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muminat
3 years ago
7

Find the midpoint of the line segment joining the points (9,6) and (-1,-6).

Mathematics
1 answer:
Hoochie [10]3 years ago
7 0

Answer:

\boxed{ \bold{ \huge{ \boxed{ \sf{(4 \: , \: 0)}}}}}

Step-by-step explanation:

Let the points be A and B

Let A ( 9 , 6 ) be ( x₁ , y₁ ) and B ( -1 , -6 ) be ( x₂ , y₂)

<u>Finding</u><u> </u><u>the</u><u> </u><u>mid</u><u> </u><u>points</u><u> </u><u>of </u><u>the</u><u> </u><u>line </u><u>segment </u><u>joining</u><u> </u><u>these </u><u>points</u>

<u>\boxed{ \sf{midpoint = ( \frac{x1 + x2}{2} , \:  \frac{y1 + y2}{2} )}}</u>

\longrightarrow{ \sf{( \frac{9 + ( - 1)}{2} , \:  \frac{6 + (  - 6)}{2}) }}

\longrightarrow{ \sf{ (\frac{9 - 1}{2}  \: , \:  \frac{6 - 6}{2} }})

\longrightarrow{ \sf{( \frac{8}{2} , \:  \frac{0}{2} }})

\longrightarrow{ \sf{(4 \: , \: 0}})

Hope I helped!

Best regards! :D

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The defect length of a corrosion defect in a pressurized steel pipe is normally distributed with mean value 30 mm and standard d
skelet666 [1.2K]

Answer:

z=-0.842

And if we solve for a we got

a=30 -0.842*7.8=23.432

So the value of height that separates the bottom 20% of data from the top 80% is 23.432.  

Step-by-step explanation:

Let X the random variable that represent the heights of a population, and for this case we know the distribution for X is given by:

X \sim N(30,7.8)  

Where \mu=30 and \sigma=7.8

For this part we want to find a value a, such that we satisfy this condition:

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P(X   (b)

As we can see on the figure attached the z value that satisfy the condition with 0.20 of the area on the left and 0.80 of the area on the right it's z=-0.842

If we use condition (b) from previous we have this:

P(X  

P(z

But we know which value of z satisfy the previous equation so then we can do this:

z=-0.842

And if we solve for a we got

a=30 -0.842*7.8=23.432

So the value of height that separates the bottom 20% of data from the top 80% is 23.432.  

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