| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.18 |
| Score | 0% | 64% |
Convert z-2 to remove the negative exponent.
| \( \frac{-1}{z^{-2}} \) | |
| \( \frac{-1}{-2z} \) | |
| \( \frac{-2}{z} \) | |
| \( \frac{1}{z^2} \) |
To convert a negative exponent to a positive exponent, calculate the positive exponent then take the reciprocal.
What is \( \frac{-5y^5}{9y^3} \)?
| -\(\frac{5}{9}\)y-2 | |
| -\(\frac{5}{9}\)y2 | |
| -\(\frac{5}{9}\)y1\(\frac{2}{3}\) | |
| -1\(\frac{4}{5}\)y8 |
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:
\( \frac{-5y^5}{9y^3} \)
\( \frac{-5}{9} \) y(5 - 3)
-\(\frac{5}{9}\)y2
A tiger in a zoo has consumed 32 pounds of food in 4 days. If the tiger continues to eat at the same rate, in how many more days will its total food consumtion be 72 pounds?
| 5 | |
| 3 | |
| 2 | |
| 7 |
If the tiger has consumed 32 pounds of food in 4 days that's \( \frac{32}{4} \) = 8 pounds of food per day. The tiger needs to consume 72 - 32 = 40 more pounds of food to reach 72 pounds total. At 8 pounds of food per day that's \( \frac{40}{8} \) = 5 more days.
If there were a total of 400 raffle tickets sold and you bought 12 tickets, what's the probability that you'll win the raffle?
| 3% | |
| 7% | |
| 10% | |
| 13% |
You have 12 out of the total of 400 raffle tickets sold so you have a (\( \frac{12}{400} \)) x 100 = \( \frac{12 \times 100}{400} \) = \( \frac{1200}{400} \) = 3% chance to win the raffle.
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.