The greater the force applied to an object, the _____ the change in speed or direction of the object.
1 answer:
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Answer:
±11.18
Step-by-step explanation:
the function is:
and to find the roots we need to find which values of makes the function result in zero:
solving for :
A square root has two solutions, one positive and one negative, so the solutions are:
±
≈ ±11.18
the roots of the quadratic equation are +11.18 and -11.18
It can be expected about 36.79% of chance that repair time exceeds
The probability that a repair time exceeds 15 hours is 0.3679
What is the exponential distribution?
It explains about the time between events or the distance between two random events is termed the exponential distribution. Here, the occurrence of the events is continuous and also independent. Moreover, the average rate is constant.
The cumulative distribution function of T is obtained below:
From the information given, let the random variable T be the required time to repair a machine follows exponential distribution with parameter λ
with mean. 1/2 hours
That is, E(x) = 1/2 hours.
The parameter of the random variable T is,
E(x) = 1/λ
λ = 1/E(x)
= 1/(1/2)
= 2
The probability density function of T is,
The cumulative density function of T is,
FT(t) = P(T <= t)
The CDF of T is,
P(T <= t) 0 <= T <= ∞
= 0 otherwise
to obtain the probability that a repair time exceeds
1/2 hours.
(a) The probability that a repair time exceeds 1/2 hours.
From the given information, the CDF of T is,
P(T <= t) 0 <= T <= ∞
= 0 otherwise
The required probability is,
P(T <= 1/2) = 1 - P(T <= 1/2)
= 1 - [ ]
= 0.3679
om total probability. It can be expected about 36.79% of chance that repair time exceeds
P(X => x) = 1 - P(X < x)
to obtain the probability that a repair takes at least 12.5 hours given that its duration exceeds 12 hours.
(b), The probability that a repair takes at least 12.5 hours given that its duration exceeds 12 hours is obtained below:
From the given information, the CDF of T is,
P(T <= t) 0 <= T <= ∞
= 0 otherwise
The required probability is,
P = P(T => 12.5∩T>12) / P(T>12)
= 0.3679
The probability that a repair takes at least 12.5 hours given that its duration exceeds 12 hours is obtained by dividing the
P = P(T => 12.5∩T>12) / P(T>12)
with
P(T>12).
It can be expected about 36.79% of chance that a repair takes at least 12.5 hours given that its duration exceeds 12 hours.
Hence, It can be expected about 36.79% of chance that repair time exceeds,
The probability that a repair time exceeds 15 hours is 0.3679
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Answer: Absolute minimum: f(-1) = -2
Absolute maximum: f() = 12.5
Step-by-step explanation: To determine minimum and maximum values in a function, take the first derivative of it and then calculate the points this new function equals 0:
f(t) =
f'(t) =
f'(t) =
f'(t) = = 0
For this function to be zero, only denominator must be zero:
t = ±
≠ 0
t = ± 5
Now, evaluate critical points in the given interval.
t = and t = - 5 don't exist in the given interval, so their f(x) don't count.
f(t) =
f(-1) =
f(-1) =
f(-1) =
f() =
f() = 12.5
f(5) =
f(5) = 0
Therefore, absolute maximum is f() = 12.5 and absolute minimum is
f(-1) = .