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Question-126723

Question Number 126723 by ajfour last updated on 23/Dec/20 Commented by prakash jain last updated on 23/Dec/20 $$\mathrm{Two}\:\mathrm{assumptions} \\ $$$${p}^{\mathrm{2}} +\mathrm{2}{pq}=\mathrm{1} \\ $$$${q}=\mathrm{2}{c} \\ $$$$\mathrm{You}\:\mathrm{are}\:\mathrm{substituting}\:\mathrm{a}\:\mathrm{given}\:\mathrm{value}…

Question-61186

Question Number 61186 by Tawa1 last updated on 30/May/19 Commented by Prithwish sen last updated on 30/May/19 $$\mathrm{Area}\:\mathrm{of}\:\mathrm{the}\:\mathrm{shadded}\:\mathrm{portion}\:=\mathrm{Area}\:\mathrm{of}\:\mathrm{the}\:\mathrm{incircle}\: \\ $$$$−\mathrm{Area}\:\mathrm{of}\:\mathrm{the}\:\mathrm{quarter}\:\mathrm{circle}\:+\frac{\mathrm{3}}{\mathrm{4}}\left(\mathrm{Area}\:\mathrm{of}\:\mathrm{the}\:\right. \\ $$$$\left.\mathrm{square}\:−\mathrm{Area}\:\mathrm{of}\:\mathrm{the}\:\mathrm{incircle}\right) \\ $$$$=\pi\mathrm{5}^{\mathrm{2}} −\frac{\mathrm{1}}{\mathrm{4}}\pi\left(\mathrm{10}\right)^{\mathrm{2}}…

If-be-the-acute-angle-between-two-regression-line-in-the-case-of-two-variables-x-and-y-Show-that-tan-1-r-r-x-y-x-2-y-2-where-r-x-y-have-their-usual-meanings-Ex

Question Number 192255 by Spillover last updated on 01/Feb/24 $${If}\:\theta\:{be}\:{the}\:{acute}\:{angle}\:{between}\:{two}\:{regression} \\ $$$${line}\:{in}\:{the}\:{case}\:{of}\:{two}\:{variables}\:{x}\:{and}\:{y} \\ $$$${Show}\:{that} \\ $$$$\:\:\mathrm{tan}\:\theta=\frac{\mathrm{1}−{r}}{{r}}.\frac{\sigma_{{x}} \sigma_{{y}} }{\sigma_{{x}} ^{\mathrm{2}} +\sigma_{{y}} ^{\mathrm{2}} }\:\:\: \\ $$$${where}\:\:{r},\sigma_{{x}} ,\sigma_{{y}}…

Question-126716

Question Number 126716 by sdfg last updated on 23/Dec/20 Answered by liberty last updated on 23/Dec/20 $$\overset{\rightarrow} {{a}}=\left(\mathrm{3},\mathrm{4}\right)\:;\:\overset{\rightarrow} {{b}}=\left({x},{y}\right)\:\rightarrow{x}^{\mathrm{2}} +{y}^{\mathrm{2}} =\mathrm{5}…\left({i}\right) \\ $$$$\:\overset{\rightarrow} {{a}}\:\bot\:\overset{\rightarrow} {{b}}\:\rightarrow\:\overset{\rightarrow}…

Establish-the-formular-x-y-2-x-2-y-2-2r-x-y-where-by-r-is-the-correlation-coefficient-between-x-and-y-1-2-2024-

Question Number 192254 by Spillover last updated on 01/Feb/24 $${Establish}\:{the}\:{formular}\:\: \\ $$$$\sigma_{{x}−{y}} ^{\mathrm{2}} =\sigma_{{x}} ^{\mathrm{2}} +\sigma_{{y}} ^{\mathrm{2}} −\mathrm{2}{r}\sigma_{{x}} \sigma_{{y}} \:\: \\ $$$${where}\:{by}\:{r}\:{is}\:{the}\:{correlation} \\ $$$${coefficient}\:{between}\:{x}\:{and}\:{y} \\…