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3 years ago

Factor by grouping and find the zeros x^3 - 10x^2 + 25x - 250 = 0

Mathematics

1 answer:

Pavel [41]3 years ago

8 0

Answer:

The answer to your question is x₁ = 10; x₂ = 5i; x₃ = -5i

Step-by-step explanation:

x³ - 10x² + 25x - 250 = 0

Factor by grouping

x²(x - 10) + 25(x - 10) = 0

(x - 10) (x² + 25) = 0

x₁ - 10 = 0

x₁ = 10

x² + 25 = 0

x² = -25

x² = ± √-25

x² = ± √25i²

x₂ = 5i

x₃ = -5i

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A line for tickets to a Broadway show had a mean waiting time of 20 minutes with a standard deviation of 5 minutes.

andrezito [222]

Answer:

5.48% of the people in line waited for more than 28 minutes

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

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$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Mean waiting time of 20 minutes with a standard deviation of 5 minutes.

This means that $\mu = 20, \sigma = 5$

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The proportion is 1 subtracted by the p-value of Z when X = 28. So

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$Z = \frac{28 - 20}{5}$

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