| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.31 |
| Score | 0% | 66% |
What is -8z7 + 6z7?
| -14z7 | |
| -2z14 | |
| -2z7 | |
| -2z49 |
To add or subtract terms with exponents, both the base and the exponent must be the same. In this case they are so add the coefficients and retain the base and exponent:
-8z7 + 6z7
(-8 + 6)z7
-2z7
Solve for \( \frac{3!}{6!} \)
| \( \frac{1}{3024} \) | |
| \( \frac{1}{120} \) | |
| \( \frac{1}{210} \) | |
| \( \frac{1}{6} \) |
A factorial is the product of an integer and all the positive integers below it. To solve a fraction featuring factorials, expand the factorials and cancel out like numbers:
\( \frac{3!}{6!} \)
\( \frac{3 \times 2 \times 1}{6 \times 5 \times 4 \times 3 \times 2 \times 1} \)
\( \frac{1}{6 \times 5 \times 4} \)
\( \frac{1}{120} \)
A menswear store is having a sale: "Buy one shirt at full price and get another shirt for 25% off." If Frank buys two shirts, each with a regular price of $37, how much will he pay for both shirts?
| $53.65 | |
| $64.75 | |
| $38.85 | |
| $9.25 |
By buying two shirts, Frank will save $37 x \( \frac{25}{100} \) = \( \frac{$37 x 25}{100} \) = \( \frac{$925}{100} \) = $9.25 on the second shirt.
So, his total cost will be
$37.00 + ($37.00 - $9.25)
$37.00 + $27.75
$64.75
Simplify \( \frac{20}{64} \).
| \( \frac{1}{3} \) | |
| \( \frac{4}{19} \) | |
| \( \frac{10}{17} \) | |
| \( \frac{5}{16} \) |
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 64 are [1, 2, 4, 8, 16, 32, 64]. They share 3 factors [1, 2, 4] making 4 their greatest common factor (GCF).
Next, divide both numerator and denominator by the GCF:
\( \frac{20}{64} \) = \( \frac{\frac{20}{4}}{\frac{64}{4}} \) = \( \frac{5}{16} \)
In a class of 22 students, 8 are taking German and 12 are taking Spanish. Of the students studying German or Spanish, 3 are taking both courses. How many students are not enrolled in either course?
| 11 | |
| 19 | |
| 5 | |
| 12 |
The number of students taking German or Spanish is 8 + 12 = 20. Of that group of 20, 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 20 - 3 = 17 who are taking at least one language. 22 - 17 = 5 students who are not taking either language.