At some point you will have to use the fact that the series ∑ c/n! converges. You can always omit a finite number of (finite-valued terms) without changing the behavior of the series (convergence or divergence does not depend on a finite number of finite terms).
Look...

What have you done so far? Just asking tutors to do your homework is not exactly the way this is supposed to work.
The domain is impossible to miss, the range may require a little more thinking, but if you show where you got stuck, we could try helping.

What have you tried so far? If you show your work, then we can help your constructively. If you expect that tutors just do your hmwk, then you will get very little out of it. What is the number whose 80% is 72? Call the number you are looking for X. Then X*80/100 = 72, so X is ......

You have been asking several questions over a short period of time. Are you trying to get tutors to do your homework? We can do it, but how do you learn?
In any case, if you walk 2 miles a day, how many miles do you walk in 10 days? 10x2=20, right?
So, what is so difficult...

Your first task is to recognize what probability distribution (either discrete or continuous) is the right one for your particular case.
Here the "experiment" looks at a certain time interval (Saturday morning, 10am -11am) and we are told that ON AVERAGE every such...

Let y = x1/3. Then, I assume you can see that you can write the expression you were given as
y2 - 7y + 12 = 0 (*)
This is a trinomial that you should easily be successful in factoring . If you don't, then there is no point in writing down the full solution...

.. Have you tried taking log() on both sides and using properties of logs?

Well, you are provided with the probability of a strike in the specific region for a specific type of fish, i.e. p = 0.48.
Then, you are told that there is a total of 22 strikes. This info alone should alert you to what is the relevant distribution
you need to use. (22 trials, probability...

Well, it is a somewhat bizarre way to assign a stat problem. I will not solve it for you for in that case you get nothing out of it. But, if you are testing:
H0: p ≤ 0.5 vs. H1: p > 0. 5
Then you reject H0 if a certain statistic is greater than...

Not sure if you mean that you are required to use Taylor's expansions or just compute the limit.
The limit can be computed using L'Hopital's Rule twice and it turns out to be 1/(2π).

Well you start with a function
f(x) = cotg(x) + 4x
compute the first derivative which is the slope of the tangent line at each point x
f'(x) = -1/sin^2(x) + 4
if there exists a point in (o, pi) for which there exists...

It is a binomial random variable, so use the formulas for the binomial.
P(X=k) = n!/(k!(n-k)!) p^k(1-p)^(n-k) n=9, p=0.1 and k=0, 1, .., 9
P(X<4) = P(X=0)+P(X=1)+P(X=2)+ P(X=3).
So use the first formula for k=0, 1, 2, and 3 to find...

You are provided with the right hint.
Let X = number of fatal crashes. You can derive the probability associated with X by using the Number of days
Total number of days = 144+172+128+37+7+1 = 489 (check the calculations!)
Prob. [X=0] = 144/489 = 0...

Let A = "exam covers chapter 1"
B = "exam covers chapter 2"
You know that P(A) = 0.45; P(B) = 0.63, and P(A or B) = 0.76.
You are asked P(A and B) and there is a formula for it,right?
Recall that P(A or B) = P(A) +...

Part (e) cannot be written as
e
∑ n . (*)
n = a
It should be written as
Σn∈{a,e} n (**).
An expression like (*) is ambiguous. In fact, someone who knows the English alphabet...

How about starting from the properties of logs:
a*ln(b) = ln(ab)
ln(a)-ln(b) = ln(a/b)
Also, recall that ln(x) is defined only if x > 0.
So ln(x^2+1) - 3ln(x) = ln(x^2+1) - ln(x^3) = ln(x^2+1/x^3) = ln(2)
...

This problem belongs to the binomial distribution category.
You are interested in the probability that you win at least 7 times out of 12 trials knowing that the probability of success on each attempt is 0.80.
X ~ Bin(n=12, p = 0.80)
and we are looking...

log1/4[(1/4)-2x] = log1/4(64)
-2x = log1/4 64
-2x = log10(64)/log10(1/4) = loge(64)/loge(1/4) = -3
Thus x = 3/2 = 1.5
In fact we can check that (1/4)-2(3/2) = (1/4)-3 = 43 = 64
Remember that to find logaB for any base a, we can always use the logs...

I misunderstood the problem. Sorry.

Well... 10,000 cannot be right. In fact,
log(log(10,000) = log(4) .
Think of it like this:
10log(log(x)) = 104
which is the same as:
log(x) = 104
And therefore x = 10^104 which is a huge number: 1010...