| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.31 |
| Score | 0% | 66% |
A circular logo is enlarged to fit the lid of a jar. The new diameter is 40% larger than the original. By what percentage has the area of the logo increased?
| 20% | |
| 15% | |
| 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 40% the radius (and, consequently, the total area) increases by \( \frac{40\text{%}}{2} \) = 20%
What is -4a5 - a5?
| -3a-10 | |
| -5a5 | |
| -3a5 | |
| -5a-5 |
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:
-4a5 - 1a5
(-4 - 1)a5
-5a5
Convert 2,390,000 to scientific notation.
| 2.39 x 10-5 | |
| 23.9 x 105 | |
| 2.39 x 106 | |
| 2.39 x 107 |
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:
2,390,000 in scientific notation is 2.39 x 106
Alex loaned Ezra $700 at an annual interest rate of 9%. If no payments are made, what is the interest owed on this loan at the end of the first year?
| $14 | |
| $63 | |
| $5 | |
| $20 |
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 $700
i = 0.09 x $700
i = $63
a(b + c) = ab + ac defines which of the following?
commutative property for multiplication |
|
distributive property for division |
|
commutative property for division |
|
distributive property for multiplication |
The distributive property for multiplication helps in solving expressions like a(b + c). It specifies that the result of multiplying one number by the sum or difference of two numbers can be obtained by multiplying each number individually and then totaling the results: a(b + c) = ab + ac. For example, 4(10-5) = (4 x 10) - (4 x 5) = 40 - 20 = 20.