1 (0+1) 3 (0+1+2) 6 (0+1+2+3) 10 (0+1+2+3+4) 15 (0+1+2+3+4+5) 21 (0+1+2+3+4+5+6) Notice these are the numbers you can arrange into equalateral triangles.
Points: (0, -1) and (-2, -4)Slope: 3/2
The range of {0, 1, 2, 3, 4, 5, 6} is 6 - 0 = 6.
2.738612788 First, find the mean (average) of all the numbers: 1+2+3+4+5+6+7+8+9 = 45 45 / 9 = 5 Mean is 5 Now take every number and calculate how far it is away from the mean, then square that number 1-5 = -4 ^2 = 16 2-5 = -3 ^2 = 9 3-5 = -2 ^2 = 4 4-5 = -1 ^2 = 1 5-5 = 0 ^2 = 0 6-5 = 1 ^2 = 1 7-5 = 2 ^2 = 4 8-5 = 3 ^2 = 9 9-5 = 4 ^2 = 16 Next, add all the results: 16+9+4+1+0+1+4+9+16 = 60 Then divide by the sample size minus 1 (n-1): 60 / 8 = 7.5 Finally, find the square root of that number: 7.5^ 0.5 = 2.738612788 Answer: 2.738612788
(x^2+x-1/2)= x(x+1)-1/2 [x + (1 - square root of 3)/2][x + (1 + square root of 3)/2] = 0 Check it: x^2 + x/2 + (square root of 3)x)/2 + x/2 + 1/4 + (square root of 3)/4 - (square root of 3)x/2 - (square root of 3)/4 - 3/4 = 0 x^2 + x/2 + x/2 + [(square root of 3)x]/2 - [(square root of 3)x]/2 + (square root of 3)/4 - (square root of 3)/4 + 1/4 - 3/4 = 0 x^2 + x - 2/4 = 0 x^2 + x - 1/2 = 0 How to find this roots: Using the completing the square method: x^2 + x - 1/2 = 0 x^2 + x = 1/2 x^2 + x + 1/4 = 1/2 + 1/4 (x + 1/2)^2 = 3/4 x + 1/2 = (plus & minus)(square root of 3/4) x = -1/2 + (square root of 3)/2 x = - 1/2 - (square root of 3)/2
Variance = sigma((value - mean)2) / (# values - 1) Mean = (0+1+1+2)/4 = 1 Variance = ((0-1)2+(1-1)2+(1-1)2+(2-1)2)/(4-1) Variance = (1+0+0+1)/3 Variance = 2/3 Variance ~ 0.667
If you mean points of (-2, 2) and (0, 4) then the slope works out as 1
The arithmetic mean is 2.
I was only able to get 13 but I think there can be more, this is what i got: 0+0+4=4 4+0+0=4 0+4+0=4 0+1+3=4 0+3+1=4 0+2+2=4 1+2+1=4 1+1+2=4 1+3+0=4 2+2+0=4 2+0+2=4 3+1+0=4 3+0+1=4
If you mean points of (-10, 1) and (0, -4) then the slope works out as -1/2
If you mean -4+20+1+4-20-1 = 0 because the numbers cancel themselves out
4-3-0-2-5-1-2
e---------------4-2-0---------------------4-2-0-------------0-0------------------ B-0---------0----------------------0---0-0-----------4---2-4-------0------------- G---1----1-----------------1--3-----------------------------------------1-------- D------2---------------------------------------------------------------------2--- A-------------------------------------------------------------------------------- E-------------------------------------------------------------------------------- e---------------0--4-2-0---------------------4-2-0-------------0-0--------------- B-0---------0----------------------0---0-0-----------4---2-4-------0------------- G---1----1-----------------1--3-----------------------------------------1-------- D------2---------------------------------------------------------------------2--- A-------------------------------------------------------------------------------- E-------------------------------------------------------------------------------- e-4--4-4-5-7-7--5-4-2-4-5-5---5-4-2-0-----------0-------------------------------- B------------------------------------------------4--2-4------------0------------- G------------------------------------------------------------1--3---------------- D-------------------------------------------------------------------------------- A-------------------------------------------------------------------------------- E-------------------------------------------------------------------------------- e---------0-0--0-----------2--5-4------------------0-2-4-5-7--------------------- B-0--0----------4-2--2-2----------5--5--4--0-0----------------------------------- G-------------------------------------------------------------------------------- D-------------------------------------------------------------------------------- A-------------------------------------------------------------------------------- E-------------------------------------------------------------------------------- e-0--2--4---5---2---0------------------------------------------------------------- B--------------------------------------------------------------------------------- G--------------------------------------------------------------------------------- D--------------------------------------------------------------------------------- A--------------------------------------------------------------------------------- E---------------------------------------------------------------------------------
2,2,0,5,1,4,1,3,0,0,1,4,4,0,1,4,3,4,2,1,0
4-3-0-2-5-1-2
12/6 = 2
+4 +3 +3 -4 -3 -2 0 -1 +3 +1+1 0 +1