| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.97 |
| Score | 0% | 59% |
A circular logo is enlarged to fit the lid of a jar. The new diameter is 75% larger than the original. By what percentage has the area of the logo increased?
| 27\(\frac{1}{2}\)% | |
| 25% | |
| 32\(\frac{1}{2}\)% | |
| 37\(\frac{1}{2}\)% |
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 75% the radius (and, consequently, the total area) increases by \( \frac{75\text{%}}{2} \) = 37\(\frac{1}{2}\)%
What is 3a7 - 7a7?
| 4a7 | |
| -4a7 | |
| 10a-14 | |
| 10a7 |
To add or subtract terms with exponents, both the base and the exponent must be the same. In this case they are so subtract the coefficients and retain the base and exponent:
3a7 - 7a7
(3 - 7)a7
-4a7
A menswear store is having a sale: "Buy one shirt at full price and get another shirt for 30% off." If Frank buys two shirts, each with a regular price of $47, how much will he pay for both shirts?
| $61.10 | |
| $14.10 | |
| $32.90 | |
| $79.90 |
By buying two shirts, Frank will save $47 x \( \frac{30}{100} \) = \( \frac{$47 x 30}{100} \) = \( \frac{$1410}{100} \) = $14.10 on the second shirt.
So, his total cost will be
$47.00 + ($47.00 - $14.10)
$47.00 + $32.90
$79.90
Solve 2 + (5 + 3) ÷ 4 x 5 - 42
| 1\(\frac{1}{4}\) | |
| \(\frac{7}{9}\) | |
| -4 | |
| \(\frac{3}{5}\) |
Use PEMDAS (Parentheses, Exponents, Multipy/Divide, Add/Subtract):
2 + (5 + 3) ÷ 4 x 5 - 42
P: 2 + (8) ÷ 4 x 5 - 42
E: 2 + 8 ÷ 4 x 5 - 16
MD: 2 + \( \frac{8}{4} \) x 5 - 16
MD: 2 + \( \frac{40}{4} \) - 16
AS: \( \frac{8}{4} \) + \( \frac{40}{4} \) - 16
AS: \( \frac{48}{4} \) - 16
AS: \( \frac{48 - 64}{4} \)
\( \frac{-16}{4} \)
-4
Solve for \( \frac{6!}{3!} \)
| \( \frac{1}{6720} \) | |
| 504 | |
| \( \frac{1}{9} \) | |
| 120 |
A factorial is the product of an integer and all the positive integers below it. To solve a fraction featuring factorials, expand the factorials and cancel out like numbers:
\( \frac{6!}{3!} \)
\( \frac{6 \times 5 \times 4 \times 3 \times 2 \times 1}{3 \times 2 \times 1} \)
\( \frac{6 \times 5 \times 4}{1} \)
\( 6 \times 5 \times 4 \)
120