ΔEFG is dilated from the origin at a scale factor of 2 to create ΔE′F′G′. Select the option that completes the statement: The tr
iangles' corresponding sides are ________, and their corresponding angles are ________; therefore, the triangles are ________.
A. congruent; similar; proportional
B. congruent; proportional; similar
C. proportional; congruent; similar
D. proportional; similar; congruent
A. congruent; similar; proportional
B. congruent; proportional; similar
C. proportional; congruent; similar
D. proportional; similar; congruent
1 answer:
Answer:
The correct option is C). proportional; congruent; similar
Step-by-step explanation:
Theory :
If triangle is dilated from the origin at a scale factor of 2 to create Triangle then, image of triangle and original triangle are similar to each other
Also, for similar triangles, corresponding angles are equal or congruent and corresponding sides are in ratio or scaled
For example : Figure show that triangle ABC is dilated by factor of 3 and centered at (-5,-4)
Question say: The triangles' corresponding sides are ________, and their corresponding angles are ________; therefore, the triangles are ________.
Answer : The triangles' corresponding sides are <u>proportional</u> and their corresponding angles are <u>congruent </u>therefore, the triangles are <u>similar</u>
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Answer:
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 scores for the univerisity A, and we know that:
Let Y the scores for the univerisity B, and we know that:
We select a sample size of size n=2, and since the distirbution for X is normal then the distribution for the sample mean would be given by:
And for the univeristy B we select a sample of n=3
Since both sample means are normally distributed then the difference is also normal distributed with the following parameters:
And we want this probability:
And we can use the z score given by:
And if we replace we got :
And if we find the probability using the normla standard table or excel we got: