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2 years ago

The slope of EF is −5/2 .

1 answer:

4 0

We know that
if two lines are perpendicular
then
m1*m2=-1
where
m1 and m2 are the slopes of the lines

so
if the slope of EF is −5/2
then
the slope of the segment perpendicular to EF is equal to
m1*m2=-1-----> m2=-1/m1------> m2=-1/(-5/2)-----> m2=2/5

case N 1) JK , where J is at (3, −2) and K is at (5, −7)

find the slope JK
m=(y2-y1)/x2-x1)-----> m=(-7+2)/(5-3)-----> m=-5/2
-5/2 is not equal to 2/5------> JK is not perpendicular to EF

case N 2) GH , where G is at (6, 7) and H is at (4, 12)
find the slope GH
m=(y2-y1)/x2-x1)-----> m=(12-7)/(4-6)-----> m=5/-2----> m=-5/2
-5/2 is not equal to 2/5------> GH is not perpendicular to EF

case N 3) LM , where L is at (1, 9) and M is at (6, 11)
find the slope LM
m=(y2-y1)/x2-x1)-----> m=(11-9)/(6-1)-----> m=2/5
2/5 is equal to 2/5------> LM is perpendicular to EF

case N 4) NP , where N is at (−3, 4) and P is at (−8, 2)
find the slope NP
m=(y2-y1)/x2-x1)-----> m=(2-4)/(-8+3)-----> m=-2/-5------> m=2/5
2/5 is equal to 2/5------> NP is perpendicular to EF

the answer is
The segments perpendicular to EF are LM and NP

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Answer:

a) 0.0392

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c) At least $39,070 to be among the 5% most expensive.

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:

$\mu = 29858, \sigma = 5600$

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This is the pvalue of Z when X = 20000. So

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

$Z = \frac{20000 - 29858}{5600}$

$Z = -1.76$

$Z = -1.76$ has a pvalue of 0.0392.

So this probability is 0.0392.

b. What is the probability that a wedding costs between $20,000 and $30,000 (to 4 decimals)?

This is the pvalue of Z when X = 30000 subtracted by the pvalue of Z when X = 20000.

X = 30000

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

$Z = \frac{30000 - 29858}{5600}$

$Z = 0.02$

$Z = 0.02$ has a pvalue of 0.5080.

X = 20000

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

$Z = \frac{20000 - 29858}{5600}$

$Z = -1.76$

$Z = -1.76$ has a pvalue of 0.0392.

So this probability is 0.5080 - 0.0392 = 0.4688

c. For a wedding to be among the 5% most expensive, how much would it have to cost (to the nearest whole number)?

This is the value of X when Z has a pvalue of 0.95. So this is X when Z = 1.645.

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

$1.645 = \frac{X - 29858}{5600}$

$X - 29858 = 5600*1.645$

$X = 39070$

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