| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.38 |
| Score | 0% | 68% |
What is the next number in this sequence: 1, 7, 13, 19, 25, __________ ?
| 31 | |
| 30 | |
| 27 | |
| 36 |
The equation for this sequence is:
an = an-1 + 6
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 + 6
a6 = 25 + 6
a6 = 31
What is 3\( \sqrt{5} \) x 6\( \sqrt{2} \)?
| 9\( \sqrt{5} \) | |
| 18\( \sqrt{2} \) | |
| 9\( \sqrt{2} \) | |
| 18\( \sqrt{10} \) |
To multiply terms with radicals, multiply the coefficients and radicands separately:
3\( \sqrt{5} \) x 6\( \sqrt{2} \)
(3 x 6)\( \sqrt{5 \times 2} \)
18\( \sqrt{10} \)
On average, the center for a basketball team hits 40% of his shots while a guard on the same team hits 50% of his shots. If the guard takes 15 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?
| 26 | |
| 12 | |
| 28 | |
| 18 |
guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 15 x \( \frac{50}{100} \) = \( \frac{50 x 15}{100} \) = \( \frac{750}{100} \) = 7 shots
The center makes 40% 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 = \( \frac{7}{\frac{40}{100}} \) = 7 x \( \frac{100}{40} \) = \( \frac{7 x 100}{40} \) = \( \frac{700}{40} \) = 18 shots
to make the same number of shots as the guard and thus score the same number of points.
Which of the following is a mixed number?
\({a \over 5} \) |
|
\({7 \over 5} \) |
|
\(1 {2 \over 5} \) |
|
\({5 \over 7} \) |
A rational number (or fraction) is represented as a ratio between two integers, a and b, and has the form \({a \over b}\) where a is the numerator and b is the denominator. An improper fraction (\({5 \over 3} \)) has a numerator with a greater absolute value than the denominator and can be converted into a mixed number (\(1 {2 \over 3} \)) which has a whole number part and a fractional part.
Simplify \( \frac{20}{68} \).
| \( \frac{5}{17} \) | |
| \( \frac{7}{16} \) | |
| \( \frac{7}{18} \) | |
| \( \frac{8}{11} \) |
To simplify this fraction, first find the greatest common factor between them. The factors of 20 are [1, 2, 4, 5, 10, 20] 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:
\( \frac{20}{68} \) = \( \frac{\frac{20}{4}}{\frac{68}{4}} \) = \( \frac{5}{17} \)