How does the area of triangle RST compare to the area of triangle LMN? The area of △RST is 2 square units less than the area of
△LMN. The area of △RST is equal to the area of △LMN. The area of △RST is 2 square units greater than the area of △LMN. The area of △RST is 4 square units greater than the area of △LMN.
2 answers:
Inscribe triangle RST in the square with dimensions 4×4, as shown in the figure.
from the area of this square, 4*4=16, we remove the triangles with dimensions
3×4, 2×1 and 2×4, whose side lengths are shown in the figure, and we are left with the area of triangle RST.
so
units squared
similarly,
units squared
Thus, the areas are equal.
from the area of this square, 4*4=16, we remove the triangles with dimensions
3×4, 2×1 and 2×4, whose side lengths are shown in the figure, and we are left with the area of triangle RST.
so
similarly,
Thus, the areas are equal.
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Answer:
Z and B are independent events because P(Z∣B) = P(Z).
Step-by-step explanation:
After a small online search, I've found a table to complete this problem, that we can see below.
For two events Z and B, we have:
P(Z|B) = probability of Z given that B
such that:
P(Z|B) = P(Z∩B)/P(B)
So, two events are independent if the outcome of one does not affect the outcome of the other.
So, if the probability of Z given B is different than P(Z) (the probability of event Z) means that the events are not independent.
So Z and B are independent if the probability of Z given B is equal to the probability of Z.
P(Z|B) = P(Z)
In the table we can see:
P(Z|B) will be equal to the quotient between all the cases of Z given B (126) and the total cases are given B (280)
P(Z|B) = 126/280 = 0.45
Similarly, we can find P(Z):
And P(Z) = 297/660 = 0.45
So we can see that:
P(Z|B) = P(Z)
Thus, B and Z are independent.
