A circle has an infinite number of lines of symmetry.
Answer:

And when we apply the limit we got that:

Step-by-step explanation:
Assuming this complete problem: "The following formula for the sum of the cubes of the first n integers is proved in Appendix E. Use it to evaluate the limit . 1^3+2^3+3^3+...+n^3=[n(n+1)/2]^2"
We have the following formula in order to find the sum of cubes:

We can express this formula like this:
![\lim_{n\to\infty} \sum_{n=1}^{\infty}i^3 =\lim_{n\to\infty} [\frac{n(n+1)}{2}]^2](https://tex.z-dn.net/?f=%20%5Clim_%7Bn%5Cto%5Cinfty%7D%20%5Csum_%7Bn%3D1%7D%5E%7B%5Cinfty%7Di%5E3%20%3D%5Clim_%7Bn%5Cto%5Cinfty%7D%20%5B%5Cfrac%7Bn%28n%2B1%29%7D%7B2%7D%5D%5E2)
And using this property we need to proof that: 1^3+2^3+3^3+...+n^3=[n(n+1)/2]^2
![\lim_{n\to\infty} [\frac{n(n+1)}{2}]^2](https://tex.z-dn.net/?f=%20%5Clim_%7Bn%5Cto%5Cinfty%7D%20%5B%5Cfrac%7Bn%28n%2B1%29%7D%7B2%7D%5D%5E2)
If we operate and we take out the 1/4 as a factor we got this:

We can cancel
and we got

We can reorder the terms like this:

We can do some algebra and we got:

We can solve the square and we got:

And when we apply the limit we got that:

Answer:
$8.50
Step-by-step explanation:
Multiply the cost by the amount of candy she bought, your equation will look like this:
2(0.75) + 3(1) + 5(1.40)
Multiplying everything makes the equation into:
1.5 + 3 + 7
Adding everything makes the total cost 11.50.
Subtract 11.50 from 20, and the answer is 8.50
(10 - 5 2/3) * -2 + x = 8 2/3
(9 3/3 - 5 2/3) * -2 + x = 8 2/3
4 1/3 * -2 + x = 26/3
13/3 * -2 + x = 26/3
-26/3 + x = 26/3
x = 26/3 + 26/3
x = 52/3 or 17 1/3 <==
Answer:
Question 1:
Here total number of students GPA is given = 50
Number of people who have GPA more than 3.69 = 5
Therefore,
Pr(That a student has GPA more than 3.69) = 5/50 = 0.1
Here X ~ NORMAL (3.12, 0.4)
so Pr(X > 3.69) = Pr(X > 3.69 ; 3.12 ; 0.4)
Z = (3.69 - 3.12)/ 0.4 = 1.425
Pr(X > 3.69) = Pr(X > 3.69 ; 3.12 ; 0.4) = 1 - Pr(Z < 1.425) = 1 - 0.9229 = 0.0771
Question 2
Here GPA would be above 95.54th percentile
so as per Z table relative to that percentile is = 1.70
so Z = (X - 3.12)/ 0.4 = 1.70
X = 3.12 + 0.4 * 1.70 = 3.80
so any person with GPA above or equal to 3.80 is eligible for that.