Write the equation of a line that is perpendicular to the given line and that passes through the given point. -x+5y=14; (-5,-2)

1 answer:

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$Let\\\\k:y=m_1x+b_1\\\\l:y=m_2x+b_2\\\\l\ \perp\ k\iff m_1m_2=-1\\\\\text{We have}\ k:-x+5y=14\qquad|+x\\\\5y=x+14\qquad|:5\\\\y=\dfrac{1}{5}x+\dfrac{14}{5}\to m_1=\dfrac{1}{5}\\\\l:y=mx+b\to\dfrac{1}{5}m=-1\qquad|\cdot5\\\\m=-5\\\\l:y=-5x+b\\\\\text{Put the coordinates of the point (-5, -2) to the equation of the line}\ l:\\\\-2=-5(-5)+b\\-2=25+b\qquad|-25\\b=-27\\\\Answer:\ y=-5x-27\to5x+y=-27$

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Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

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

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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.

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