Answer:
The probability that he rolls a sum of 9 given the sample space is . 9/36, or 1/4.
What is the probability?
Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.
The probability that he rolls a sum of 9 = cubes that have a sum of 9 / total number of cubes
9/36 = 1/4
Step-by-step explanation:
x2 + 2xn + n2
x2 + xn + xn + n2
x(x + n) + n (x + n)
So (x + n)^2 is the factor
Answer:
Yes, you're correct.
Step-by-step explanation:
Answer:

Step-by-step explanation:
Consider the quadratic expression

First, find its discriminant:

Note that
then 
Use quadratic formula to find the roots:

Now, given quadratic expression is equivalent to

Answer:
7.71 inches far from each edge of the wall you should place the shelf.
Step-by-step explanation:
Given:

Let,
AB = distance between the edges or distance of wall.
ED = size of the shelf.
C is the centre of the wall.
To Find:
Distance from the edge of the wall to the shelf, when the shell is placed at the center of the wall.
AE = DB = ?
Solution:
As we need to place the shelf exactly in the center.
First we will calculate the distance from the center of the wall to the edge.
So the distance from the centre of the wall to the edge will be exactly half of the size of the wall.

now the distance from the centre to the end of the shelf will be exactly half of the size of the shelf.

Now we want to calculate the distance from the edge of the wall to the shelf,that is the distance from the end of the shelf to the edge of the wall.

Therefore, 7.71 inches far from each edge of the wall you should place the shelf.