Probability =
(number of ways it can come out the way you want it to)
divided by
(total number of ways it can come out).
Total number of ways it can come out =
number of bottles in the cooler
= (10 + 15 + 13) = 38 .
Number of ways it can come out the way you want it to =
(soda + lemonade)
= (10 + 15) = 25 .
Probability of coming out the way you want it to =
25 / 38 = about 65.8 % .
Okay, let's work this out...
What we know:
-32 stamps in all
- rows (horizontal)
- same # in each
What we "want to know" :
- # of combinations (different)
Problem Solving :
This is actually very easy its just the words than get ya!
1st : we need to figure out the factors of 32...
In other words, we need to figure out _x_=32 and how many different combinations and ways there are!
Note:(* means multiplication)
#1: What are the factors of 32?
32: 1*32 , 2*16 , 4*8
32: 32*1 , 16*2 , 8*4
The factors (not including 1 are 2,4,8,16)
Now, as you can see, there are 4 ways to get 32 as shown first.
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That ¦ is 1 way with 16 in 2 rows. Basic multiplication, 16*2=32 or 16+16=32.
But, this is also a way,
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Now there should be 2 in each row and 16 rows. Again 2*16=32 or 2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2=32
That's two ways so far.
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Another way which is 4 rows with 8 in each.
4*8=32 or 8+8+8+8=32
But, this is also a way,
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Now that is 8 rows with 4 in each. 8*4=32 or 4+4+4+4+4+4+4+4=32
That was our fourth way.
Again NOT including 1. If you include 1 then there will be 6 ways but aside from that there are 4 ways.
I hope that helped I worked hard typing this all for you. Any questions just ask!
<span>Simplifying
4x = 92
Solving
4x = 92
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Divide each side by '4'.
x = 23
Simplifying
x = 23</span>
Answer:
A), B) and D) are true
Step-by-step explanation:
A) We can prove it as follows:
B) When you compute the product Ax, the i-th component is the matrix of the i-th column of A with x, denote this by Ai x. Then, we have that 
. Now, the colums of A are orthonormal so we have that (Ai x)^2=x_i^2. Then 
.
C) Consider 
. This set is orthogonal because 
, but S is not orthonormal because the norm of (0,2) is 2≠1.
D) Let A be an orthogonal matrix in 
. Then the columns of A form an orthonormal set. We have that 
. To see this, note than the component 
of the product 
is the dot product of the i-th row of 
and the jth row of 
. But the i-th row of is equal to the i-th column of . If i≠j, this product is equal to 0 (orthogonality) and if i=j this product is equal to 1 (the columns are unit vectors), then 
E) Consider S={e_1,0}. S is orthogonal but is not linearly independent, because 0∈S.
In fact, every orthogonal set in R^n without zero vectors is linearly independent. Take a orthogonal set 
and suppose that there are coefficients a_i such that 
. For any i, take the dot product with u_i in both sides of the equation. All product are zero except u_i·u_i=||u_i||. Then 
then 
.
I need points so imma answer
