two nonoverlapping acute angles that share a ray form an obtuse angle if one of the acute angles have a a measure of 50 degres w
hat could be the measure of the other acute angle?
2 answers:
Answer:
The measure of other acute angle has to be less than 40°
Step-by-step explanation:
Let a and b denote the two acute angle that is formed by a same ray.
such that a=50 degree.
Let c be the obtuse angle that is formed.
i.e. m∠c >90°
So, we get a triangle such that the three angles of a triangle are a , b and c.
As we know that the sum of all the angles of a triangle is 180°.
Hence,
m∠a+m∠b+m∠c=180°
Hence,
50+m∠b+m∠c=180°
m∠b+m∠c=180°-50°
m∠b+m∠c=130°
Hence,
m∠b=130°-m∠c
As,
m∠c>90°
⇒ -m∠c<-90°
⇒ 130°-m∠c<130°-90°
⇒ 130°-m∠c<40°
⇒ m∠b<40°
Hence, the measure of the other acute angle has to be less than 40°
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Answer:
64.56% probability that between 17 and 25 circuits in the sample are defective.
Step-by-step explanation:
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The expected value of the binomial distribution is:
The standard deviation of the binomial distribution is:
Normal probability distribution
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.
When we are approximating a binomial distribution to a normal one, we have that ,
.
In this problem, we have that:
So
Probability that between 17 and 25 circuits in the sample are defective.
This is the pvalue of Z when X = 25 subtrated by the pvalue of Z when X = 17. So
X = 25
has a pvalue of 0.7626.
X = 17
has a pvalue of 0.1170.
0.7626 - 0.1170 = 0.6456
64.56% probability that between 17 and 25 circuits in the sample are defective.
Given:
The equation is
To find:
The coefficient and reciprocal.
Solution:
We have,
Here, is multiplied with x.
So, the coefficient of x is .
To find the reciprocal, we need to interchange numerator and denominator of a fraction.
So, the reciprocal of is
Therefore, the reciprocal is 3.