Answer:
The expression is shown in the explanation below:
Explanation:
Thinking process:
Let the time period of a simple pendulum be given by the expression:
Let the fundamental units be mass= M, time = t, length = L
Then the equation will be in the form
where k is the constant of proportionality.
Now putting the dimensional formula:
Equating the powers gives:
a = 0
b + c = 0
2c = 1, c = -1/2
b = 1/2
so;
a = 0 , b = 1/2 , c = -1/2
Therefore:
T =
where k =
Answer:
Explanation:
The <em>batch</em> is <em>rejected</em> if any of the <em>random samples are found defective</em>, or, what is the same, it will be accepted only if all 15 samples are good.
The probability that none be defective is the same probability that all the samples are good. Thus, start to calculate the probability that the batch is accepted.
The probability that the first sample is good is 214 /225, because there are 225 - 11 = 214 good samples in 225 doses.
The probability that the second samples is good too is 213/224, because there is 1 less good sample, in the 224 remaining samples.
By the same process, you conclude that the consecutive probabilities of selecting a good sample are: 212/223, 211/222, 210/221, . . . up to 199/211.
The joint probability of all the samples are good is the product of each probability:
The result is: 0.41278 ≈ 0.41
The conclusion is that the probability that all the samples are good and the batch is accepted is 0.41.
Therefore, <em>the probability that the batch is rejected</em> is 1 - 0.41 = 0.59.