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Alexandra [31]
4 years ago
15

PLEASE HELP!!!! Factor this expression completely. x^3 1/8 - y^3 1/27

Mathematics
1 answer:
omeli [17]4 years ago
7 0
This expression is the difference of two cubes:

x^3     y^3
----- - -------
2^3     3^3

The rule here is  a^3 - b^3 = (a - b)(a^2 + ab + b^2), so


x^3     y^3                          x^2       x^3y^3        y^2
----- - ------- = (x/2 - y/3)*(-------- + ----------- + --------- )
2^3     3^3                          2^2          6^3          3^2
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Adimas found the mean of her 11 math test scores for the first semester. X = StartFraction (76 87 65 88 67 84 77 82 91 85 90) Ov
Reika [66]

To find the solution we will first find the difference between each number and mean, and then substitute the value in the formula of standard deviation.

The standard deviation is 8.4477 and the variance is 71.40.

Given to us

  • Test scores of Adimas = (76, 87, 65, 88, 67, 84, 77, 82, 91, 85, 90)
  • Mean = 81

<h3>Standard Deviation</h3>

difference between each number and mean,

x_1 -\mu= 76-81 = -5\\&#10;x_2-\mu = 87-81 = 6\\&#10;x_3-\mu = 65-81 = -16\\&#10;x_4-\mu = 88 -81 = 7\\&#10;x_5-\mu = 67-81 = -14\\&#10;x_6 -\mu= 84-81 = 3\\&#10;x_7 -\mu= 77-81 = -4\\&#10;x_8 -\mu= 81-81 = 1\\&#10;x_9 -\mu= 91-81 = 10\\&#10;x_{10}-\mu=85-81 = 4\\&#10;x_{11} -\mu= 90-81 = 9

\sum(x-\mu)^2 = x_1^2+x_2^2+x_3^2+x_4^2+x_5^2+x_6^2+x_7^2+x_8^2+x_9^2+x_{10}^2+x_{11}^2

                 =  25 + 36 + 256 + 49 + 196 + 9 + 16 + 1 + 100 +16 + 81

                 = 785

\rm{ Standard\ Deviation = \sqrt{\dfrac{\sum{(X-\mu)^2}} {n}

                             \sigma= \sqrt{\dfrac{785}{11}}\\\\&#10;\sigma = 8.4477

<h3>Variance</h3>

Variance = \sigma ^2

              = 71.40

Hence, the standard deviation is 8.4477 and the variance is 71.40.

Learn more about Standard Deviation:

brainly.com/question/12402189

3 0
3 years ago
Rearrange w=3(2a+b)-4 can u please make a the subject of the formulae
lys-0071 [83]
I'll try to do each individual step, hopefully that'll clear it up
 w= 3(2a+b)-4
w+4= 3(2a+b)
(w+4)/3 = 2a+ b
2a= ((w+4)/3) - b
a= (((w+4)/3) - b)/ 2
3 0
4 years ago
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Answer:

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Step-by-step explanation:

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