<span>As far as i know it is related to Gauss.
Write the sequences forward and backward first.
1 +2 +3 +.....+1002
1002+1001+1000+.....+1
--------------------------------------... Adding them
1003+1003+......(1002 times)
=1002x1003
But this contains the series twice.
So, the sum is = 1002x1003/2=501x1003=502503. answer</span>
Answer:
see explanation
Step-by-step explanation:
(10)
To evaluate f(- 4) substitute x = - 4 into f(x)
f(x) = 7x - 4x + 3 = 3x + 3
f(- 4) = 3(- 4) + 3 = - 12 + 3 = - 9
(11)
To evaluate f(- 2) substitute x = - 2 into f(x)
f(- 2) = 2(- 2)² - 8 = 2(4) - 8 = 8 - 8 = 0
(12)
To evaluate g(- 3) substitute x = - 3 into g(x)
g(- 3) = - 2(- 3)² + 3(- 3) = - 2(9) - 9 = - 18 - 9 = - 27
Apply to Row 2 : Row 2 + Row 1
2x + 2y + 3z = 0
y + 4z = -3
2x + 3y + 3z = 5
Apply to Row 3: Row 3 - Row 1
2x + 2y + 3z = 0
y + 4z = -3
y = 5
Apply to Row 3: Row 3 - Row 2
2x + 2y + 3z = 0
y + 4z = -3
-4z = 8
Simplify rows
2x + 2y + 3z = 0
y + 4z = -3
z = -2
<em>Note that the matrix is in echelon form now. The next steps are for back substitution.</em>
Apply to Row 2: Row 2 - 4 Row 3
2x + 2y + 3z = 0
y = 5
z = -2
Apply to Row 1: Row 1 - 3 Row 3
2x + 2y = 6
y = 5
z = -2
Apply to Row 1: Row 1 - 2 Row 2
2x = -4
y = 5
z = 2
Simplify the rows
<u>x = -2</u>
<u>y = 5</u>
<u>z = -2</u>
We want to find
, where
is a binomial distribution with
and
. So
4/7 for the 1st one., 8/9 for he 3rd dunno about middle one soz
