| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.59 |
| Score | 0% | 52% |
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?
| 25% | |
| 27\(\frac{1}{2}\)% | |
| 22\(\frac{1}{2}\)% | |
| 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 \( 9 \)\( \sqrt{75} \) + \( 4 \)\( \sqrt{3} \)
| 49\( \sqrt{3} \) | |
| 13\( \sqrt{25} \) | |
| 36\( \sqrt{3} \) | |
| 36\( \sqrt{75} \) |
To add these radicals together their radicands must be the same:
9\( \sqrt{75} \) + 4\( \sqrt{3} \)
9\( \sqrt{25 \times 3} \) + 4\( \sqrt{3} \)
9\( \sqrt{5^2 \times 3} \) + 4\( \sqrt{3} \)
(9)(5)\( \sqrt{3} \) + 4\( \sqrt{3} \)
45\( \sqrt{3} \) + 4\( \sqrt{3} \)
Now that the radicands are identical, you can add them together:
45\( \sqrt{3} \) + 4\( \sqrt{3} \)Which of these numbers is a factor of 16?
| 16 | |
| 13 | |
| 6 | |
| 20 |
The factors of a number are all positive integers that divide evenly into the number. The factors of 16 are 1, 2, 4, 8, 16.
Cooks are needed to prepare for a large party. Each cook can bake either 5 large cakes or 13 small cakes per hour. The kitchen is available for 2 hours and 32 large cakes and 380 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?
| 12 | |
| 5 | |
| 15 | |
| 19 |
If a single cook can bake 5 large cakes per hour and the kitchen is available for 2 hours, a single cook can bake 5 x 2 = 10 large cakes during that time. 32 large cakes are needed for the party so \( \frac{32}{10} \) = 3\(\frac{1}{5}\) cooks are needed to bake the required number of large cakes.
If a single cook can bake 13 small cakes per hour and the kitchen is available for 2 hours, a single cook can bake 13 x 2 = 26 small cakes during that time. 380 small cakes are needed for the party so \( \frac{380}{26} \) = 14\(\frac{8}{13}\) 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 4 + 15 = 19 cooks.
Convert 4,189,000 to scientific notation.
| 0.419 x 107 | |
| 41.89 x 105 | |
| 4.189 x 106 | |
| 4.189 x 105 |
A number in scientific notation has the format 0.000 x 10exponent. To convert to scientific notation, move the decimal point to the right or the left until the number is a decimal between 1 and 10. The exponent of the 10 is the number of places you moved the decimal point and is positive if you moved the decimal point to the left and negative if you moved it to the right:
4,189,000 in scientific notation is 4.189 x 106