| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.21 |
| Score | 0% | 64% |
A circular logo is enlarged to fit the lid of a jar. The new diameter is 70% larger than the original. By what percentage has the area of the logo increased?
| 30% | |
| 15% | |
| 22\(\frac{1}{2}\)% | |
| 35% |
The area of a circle is given by the formula A = πr2 where r is the radius of the circle. The radius of a circle is its diameter divided by two so A = π(\( \frac{d}{2} \))2. If the diameter of the logo increases by 70% the radius (and, consequently, the total area) increases by \( \frac{70\text{%}}{2} \) = 35%
Find the average of the following numbers: 15, 7, 14, 8.
| 10 | |
| 14 | |
| 11 | |
| 12 |
To find the average of these 4 numbers add them together then divide by 4:
\( \frac{15 + 7 + 14 + 8}{4} \) = \( \frac{44}{4} \) = 11
What is the next number in this sequence: 1, 5, 13, 25, 41, __________ ?
| 65 | |
| 69 | |
| 62 | |
| 61 |
The equation for this sequence is:
an = an-1 + 4(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 + 4(6 - 1)
a6 = 41 + 4(5)
a6 = 61
What is \( \frac{12\sqrt{24}}{4\sqrt{8}} \)?
| \(\frac{1}{3}\) \( \sqrt{3} \) | |
| \(\frac{1}{3}\) \( \sqrt{\frac{1}{3}} \) | |
| 3 \( \sqrt{3} \) | |
| 3 \( \sqrt{\frac{1}{3}} \) |
To divide terms with radicals, divide the coefficients and radicands separately:
\( \frac{12\sqrt{24}}{4\sqrt{8}} \)
\( \frac{12}{4} \) \( \sqrt{\frac{24}{8}} \)
3 \( \sqrt{3} \)
A menswear store is having a sale: "Buy one shirt at full price and get another shirt for 25% off." If Alex buys two shirts, each with a regular price of $30, how much will he pay for both shirts?
| $43.50 | |
| $7.50 | |
| $52.50 | |
| $45.00 |
By buying two shirts, Alex will save $30 x \( \frac{25}{100} \) = \( \frac{$30 x 25}{100} \) = \( \frac{$750}{100} \) = $7.50 on the second shirt.
So, his total cost will be
$30.00 + ($30.00 - $7.50)
$30.00 + $22.50
$52.50