| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.27 |
| Score | 0% | 65% |
What is the next number in this sequence: 1, 4, 10, 19, 31, __________ ?
| 43 | |
| 46 | |
| 54 | |
| 47 |
The equation for this sequence is:
an = an-1 + 3(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 + 3(6 - 1)
a6 = 31 + 3(5)
a6 = 46
What is \( \frac{2}{3} \) - \( \frac{3}{7} \)?
| 2 \( \frac{5}{21} \) | |
| 2 \( \frac{1}{10} \) | |
| \(\frac{5}{21}\) | |
| 2 \( \frac{3}{21} \) |
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:
\( \frac{2 x 7}{3 x 7} \) - \( \frac{3 x 3}{7 x 3} \)
\( \frac{14}{21} \) - \( \frac{9}{21} \)
Now, because the fractions share a common denominator, you can subtract them:
\( \frac{14 - 9}{21} \) = \( \frac{5}{21} \) = \(\frac{5}{21}\)
A menswear store is having a sale: "Buy one shirt at full price and get another shirt for 15% off." If Ezra buys two shirts, each with a regular price of $39, how much will he pay for both shirts?
| $50.70 | |
| $33.15 | |
| $5.85 | |
| $72.15 |
By buying two shirts, Ezra will save $39 x \( \frac{15}{100} \) = \( \frac{$39 x 15}{100} \) = \( \frac{$585}{100} \) = $5.85 on the second shirt.
So, his total cost will be
$39.00 + ($39.00 - $5.85)
$39.00 + $33.15
$72.15
If \( \left|x + 7\right| \) + 0 = 9, which of these is a possible value for x?
| -5 | |
| -3 | |
| 2 | |
| -21 |
First, solve for \( \left|x + 7\right| \):
\( \left|x + 7\right| \) + 0 = 9
\( \left|x + 7\right| \) = 9 + 0
\( \left|x + 7\right| \) = 9
The value inside the absolute value brackets can be either positive or negative so (x + 7) must equal + 9 or -9 for \( \left|x + 7\right| \) to equal 9:
| x + 7 = 9 x = 9 - 7 x = 2 | x + 7 = -9 x = -9 - 7 x = -16 |
So, x = -16 or x = 2.
Which of the following is not an integer?
\({1 \over 2}\) |
|
0 |
|
1 |
|
-1 |
An integer is any whole number, including zero. An integer can be either positive or negative. Examples include -77, -1, 0, 55, 119.