B = 2
B is basically whatever number the line passes through on the Y - Axis
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I'm assuming you meant to say
P(A) = 2/3
P(A and B) = 1/3
If that is the case, then A and B are independent if and only if the following equation is true
P(A and B) = P(A)*P(B)
So we multiply P(A) and P(B) to get the value of P(A and B). We don't know what P(B) is, but we can use algebra to find it
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P(A and B) = P(A)*P(B)
P(A)*P(B) = P(A and B)
(2/3)*P(B) = 1/3
P(B) = (1/3)*(3/2) .... multiply both sides by the reciprocal of 2/3
P(B) = (1*3)/(3*2)
<h3>P(B) = 1/2 is the answer</h3>
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If P(B) = 1/2, then
P(A and B) = P(A)*P(B)
P(A and B) = (2/3)*(1/2)
P(A and B) = (2*1)/(3*2)
P(A and B) = 1/3
Which is the given probability for both events happening. This confirms we have the correct P(B) value.
Answer:
20 cm
Step-by-step explanation:
An hexagon has 6 equal sides therefore its perimeter is obtained by summing up all the values of the 6 sides
For the bigger hexagon, the perimeter = 32 + 32 + 32 +32 + 32 + 32
or 6 *32
= 192 cm
Next, we'll calculate the perimeter of the smaller hexagon
Since their perimeters are in the ratio 8: 5
Let x represent the perimeter of the smaller hexagon
This gives;
8 : 5 = 192 : x
change to fraction
8/5 = 192 /x
cross multiply
8x = 192*5
8x = 960
Divide both sides by the coefficient if x which is 8
x = 120 cm
Since all sides of an hexagon are equal, we'll simple divide the value of the perimeter by the number of sides of the hexagon
120/6
20 cm
Therefore, the length of the corresponding smaller hexagon is 20 cm
