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Illusion [34]
2 years ago
12

Find the roots of the equation x^3-3x^2+x+5

Mathematics
1 answer:
leonid [27]2 years ago
5 0
First observe that x=-1 is a root of the equation. Use long division to divide x^3-3x^2+x+5 by x+1, we find that (x^3-3x^2+x+5)/(x+1)=(x^2-4x+5). Now we need to find the roots of x^2-4x+5.
x^2-4x+5=0, 
x^2-4x+4=-1,
(x-2)^2=i,
x-2=i or -1,
x=2+i or 2-i. 
The three roots are 2+i, 2-i, -1.
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3 years ago
In 2014, the CDC estimated that the mean height for adult women in the U.S. was 64 inches with a standard deviation of 4 inches.
Vladimir79 [104]

Answer:

A. 16%

Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

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 pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

\mu = 64, \sigma = 4

Which of the following gives the probability that a randomly selected woman has a height of greater than 68 inches?

This is 1 subtracted by the pvalue of Z when X = 68. So

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

Z = \frac{68 - 64}{4}

Z = 1

Z = 1 has a pvalue of 0.84.

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So the correct answer is:

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3 years ago
What is the value of f (4) if it is defined by f (x) =2x+3
AleksAgata [21]

Answer:

11

Step-by-step explanation:

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3 0
2 years ago
Read 2 more answers
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