| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.74 |
| Score | 0% | 55% |
If \(\left|a\right| = 7\), which of the following best describes a?
a = 7 |
|
none of these is correct |
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a = -7 |
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a = 7 or a = -7 |
The absolute value is the positive magnitude of a particular number or variable and is indicated by two vertical lines: \(\left|-5\right| = 5\). In the case of a variable absolute value (\(\left|a\right| = 5\)) the value of a can be either positive or negative (a = -5 or a = 5).
What is 6\( \sqrt{5} \) x 5\( \sqrt{4} \)?
| 30\( \sqrt{9} \) | |
| 11\( \sqrt{4} \) | |
| 60\( \sqrt{5} \) | |
| 11\( \sqrt{20} \) |
To multiply terms with radicals, multiply the coefficients and radicands separately:
6\( \sqrt{5} \) x 5\( \sqrt{4} \)
(6 x 5)\( \sqrt{5 \times 4} \)
30\( \sqrt{20} \)
Now we need to simplify the radical:
30\( \sqrt{20} \)
30\( \sqrt{5 \times 4} \)
30\( \sqrt{5 \times 2^2} \)
(30)(2)\( \sqrt{5} \)
60\( \sqrt{5} \)
Cooks are needed to prepare for a large party. Each cook can bake either 5 large cakes or 11 small cakes per hour. The kitchen is available for 2 hours and 22 large cakes and 210 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?
| 8 | |
| 13 | |
| 7 | |
| 11 |
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. 22 large cakes are needed for the party so \( \frac{22}{10} \) = 2\(\frac{1}{5}\) 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 2 hours, a single cook can bake 11 x 2 = 22 small cakes during that time. 210 small cakes are needed for the party so \( \frac{210}{22} \) = 9\(\frac{6}{11}\) 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 3 + 10 = 13 cooks.
A circular logo is enlarged to fit the lid of a jar. The new diameter is 55% larger than the original. By what percentage has the area of the logo increased?
| 32\(\frac{1}{2}\)% | |
| 27\(\frac{1}{2}\)% | |
| 25% | |
| 17\(\frac{1}{2}\)% |
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 55% the radius (and, consequently, the total area) increases by \( \frac{55\text{%}}{2} \) = 27\(\frac{1}{2}\)%
Which of the following is an improper fraction?
\(1 {2 \over 5} \) |
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\({7 \over 5} \) |
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\({a \over 5} \) |
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\({2 \over 5} \) |
A rational number (or fraction) is represented as a ratio between two integers, a and b, and has the form \({a \over b}\) where a is the numerator and b is the denominator. An improper fraction (\({5 \over 3} \)) has a numerator with a greater absolute value than the denominator and can be converted into a mixed number (\(1 {2 \over 3} \)) which has a whole number part and a fractional part.