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3 years ago

Find an equation in slope intercept form for the line through point P(-3, 2) and perpendicular to the line

Mathematics

1 answer:

vova2212 [387]3 years ago

4 0

Answer:

y=-1/5 x +7/5

Step-by-step explanation:

First lets find the slope for line containing the two points (2,3) and (1,2)

$m=\frac{3-(-2)}{(2-1)}\\$

m=5

Two lines are perpendicular between each other if m1*m2=-1

we have one slope m1=5, we obtain m2= -1/5

Next we need to eval the equation for lines y=mx+b, where m= -1/5 using the point P(-3,2)

2=-1/5 * -3 +b

From that we obtain that b= 2-3/5=7/5

So the equation for the desired line is:

y=-1/5 x +7/5

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A survey showed that 77% of us need correction (eyeglasses, contacts, surgery, etc.) for their eyesight. 13 adults are randomly

earnstyle [38]

Using the binomial distribution, it is found that the probability that at least 12 of the 13 adults require eyesight correction is of 0.163 = 16.3%. Since this probability is greater than 5%, it is found that 12 is not a significantly high number of adults requiring eyesight correction.

For each person, there are only two possible outcomes, either they need correction for their eyesight, or they do not. The probability of a person needing correction is independent of any other person, hence, the binomial distribution is used to solve this question.

<h3>What is the binomial distribution formula?</h3>

The formula is:

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$C_{n,x} = \frac{n!}{x!(n-x)!}$

The parameters are:

x is the number of successes.

n is the number of trials.

p is the probability of a success on a single trial.

In this problem:

A survey showed that 77% of us need correction, hence p = 0.77.

13 adults are randomly selected, hence n = 13.

The probability that at least 12 of them need correction for their eyesight is given by:

$P(X \geq 12) = P(X = 12) + P(X = 13)$

In which:

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 12) = C_{13,12}.(0.77)^{12}.(0.23)^{1} = 0.1299$

$P(X = 13) = C_{13,13}.(0.77)^{13}.(0.23)^{0} = 0.0334$

Then:

$P(X \geq 12) = P(X = 12) + P(X = 13) = 0.1299 + 0.0334 = 0.163$

The probability that at least 12 of the 13 adults require eyesight correction is of 0.163 = 16.3%. Since this probability is greater than 5%, it is found that 12 is not a significantly high number of adults requiring eyesight correction.

More can be learned about the binomial distribution at brainly.com/question/24863377

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