Compute the amount of interest earned in the following simple interest problem. A deposit of $1,600 at 6% for 180 days =
2 answers:
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Answer:
The volume in such a package is 27648 in³
Step-by-step explanation:
Consider the provided information.
Postal regulations specify that a parcel sent by priority mail may have a combined length and girth of no more than 144 in.
Let the dimension are x by x by y.
Where x is the variable for the square base package and y is the variable for length.
Thus l=x, b=x and h=y
Then the volume of the box is: (∵V=lbh)
The maximum combined length and girth is 144.
Therefore,
Substitute the value of y in volume of the box.
Substitute V'(x)=0.
Now apply second derivative test.
(Min)
(Max)
Hence, the maximum volume is at x=24
If x=24 then
Substituting value of x = 24 and y = 48 gives 27648.
Hence, the volume in such a package is 27648 in³
Answer:
Step-by-step explanation:
A negative binomial random variable "is the number X of repeated trials to produce r successes in a negative binomial experiment. The probability distribution of a negative binomial random variable is called a negative binomial distribution, this distribution is known as the Pascal distribution".
And the probability mass function is given by:
Where r represent the number successes after the k failures and p is the probability of a success on any given trial.
Solution to the problem
For this case the likehoof function is given by:
If we replace the mass function we got:
When we take the derivate of the likehood function we got:
And in order to estimate the likehood estimator for p we need to take the derivate from the last expression and we got:
And we can separete the sum and we got:
Now we need to find the critical point setting equal to zero this derivate and we got:
For the left and right part of the expression we just have this using the properties for a sum and taking in count that p is a fixed value:
Now we need to solve the value of from the last equation like this:
And if we solve for we got:
And if we divide numerator and denominator by n we got:
Since