| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.35 |
| Score | 0% | 67% |
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?
| 35% | |
| 37\(\frac{1}{2}\)% | |
| 30% | |
| 27\(\frac{1}{2}\)% |
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\(\frac{1}{2}\)%
Convert 2,287,000 to scientific notation.
| 2.287 x 106 | |
| 2.287 x 105 | |
| 22.87 x 105 | |
| 2.287 x 10-6 |
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:
2,287,000 in scientific notation is 2.287 x 106
Which of the following is a mixed number?
\(1 {2 \over 5} \) |
|
\({5 \over 7} \) |
|
\({a \over 5} \) |
|
\({7 \over 5} \) |
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.
Solve for \( \frac{2!}{6!} \)
| 8 | |
| 6 | |
| \( \frac{1}{360} \) | |
| 6720 |
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:
\( \frac{2!}{6!} \)
\( \frac{2 \times 1}{6 \times 5 \times 4 \times 3 \times 2 \times 1} \)
\( \frac{1}{6 \times 5 \times 4 \times 3} \)
\( \frac{1}{360} \)
Ezra loaned Latoya $400 at an annual interest rate of 6%. If no payments are made, what is the total amount owed at the end of the first year?
| $424 | |
| $420 | |
| $416 | |
| $408 |
The yearly interest charged on this loan is the annual interest rate multiplied by the amount borrowed:
interest = annual interest rate x loan amount
i = (\( \frac{6}{100} \)) x $400
i = 0.06 x $400
No payments were made so the total amount due is the original amount + the accumulated interest:
total = $400 + $24