Answer:
b = y - mx
Step-by-step explanation:
Given
y = mx + b ( subtract mx from both sides )
y - mx = b
Answer:
Option C) Nominal
Step-by-step explanation:
We are given the following in the question:
Variable:
Nation of origin
Nominal and ordinal:
- Categorical variables can further be divided as nominal and ordinal.
- Nominal variable are simple name variable and no numeric value is used to express such variable.
- Ordinal variable are the variable where position plays an important role but again numerical value is not used to express them.
Ratio and interval:
- Numerical data can be divided as ratio and interval.
- Ratio is the data that have true zero value.
- For interval, absolute zero have no meaning.
Thus, the given variable that is name of origin is a categorical variable.
It is a nominal variable as position plays no role in this.
Thus, the correct answer is
Option C) Nominal
Answer:
a) The order of αβ is 9 and αβ is an even permutation
b) See proof
Step-by-step explanation:
a) Given that: α is a cycle of length 3 and β a cycle of length 9.
We want to find the order of αβ .
The order of αβ is the LCM of the length of the disjoint cycles.
Therefore the order is the LCM of 3 and 9 which is 9.
Since α is a cycle of length 3 and β a cycle of length 9, and (3-1)+(9-1)=10, the permutation αβ is even.
b) We want to show that, for every positive integer n,
![(\alpha \cdot \beta)^n=\alpha^n \cdot \beta^n](https://tex.z-dn.net/?f=%28%5Calpha%20%5Ccdot%20%5Cbeta%29%5En%3D%5Calpha%5En%20%5Ccdot%20%5Cbeta%5En)
Proof:
Expanding from left, we have
![(\alpha \cdot \beta)^n=\alpha \cdot \beta \cdot \alpha \cdot \beta \cdot \alpha \cdot \beta ....\alpha \cdot \beta \:n-times](https://tex.z-dn.net/?f=%28%5Calpha%20%5Ccdot%20%5Cbeta%29%5En%3D%5Calpha%20%5Ccdot%20%5Cbeta%20%5Ccdot%20%5Calpha%20%5Ccdot%20%5Cbeta%20%5Ccdot%20%5Calpha%20%5Ccdot%20%5Cbeta%20....%5Calpha%20%5Ccdot%20%5Cbeta%20%5C%3An-times)
Since α and β commutes, we rearrange to get:
![(\alpha\cdot \beta)^n=\alpha\cdot \alpha \cdot \alpha...n-times \cdot \beta \cdot \beta \cdot \beta-----n\:times](https://tex.z-dn.net/?f=%28%5Calpha%5Ccdot%20%5Cbeta%29%5En%3D%5Calpha%5Ccdot%20%5Calpha%20%5Ccdot%20%5Calpha...n-times%20%5Ccdot%20%5Cbeta%20%5Ccdot%20%5Cbeta%20%5Ccdot%20%5Cbeta-----n%5C%3Atimes)
We simplify on the right to get:
![(\alpha \cdot \beta)^n=\alpha^n \cdot \beta^n](https://tex.z-dn.net/?f=%28%5Calpha%20%5Ccdot%20%5Cbeta%29%5En%3D%5Calpha%5En%20%5Ccdot%20%5Cbeta%5En)
![Q\cdot E\cdot D](https://tex.z-dn.net/?f=Q%5Ccdot%20E%5Ccdot%20D)
Answer:
Yes
Step-by-step explanation:
two of the different sides match
Answer:
135 pennies
Step-by-step explanation:
x= pennies in the door at the start
x-1/3x-1/3(x-1/3x)-1/3(x-1/3x-1/3(x-1/3x))=40
x = 135
Proof:
135-45-20 =40
135-45=90
90=30=60
60-20=40