What is the slope of a line perpendicular to the line whose equation is 5x - y = -7.

1 answer:

3 0

keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above

$5x-y=-7\implies 5x-y+7=0 \\\\\\ \stackrel{\stackrel{m}{\downarrow }}{5} x+7=y\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}$

so a line perpendicular to that one above will have a slope of

$\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{5\implies \cfrac{5}{1}} ~\hfill \stackrel{reciprocal}{\cfrac{1}{5}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{1}{5}}}$

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$P(x \geq 6)=P(X=6)+P(X=7)$

And we can find the individual probabilities:

$P(X=6)=(7C6)(0.91)^6 (1-0.91)^{7-6}=0.358$

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And replacing we got:

$P(x \geq 6)=P(X=6)+P(X=7)= 0.358+0.517=0.875$

Step-by-step explanation:

Previous concepts

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

Solution to the problem

Let X the random variable of interest, on this case we now that:

$X \sim Binom(n=7, p=1-0.09=0.91)$