Answer:
c
Step-by-step explanation:
The answers to the question have been written below
<h3>The changes to a polygon</h3>
1. If the number of sides of the polygon should increase then the measure of the interior angle would increase by 180.
2. A regular polygon has the sum of its external angles as 360. This is solved as 360/n = 0
Hence the value of the exterior would move towards 0 as its sides increases.
4. As the total sum of the of the polygon changes, it would tend towards infinity.
5. The total sum of the exterior angles as the number of sides changes would tends towards 360 degrees.
Read more on polygon here:
brainly.com/question/1592456
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Addition,subtraction,and multiplication
Answer:
![x=10](https://tex.z-dn.net/?f=x%3D10)
Step-by-step explanation:
Notice that all three sides of the given triangle has one tick mark.
This means that all three sides are congruent, meaning that we have an equilateral triangle.
And for equilateral triangles, all three angles are also congruent.
So:
![\angle CBA=\angle BAC=\angle ACB](https://tex.z-dn.net/?f=%5Cangle%20CBA%3D%5Cangle%20BAC%3D%5Cangle%20ACB)
Also, recall that the interior angles of a triangle is always 180. Thus:
![\angle CBA+\angle BAC+\angle ACB=180](https://tex.z-dn.net/?f=%5Cangle%20CBA%2B%5Cangle%20BAC%2B%5Cangle%20ACB%3D180)
Substitute:
![\angle CBA+\angle CBA+\angle CBA=180](https://tex.z-dn.net/?f=%5Cangle%20CBA%2B%5Cangle%20CBA%2B%5Cangle%20CBA%3D180)
Combine like terms:
![3\angle CBA=180](https://tex.z-dn.net/?f=3%5Cangle%20CBA%3D180)
Substitute:
![3(6x)=180](https://tex.z-dn.net/?f=3%286x%29%3D180)
Multiply:
![18x=180](https://tex.z-dn.net/?f=18x%3D180)
Thus:
![x=10](https://tex.z-dn.net/?f=x%3D10)
And we are done!
Answer:
The required probability is 0.031918.
Step-by-step explanation:
Consider the provided information.
It is given that According to an article in The Wall Street Journal, this theory held for 22 out of the last 34 years.
Therefore n=34
The probability it is either up or down is 0.5.
Thus the value of p =0.5 and q = 0.5
Now calculate the probability
Let X is the number of years that theory held.
X has a binomial distribution with n=34 and p=0.5
![P(X=22)=\binom{34}{22}(0.5)^{22}(0.5)^{12}\\P(X=22)=\frac{34!}{22!\times 12!}(0.5)^{22}(0.5)^{12}\\P(X=22)=548354040\times 5.8207660913\times 10^{11}\\P(X=22)=0.0319184060208\\P(X=22)\approx0.031918](https://tex.z-dn.net/?f=P%28X%3D22%29%3D%5Cbinom%7B34%7D%7B22%7D%280.5%29%5E%7B22%7D%280.5%29%5E%7B12%7D%5C%5CP%28X%3D22%29%3D%5Cfrac%7B34%21%7D%7B22%21%5Ctimes%2012%21%7D%280.5%29%5E%7B22%7D%280.5%29%5E%7B12%7D%5C%5CP%28X%3D22%29%3D548354040%5Ctimes%205.8207660913%5Ctimes%2010%5E%7B11%7D%5C%5CP%28X%3D22%29%3D0.0319184060208%5C%5CP%28X%3D22%29%5Capprox0.031918)
Hence, the required probability is 0.031918.