Question Number 190573 by sami123 last updated on 06/Apr/23 $$\hat {{a}}\mathrm{2}+\mathrm{2}{ab}+\hat {{b}}\mathrm{2} \\ $$ Commented by a.lgnaoui last updated on 06/Apr/23 $$\mathrm{1}\bullet{pour}\:{editer}\:\:{exposant}\left({a}^{\mathrm{2}} \right) \\ $$$${dans}\:{clavier}\:{ecrire}\:\:{a}\:\:{puis}\:\:\:\:…
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Question Number 124409 by oustmuchiya@gmail.com last updated on 03/Dec/20 $${write}\:\mathrm{A}'\cup\:{B}'\:{in}\:{a}\:{disjoint}\:{set} \\ $$ Answered by Ar Brandon last updated on 03/Dec/20 $$\left(\mathrm{A}\cup\mathrm{B}\right)−\left(\mathrm{A}\cap\mathrm{B}\right) \\ $$ Terms of…
Question Number 189672 by Bidhan12 last updated on 20/Mar/23 Commented by Rasheed.Sindhi last updated on 20/Mar/23 $${B}\supseteq{A}\:{or}\:{A}\subseteq{B} \\ $$ Commented by som(math1967) last updated on…
Question Number 189091 by mnjuly1970 last updated on 12/Mar/23 $$ \\ $$$$\:\:\:\:\mathrm{1}\::\:\:\:\:\Omega\:=\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\:\left(−\:\mathrm{1}\:\right)^{\:{n}} \mathrm{H}_{\:{n}} }{{n}^{\:\mathrm{2}} }\:=\:? \\ $$$$\:\:\:\:\mathrm{2}\::\:\:\:\:\:\eta\:\left(−\mathrm{1}\:\right)=\:? \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$…
Question Number 123287 by mnjuly1970 last updated on 24/Nov/20 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:…\:{nice}\:\:{calculus}\:… \\ $$$$\:\:\:\:\:\:\:{number}\:{theory} \\ $$$$\:\:\:\:\:\:\:\:\:\:{prove}\:{thar}\:::: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{2}^{\mathrm{32}} +\mathrm{1}\overset{\mathrm{641}} {\equiv}\mathrm{0}\:\checkmark \\ $$$$\:\:\:{notice}:\:{without}\:{calculator}\:{and}\:{only} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:{with}\:{the}\:{use}\:{of}\:{congruence}\:{properties}.. \\ $$ Answered…
Question Number 122436 by sahiljakhar04 last updated on 17/Nov/20 $$\boldsymbol{\mathrm{Mean}}\::\:\mathrm{It}\:\mathrm{is}\:\mathrm{found}\:\mathrm{by}\:\mathrm{adding}\:\mathrm{all}\:\mathrm{the}\:\mathrm{values}\:\mathrm{of}\:\mathrm{the}\:\mathrm{observation}\:\mathrm{and}\:\mathrm{dividing}\:\mathrm{it}\:\mathrm{by}\:\mathrm{the} \\ $$$$\mathrm{total}\:\mathrm{number}\:\mathrm{of}\:\mathrm{observations}.\:\mathrm{It}\:\mathrm{is}\:\mathrm{denoted}\:\mathrm{by}\:\bar {{x}}. \\ $$$$\mathrm{So},\:\bar {{x}}\:=\:\frac{\underset{{i}=\mathrm{1}} {\overset{{n}} {\sum}}{x}_{{i}} }{{n}}.\:\mathrm{For}\:\mathrm{an}\:\boldsymbol{\mathrm{ungrouped}}\:\boldsymbol{\mathrm{frequency}}\:\boldsymbol{\mathrm{distribution}},\:\mathrm{it}\:\mathrm{is}\:\bar {\boldsymbol{{x}}}\:=\:\frac{\underset{\boldsymbol{{i}}\:=\:\mathrm{1}} {\overset{\boldsymbol{{n}}} {\sum}}\boldsymbol{{f}}_{\boldsymbol{{i}}} \boldsymbol{{x}}_{\boldsymbol{{i}}} }{\underset{\boldsymbol{{i}}\:=\:\mathrm{1}} {\overset{\boldsymbol{{n}}}…
Question Number 122426 by Lordose last updated on 16/Nov/20 $$ \\ $$$$\mathrm{In}\:\mathrm{an}\:\mathrm{exam}\:\mathrm{36\%}\:\mathrm{of}\:\mathrm{people}\:\mathrm{failed}\:\mathrm{in}\: \\ $$$$\mathrm{physics}\:\mathrm{and}\:\mathrm{49\%}\:\mathrm{failed}\:\mathrm{in}\:\mathrm{maths}\:\mathrm{and}\:\mathrm{15\%} \\ $$$$\mathrm{failed}\:\mathrm{in}\:\mathrm{both}\:\mathrm{subject}.\:\mathrm{If}\:\mathrm{the}\:\mathrm{total}\: \\ $$$$\mathrm{number}\:\mathrm{of}\:\mathrm{student}\:\mathrm{that}\:\mathrm{passed}\:\mathrm{physics} \\ $$$$\mathrm{only}\:\mathrm{is}\:\mathrm{680}\:\mathrm{find}\:\mathrm{the}\:\mathrm{total}\:\mathrm{number}\:\mathrm{of} \\ $$$$\mathrm{students}\:\mathrm{that}\:\mathrm{appeared}\:\mathrm{in}\:\mathrm{the}\:\mathrm{exam}\:. \\ $$ Terms…
Question Number 56744 by Umar last updated on 22/Mar/19 $$\mathrm{If}\:\mathrm{R}\:\mathrm{be}\:\mathrm{a}\:\mathrm{relation}\:\mathrm{on}\:\mathrm{a}\:\mathrm{set}\:\mathrm{of}\:\mathrm{real}\:\mathrm{number} \\ $$$$\mathrm{defined}\:\mathrm{by}\:\mathrm{R}=\left\{\left(\mathrm{x},\mathrm{y}\right):\:\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} =\mathrm{0}\right\}, \\ $$$$\mathrm{find}\: \\ $$$$\:\:\mathrm{i}−\:\mathrm{R}\:\mathrm{in}\:\mathrm{roster}\:\mathrm{form} \\ $$$$\:\:\mathrm{ii}−\mathrm{Domain}\:\mathrm{of}\:\mathrm{R} \\ $$$$\:\:\mathrm{iii}−\mathrm{Range}\:\mathrm{of}\:\mathrm{R}\: \\ $$ Answered…
Question Number 121870 by mnjuly1970 last updated on 12/Nov/20 $$\:\:\:\:\:\:{number}\:\:{theory}: \\ $$$$\:\:\:\:\:\:{m},{n}\:\in\:\mathbb{N}\:\:,\:\:\left({m},{n}\right)=\mathrm{1} \\ $$$$\:\:\:\:\:\:\:\:\:{prove}\::\:\:\:{m}^{\varphi\left({n}\right)} +{n}^{\varphi\left({m}\right)} \overset{{mn}} {\equiv}\mathrm{1} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\varphi\left({n}\right)=\mid\left\{{x}\in\mathbb{N}\mid\:{x}<{n}\:,\:\left({x},{n}\right)=\mathrm{1}\right\}\mid \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:.{m}.{n}. \\ $$ Answered by…