Answer:
The condition are
The Null hypothesis is 
The Alternative hypothesis is
The check revealed that
There is sufficient evidence to support the claim that in a small city renowned for its music school, the average child takes at least 5 years of piano lessons
Step-by-step explanation:
From the question we are told that
The population mean is 
The sample size is n = 20
The sample mean is 
The standard deviation is 
The Null hypothesis is 
The Alternative hypothesis is
So i will be making use of
level of significance to test this claim
The critical value of
from the normal distribution table is 
Generally the test statistics is mathematically evaluated as

substituting values


Looking at the value of t and
we see that
so we fail to reject the null hypothesis
This implies that there is sufficient evidence to support the claim that in a small city renowned for its music school, the average child takes at least 5 years of piano lessons.
A)
Earlier, The length of the angelfish =
inches
Now, the length of angelfish =
inches
We have to determine the grown length of angelfish
=
- 
= 
LCM of '2' and '3' is '6',
= 
=
inch
Therefore, the angelfish has grown by
inch.
B)
We have to determine the increased length of angelfish in feet.
Since
foot
So, 
= 0.069 foot.
The answer to the question above is the third choice, "a shelf on a wall". The shelf is usually made of rectangular pieces of materials that are then connected to each other to form quadrilaterals. The sides of the shelf are planes.
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


![\displaystyle\sum_{n\ge2}\bigg[n(n-1)a_n-(n-1)a_{n-1}\bigg]x^{n-2}=0](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Csum_%7Bn%5Cge2%7D%5Cbigg%5Bn%28n-1%29a_n-%28n-1%29a_%7Bn-1%7D%5Cbigg%5Dx%5E%7Bn-2%7D%3D0)
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:
Explanation:
Let the equation be
a
⋅
x
2
+
b
⋅
x
+
c
. To factorize multiplication of a and c i.e. ac so that sum of factors, if ac is positive (and difference if ac is negative) is equal to b. Now split b into these two components and factorization will be easy.