The answer
the full question is
If A(x1, y1), B(x2, y2), C(x3, y3), and D(x4, y4) create two line segments, and AB ⊥ CD, what condition must be satisfied to establish that AB ⊥ CD?
Let A(x1, y1) and B(x2, y2) represent the first line, while C(x3, y3) and D(x4, y4) represent the second line.
The slope for the first line is given by m = (y2 - y1) / (x2 - x1).
For the second line, the slope is m' = (y4 - y3) / (x4 - x3).
The necessary condition to demonstrate that AB ⊥ CD is
(y2 - y1) * (y4 - y3)
m × m' = --------- × ------------ = -1
(x2 - x1) (y4 - y3)
Answer:
0.40
Step-by-step explanation:
The percentage of members who engage only in long-distance running is 8%
Therefore, the probability that a member focuses solely on long-distance running is P(A) = 0.08
The percentage of members who participate exclusively in field events is 32%
Thus, the probability of a member competing only in field events is P(B) = 0.32
The percentage of members acting as sprinters is 12%
So, the probability that a member is a sprinter is P(C) = 0.12
We need to determine the probability that a team member is either an exclusive long-distance runner or an only field event competitor, which equates to finding P(A or B). Since these two events cannot occur simultaneously, we can express this as:
P(A or B) = P(A) + P(B)
Substituting the known values results in:
P(A or B) = 0.08 + 0.32 = 0.40
Thus, the likelihood that a randomly selected team member runs exclusively long-distance or participates solely in field events stands at 0.40
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