Answer: I think the perimeter is 17ab4
Step-by-step explanation:
Answer:
![P(A\textrm{ and }B)=\frac{3}{14}](https://tex.z-dn.net/?f=P%28A%5Ctextrm%7B%20and%20%7DB%29%3D%5Cfrac%7B3%7D%7B14%7D)
Step-by-step explanation:
Given:
![P(A)=\frac{4}{7}](https://tex.z-dn.net/?f=P%28A%29%3D%5Cfrac%7B4%7D%7B7%7D)
![P(B|A)=\frac{3}{8}](https://tex.z-dn.net/?f=P%28B%7CA%29%3D%5Cfrac%7B3%7D%7B8%7D)
We know that, conditional probability of B given that A has occurred is given as:
. Expressing this in terms of
, we get
![P(A\cap B)=P(B|A)\times P(A)](https://tex.z-dn.net/?f=P%28A%5Ccap%20B%29%3DP%28B%7CA%29%5Ctimes%20P%28A%29)
Plug in the known values and solve for
. This gives,
![P(A\cap B)=P(B|A)\times P(A)\\P(A\cap B)=\frac{3}{8}\times \frac{4}{7}\\P(A\cap B)=\frac{12}{56}=\frac{3}{14}](https://tex.z-dn.net/?f=P%28A%5Ccap%20B%29%3DP%28B%7CA%29%5Ctimes%20P%28A%29%5C%5CP%28A%5Ccap%20B%29%3D%5Cfrac%7B3%7D%7B8%7D%5Ctimes%20%5Cfrac%7B4%7D%7B7%7D%5C%5CP%28A%5Ccap%20B%29%3D%5Cfrac%7B12%7D%7B56%7D%3D%5Cfrac%7B3%7D%7B14%7D)
Therefore, the probability of events A and B occurring is
.
Answer:
B'(-3, 2)
Explanation:
In the triangle, point B is at (3, 2).
We want to find the coordinates of B', the image of B when triangle ABC is reflected over the y-axis.
When a point (x,y) is reflected over the y-axis, the transformation rule is:
![(x,y)\to(-x,y)](https://tex.z-dn.net/?f=%28x%2Cy%29%5Cto%28-x%2Cy%29)
This means that the x-coordinate changes to the opposite sign while the y-coordinate stays the same.
Applying this rule, we have:
![B(3,2)\to B^{\prime}(-3,2)](https://tex.z-dn.net/?f=B%283%2C2%29%5Cto%20B%5E%7B%5Cprime%7D%28-3%2C2%29)
Thus, the coordinates of point B' after triangle ABC is reflected across the y-axis will be B'(-3, 2).
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