Answer: (20.86, 22.52)
Step-by-step explanation:
Formula to find the confidence interval for population mean :-
, where = sample mean.
z*= critical z-value
n= sample size.
= Population standard deviation.
By considering the given question , we have
n= 58
Using z-table, the critical z-value for 95% confidence = z* = 1.96
Then, 95% confidence interval for the amount of time spent on administrative issues will be :
Hence, the 95% confidence interval for the amount of time spent on administrative issues = (20.86, 22.52)
I don't know what method is referred to in "section 4.3", but I'll suppose it's reduction of order and use that to find the exact solution. Take
, so that
and we're left with the ODE linear in
:
Now suppose
has a power series expansion
Then the ODE can be written as
All the coefficients of the series vanish, and setting
in the power series forms for
and
tell us that
and
, so we get the recurrence
We can solve explicitly for
quite easily:
and so on. Continuing in this way we end up with
so that the solution to the ODE is
We also require the solution to satisfy
, which we can do easily by adding and subtracting a constant as needed:
Answer:
I believe the correct answer is B.
Answer:
See below.
Step-by-step explanation:
So, we have:
PART A:
Find the GCF. Notice that we have a 3 in every term and a p in every term. Thus, the GCF is 3p:
This is the most we can do.
PART B:
Continue from where we left off. Factor the entire expression:
(-2ab^3)(-3a^2b^5)<span>Simplifying
(-2ab3)(-3a2b5)
Remove parenthesis around (-2ab3)
-2ab3(-3a2b5)
Remove parenthesis around (-3a2b5)
-2ab3 * -3a2b5
Reorder the terms for easier multiplication:
-2 * -3ab3 * a2b5
Multiply -2 * -3
6ab3 * a2b5
Multiply ab3 * a2b5
6a3b<span>8</span></span>