Line segments MP and ML are perpendicular chords in circle O. MP = 10 and ML = 24. Triangle L M P is inscribed within circle O.
2 answers:
Answer:
The radius of circle O is 13.
∠LMP intercepts a semicircle.
LP is a diameter of circle O
Step-by-step explanation:
Find the diagram attached
From the circle, PL is the diameter of the circle;
Also, LMP intercepts a semicircle since the triangle LMP is a triangle in the semicircle of the circle.
According to pythagoras theorem;
ML²+MP² = PL²
24²+10² = PL²
576 + 100 = PL²
676 = PL²
Swap
PL² = 676
PL = √676
PL = 26
Since radius = diameter/2
Radius of the circle = 26/2
Radius of the circle = 13
Hence the radius of circle O is 13.
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Answer:
P ( 1.2 < X < 2.1 ) = 0.3
Step-by-step explanation:
Given:
Uniform distribution over interval (0,3) can be modeled by a probability density function f(x)
f(x) = 1 / (b - a)
Where a < x < b is the domain at which function is defined:
f(x) = 1 / (3) = 1 / 3
Where, X - U ( u , δ )
u = ( a + b ) / 2 = (0 +3) / 2 = 1.5
δ = ( b - a ) / sqrt (12) = (3 - 0) / sqrt (12) = 0.866
Hence,
X - U ( 1.5 , 0.866 )
There-fore calculating P ( 1.2 < X < 2.1 ):
Where, a = 1.2 and b = 2.1
P ( 1.2 < X < 2.1 ) = x / 3 |
P ( 1.2 < X < 2.1 ) = 2.1 /3 - 1.2 / 3 = 0.3
Answer: P ( 1.2 < X < 2.1 ) = 0.3
See attachment for math work and answer.
