Question Number 81927 by zainal tanjung last updated on 16/Feb/20 $$\mathrm{One}\:\mathrm{man}\:\mathrm{adds}\:\mathrm{3}\:\mathrm{litres}\:\mathrm{of}\:\mathrm{water}\:\mathrm{to}\:\mathrm{12}\:\mathrm{litres}\:\mathrm{of}\:\mathrm{milk} \\ $$$$\mathrm{and}\:\mathrm{another}\:\mathrm{4}\:\mathrm{litres}\:\mathrm{of}\:\mathrm{water}\:\mathrm{to}\:\mathrm{10}\:\mathrm{litres}\:\mathrm{of}\:\mathrm{milk}. \\ $$$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{ratio}\:\mathrm{of}\:\mathrm{the}\:\mathrm{strengths}\:\mathrm{of}\:\mathrm{milk}\:\mathrm{in}\:\mathrm{the} \\ $$$$\mathrm{two}\:\mathrm{mixtures}? \\ $$ Answered by TANMAY PANACEA last updated…
Question Number 81926 by zainal tanjung last updated on 16/Feb/20 $$\mathrm{3}\:\mathrm{integers}\:\mathrm{are}\:\mathrm{chosen}\:\mathrm{at}\:\mathrm{random}\:\mathrm{from} \\ $$$$\mathrm{the}\:\mathrm{first}\:\mathrm{20}\:\mathrm{integers}.\:\mathrm{The}\:\mathrm{probability} \\ $$$$\mathrm{that}\:\mathrm{their}\:\mathrm{ptoduct}\:\mathrm{is}\:\mathrm{even},\:\mathrm{is} \\ $$ Commented by mr W last updated on 16/Feb/20…
Question Number 81925 by zainal tanjung last updated on 16/Feb/20 $$\mathrm{If}\:{A}\:\mathrm{and}\:{B}\:\mathrm{are}\:\mathrm{two}\:\mathrm{indpendent}\:\mathrm{events}, \\ $$$$\mathrm{the}\:\mathrm{probability}\:\mathrm{that}\:\mathrm{both}\:{A}\:\mathrm{and}\:{B}\:\mathrm{occur} \\ $$$$\mathrm{is}\:\frac{\mathrm{1}}{\mathrm{8}}\:\mathrm{and}\:\mathrm{the}\:\mathrm{probability}\:\mathrm{that}\:\mathrm{neither}\:\mathrm{of} \\ $$$$\mathrm{them}\:\mathrm{occurs}\:\mathrm{is}\:\frac{\mathrm{3}}{\mathrm{8}}\:.\:\mathrm{The}\:\mathrm{probability}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{occurrence}\:\mathrm{of}\:{A}\:\mathrm{is} \\ $$ Answered by MJS last…
Question Number 16383 by aamaguestt last updated on 21/Jun/17 $$\mathrm{If}\:\mathrm{P}\::\:\mathrm{Q}\::\:\mathrm{R}\:=\:\mathrm{2}\::\:\mathrm{3}\::\:\mathrm{4}\:\mathrm{and}\:\mathrm{P}^{\mathrm{2}} +\mathrm{Q}^{\mathrm{2}} +\mathrm{R}^{\mathrm{2}} =\mathrm{11600}, \\ $$$$\mathrm{then}\:\mathrm{find}\:\left(\mathrm{P}+\mathrm{Q}−\mathrm{R}\right). \\ $$ Answered by ajfour last updated on 21/Jun/17 $$\:{p}^{\mathrm{2}}…
Question Number 81876 by zainal tanjung last updated on 16/Feb/20 $$\mathrm{The}\:\mathrm{system}\:\mathrm{of}\:\mathrm{linear}\:\mathrm{equations}\:{x}+{y}+{z}=\mathrm{2}, \\ $$$$\mathrm{2}{x}+{y}−{z}=\mathrm{3},\:\mathrm{3}{x}+\mathrm{2}{y}+{kz}=\mathrm{4}\:\mathrm{has}\:\mathrm{a}\:\mathrm{unique} \\ $$$$\mathrm{solution}\:\mathrm{if} \\ $$ Commented by Tony Lin last updated on 16/Feb/20…
Question Number 81879 by zainal tanjung last updated on 16/Feb/20 $$\mathrm{The}\:\mathrm{value}\:\mathrm{of}\:\mathrm{determinant}\begin{vmatrix}{−\mathrm{1}}&{\:\:\:\:\mathrm{1}}&{\:\:\:\:\mathrm{1}}\\{\:\:\:\:\mathrm{1}}&{−\mathrm{1}}&{\:\:\:\:\mathrm{1}}\\{\:\:\:\:\mathrm{1}}&{\:\:\:\:\:\mathrm{1}}&{−\mathrm{1}}\end{vmatrix} \\ $$$$\mathrm{is}\:\mathrm{equal}\:\mathrm{to} \\ $$ Commented by john santu last updated on 16/Feb/20 $$−\mathrm{1}\left(\mathrm{0}\right)−\mathrm{1}\left(−\mathrm{2}\right)+\mathrm{1}\left(\mathrm{2}\right)\:=\:\mathrm{4} \\…
Question Number 81874 by zainal tanjung last updated on 16/Feb/20 $$\mathrm{If}\:{A}=\begin{bmatrix}{\:\:\mathrm{1}}&{−\mathrm{5}}&{\:\:\:\mathrm{7}}\\{\:\:\mathrm{0}}&{\:\:\:\:\mathrm{7}}&{\:\:\:\mathrm{9}}\\{\mathrm{11}}&{\:\:\:\:\mathrm{8}}&{\:\:\:\mathrm{9}}\end{bmatrix}\:\mathrm{then}\:\mathrm{trace}\:\mathrm{of}\: \\ $$$$\mathrm{matrix}\:{A}\:\mathrm{is} \\ $$ Commented by jagoll last updated on 16/Feb/20 $${trc}\:\left({A}\right)=\mathrm{17} \\ $$…
Question Number 81873 by zainal tanjung last updated on 16/Feb/20 $$\begin{vmatrix}{\mathrm{sin}^{\mathrm{2}} {x}}&{\mathrm{cos}^{\mathrm{2}} {x}}&{\mathrm{1}}\\{\mathrm{cos}^{\mathrm{2}} {x}}&{\mathrm{sin}^{\mathrm{2}} {x}}&{\mathrm{1}}\\{−\mathrm{10}}&{\:\:\mathrm{12}}&{\mathrm{2}}\end{vmatrix}= \\ $$ Commented by john santu last updated on 16/Feb/20…
Question Number 81872 by zainal tanjung last updated on 16/Feb/20 $$\mathrm{If}\:\mathrm{every}\:\mathrm{element}\:\mathrm{of}\:\mathrm{a}\:\mathrm{third}\:\mathrm{order} \\ $$$$\mathrm{determinant}\:\mathrm{of}\:\mathrm{value}\:\bigtriangleup\:\mathrm{is}\:\mathrm{multiplied}\:\mathrm{by} \\ $$$$\mathrm{5},\:\mathrm{then}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{new}\:\mathrm{determinant}\:\mathrm{is} \\ $$ Answered by MJS last updated on 16/Feb/20 $$\mathrm{5}^{\mathrm{3}}…
Question Number 81731 by zainal tanjung last updated on 15/Feb/20 $$\mathrm{If}\:\:{a},\:{b},\:{c}\:\mathrm{are}\:\mathrm{in}\:\mathrm{AP};\:\:{p},\:{q},\:{r}\:\mathrm{are}\:\mathrm{in}\:\mathrm{HP}\: \\ $$$$\mathrm{and}\:\:{ap},\:{bq},\:{cr}\:\:\mathrm{are}\:\mathrm{in}\:\mathrm{GP},\:\mathrm{then}\:\frac{{p}}{{r}}+\frac{{r}}{{p}} \\ $$$$\mathrm{is}\:\mathrm{equal}\:\mathrm{to} \\ $$ Commented by jagoll last updated on 15/Feb/20 $$\left({i}\right)\:{a},{b},{c}\:{in}\:{AP}\:\Rightarrow\:\mathrm{2}{b}\:=\:{a}+{c}…