| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.02 |
| Score | 0% | 60% |
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?
| 35% | |
| 22\(\frac{1}{2}\)% | |
| 27\(\frac{1}{2}\)% | |
| 25% |
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%
What is the next number in this sequence: 1, 5, 13, 25, 41, __________ ?
| 55 | |
| 69 | |
| 66 | |
| 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
Cooks are needed to prepare for a large party. Each cook can bake either 3 large cakes or 10 small cakes per hour. The kitchen is available for 4 hours and 35 large cakes and 400 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?
| 5 | |
| 11 | |
| 8 | |
| 13 |
If a single cook can bake 3 large cakes per hour and the kitchen is available for 4 hours, a single cook can bake 3 x 4 = 12 large cakes during that time. 35 large cakes are needed for the party so \( \frac{35}{12} \) = 2\(\frac{11}{12}\) cooks are needed to bake the required number of large cakes.
If a single cook can bake 10 small cakes per hour and the kitchen is available for 4 hours, a single cook can bake 10 x 4 = 40 small cakes during that time. 400 small cakes are needed for the party so \( \frac{400}{40} \) = 10 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.
What is -4y3 - 3y3?
| 7y-3 | |
| -7y3 | |
| 7y3 | |
| -y9 |
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:
-4y3 - 3y3
(-4 - 3)y3
-7y3
Which of the following is an improper fraction?
\({2 \over 5} \) |
|
\({a \over 5} \) |
|
\(1 {2 \over 5} \) |
|
\({7 \over 5} \) |
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.