| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.32 |
| Score | 0% | 66% |
What is the next number in this sequence: 1, 8, 15, 22, 29, __________ ?
| 27 | |
| 36 | |
| 41 | |
| 30 |
The equation for this sequence is:
an = an-1 + 7
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 + 7
a6 = 29 + 7
a6 = 36
What is 4b2 + 3b2?
| 7b4 | |
| 7b2 | |
| b-2 | |
| -b-2 |
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:
4b2 + 3b2
(4 + 3)b2
7b2
What is \( 5 \)\( \sqrt{50} \) - \( 5 \)\( \sqrt{2} \)
| 25\( \sqrt{100} \) | |
| 25\( \sqrt{2} \) | |
| 0\( \sqrt{100} \) | |
| 20\( \sqrt{2} \) |
To subtract these radicals together their radicands must be the same:
5\( \sqrt{50} \) - 5\( \sqrt{2} \)
5\( \sqrt{25 \times 2} \) - 5\( \sqrt{2} \)
5\( \sqrt{5^2 \times 2} \) - 5\( \sqrt{2} \)
(5)(5)\( \sqrt{2} \) - 5\( \sqrt{2} \)
25\( \sqrt{2} \) - 5\( \sqrt{2} \)
Now that the radicands are identical, you can subtract them:
25\( \sqrt{2} \) - 5\( \sqrt{2} \)If the ratio of home fans to visiting fans in a crowd is 5:1 and all 30,000 seats in a stadium are filled, how many home fans are in attendance?
| 27,333 | |
| 32,250 | |
| 25,000 | |
| 27,200 |
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:
30,000 fans x \( \frac{5}{6} \) = \( \frac{150000}{6} \) = 25,000 fans.
If a car travels 315 miles in 7 hours, what is the average speed?
| 45 mph | |
| 25 mph | |
| 40 mph | |
| 70 mph |
Average speed in miles per hour is the number of miles traveled divided by the number of hours:
speed = \( \frac{\text{distance}}{\text{time}} \)