Answer:
It will take 6/13 hours to walk one mile
Step-by-step explanation:
Here, we want to calculate the number of hours it take to walk one mile
From the question, 1 1/2 miles take 3 1/4 hours
the number of hours it will take to walk 1 mile will be;
1 1/2 divided by 3 1/4
= 3/2 divided by 13/4
= 3/2 * 4/13 = 6/13 hours
Answer:
Please check the explanation!
Step-by-step explanation:
Given the polynomial
![\left(x+y\right)^5](https://tex.z-dn.net/?f=%5Cleft%28x%2By%5Cright%29%5E5)
![\mathrm{Apply\:binomial\:theorem}:\quad \left(a+b\right)^n=\sum _{i=0}^n\binom{n}{i}a^{\left(n-i\right)}b^i](https://tex.z-dn.net/?f=%5Cmathrm%7BApply%5C%3Abinomial%5C%3Atheorem%7D%3A%5Cquad%20%5Cleft%28a%2Bb%5Cright%29%5En%3D%5Csum%20_%7Bi%3D0%7D%5En%5Cbinom%7Bn%7D%7Bi%7Da%5E%7B%5Cleft%28n-i%5Cright%29%7Db%5Ei)
![a=x,\:\:b=y](https://tex.z-dn.net/?f=a%3Dx%2C%5C%3A%5C%3Ab%3Dy)
![=\sum _{i=0}^5\binom{5}{i}x^{\left(5-i\right)}y^i](https://tex.z-dn.net/?f=%3D%5Csum%20_%7Bi%3D0%7D%5E5%5Cbinom%7B5%7D%7Bi%7Dx%5E%7B%5Cleft%285-i%5Cright%29%7Dy%5Ei)
so expanding summation
![=\frac{5!}{0!\left(5-0\right)!}x^5y^0+\frac{5!}{1!\left(5-1\right)!}x^4y^1+\frac{5!}{2!\left(5-2\right)!}x^3y^2+\frac{5!}{3!\left(5-3\right)!}x^2y^3+\frac{5!}{4!\left(5-4\right)!}x^1y^4+\frac{5!}{5!\left(5-5\right)!}x^0y^5](https://tex.z-dn.net/?f=%3D%5Cfrac%7B5%21%7D%7B0%21%5Cleft%285-0%5Cright%29%21%7Dx%5E5y%5E0%2B%5Cfrac%7B5%21%7D%7B1%21%5Cleft%285-1%5Cright%29%21%7Dx%5E4y%5E1%2B%5Cfrac%7B5%21%7D%7B2%21%5Cleft%285-2%5Cright%29%21%7Dx%5E3y%5E2%2B%5Cfrac%7B5%21%7D%7B3%21%5Cleft%285-3%5Cright%29%21%7Dx%5E2y%5E3%2B%5Cfrac%7B5%21%7D%7B4%21%5Cleft%285-4%5Cright%29%21%7Dx%5E1y%5E4%2B%5Cfrac%7B5%21%7D%7B5%21%5Cleft%285-5%5Cright%29%21%7Dx%5E0y%5E5)
solving
![\frac{5!}{0!\left(5-0\right)!}x^5y^0](https://tex.z-dn.net/?f=%5Cfrac%7B5%21%7D%7B0%21%5Cleft%285-0%5Cright%29%21%7Dx%5E5y%5E0)
![=1\cdot \frac{5!}{0!\left(5-0\right)!}x^5](https://tex.z-dn.net/?f=%3D1%5Ccdot%20%5Cfrac%7B5%21%7D%7B0%21%5Cleft%285-0%5Cright%29%21%7Dx%5E5)
![=1\cdot \:1\cdot \:x^5](https://tex.z-dn.net/?f=%3D1%5Ccdot%20%5C%3A1%5Ccdot%20%5C%3Ax%5E5)
![=x^5](https://tex.z-dn.net/?f=%3Dx%5E5)
also solving
![=\frac{5!}{1!\left(5-1\right)!}x^4y](https://tex.z-dn.net/?f=%3D%5Cfrac%7B5%21%7D%7B1%21%5Cleft%285-1%5Cright%29%21%7Dx%5E4y)
![=\frac{5}{1!}x^4y](https://tex.z-dn.net/?f=%3D%5Cfrac%7B5%7D%7B1%21%7Dx%5E4y)
![=\frac{5}{1!}x^4y](https://tex.z-dn.net/?f=%3D%5Cfrac%7B5%7D%7B1%21%7Dx%5E4y)
![=\frac{5x^4y}{1}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B5x%5E4y%7D%7B1%7D)
![=\frac{5x^4y}{1}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B5x%5E4y%7D%7B1%7D)
![=5x^4y](https://tex.z-dn.net/?f=%3D5x%5E4y)
similarly, the result of the remaining terms can be solved such as
![\frac{5!}{2!\left(5-2\right)!}x^3y^2=10x^3y^2](https://tex.z-dn.net/?f=%5Cfrac%7B5%21%7D%7B2%21%5Cleft%285-2%5Cright%29%21%7Dx%5E3y%5E2%3D10x%5E3y%5E2)
![\frac{5!}{3!\left(5-3\right)!}x^2y^3=10x^2y^3](https://tex.z-dn.net/?f=%5Cfrac%7B5%21%7D%7B3%21%5Cleft%285-3%5Cright%29%21%7Dx%5E2y%5E3%3D10x%5E2y%5E3)
![\frac{5!}{4!\left(5-4\right)!}x^1y^4=5xy^4](https://tex.z-dn.net/?f=%5Cfrac%7B5%21%7D%7B4%21%5Cleft%285-4%5Cright%29%21%7Dx%5E1y%5E4%3D5xy%5E4)
![\frac{5!}{5!\left(5-5\right)!}x^0y^5=y^5](https://tex.z-dn.net/?f=%5Cfrac%7B5%21%7D%7B5%21%5Cleft%285-5%5Cright%29%21%7Dx%5E0y%5E5%3Dy%5E5)
so substituting all the solved results in the expression
![=\frac{5!}{0!\left(5-0\right)!}x^5y^0+\frac{5!}{1!\left(5-1\right)!}x^4y^1+\frac{5!}{2!\left(5-2\right)!}x^3y^2+\frac{5!}{3!\left(5-3\right)!}x^2y^3+\frac{5!}{4!\left(5-4\right)!}x^1y^4+\frac{5!}{5!\left(5-5\right)!}x^0y^5](https://tex.z-dn.net/?f=%3D%5Cfrac%7B5%21%7D%7B0%21%5Cleft%285-0%5Cright%29%21%7Dx%5E5y%5E0%2B%5Cfrac%7B5%21%7D%7B1%21%5Cleft%285-1%5Cright%29%21%7Dx%5E4y%5E1%2B%5Cfrac%7B5%21%7D%7B2%21%5Cleft%285-2%5Cright%29%21%7Dx%5E3y%5E2%2B%5Cfrac%7B5%21%7D%7B3%21%5Cleft%285-3%5Cright%29%21%7Dx%5E2y%5E3%2B%5Cfrac%7B5%21%7D%7B4%21%5Cleft%285-4%5Cright%29%21%7Dx%5E1y%5E4%2B%5Cfrac%7B5%21%7D%7B5%21%5Cleft%285-5%5Cright%29%21%7Dx%5E0y%5E5)
![=x^5+5x^4y+10x^3y^2+10x^2y^3+5xy^4+y^5](https://tex.z-dn.net/?f=%3Dx%5E5%2B5x%5E4y%2B10x%5E3y%5E2%2B10x%5E2y%5E3%2B5xy%5E4%2By%5E5)
Therefore,
![\left(x\:+y\right)^5=x^5+5x^4y+10x^3y^2+10x^2y^3+5xy^4+y^5](https://tex.z-dn.net/?f=%5Cleft%28x%5C%3A%2By%5Cright%29%5E5%3Dx%5E5%2B5x%5E4y%2B10x%5E3y%5E2%2B10x%5E2y%5E3%2B5xy%5E4%2By%5E5)
Answer:
1. 458 - 247 = 211
2. 58.92 - 43.87 = 15.05
3. 51/8 - 15/8 = 4.5
Here you go ! Hope this helps !