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2 answers:
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The measure of ∠angle B when Angle C is inscribed in circle O and AB is a diameter of circle O, is 19 degrees.
<h3>What is triangle angle sum theorem?</h3>According to the triangle angle sum theorem, the sum of all the angle(interior) of a triangle is equal to the 180 degrees.
In the image attached below:
- Angle C is inscribed in circle O.
- AB is a diameter of circle O.
The measure of the angle A is,
The measure of the angle C in a semicircle is,
The sum of all the angle(interior) of a triangle is equal to the 180 degrees. Thus,
Thus, the measure of ∠angle B when Angle C is inscribed in circle O and AB is a diameter of circle O, is 19 degrees.
Learn more about the triangle angle sum theorem here;
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Answer with Step-by-step explanation:
We are given that A and B are two countable sets
We have to show that if A and B are countable then is countable.
Countable means finite set or countably infinite.
Case 1: If A and B are two finite sets
Suppose A={1} and B={2}
={1,2}=Finite=Countable
Hence, is countable.
Case 2: If A finite and B is countably infinite
Suppose, A={1,2,3}
B=N={1,2,3,...}
Then, ={1,2,3,....}=N
Hence, is countable.
Case 3:If A is countably infinite and B is finite set.
Suppose , A=Z={..,-2,-1,0,1,2,....}
B={-2,-3}
=Z=Countable
Hence, countable.
Case 4:If A and B are both countably infinite sets.
Suppose A=N and B=Z
Then,=
=Z
Hence, is countable.
Therefore, if A and B are countable sets, then is also countable.
Answer:
The probability that the student's IQ is at least 140 points is of 55.17%.
Step-by-step explanation:
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean and standard deviation
, the zscore of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this problem, we have that:
University A:
a) Select a student at random from university A. Find the probability that the student's IQ is at least 140 points.
This is 1 subtracted by the pvalue of Z when X = 140. So
has a pvalue of 0.4483.
1 - 0.4483 = 0.5517
The probability that the student's IQ is at least 140 points is of 55.17%.