| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.40 |
| Score | 0% | 68% |
A bread recipe calls for 2\(\frac{1}{2}\) cups of flour. If you only have \(\frac{3}{8}\) cup, how much more flour is needed?
| 1 cups | |
| 1\(\frac{3}{8}\) cups | |
| 2\(\frac{1}{8}\) cups | |
| 2\(\frac{7}{8}\) cups |
The amount of flour you need is (2\(\frac{1}{2}\) - \(\frac{3}{8}\)) cups. Rewrite the quantities so they share a common denominator and subtract:
(\( \frac{20}{8} \) - \( \frac{3}{8} \)) cups
\( \frac{17}{8} \) cups
2\(\frac{1}{8}\) cups
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?
| 22\(\frac{1}{2}\)% | |
| 35% | |
| 32\(\frac{1}{2}\)% | |
| 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 70% the radius (and, consequently, the total area) increases by \( \frac{70\text{%}}{2} \) = 35%
Roger loaned Charlie $1,500 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?
| $135 | |
| $60 | |
| $14 | |
| $12 |
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 $1,500
i = 0.09 x $1,500
i = $135
Simplify \( \frac{24}{80} \).
| \( \frac{9}{11} \) | |
| \( \frac{5}{9} \) | |
| \( \frac{8}{17} \) | |
| \( \frac{3}{10} \) |
To simplify this fraction, first find the greatest common factor between them. The factors of 24 are [1, 2, 3, 4, 6, 8, 12, 24] and the factors of 80 are [1, 2, 4, 5, 8, 10, 16, 20, 40, 80]. They share 4 factors [1, 2, 4, 8] making 8 their greatest common factor (GCF).
Next, divide both numerator and denominator by the GCF:
\( \frac{24}{80} \) = \( \frac{\frac{24}{8}}{\frac{80}{8}} \) = \( \frac{3}{10} \)
a(b + c) = ab + ac defines which of the following?
distributive property for multiplication |
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commutative property for multiplication |
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distributive property for division |
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commutative property for division |
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.