| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.15 |
| Score | 0% | 63% |
In a class of 26 students, 8 are taking German and 10 are taking Spanish. Of the students studying German or Spanish, 3 are taking both courses. How many students are not enrolled in either course?
| 15 | |
| 18 | |
| 11 | |
| 10 |
The number of students taking German or Spanish is 8 + 10 = 18. Of that group of 18, 3 are taking both languages so they've been counted twice (once in the German group and once in the Spanish group). Subtracting them out leaves 18 - 3 = 15 who are taking at least one language. 26 - 15 = 11 students who are not taking either language.
If \(\left|a\right| = 7\), which of the following best describes a?
none of these is correct |
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a = -7 |
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a = 7 |
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a = 7 or a = -7 |
The absolute value is the positive magnitude of a particular number or variable and is indicated by two vertical lines: \(\left|-5\right| = 5\). In the case of a variable absolute value (\(\left|a\right| = 5\)) the value of a can be either positive or negative (a = -5 or a = 5).
The __________ is the smallest positive integer that is a multiple of two or more integers.
least common factor |
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least common multiple |
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absolute value |
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greatest common factor |
The least common multiple (LCM) is the smallest positive integer that is a multiple of two or more integers.
What is -5z7 x z3?
| -5z7 | |
| -5z21 | |
| -5z10 | |
| -4z21 |
To multiply terms with exponents, the base of both exponents must be the same. In this case they are so multiply the coefficients and add the exponents:
-5z7 x z3
(-5 x 1)z(7 + 3)
-5z10
A sports card collection contains football, baseball, and basketball cards. If the ratio of football to baseball cards is 7 to 2 and the ratio of baseball to basketball cards is 7 to 1, what is the ratio of football to basketball cards?
| 49:2 | |
| 9:2 | |
| 1:1 | |
| 1:4 |
The ratio of football cards to baseball cards is 7:2 and the ratio of baseball cards to basketball cards is 7:1. 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 49:14 and the ratio of baseball cards to basketball cards as 14:2. So, the ratio of football cards to basketball cards is football:baseball, baseball:basketball or 49:14, 14:2 which reduces to 49:2.