Answer:
828
Step-by-step explanation:
To cut the margin of Error in half, the clinic needs quadruple of the sample size.
If the sample size is 207 women,
Then quadruple of 207 = 4 * 207 = 828
A line has 0 endpoints and extends forever in 2 directions and a point has 1 endpoint and extends forever in 0 directions.
![\displaystyle\int_0^{1/16}\frac{\arcsin8x}{\sqrt{1-64x^2}}\,\mathrm dx](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cint_0%5E%7B1%2F16%7D%5Cfrac%7B%5Carcsin8x%7D%7B%5Csqrt%7B1-64x%5E2%7D%7D%5C%2C%5Cmathrm%20dx)
First let
![y=8x](https://tex.z-dn.net/?f=y%3D8x)
, so that
![\mathrm dx=\dfrac{\mathrm dy}8](https://tex.z-dn.net/?f=%5Cmathrm%20dx%3D%5Cdfrac%7B%5Cmathrm%20dy%7D8)
to write the integral as
![\displaystyle\frac18\int_0^{1/2}\frac{\arcsin y}{\sqrt{1-y^2}}\,\mathrm dy](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cfrac18%5Cint_0%5E%7B1%2F2%7D%5Cfrac%7B%5Carcsin%20y%7D%7B%5Csqrt%7B1-y%5E2%7D%7D%5C%2C%5Cmathrm%20dy)
Now recall that
![(\arcsin y)'=\dfrac1{\sqrt{1-y^2}}](https://tex.z-dn.net/?f=%28%5Carcsin%20y%29%27%3D%5Cdfrac1%7B%5Csqrt%7B1-y%5E2%7D%7D)
, so substituting
![z=\arcsin y](https://tex.z-dn.net/?f=z%3D%5Carcsin%20y)
should do the trick. The integral then becomes
5/2 is the answer.
Have a nive day!
Two squares are congruent if they have the same side length.