Answer:
The system is consistent because the rightmost column of the augmented matrix is not a pivot column.
Step-by-step explanation:
It is given that the coefficient of the matrix of a linear equation has a pivot position in every row.
It is provided by the Existence and Uniqueness theorem that linear system is said to be consistent when only the column in the rightmost of the matrix which is augmented is not a pivot column.
When the linear system is considered consistent, then every solution set consists of either unique solution where there will be no any variables which are free or infinitely many solutions, when there is at least one free variable. This explains why the system is consistent.
For any m x n augmented matrix of any system, if its co-efficient matrix has a pivot position in every row, then there will never be a row of the form [0 .... 0 b].
Using conditional probability, it is found that there is a 0.1 = 10% probability that the chosen coin was the fair coin.
Conditional Probability
In which
- P(B|A) is the probability of event B happening, given that A happened.
is the probability of both A and B happening.
- P(A) is the probability of A happening.
In this problem:
- Event A: Three heads.
- Event B: Fair coin.
The probability associated with 3 heads are:
out of 0.5(fair coin).- 1 out of 0.5(biased).
Hence:
The probability of 3 heads and the fair coin is:
Then, the conditional probability is:
0.1 = 10% probability that the chosen coin was the fair coin.
A similar problem is given at brainly.com/question/14398287
Answer:
Option C(66.0)
Step-by-step explanation:
C = 2πr
C=Circumference
π=3.14(pi)
r=radius
C=2x3.14x10.5
3.14x10.5=32.97
32.97x2=65.94
65.94 rounded to nearest tenth is 65.9, so basically 66.0.
