First move the constant to the other side causing it to change sides
4x<-6-6
Then calculate the difference (-6-6)
4x<-12
Now divide both sides by 4
X<-3
Then you are left with your answer:
x<-3
Hope this helps! :3
.30 move the decimal two times to the left.
Answer:
37.27% probability that he or she will have a heart attack.
Step-by-step explanation:
Bayes Theorem:
Two events, A and B.
![P(B|A) = \frac{P(B)*P(A|B)}{P(A)}](https://tex.z-dn.net/?f=P%28B%7CA%29%20%3D%20%5Cfrac%7BP%28B%29%2AP%28A%7CB%29%7D%7BP%28A%29%7D)
In which P(B|A) is the probability of B happening when A has happened and P(A|B) is the probability of A happening when B has happened.
In this question:
Event A: Periodontal disease
Event B: Heart attack
Researchers discovered that 82% of people who have suffered a heart attack had periodontal disease, an inflammation of the gums.
This means that ![P(A|B) = 0.82](https://tex.z-dn.net/?f=P%28A%7CB%29%20%3D%200.82)
Only 33% of healthy people have this disease.
This means that ![P(A) = 0.33](https://tex.z-dn.net/?f=P%28A%29%20%3D%200.33)
Suppose that in a certain community heart attacks are quite rare, occurring with only 15% probability.
This means that ![P(B) = 0.15](https://tex.z-dn.net/?f=P%28B%29%20%3D%200.15)
If someone has periodontal disease, what is the probability that he or she will have a heart attack
![P(B|A) = \frac{0.15*0.82}{0.33} = 0.3727](https://tex.z-dn.net/?f=P%28B%7CA%29%20%3D%20%5Cfrac%7B0.15%2A0.82%7D%7B0.33%7D%20%3D%200.3727)
37.27% probability that he or she will have a heart attack.
Answer:
Option (2)
Step-by-step explanation:
Given expression is, AX + B = C
![A=\begin{bmatrix}-3 & -4\\ 1 & 0\end{bmatrix}](https://tex.z-dn.net/?f=A%3D%5Cbegin%7Bbmatrix%7D-3%20%26%20-4%5C%5C%201%20%26%200%5Cend%7Bbmatrix%7D)
![B=\begin{bmatrix}-7 & -9\\ 4 & -1\end{bmatrix}](https://tex.z-dn.net/?f=B%3D%5Cbegin%7Bbmatrix%7D-7%20%26%20-9%5C%5C%204%20%26%20-1%5Cend%7Bbmatrix%7D)
![C=\begin{bmatrix}-42 & -20\\ 5 & 4\end{bmatrix}](https://tex.z-dn.net/?f=C%3D%5Cbegin%7Bbmatrix%7D-42%20%26%20-20%5C%5C%205%20%26%204%5Cend%7Bbmatrix%7D)
AX + B = C
AX = C - B
C - B =
= ![\begin{bmatrix}-42+7 & -20+9\\ 5-4 & 4+1\end{bmatrix}](https://tex.z-dn.net/?f=%5Cbegin%7Bbmatrix%7D-42%2B7%20%26%20-20%2B9%5C%5C%205-4%20%26%204%2B1%5Cend%7Bbmatrix%7D)
C - B = ![\begin{bmatrix}-35 & -11\\ 1 & 5\end{bmatrix}](https://tex.z-dn.net/?f=%5Cbegin%7Bbmatrix%7D-35%20%26%20-11%5C%5C%201%20%26%205%5Cend%7Bbmatrix%7D)
Let ![X=\begin{bmatrix}a & b\\ c & d\end{bmatrix}](https://tex.z-dn.net/?f=X%3D%5Cbegin%7Bbmatrix%7Da%20%26%20b%5C%5C%20c%20%26%20d%5Cend%7Bbmatrix%7D)
AX =
= ![\begin{bmatrix}(-3a-4c) & (-3b-4d)\\ a & b\end{bmatrix}](https://tex.z-dn.net/?f=%5Cbegin%7Bbmatrix%7D%28-3a-4c%29%20%26%20%28-3b-4d%29%5C%5C%20a%20%26%20b%5Cend%7Bbmatrix%7D)
Since AX = C - B
![\begin{bmatrix}(-3a-4c) & (-3b-4d)\\ a & b\end{bmatrix}=\begin{bmatrix}-35 & -11\\ 1 & 5\end{bmatrix}](https://tex.z-dn.net/?f=%5Cbegin%7Bbmatrix%7D%28-3a-4c%29%20%26%20%28-3b-4d%29%5C%5C%20a%20%26%20b%5Cend%7Bbmatrix%7D%3D%5Cbegin%7Bbmatrix%7D-35%20%26%20-11%5C%5C%201%20%26%205%5Cend%7Bbmatrix%7D)
Therefore, a = 1, b = 5
(-3a - 4c) = -35
3(1) + 4c = 35
3 + 4c = 35
4c = 32
c = 8
And (-3b - 4d) = -11
3(5) + 4d = 11
4d = -4
d = -1
Therefore, Option (2). X =
will be the answer.