| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.12 |
| Score | 0% | 62% |
What is the next number in this sequence: 1, 3, 7, 13, 21, __________ ?
| 27 | |
| 37 | |
| 29 | |
| 31 |
The equation for this sequence is:
an = an-1 + 2(n - 1)
where n is the term's order in the sequence, an is the value of the term, and an-1 is the value of the term before an. This makes the next number:
a6 = a5 + 2(6 - 1)
a6 = 21 + 2(5)
a6 = 31
If \(\left|a\right| = 7\), which of the following best describes a?
none of these is correct |
|
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).
Christine scored 78% on her final exam. If each question was worth 4 points and there were 240 possible points on the exam, how many questions did Christine answer correctly?
| 56 | |
| 59 | |
| 45 | |
| 47 |
Christine scored 78% on the test meaning she earned 78% of the possible points on the test. There were 240 possible points on the test so she earned 240 x 0.78 = 188 points. Each question is worth 4 points so she got \( \frac{188}{4} \) = 47 questions right.
In a class of 22 students, 10 are taking German and 5 are taking Spanish. Of the students studying German or Spanish, 5 are taking both courses. How many students are not enrolled in either course?
| 11 | |
| 18 | |
| 13 | |
| 12 |
The number of students taking German or Spanish is 10 + 5 = 15. Of that group of 15, 5 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 15 - 5 = 10 who are taking at least one language. 22 - 10 = 12 students who are not taking either language.
\({b + c \over a} = {b \over a} + {c \over a}\) defines which of the following?
distributive property for division |
|
commutative property for multiplication |
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commutative property for division |
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distributive property for multiplication |
The distributive property for division helps in solving expressions like \({b + c \over a}\). It specifies that the result of dividing a fraction with multiple terms in the numerator and one term in the denominator can be obtained by dividing each term individually and then totaling the results: \({b + c \over a} = {b \over a} + {c \over a}\). For example, \({a^3 + 6a^2 \over a^2} = {a^3 \over a^2} + {6a^2 \over a^2} = a + 6\).