| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.10 |
| Score | 0% | 62% |
Which of the following statements about exponents is false?
b1 = 1 |
|
all of these are false |
|
b1 = b |
|
b0 = 1 |
A number with an exponent (be) consists of a base (b) raised to a power (e). The exponent indicates the number of times that the base is multiplied by itself. A base with an exponent of 1 equals the base (b1 = b) and a base with an exponent of 0 equals 1 ( (b0 = 1).
What is \( \frac{6}{6} \) - \( \frac{7}{12} \)?
| \(\frac{5}{12}\) | |
| 2 \( \frac{5}{10} \) | |
| \( \frac{6}{12} \) | |
| 1 \( \frac{7}{16} \) |
To subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 6 are [6, 12, 18, 24, 30, 36, 42, 48, 54, 60] and the first few multiples of 12 are [12, 24, 36, 48, 60, 72, 84, 96]. The first few multiples they share are [12, 24, 36, 48, 60] making 12 the smallest multiple 6 and 12 share.
Next, convert the fractions so each denominator equals the lowest common multiple:
\( \frac{6 x 2}{6 x 2} \) - \( \frac{7 x 1}{12 x 1} \)
\( \frac{12}{12} \) - \( \frac{7}{12} \)
Now, because the fractions share a common denominator, you can subtract them:
\( \frac{12 - 7}{12} \) = \( \frac{5}{12} \) = \(\frac{5}{12}\)
Simplify \( \frac{20}{76} \).
| \( \frac{2}{5} \) | |
| \( \frac{2}{3} \) | |
| \( \frac{3}{5} \) | |
| \( \frac{5}{19} \) |
To simplify this fraction, first find the greatest common factor between them. The factors of 20 are [1, 2, 4, 5, 10, 20] and the factors of 76 are [1, 2, 4, 19, 38, 76]. They share 3 factors [1, 2, 4] making 4 their greatest common factor (GCF).
Next, divide both numerator and denominator by the GCF:
\( \frac{20}{76} \) = \( \frac{\frac{20}{4}}{\frac{76}{4}} \) = \( \frac{5}{19} \)
Roger loaned Frank $600 at an annual interest rate of 5%. If no payments are made, what is the interest owed on this loan at the end of the first year?
| $14 | |
| $104 | |
| $77 | |
| $30 |
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 $600
i = 0.05 x $600
i = $30
A sports card collection contains football, baseball, and basketball cards. If the ratio of football to baseball cards is 9 to 2 and the ratio of baseball to basketball cards is 9 to 1, what is the ratio of football to basketball cards?
| 3:4 | |
| 1:2 | |
| 5:4 | |
| 81:2 |
The ratio of football cards to baseball cards is 9:2 and the ratio of baseball cards to basketball cards is 9:1. To solve this problem, we need the baseball card side of each ratio to be equal so we need to rewrite the ratios in terms of a common number of baseball cards. (Think of this like finding the common denominator when adding fractions.) The ratio of football to baseball cards can also be written as 81:18 and the ratio of baseball cards to basketball cards as 18:2. So, the ratio of football cards to basketball cards is football:baseball, baseball:basketball or 81:18, 18:2 which reduces to 81:2.