Solution: The number of ways we can arrange 3 blue marbles if a set of 5 marbles is selected is:



Therefore, there are 10 ways we could arrange 3 blue marbles.
Answer:
The solution of the given initial value problems in explicit form is
and the solutions are defined for all real numbers.
Step-by-step explanation:
The given differential equation is

It can be written as

Use variable separable method to solve this differential equation.

Integrate both the sides.

![[\because \int x^n=\frac{x^{n+1}}{n+1}]](https://tex.z-dn.net/?f=%5B%5Cbecause%20%5Cint%20x%5En%3D%5Cfrac%7Bx%5E%7Bn%2B1%7D%7D%7Bn%2B1%7D%5D)
... (1)
It is given that y(1) = -2. Substitute x=1 and y=-2 to find the value of C.



The value of C is -2. Substitute C=-2 in equation (1).
Therefore the solution of the given initial value problems in explicit form is
.
The solution is quadratic function, so it is defined for all real values.
Therefore the solutions are defined for all real numbers.
Answer: In mathematics, an inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions. It is used most often to compare two numbers on the number line by their size
Step-by-step explanation: