The figure below is a scatterplot for paired data (x, y), with x values on the horizontal axis and y on the vertical axis. The t
ick marks are spaced 10 units apart on both axes. (Note that to answer the following questions you don't need the actual values for each tick mark, only differences between them.) 00 00 Oo oo 8 Oo oo (1) What are plausible values for the standard deviations of x and y, respectively? (2) What is a plausible value for the slope of the SD line? (3) Given your answer to part (b), what is a plausible value for the slope of the regression line?
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Check the picture below.
so the chord is the one in red there, making the segment, in green there, with a central angle of 45°, and the minor segment will be that green one.
![\bf \textit{area of a segment of a circle}\\\\ A=\cfrac{r^2}{2}\left[ \cfrac{\pi \theta }{180} - sin(\theta) \right]~~ \begin{cases} r=radius\\ \theta =angle~in\\ \qquad degrees\\ ------\\ r=3\\ \theta =45 \end{cases} \\\\\\ A=\cfrac{3^2}{2}\left[ \cfrac{\pi(45) }{180} - sin(45^o) \right]\implies A=\cfrac{9}{2}\left[ \cfrac{\pi }{4}-\cfrac{\sqrt{2}}{2} \right] \\\\\\ A=\cfrac{9}{2}\left( \cfrac{\pi -2\sqrt{2}}{4} \right)\implies A\approx 0.3523112199491](https://tex.z-dn.net/?f=%5Cbf%20%5Ctextit%7Barea%20of%20a%20segment%20of%20a%20circle%7D%5C%5C%5C%5C%0AA%3D%5Ccfrac%7Br%5E2%7D%7B2%7D%5Cleft%5B%20%5Ccfrac%7B%5Cpi%20%5Ctheta%20%7D%7B180%7D%20-%20sin%28%5Ctheta%29%20%5Cright%5D~~%0A%5Cbegin%7Bcases%7D%0Ar%3Dradius%5C%5C%0A%5Ctheta%20%3Dangle~in%5C%5C%0A%5Cqquad%20degrees%5C%5C%0A------%5C%5C%0Ar%3D3%5C%5C%0A%5Ctheta%20%3D45%0A%5Cend%7Bcases%7D%0A%5C%5C%5C%5C%5C%5C%0AA%3D%5Ccfrac%7B3%5E2%7D%7B2%7D%5Cleft%5B%20%5Ccfrac%7B%5Cpi%2845%29%20%7D%7B180%7D%20-%20sin%2845%5Eo%29%20%5Cright%5D%5Cimplies%20A%3D%5Ccfrac%7B9%7D%7B2%7D%5Cleft%5B%20%5Ccfrac%7B%5Cpi%20%7D%7B4%7D-%5Ccfrac%7B%5Csqrt%7B2%7D%7D%7B2%7D%20%5Cright%5D%0A%5C%5C%5C%5C%5C%5C%0AA%3D%5Ccfrac%7B9%7D%7B2%7D%5Cleft%28%20%5Ccfrac%7B%5Cpi%20-2%5Csqrt%7B2%7D%7D%7B4%7D%20%5Cright%29%5Cimplies%20A%5Capprox%200.3523112199491)
so the chord is the one in red there, making the segment, in green there, with a central angle of 45°, and the minor segment will be that green one.