Answer:
Step-by-step explanation:
From the given information:
a.
Compute 
:
b.
Compute P(A ∩ B)
P(A ∩ B) = P(A) +P(B) - P(A∪B)
P(A ∩ B) = 0.32 + 0.46 - 0.57
P(A ∩ B) = 0.21
Thus, since P(A ∩ B) ≠ 0, we can say that they are not mutually exclusive.
c.
P(A ∩ C) = P(A) +P(C) - P(A∪C)
P(A ∩ C) = 0.32 + 0.23 -0.55
P(A ∩ C) = 0
Thus, since P(A ∩ C) = 0, we can say that they are both mutually exclusive.
d. To determine P[(A ∪ B ∪ C)′]
i.e. none of the events occurring
Then :
P(B ∩ C) = 0.46 +0.23 -0.49
P(B ∩ C) = 0.20
Therefore:
P(A ∪ B ∪ C) = P(A) + P(B) + P(C) - P(A ∩ B ) - P(A ∩ C) - P(B ∩ C) + P(A ∩ B ∩ C)
P(A ∪ B ∪ C) = 0.32 + 0.46 + 0.23 - 0.21 - 0 - 0.20 + 0
P(A ∪ B ∪ C) = 0.60
Answer:
32
Step-by-step explanation:
34 = -62 + 3x
34+62 = 3x
96 = 3x
x = 32
Answer:
2000 feet.
Step-by-step explanation:
Let the length of fence need be x feet.
Then we have the equation:
2lx = 19x + 4000
21x - 19x = 4000
2x = 4000
x = 2000.
Answer:
A) Same shape
C) Similar
Step-by-step explanation:
The figure is missing: find it in attachment.
Here we want to compare the two triangles: Let's analyze each statement.
A) Same shape --> TRUE
In fact, we see that the 3 angles of the two triangles are the same: therefore, the two triangles have same shape.
B) Congruent --> FALSE
Two triangles are said to be congruent if they have same sizes and same angles: here we see that they do not have the same sizes, so they are not congruent.
C) Similar --> TRUE
Two triangles are said to be similar if the proportions between their sides are the same.
For the triangles in the figure, we see that this is valid. In fact, the ratio of the 3 sides for the triangle on the left is 10:8:6, while the ratio for the triangle on the right is 20:16:12, which can be reduced to 10:8:6: therefore, the same ratio.
D) Same size --> FALSE
As we see, the two triangles do not have the same size.
There are 5 + 7 = 12 triangles or hexagons. So the probability is 12/15 = 4/5. As a percent, it would be 80%.
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Hope this helps!
==jding713==
