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Author: Tinku Tara

Question-133431

Question Number 133431 by Algoritm last updated on 22/Feb/21 Answered by benjo_mathlover last updated on 22/Feb/21 $$\mathrm{x}^{\mathrm{2}} \mathrm{y}−\mathrm{5xy}−\mathrm{y}=\mathrm{x}^{\mathrm{2}} −\mathrm{3x}−\mathrm{1} \\ $$$$\left(\mathrm{y}−\mathrm{1}\right)\mathrm{x}^{\mathrm{2}} −\left(\mathrm{5y}−\mathrm{3}\right)\mathrm{x}+\mathrm{1}−\mathrm{y}=\mathrm{0} \\ $$$$\mathrm{x}\:=\:\frac{\mathrm{5y}−\mathrm{3}\pm\sqrt{\left(\mathrm{5y}−\mathrm{3}\right)^{\mathrm{2}} −\mathrm{4}\left(\mathrm{y}−\mathrm{1}\right)\left(\mathrm{1}−\mathrm{y}\right)}}{\mathrm{2}\left(\mathrm{y}−\mathrm{1}\right)}…

Given-10-white-balls-and-ten-black-balls-numbered-1-2-10-How-many-ways-can-we-choose-6-balls-such-that-i-no-two-chosen-balls-have-the-same-number-ii-two-pairs-of-chosen-balls-have-the-same-n

Question Number 133424 by liberty last updated on 22/Feb/21 $$\mathrm{Given}\:\mathrm{10}\:\mathrm{white}\:\mathrm{balls}\:\mathrm{and}\:\mathrm{ten}\:\mathrm{black}\:\mathrm{balls} \\ $$$$\mathrm{numbered}\:\mathrm{1},\mathrm{2},…,\mathrm{10}.\:\mathrm{How}\:\mathrm{many}\: \\ $$$$\mathrm{ways}\:\mathrm{can}\:\mathrm{we}\:\mathrm{choose}\:\mathrm{6}\:\mathrm{balls}\:\mathrm{such}\:\mathrm{that} \\ $$$$\left(\mathrm{i}\right)\:\mathrm{no}\:\mathrm{two}\:\mathrm{chosen}\:\mathrm{balls}\:\mathrm{have}\:\mathrm{the}\:\mathrm{same}\:\mathrm{number} \\ $$$$\left(\mathrm{ii}\right)\:\mathrm{two}\:\mathrm{pairs}\:\mathrm{of}\:\mathrm{chosen}\:\mathrm{balls}\:\mathrm{have} \\ $$$$\mathrm{the}\:\mathrm{same}\:\mathrm{number}? \\ $$ Answered by EDWIN88…

x-dx-

Question Number 133426 by metamorfose last updated on 22/Feb/21 $$\int\lfloor{x}\rfloor{dx}=?… \\ $$ Answered by MJS_new last updated on 22/Feb/21 $$\mathrm{for}\:{a}<{b}:\:\underset{{a}} {\overset{{b}} {\int}}\lfloor{x}\rfloor{dx}=\lfloor{a}\rfloor\underset{{a}} {\overset{\lceil{a}\rceil} {\int}}{dx}+\underset{\lceil{a}\rceil} {\overset{\lfloor{b}\rfloor−\mathrm{1}}…

Let-A-denote-the-event-of-test-positive-in-a-specific-experiment-and-B-that-of-have-cancer-It-is-known-that-P-B-0-005-P-A-B-0-95-and-P-A-B-0-95-Suppose-someone-tests-positive-in-the

Question Number 133420 by liberty last updated on 22/Feb/21 $$\mathrm{Let}\:\mathrm{A}\:\mathrm{denote}\:\mathrm{the}\:\mathrm{event}\:\mathrm{of}\:'\mathrm{test}\:\mathrm{positive}' \\ $$$$\mathrm{in}\:\mathrm{a}\:\mathrm{specific}\:\mathrm{experiment},\:\mathrm{and}\:\mathrm{B} \\ $$$$\mathrm{that}\:\mathrm{of}\:'\mathrm{have}\:\mathrm{cancer}'.\:\mathrm{It}\:\mathrm{is}\:\mathrm{known}\:\mathrm{that} \\ $$$$\mathrm{P}\left(\mathrm{B}\right)=\mathrm{0}.\mathrm{005}\:,\:\mathrm{P}\left(\mathrm{A}\mid\mathrm{B}\right)=\:\mathrm{0}.\mathrm{95}\:\mathrm{and}\:\mathrm{P}\left(\overset{−} {\mathrm{A}}\mid\overset{−} {\mathrm{B}}\right)=\:\mathrm{0}.\mathrm{95} \\ $$$$\mathrm{Suppose}\:\mathrm{someone}\:\mathrm{tests}\:\mathrm{positive}\:\mathrm{in} \\ $$$$\mathrm{the}\:\mathrm{experiment}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{probability}\:\mathrm{that} \\ $$$$\mathrm{he}\:\mathrm{has}\:\mathrm{cancer}\:. \\…

Prove-the-set-1-2-3-1989-can-be-expressed-as-the-disjoint-union-of-A-1-A-2-A-117-such-that-i-each-A-i-contains-the-same-number-of-elements-and-ii-the-sum-of-all-elements-of-each-A

Question Number 133419 by liberty last updated on 22/Feb/21 $$\mathrm{Prove}\:\mathrm{the}\:\mathrm{set}\:\left\{\mathrm{1},\mathrm{2},\mathrm{3},…,\mathrm{1989}\right\} \\ $$$$\mathrm{can}\:\mathrm{be}\:\mathrm{expressed}\:\mathrm{as}\:\mathrm{the}\:\mathrm{disjoint} \\ $$$$\mathrm{union}\:\mathrm{of}\:\mathrm{A}_{\mathrm{1}} ,\mathrm{A}_{\mathrm{2}} ,…,\mathrm{A}_{\mathrm{117}} \:\mathrm{such}\:\mathrm{that} \\ $$$$\left(\mathrm{i}\right)\:\mathrm{each}\:\mathrm{A}_{\mathrm{i}} \:\mathrm{contains}\:\mathrm{the}\:\mathrm{same}\:\mathrm{number}\:\mathrm{of}\:\mathrm{elements}\:,\mathrm{and} \\ $$$$\left(\mathrm{ii}\right)\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{all}\:\mathrm{elements}\:\mathrm{of}\:\mathrm{each}\:\mathrm{A}_{\mathrm{i}} \:\mathrm{is} \\ $$$$\mathrm{the}\:\mathrm{same}\:\mathrm{for}\:\mathrm{i}=\mathrm{1},\mathrm{2},\mathrm{3},…,\mathrm{m}…