"cube has a volume of 125 cubic inches. What is the length of each edge?"
1 answer:
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Answer:
Part 1) m∠1 =(1/2)[arc SP+arc QR]
Part 2)
Part 3) PQ=PR
Part 4) m∠QPT=(1/2)[arc QT-arc QS]
Step-by-step explanation:
Part 1)
we know that
The measure of the inner angle is the semi-sum of the arcs comprising it and its opposite.
we have
m∠1 -----> is the inner angle
The arcs that comprise it and its opposite are arc SP and arc QR
so
m∠1 =(1/2)[arc SP+arc QR]
Part 2)
we know that
The <u>Intersecting Secant-Tangent Theorem,</u> states that the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment.
so
In this problem we have that
Part 3)
we know that
The <u>Tangent-Tangent Theorem</u> states that if from one external point, two tangents are drawn to a circle then they have equal tangent segments
so
In this problem
PQ=PR
Part 4)
we know that
The measurement of the outer angle is the semi-difference of the arcs it encompasses.
In this problem
m∠QPT -----> is the outer angle
The arcs that it encompasses are arc QT and arc QS
therefore
m∠QPT=(1/2)[arc QT-arc QS]
Answer:
a) The probability that at least 3 months elapse before the first earthquake of destructive magnitude occurs is P=0.7788
b) The probability that at least 7 months elapsed before the first earthquake of destructive magnitude occurs knowing that 3 months have already elapsed is P=0.7165
Step-by-step explanation:
Tha most appropiate distribution to model the probability of this events is the exponential distribution.
The cumulative distribution function of the exponential distribution is given by:
The destructive earthquakes happen in average once a year. This can be expressed by the parameter λ=1/year.
We can express the probability of having a 3 month period (t=3/12=0.25) without destructive earthquakes as:
Applying the memory-less property of the exponential distribution, in which the past events don't affect the future probabilities, the probability of having at least 7 months (t=0.58) elapsed before the first earthquake given that 3 months have already elapsed, is the same as the probability of having 4 months elapsed before an earthquake.