Find the area of the parallelogram with vertices A(−1,2,3), B(0,4,6), C(1,1,2), and D(2,3,5).
1 answer:
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Answer:
<em>The required points of the given line segment are ( - 1, - 5 ).</em>
Step-by-step explanation:
Given that the line segment AB whose midpoint M is ( 3, -2 ) and point A is ( 7, - 9), then we have to find point B of the line segment AB -
As we know that-
If a line segment AB is with endpoints ( ) and (
)then the mid points M are-
<em>M = ( ,
)</em>
Here,
<em>Let A ( 7, - 9 ), B ( x, y ) with midpoint M ( 3, - 2 ) -</em>
then by the midpoint formula M are-
<em>( 3, - 2 ) = ( ,
)</em>
On comparing x coordinate and y coordinate -
We get,
<em>( = 3 ,
= - 2)</em>
<em>( 7 + x = 6, - 9 + y = - 4 )</em>
<em>( x = 6 - 7, y = - 4 + 9 )</em>
<em>( x = - 1, y = -5 )</em>
<em>Hence the required points A are ( - 1, - 5 ).</em>
<em>We can also verify by putting these points into Midpoint formula.</em>
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Answer:
z≈3.16
p≈0.001
we reject the null hypothesis and conclude that the student knows more than half of the answers and is not just guessing in 0.05 significance level.
Step-by-step explanation:
As a result of step 2, we can assume normal distribution for the null hypothesis
<em>step 3:</em>
z statistic is computed as follows:
z= where
- X is the proportion of correct answers in the test (
)
- M is the expected proportion of correct answers according to the null hypothesis (0.5)
- p is the probability of correct answer (0.5)
- N is the total number of questions in the test (40)
z= ≈ 3.16
And corresponding p value for the z-statistic is p≈0.001.
Since p<0.05, we reject the null hypothesis and conclude that the student knows more than half of the answers and is not just guessing in 0.05 significance level.