Splitting up the interval [0, 6] into 6 subintervals means we have
![[0,1]\cup[1,2]\cup[2,3]\cup\cdots\cup[5,6]](https://tex.z-dn.net/?f=%5B0%2C1%5D%5Ccup%5B1%2C2%5D%5Ccup%5B2%2C3%5D%5Ccup%5Ccdots%5Ccup%5B5%2C6%5D)
and the respective midpoints are
![\dfrac12,\dfrac32,\dfrac52,\ldots,\dfrac{11}2](https://tex.z-dn.net/?f=%5Cdfrac12%2C%5Cdfrac32%2C%5Cdfrac52%2C%5Cldots%2C%5Cdfrac%7B11%7D2)
. We can write these sequentially as
![{x_i}^*=\dfrac{2i+1}2](https://tex.z-dn.net/?f=%7Bx_i%7D%5E%2A%3D%5Cdfrac%7B2i%2B1%7D2)
where
![0\le i\le5](https://tex.z-dn.net/?f=0%5Cle%20i%5Cle5)
.
So the integral is approximately
![\displaystyle\int_0^6x^2\,\mathrm dx\approx\sum_{i=0}^5({x_i}^*)^2\Delta x_i=\frac{6-0}6\sum_{i=0}^5({x_i}^*)^2=\sum_{i=0}^5\left(\frac{2i+1}2\right)^2](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cint_0%5E6x%5E2%5C%2C%5Cmathrm%20dx%5Capprox%5Csum_%7Bi%3D0%7D%5E5%28%7Bx_i%7D%5E%2A%29%5E2%5CDelta%20x_i%3D%5Cfrac%7B6-0%7D6%5Csum_%7Bi%3D0%7D%5E5%28%7Bx_i%7D%5E%2A%29%5E2%3D%5Csum_%7Bi%3D0%7D%5E5%5Cleft%28%5Cfrac%7B2i%2B1%7D2%5Cright%29%5E2)
Recall that
![\displaystyle\sum_{i=1}^ni^2=\frac{n(n+1)(2n+1)}6](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Csum_%7Bi%3D1%7D%5Eni%5E2%3D%5Cfrac%7Bn%28n%2B1%29%282n%2B1%29%7D6)
![\displaystyle\sum_{i=1}^ni=\frac{n(n+1)}2](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Csum_%7Bi%3D1%7D%5Eni%3D%5Cfrac%7Bn%28n%2B1%29%7D2)
![\displaystyle\sum_{i=1}^n1=n](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Csum_%7Bi%3D1%7D%5En1%3Dn)
so our sum becomes
![\displaystyle\sum_{i=0}^5\left(\frac{2i+1}2\right)^2=\sum_{i=0}^5\left(i^2+i+\frac14\right)](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Csum_%7Bi%3D0%7D%5E5%5Cleft%28%5Cfrac%7B2i%2B1%7D2%5Cright%29%5E2%3D%5Csum_%7Bi%3D0%7D%5E5%5Cleft%28i%5E2%2Bi%2B%5Cfrac14%5Cright%29)
Answer:
10 ≥ w ≥ 9 ( ? )
Step-by-step explanation:
the probability that a Great blue heron is at least 9 pounds, but no more than 10 pounds -> w= weight of great blue heron
w is at lest 9 pound's -> w ≥ 9
w is no more than 10 pound's -> w ≥ 10
w ≥ 9 ( + ) w ≥ 10 = 10 ≥ w ≥ 9
Dependency: A variable whose value depends on the value assigned to another variable (independent variable).
Correlation: The relationship between two or more variables is considered as correlation.
In statistics, when we talk about dependency, we are referring to any statistical relationship between two random variables or two sets of data. Correlation, on the other hand refers to any of a broad class of statistical relationships involving dependence.
Answer: C
Step-by-step explanation:
3(x+4y-2)
3x+12y-6