| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.88 |
| Score | 0% | 58% |
What is \( 6 \)\( \sqrt{75} \) - \( 8 \)\( \sqrt{3} \)
| -2\( \sqrt{3} \) | |
| 22\( \sqrt{3} \) | |
| -2\( \sqrt{-16} \) | |
| 48\( \sqrt{75} \) |
To subtract these radicals together their radicands must be the same:
6\( \sqrt{75} \) - 8\( \sqrt{3} \)
6\( \sqrt{25 \times 3} \) - 8\( \sqrt{3} \)
6\( \sqrt{5^2 \times 3} \) - 8\( \sqrt{3} \)
(6)(5)\( \sqrt{3} \) - 8\( \sqrt{3} \)
30\( \sqrt{3} \) - 8\( \sqrt{3} \)
Now that the radicands are identical, you can subtract them:
30\( \sqrt{3} \) - 8\( \sqrt{3} \)What is the next number in this sequence: 1, 3, 7, 13, 21, __________ ?
| 31 | |
| 22 | |
| 28 | |
| 23 |
The equation for this sequence is:
an = an-1 + 2(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 + 2(6 - 1)
a6 = 21 + 2(5)
a6 = 31
If the ratio of home fans to visiting fans in a crowd is 3:1 and all 37,000 seats in a stadium are filled, how many home fans are in attendance?
| 27,750 | |
| 33,600 | |
| 24,750 | |
| 34,167 |
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:
37,000 fans x \( \frac{3}{4} \) = \( \frac{111000}{4} \) = 27,750 fans.
4! = ?
4 x 3 x 2 x 1 |
|
3 x 2 x 1 |
|
5 x 4 x 3 x 2 x 1 |
|
4 x 3 |
A factorial has the form n! and is the product of the integer (n) and all the positive integers below it. For example, 5! = 5 x 4 x 3 x 2 x 1 = 120.
Which of the following statements about exponents is false?
b1 = 1 |
|
b1 = b |
|
all of these are false |
|
b0 = 1 |
A number with an exponent (be) consists of a base (b) raised to a power (e). The exponent indicates the number of times that the base is multiplied by itself. A base with an exponent of 1 equals the base (b1 = b) and a base with an exponent of 0 equals 1 ( (b0 = 1).