Answer:
c. 12x; 111 cm
Step-by-step explanation:
The regular dodecagon has 12 sides. Each side has a length of x=9.25 cm, and we know that the perimeter of the figure is the sum of the lengths of all the sides: Therefore, since we have 12 sides, the perimeter will be given by the product between the length of each side, x, and the number of sides, 12:
and if we substitute x = 9.25 cm, we find
The interval of the convergence is x < -3 or x > 3 if the series n 3^n/x^n goes infinitely.
<h3>What is convergent of a series?</h3>A series is convergent if the series of its partial sums approaches a limit; that really is, when the values are added one after the other in the order defined by the numbers, the partial sums getting closer and closer to a certain number.
We can find the interval for the convergent by root test.
Like the Ratio Test, the root Test is used to determine absolute convergence (or not) with factorials, the ratio test is useful.
For the given series:
As the series goes infinitely, we can use root test.
By the root test, the convergence interval will be;
The interval of convergence is:
x < -3 or x > 3 we can write this as:
|x| < 3
Thus, the interval of the convergence is x < -3 or x > 3 if the series n 3^n/x^n goes infinitely.
Learn more about the convergent of a series here:
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Answer:
With alpha 0.95 and 8 degrees of freedom χ²= 2.73
And with alpha 0.05 and 8 degrees of freedom χ²=15.51
Step-by-step explanation:
The significance level ∝ = 1- 0.9 = 0.1
But we need the area of the middle so we divide this significance level with 2
so that we get exactly the middle area .
Dividing 0.1/2= 0.05
So we will have two values for chi square
One with 0.9 + 0.05 = 0.95 alpha and one with 0.05 alpha . This is because the chi square is right tailed.
So with alpha 0.95 and 8 degrees of freedom χ²= 2.73
And with alpha 0.05 and 8 degrees of freedom χ²=15.51
This can be shown with a graph.
