Answer: Probability that Box A was chosen given that black marble is chosen is 0.5.
Step-by-step explanation:
Since we have given that
Number of boxes = 2
In Box A,
Number of black marbles = 1
Number of white marbles = 3
In Box B,
Number of black marbles = 2
Number of white marbles = 4
Since black marble is selected.
So, using Bayes theorem , we get that

Hence, probability that Box A was chosen given that black marble is chosen is 0.5.
The first question's answer is the second choice. The second question's answer is the first choice. The third question's answer is the second choice.
Answer:
The angle
measures approximately 
Step-by-step explanation:
Since this problem involves the finding of an angle in a right angle triangle for which we know the opposite side and the adjacent side, the trigonometric function that relates them is the tangent:

Then, for our case we get a starting equation that reads:

and for which we need to solve for
. Then we use the arctangent function to get the final answer:

Answer: 4m-8
Step-by-step explanation:
Remember to distribute the negative sign!
m-8+3m
4m-8
<h3>
Answer:</h3>
(1, 1), (4, -25)
<h3>
Step-by-step explanation:</h3>
You can evaluate the function to see.
f(-1) = -3^(-1-1)+2 = -3^(-2)+2 = -1/9 +2 ≠ 2
f(1) = -3^(1-1) +2 = -1 +2 = 1
f(0) = -3^(0-1) +2 = -1/3 +2 ≠ 0
f(4) = -3^(4 -1) +2 = -27 +2 = -25
_____
Or, you can graph the points and the curve.