Answer: 31,755
Step-by-step explanation: You would just multiply 365 by 87 like this.
365 x 87
and the answer would be 31,755.
365 x 87 = 31,755
Given that <span>Henry divided the town into eight regions and randomly chose 10 households from each region in order to survey about traffic concerns. This type of sample is called</span> stratified sampling.
Stratified sampling<span> is a type of </span>sampling <span>method where</span><span> the researcher divides the population into separate groups, called strata and then, a probability </span>sample<span> (often a simple random </span>sample<span> ) is drawn from each group.</span>
The moment of inertia about the y-axis of the thin semicircular region of constant density is given below.
![\rm I_y = \dfrac{1}{8} \times \pi r^4](https://tex.z-dn.net/?f=%5Crm%20I_y%20%3D%20%5Cdfrac%7B1%7D%7B8%7D%20%5Ctimes%20%5Cpi%20r%5E4)
<h3>What is rotational inertia?</h3>
Any item that can be turned has rotational inertia as a quality. It's a scalar value that indicates how complex it is to adjust an object's rotational velocity around a certain axis.
Then the moment of inertia about the y-axis of the thin semicircular region of constant density will be
![\rm I_x = \int y^2 dA\\\\I_y = \int x^2 dA](https://tex.z-dn.net/?f=%5Crm%20I_x%20%3D%20%5Cint%20y%5E2%20dA%5C%5C%5C%5CI_y%20%3D%20%5Cint%20x%5E2%20dA)
x = r cos θ
y = r sin θ
dA = r dr dθ
Then the moment of inertia about the x-axis will be
![\rm I_x = \int _0^r \int _0^{\pi} (r\sin \theta )^2 \ r \ dr \ d\theta\\\\\rm I_x = \int _0^r \int _0^{\pi} r^3 \sin ^2\theta \ dr \ d\theta](https://tex.z-dn.net/?f=%5Crm%20I_x%20%3D%20%5Cint%20_0%5Er%20%5Cint%20_0%5E%7B%5Cpi%7D%20%20%28r%5Csin%20%5Ctheta%20%29%5E2%20%20%5C%20r%20%5C%20%20dr%20%5C%20%20d%5Ctheta%5C%5C%5C%5C%5Crm%20I_x%20%3D%20%5Cint%20_0%5Er%20%5Cint%20_0%5E%7B%5Cpi%7D%20%20r%5E3%20%5Csin%20%5E2%5Ctheta%20%20%5C%20%20dr%20%5C%20%20d%5Ctheta)
On integration, we have
![\rm I_x = \dfrac{1}{8} \times \pi r^4](https://tex.z-dn.net/?f=%5Crm%20I_x%20%3D%20%5Cdfrac%7B1%7D%7B8%7D%20%5Ctimes%20%5Cpi%20r%5E4)
Then the moment of inertia about the y-axis will be
![\rm I_y = \int _0^r \int _0^{\pi} (r\cos\theta )^2 \ r \ dr \ d\theta\\\\\rm I_y = \int _0^r \int _0^{\pi} r^3 \cos ^2\theta \ dr \ d\theta](https://tex.z-dn.net/?f=%5Crm%20I_y%20%3D%20%5Cint%20_0%5Er%20%5Cint%20_0%5E%7B%5Cpi%7D%20%20%28r%5Ccos%5Ctheta%20%29%5E2%20%20%5C%20r%20%5C%20%20dr%20%5C%20%20d%5Ctheta%5C%5C%5C%5C%5Crm%20I_y%20%3D%20%5Cint%20_0%5Er%20%5Cint%20_0%5E%7B%5Cpi%7D%20%20r%5E3%20%5Ccos%20%5E2%5Ctheta%20%20%5C%20%20dr%20%5C%20%20d%5Ctheta)
On integration, we have
![\rm I_y = \dfrac{1}{8} \times \pi r^4](https://tex.z-dn.net/?f=%5Crm%20I_y%20%3D%20%5Cdfrac%7B1%7D%7B8%7D%20%5Ctimes%20%5Cpi%20r%5E4)
Then the moment of inertia about O will be
![\rm I_o = I_x + I_y\\\\I_o = \dfrac{1}{8} \times \pi r^4 + \dfrac{1}{8} \times \pi r^4\\\\I_o = \dfrac{1}{4} \times \pi r^4](https://tex.z-dn.net/?f=%5Crm%20I_o%20%3D%20I_x%20%2B%20I_y%5C%5C%5C%5CI_o%20%3D%20%5Cdfrac%7B1%7D%7B8%7D%20%5Ctimes%20%5Cpi%20r%5E4%20%2B%20%5Cdfrac%7B1%7D%7B8%7D%20%5Ctimes%20%5Cpi%20r%5E4%5C%5C%5C%5CI_o%20%3D%20%5Cdfrac%7B1%7D%7B4%7D%20%5Ctimes%20%5Cpi%20r%5E4)
More about the rotational inertia link is given below.
brainly.com/question/22513079
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