Answer:
Recall that a relation is an <em>equivalence relation</em> if and only if is symmetric, reflexive and transitive. In order to simplify the notation we will use A↔B when A is in relation with B.
<em>Reflexive: </em>We need to prove that A↔A. Let us write J for the identity matrix and recall that J is invertible. Notice that 
. Thus, A↔A.
<em>Symmetric</em>: We need to prove that A↔B implies B↔A. As A↔B there exists an invertible matrix P such that 
. In this equality we can perform a right multiplication by 
and obtain 
. Then, in the obtained equality we perform a left multiplication by P and get 
. If we write 
and 
we have 
. Thus, B↔A.
<em>Transitive</em>: We need to prove that A↔B and B↔C implies A↔C. From the fact A↔B we have and from B↔C we have 
. Now, if we substitute the last equality into the first one we get
.
Recall that if P and Q are invertible, then QP is invertible and 
. So, if we denote R=QP we obtained that
. Hence, A↔C.
Therefore, the relation is an <em>equivalence relation</em>.
The baker needs to use 100/3 pounds of 90% chocolate to make the cake.
<h3>
Equation </h3>
An equation is an expression used to show the relationship between two or more numbers and variables.
Let x represent the amount of 90% chocolate. Using equation:
100 * 70% + x * 90% = (x + 100) * 75%
100 * 0.7 + 0.9 * x = (x + 100) * 0.75
70 + 0.9x = 0.75x + 75
x = 100/3
The baker needs to use 100/3 pounds of 90% chocolate to make the cake.
Find out more on Equation at: brainly.com/question/22688504
Answer:
I have no clue but keep up the good work in the test
Answer:
To make the answer to 36 divided by 2/3 in decimal form, you simply divide the numerator by the denominator from the fraction answer above:
108 / 2 = 54
Step-by-step explanation:
I am so sorry if i am wrong
Answer:
3/8 probability or a 37.5% chance.
