 |
| Score | 0% | 71% |
What is -z5 + 6z5?
| 5z25 | |
| 5z5 | |
| -7z5 | |
| 5z10 |
To add or subtract terms with exponents, both the base and the exponent must be the same. In this case they are so add the coefficients and retain the base and exponent:
-1z5 + 6z5
(-1 + 6)z5
5z5
21 members of a bridal party need transported to a wedding reception but there are only 4 4-passenger taxis available to take them. How many will need to find other transportation?
| 7 | |
| 8 | |
| 4 | |
| 5 |
There are 4 4-passenger taxis available so that's 4 x 4 = 16 total seats. There are 21 people needing transportation leaving 21 - 16 = 5 who will have to find other transportation.
Simplify \( \frac{24}{68} \).
| \( \frac{9}{11} \) | |
| \( \frac{2}{3} \) | |
| \( \frac{1}{2} \) | |
| \( \frac{6}{17} \) |
To simplify this fraction, first find the greatest common factor between them. The factors of 24 are [1, 2, 3, 4, 6, 8, 12, 24] and the factors of 68 are [1, 2, 4, 17, 34, 68]. They share 3 factors [1, 2, 4] making 4 their greatest common factor (GCF).
Next, divide both numerator and denominator by the GCF:
\( \frac{24}{68} \) = \( \frac{\frac{24}{4}}{\frac{68}{4}} \) = \( \frac{6}{17} \)
If a car travels 150 miles in 5 hours, what is the average speed?
| 40 mph | |
| 65 mph | |
| 45 mph | |
| 30 mph |
Average speed in miles per hour is the number of miles traveled divided by the number of hours:
speed = \( \frac{\text{distance}}{\text{time}} \)A circular logo is enlarged to fit the lid of a jar. The new diameter is 40% larger than the original. By what percentage has the area of the logo increased?
| 17\(\frac{1}{2}\)% | |
| 32\(\frac{1}{2}\)% | |
| 25% | |
| 20% |
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 40% the radius (and, consequently, the total area) increases by \( \frac{40\text{%}}{2} \) = 20%