| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.29 |
| Score | 0% | 66% |
Which of the following is not an integer?
1 |
|
0 |
|
-1 |
|
\({1 \over 2}\) |
An integer is any whole number, including zero. An integer can be either positive or negative. Examples include -77, -1, 0, 55, 119.
What is the next number in this sequence: 1, 10, 19, 28, 37, __________ ?
| 43 | |
| 50 | |
| 53 | |
| 46 |
The equation for this sequence is:
an = an-1 + 9
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 + 9
a6 = 37 + 9
a6 = 46
Simplify \( \frac{36}{44} \).
| \( \frac{3}{10} \) | |
| \( \frac{5}{18} \) | |
| \( \frac{4}{19} \) | |
| \( \frac{9}{11} \) |
To simplify this fraction, first find the greatest common factor between them. The factors of 36 are [1, 2, 3, 4, 6, 9, 12, 18, 36] and the factors of 44 are [1, 2, 4, 11, 22, 44]. They share 3 factors [1, 2, 4] making 4 their greatest common factor (GCF).
Next, divide both numerator and denominator by the GCF:
\( \frac{36}{44} \) = \( \frac{\frac{36}{4}}{\frac{44}{4}} \) = \( \frac{9}{11} \)
What is \( 9 \)\( \sqrt{18} \) + \( 8 \)\( \sqrt{2} \)
| 72\( \sqrt{18} \) | |
| 35\( \sqrt{2} \) | |
| 72\( \sqrt{9} \) | |
| 72\( \sqrt{36} \) |
To add these radicals together their radicands must be the same:
9\( \sqrt{18} \) + 8\( \sqrt{2} \)
9\( \sqrt{9 \times 2} \) + 8\( \sqrt{2} \)
9\( \sqrt{3^2 \times 2} \) + 8\( \sqrt{2} \)
(9)(3)\( \sqrt{2} \) + 8\( \sqrt{2} \)
27\( \sqrt{2} \) + 8\( \sqrt{2} \)
Now that the radicands are identical, you can add them together:
27\( \sqrt{2} \) + 8\( \sqrt{2} \)On average, the center for a basketball team hits 45% of his shots while a guard on the same team hits 50% of his shots. If the guard takes 10 shots during a game, how many shots will the center have to take to score as many points as the guard assuming each shot is worth the same number of points?
| 11 | |
| 24 | |
| 9 | |
| 17 |
guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 10 x \( \frac{50}{100} \) = \( \frac{50 x 10}{100} \) = \( \frac{500}{100} \) = 5 shots
The center makes 45% of his shots so he'll have to take:
shots made = shots taken x \( \frac{\text{% made}}{100} \)
shots taken = \( \frac{\text{shots taken}}{\frac{\text{% made}}{100}} \)
to make as many shots as the guard. Plugging in values for the center gives us:
center shots taken = \( \frac{5}{\frac{45}{100}} \) = 5 x \( \frac{100}{45} \) = \( \frac{5 x 100}{45} \) = \( \frac{500}{45} \) = 11 shots
to make the same number of shots as the guard and thus score the same number of points.