Answer:

Step-by-step explanation:
First, find the probability of him pulling out a book.
There are 11 objects in total, and there are 4 books.
So, the probability of pulling out a book is 
Next, find the probability of him pulling out a DVD after.
Since a book was taken out, there are only 10 objects left. There are 5 DVDs.
So, the probability of pulling out a DVD is
, or simplified to 
To find the probability that this happens in order, multiply the probabilities:
x 
= 
So, the probability is 
Answer:
The original length was 41 inches and the original width was 16 inches
Step-by-step explanation:
Let
x ----> the original length of the piece of metal
y ----> the original width of the piece of metal
we know that
When squares with sides 5 in long are cut from the four corners and the flaps are folded upward to form an open box
The dimensions of the box are

The volume of the box is equal to


so

simplify
-----> equation A
Remember that
The piece of metal is 25 in longer than it is wide
so
----> equation B
substitute equation B in equation A

solve for y

Solve the quadratic equation by graphing
using a graphing tool
The solution is y=16
see the attached figure
Find the value of x

therefore
The original length was 41 inches and the original width was 16 inches
The distance between any two points is:
d^2=(x2-x1)^2+(y2-y1)^2
d^2=(6--2)^2+(4--4)^2
d^2=8^2+8^2
d^2=64+64
d^2=128
d=√128 units
To prove two equations have infinite solutions, you have to prove that those two equations are the same equations, but in a different form.
For example: Prove the equations are infinite
5y=2x+7
10y=4x+14
If you multiply the first equation by 2, and substitiute any of the numbers, you will get 0=0