answer: Riley practiced soccer for 2 1/4 hours Monday and Tuesday. she practiced 2/4 more hours on Wednesday than Tuesday.
explanation: 1/2 is essentially 2/4, add 3/4 it becomes 1 1/4 now add one for 2 1/4.
this is quite self explanatory. 1 1/4 - 3/4 is step by step like this. 1 1/4 - 1/4= 1.
1- 2/4 (half of one whole.) = 2/4.
I hope that explains it.
C.90 bc it’s a right angle
Given:
The equation is:
![2\sum_{n=3}^7n^2=\sum_{n=3}^72n^2](https://tex.z-dn.net/?f=2%5Csum_%7Bn%3D3%7D%5E7n%5E2%3D%5Csum_%7Bn%3D3%7D%5E72n%5E2)
To find:
Whether the equation is true or not.
Solution:
We have,
![2\sum_{n=3}^7n^2=\sum_{n=3}^72n^2](https://tex.z-dn.net/?f=2%5Csum_%7Bn%3D3%7D%5E7n%5E2%3D%5Csum_%7Bn%3D3%7D%5E72n%5E2)
Taking LHS, we get
![LHS=2\sum_{n=3}^7n^2](https://tex.z-dn.net/?f=LHS%3D2%5Csum_%7Bn%3D3%7D%5E7n%5E2)
![LHS=2[(3)^2+(4)^2+(5)^2+(6)^2+(7)^2]](https://tex.z-dn.net/?f=LHS%3D2%5B%283%29%5E2%2B%284%29%5E2%2B%285%29%5E2%2B%286%29%5E2%2B%287%29%5E2%5D)
![LHS=2[9+16+25+36+49]](https://tex.z-dn.net/?f=LHS%3D2%5B9%2B16%2B25%2B36%2B49%5D)
![LHS=2[135]](https://tex.z-dn.net/?f=LHS%3D2%5B135%5D)
![LHS=270](https://tex.z-dn.net/?f=LHS%3D270)
Taking RHS, we get
![RHS=\sum_{n=3}^72n^2](https://tex.z-dn.net/?f=RHS%3D%5Csum_%7Bn%3D3%7D%5E72n%5E2)
![RHS=2(3)^2+2(4)^2+2(5)^2+2(6)^2+2(7)^2](https://tex.z-dn.net/?f=RHS%3D2%283%29%5E2%2B2%284%29%5E2%2B2%285%29%5E2%2B2%286%29%5E2%2B2%287%29%5E2)
![RHS=2(9)+2(16)+2(25)+2(36)+2(49)](https://tex.z-dn.net/?f=RHS%3D2%289%29%2B2%2816%29%2B2%2825%29%2B2%2836%29%2B2%2849%29)
![RHS=18+32+50+72+98](https://tex.z-dn.net/?f=RHS%3D18%2B32%2B50%2B72%2B98)
![RHS=270](https://tex.z-dn.net/?f=RHS%3D270)
Here,
.
Therefore, the given equation is true.
Answer: 6.51
Step-by-step explanation:
For x be a binomial variable with parameters n (number of trials ) and p (probability of getting success in each event)
The standard deviation is given by :-
![\sigma=\sqrt{np(1-p)}](https://tex.z-dn.net/?f=%5Csigma%3D%5Csqrt%7Bnp%281-p%29%7D)
As per given , we have
Number of seniors in the graduating class : n= 265
The probability the graduating seniors have chosen to attend The Ohio State University : p=20%= 0.20
Now, the standard deviation of the number of students who will attend Ohio State :-
Hence, the standard deviation of the number of students who will attend Ohio State = 6.51