SOLUTION: X: 8,9,10,11,12,13,14 Y: 1,2,3,4,5,6,7 1. ∑X ∑Y 2. ∑X²Y 3. 3∑(x+y)

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Question 1203687: X: 8,9,10,11,12,13,14
Y: 1,2,3,4,5,6,7
1. ∑X ∑Y
2. ∑X²Y
3. 3∑(x+y)
Found 2 solutions by mananth, math_tutor2020:
Answer by mananth(16946)   (Show Source): You can put this solution on YOUR website!
X: 8,9,10,11,12,13,14
Y: 1,2,3,4,5,6,7
1. ∑X ∑Y
2. ∑X²Y
3. 3∑(x+y)
X =8 + 9 + 10 + 11 + 12 + 13 + 14 = 77
Y = 1 + 2 + 3 + 4 + 5 + 6 + 7 = 28
X^2=(8²) + (9²) + (10²) + (11²) + (12²) + (13²) + (14²) =875
(X+Y) = 77+28 = 105
∑X ∑Y = 77*28=
∑X²Y= 875*28
3∑(x+y) = 3*105=



Answer by math_tutor2020(3817)   (Show Source): You can put this solution on YOUR website!

Tutor @mananth is mostly correct.

The only mistake is ∑(X²Y)= 875*28 is false

We cannot say ∑(X²Y) = ∑X²*∑Y because ∑(A*B) = ∑A*∑B isn't true.

Consider the small sets
A = {1,2,3}
B = {4,5,6}

They have these sums
∑A = 1+2+3 = 6
∑B = 4+5+6 = 15

Then,
C = A*B = pairwise multiplication
C = {1*4, 2*5, 3*6}
C = {4,10,18}
∑C = 4+10+18 = 32
But,
∑A*∑B = 6*15 = 90
which does not match with ∑C = 32

This is one counter-example to show why ∑A*∑B = ∑(A*B) is false.


This is how I would compute ∑(X²Y)
xyx^2x^2y
816464
9281162
103100300
114121484
125144720
1361691014
1471961372

I recommend using a spreadsheet.
Then we sum the items in the X²Y column:
64 + 162 + 300 + 484 + 720 + 1014 + 1372 = 4116
This value is not equal to the result of 875*28.


Therefore, ∑(X²Y) = 4116
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