Determine whether the triangles are similar. If so, write a similarity statement and name the postulate or the theorem you used.
If not, explain.
2 answers:
Answer: Both the pairs of triangles (a) and (b) are similar.
(a) By AA similarity statement.
(b) By proportionality statement.
Step-by-step explanation: We are given to check whether the pairs of triangles in cases (a) and (b) are similar or not.
(a) We see that in triangles ABC and PQR, we have
m∠A = m∠P = 41°, m∠B = m∠Q = 85° and m∠C = m∠R = 54°.
So, ΔABC and ΔPQR are similar by AA similarity statement.
(b) We see that in triangles ABC and DEF, we have
AB = 4, BC = 5, CA = 3, DE = 24, EF = 30 and FD = 18.
So, we have
That is, the corresponding sides of two triangles are proportional.
Thus, ΔABC and ΔDEF are similar by proportionality statement.
You might be interested in
Answer:
And if we solve for a we got
Step-by-step explanation:
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".
Solution to the problem
Let X the random variable that represent the hourly rates of a population, and for this case we know the distribution for X is given by:
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 0.80 of the area on the left and 0.20 of the area on the right it's z=0.842. On this case P(Z<0.842)=0.8 and P(z>0.842)=0.20
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