Tell whether the triangles are similar. Explain.
2 answers:
Answer:
Step-by-step explanation:
We can use the AA Similarity Theorem that says that if two corresponding pairs of angles are congruent then the two triangles are similar.
11.
On the big triangles we are given one angle is 90° , one angle is 51° and
we know that the sum of all angles in a triangle is 180.
Calculate the missing angle in the big triangle:
180 -90-51 = 39°
Also in the picture we see a given angle of 102° that is adjacent to the 39° angle and another missing angle adjacent that form together 180° given the 2 triangles sin on a straight line.
Calculate the third missing angle
180 -39-102 = 39°
The green triangles are similar because of AA Similarity Theorem.
A= 39°=39° angles with same measure are congruent
A=90°=90° all right angles are congruent
12.
We have 2 vertical angles here and we know that vertical angles are congruent. Is given one of the vertical angle is 29° so the other vertical angle is 29° as well.
We are also given an angle of 88° and given that the sum of angles in a Δ is 180° we can find the third angle in that Δ.
180-29-88 = 63°
On the Δ that is on the right side we are given an angle of 91° and an adjacent angle along a straight line so they must form together 180°. 91+89 = 180
So the third angle in the Δ is 180-29-89 = 62.
We can see here that the angles are not congruent so the yellow triangles are NOT similar.
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Using the binomial distribution, it is found that about 75 batteries each day are defective.
For each battery, there are only two possible outcomes, either it is defective, or it is not. The probability of a battery being defective is independent of any other battery, hence the <em>binomial distribution</em> is used to solve this question.
<h3>What is the binomial probability distribution?</h3>It is the probability of exactly <u>x successes on n repeated trials, with p probability</u> of a success on each trial.
The expected value of the binomial distribution is:
In this problem:
- 3 out of 20 batteries are defective, hence p = 3/20 = 0.15.
- Each day, 500 batteries are produced, hence n = 500.
Then, the expected number of defective batteries in a day is given by:
E(X) = np = 500(0.15) = 75.
More can be learned about the binomial distribution at brainly.com/question/14424710