decide whether enough information is given to prove that triangle XYZ is congruent to triangle JKL. If so, state the term you us
1 answer:
The information given to us shows that triangles XYZ and JKL is not enough to prove they are congruent by AAS, ASA, nor SAS.
<h3>The Triangle Congruence Theorems</h3>- Two triangles are congruent by the AAS congruence theorem if they both have two pairs of congruent angles and a pair of congruent non-included sides.
- Two triangles are congruent by the ASA congruence theorem if they both have two pairs of congruent angles and a pair of congruent included sides.
- Two triangles are congruent by the SAS congruence theorem if they both have two pairs of congruent sides and a pair of congruent included angles.
Thus, the information given to us shows that triangles XYZ and JKL is not enough to prove they are congruent by AAS, ASA, nor SAS.
Learn more about triangle congruence theorem on:
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Answer:
So the value of height that separates the bottom 45% of data from the top 55% is 1022.532.
Step-by-step explanation:
1) Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
2) Solution to the problem
Let X the random variable that represent the consumption levels of a population, and for this case we know the distribution for X is given by:
Where and
For this part we want to find a value a, such that we satisfy this condition:
(a)
(b)
Both conditions are equivalent on this case. We can use the z score again in order to find the value a.
As we can see on the figure attached the z value that satisfy the condition with 0.45 of the area on the left and 0.55 of the area on the right it's z=-0.26. On this case P(Z<-0.126)=0.45 and P(z>-0.126)=0.55
If we use condition (b) from previous we have this:
But we know which value of z satisfy the previous equation so then we can do this:
And if we solve for a we got
So the value of height that separates the bottom 45% of data from the top 55% is 1022.532.