| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.26 |
| Score | 0% | 65% |
What is the next number in this sequence: 1, 10, 19, 28, 37, __________ ?
| 46 | |
| 50 | |
| 47 | |
| 41 |
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
What is \( \frac{8}{3} \) - \( \frac{3}{7} \)?
| 1 \( \frac{6}{12} \) | |
| 2\(\frac{5}{21}\) | |
| 2 \( \frac{7}{15} \) | |
| \( \frac{4}{12} \) |
To subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 3 are [3, 6, 9, 12, 15, 18, 21, 24, 27, 30] and the first few multiples of 7 are [7, 14, 21, 28, 35, 42, 49, 56, 63, 70]. The first few multiples they share are [21, 42, 63, 84] making 21 the smallest multiple 3 and 7 share.
Next, convert the fractions so each denominator equals the lowest common multiple:
\( \frac{8 x 7}{3 x 7} \) - \( \frac{3 x 3}{7 x 3} \)
\( \frac{56}{21} \) - \( \frac{9}{21} \)
Now, because the fractions share a common denominator, you can subtract them:
\( \frac{56 - 9}{21} \) = \( \frac{47}{21} \) = 2\(\frac{5}{21}\)
What is \( \frac{14\sqrt{16}}{7\sqrt{8}} \)?
| 2 \( \sqrt{2} \) | |
| 2 \( \sqrt{\frac{1}{2}} \) | |
| \(\frac{1}{2}\) \( \sqrt{2} \) | |
| \(\frac{1}{2}\) \( \sqrt{\frac{1}{2}} \) |
To divide terms with radicals, divide the coefficients and radicands separately:
\( \frac{14\sqrt{16}}{7\sqrt{8}} \)
\( \frac{14}{7} \) \( \sqrt{\frac{16}{8}} \)
2 \( \sqrt{2} \)
If \( \left|y + 5\right| \) + 9 = -8, which of these is a possible value for y?
| 7 | |
| 12 | |
| 6 | |
| -1 |
First, solve for \( \left|y + 5\right| \):
\( \left|y + 5\right| \) + 9 = -8
\( \left|y + 5\right| \) = -8 - 9
\( \left|y + 5\right| \) = -17
The value inside the absolute value brackets can be either positive or negative so (y + 5) must equal - 17 or --17 for \( \left|y + 5\right| \) to equal -17:
| y + 5 = -17 y = -17 - 5 y = -22 | y + 5 = 17 y = 17 - 5 y = 12 |
So, y = 12 or y = -22.
Cooks are needed to prepare for a large party. Each cook can bake either 2 large cakes or 11 small cakes per hour. The kitchen is available for 3 hours and 37 large cakes and 200 small cakes need to be baked.
How many cooks are required to bake the required number of cakes during the time the kitchen is available?
| 15 | |
| 14 | |
| 6 | |
| 5 |
If a single cook can bake 2 large cakes per hour and the kitchen is available for 3 hours, a single cook can bake 2 x 3 = 6 large cakes during that time. 37 large cakes are needed for the party so \( \frac{37}{6} \) = 6\(\frac{1}{6}\) cooks are needed to bake the required number of large cakes.
If a single cook can bake 11 small cakes per hour and the kitchen is available for 3 hours, a single cook can bake 11 x 3 = 33 small cakes during that time. 200 small cakes are needed for the party so \( \frac{200}{33} \) = 6\(\frac{2}{33}\) cooks are needed to bake the required number of small cakes.
Because you can't employ a fractional cook, round the number of cooks needed for each type of cake up to the next whole number resulting in 7 + 7 = 14 cooks.