| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.98 |
| Score | 0% | 60% |
Which of the following statements about exponents is false?
b1 = 1 |
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b0 = 1 |
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all of these are false |
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b1 = b |
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).
a(b + c) = ab + ac defines which of the following?
commutative property for multiplication |
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commutative property for division |
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distributive property for multiplication |
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distributive 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.
What is \( \frac{-9z^6}{8z^4} \)?
| -1\(\frac{1}{8}\)z2 | |
| -\(\frac{8}{9}\)z-2 | |
| -1\(\frac{1}{8}\)z\(\frac{2}{3}\) | |
| -1\(\frac{1}{8}\)z1\(\frac{1}{2}\) |
To divide terms with exponents, the base of both exponents must be the same. In this case they are so divide the coefficients and subtract the exponents:
\( \frac{-9z^6}{8z^4} \)
\( \frac{-9}{8} \) z(6 - 4)
-1\(\frac{1}{8}\)z2
A menswear store is having a sale: "Buy one shirt at full price and get another shirt for 50% off." If Ezra buys two shirts, each with a regular price of $27, how much will he pay for both shirts?
| $33.75 | |
| $40.50 | |
| $13.50 | |
| $36.45 |
By buying two shirts, Ezra will save $27 x \( \frac{50}{100} \) = \( \frac{$27 x 50}{100} \) = \( \frac{$1350}{100} \) = $13.50 on the second shirt.
So, his total cost will be
$27.00 + ($27.00 - $13.50)
$27.00 + $13.50
$40.50
In a class of 20 students, 10 are taking German and 8 are taking Spanish. Of the students studying German or Spanish, 6 are taking both courses. How many students are not enrolled in either course?
| 13 | |
| 19 | |
| 14 | |
| 8 |
The number of students taking German or Spanish is 10 + 8 = 18. Of that group of 18, 6 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 - 6 = 12 who are taking at least one language. 20 - 12 = 8 students who are not taking either language.