Answer:
![P(A \cap B)](https://tex.z-dn.net/?f=%20P%28A%20%5Ccap%20B%29)
And we can use the following formula:
![P(A \cap B)= P(A)* P(B)](https://tex.z-dn.net/?f=%20P%28A%20%5Ccap%20B%29%3D%20P%28A%29%2A%20P%28B%29)
And replacing the info we got:
![P(A \cap B) = \frac{5}{7} \frac{2}{3}= \frac{10}{21}=0.476](https://tex.z-dn.net/?f=%20P%28A%20%5Ccap%20B%29%20%3D%20%5Cfrac%7B5%7D%7B7%7D%20%5Cfrac%7B2%7D%7B3%7D%3D%20%5Cfrac%7B10%7D%7B21%7D%3D0.476)
Step-by-step explanation:
We define two events for this case A and B. And we know the probability for each individual event given by the problem:
![p(A) = \frac{5}{7}](https://tex.z-dn.net/?f=%20p%28A%29%20%3D%20%5Cfrac%7B5%7D%7B7%7D)
![p(B) = \frac{2}{3}](https://tex.z-dn.net/?f=%20p%28B%29%20%3D%20%5Cfrac%7B2%7D%7B3%7D)
And we want to find the probability that A and B both occurs if A and B are independent events, who menas the following conditions:
![P(A|B) = P(A)](https://tex.z-dn.net/?f=%20P%28A%7CB%29%20%3D%20P%28A%29)
![P(B|A) = P(B)](https://tex.z-dn.net/?f=%20P%28B%7CA%29%20%3D%20P%28B%29)
And for this special case we want to find this probability:
![P(A \cap B)](https://tex.z-dn.net/?f=%20P%28A%20%5Ccap%20B%29)
And we can use the following formula:
![P(A \cap B)= P(A)* P(B)](https://tex.z-dn.net/?f=%20P%28A%20%5Ccap%20B%29%3D%20P%28A%29%2A%20P%28B%29)
And replacing the info we got:
![P(A \cap B) = \frac{5}{7} \frac{2}{3}= \frac{10}{21}=0.476](https://tex.z-dn.net/?f=%20P%28A%20%5Ccap%20B%29%20%3D%20%5Cfrac%7B5%7D%7B7%7D%20%5Cfrac%7B2%7D%7B3%7D%3D%20%5Cfrac%7B10%7D%7B21%7D%3D0.476)
Answer:
The graph i the attached figure
Step-by-step explanation:
we have
----> inequality A
The solution of the inequality A is the shaded area above the dotted line ![y=2x-5](https://tex.z-dn.net/?f=y%3D2x-5)
The slope of the dotted line is positive
The x- intercept of the dotted line is the point (2.5,0)
The y- intercept of the dotted line is the point (0,-5)
-----> inequality B
The solution of the inequality B is the shaded area below the dotted line ![y=-3x](https://tex.z-dn.net/?f=y%3D-3x)
The slope of the dotted line is negative
The x- intercept of the dotted line is the point (0,0)
The y- intercept of the dotted line is the point (0,0)
The solution of the system of inequalities is the shaded area between the two dotted lines
see the attached figure
Answer:
A, 3/4(4/3)x=-6(4/3)
Step-by-step explanation:
Multiplying each side of the equation by 4/3 isolates x and solves the equation in one step.
-24a^3b^7 you multiply the two numbers and add the exponents.
Answer:
42
Step-by-step explanation:
The figure is broken into different shapes so you find the area of each shape shown and add them up!
Step one: find the area of the triangle. 1/2*base*height* The base is 3 and the height is 4. it will be 6. This applies to the second triangle on the bottom as well. The total of both triangle is 12.
Step two: find the area of the rectangle.base*height. All you have to do is 10*3 which is 30.
Step three: now add up all the areas you got. 30+12. which is 42.
hope this helps :)