☃ [tex] \: \: \: \: \: \: \: \: \red{ \underline{ \large{ \blue{ \tt{ ꧁ \: A \: N \: S \: W \: E \:R ꧂}}}}}[/tex]
✧ [tex] \large\tt{Step \: - \: By \: - \: Step \: Explanation} : [/tex]
Let the total number of students who failed in SLC be n ( U ) , number of students failed in science only be n ( only S ) , number of students failed in mathematics only be n ( only M ) , number of students who failed in both subjects be n ( M ∩ S ) and number of students who failed in other subjects be [tex] \tt{n( \overline{s \: ∪ \: m})}[/tex].
❀ [tex] \underline{ \underline{ \large{ \tt{ \: G \: I\: V \: E \: N}}}} : [/tex]
↳ [tex] \large{ \tt{n(u) = 20 \: \% \:of \: 115000 = \red{ \underline{23000}}}}[/tex]
↳ [tex] \large{ \tt{ n_{0}(s) = 40\% \: of \: 23000 = \red{ \underline{9200}}}} [/tex]
↳ [tex] \large{ \tt{ n_{o}(m) = 35\% \: of \: 23000 = \red {\underline{8050}}}}[/tex]
↳ [tex] \large{ \tt{n( \overline{s \:∪ \: m) }= 5\% \: of \: 23000 = \red{ \underline{1150}}}}[/tex]
✎ [tex] \underline{ \underline{ \large{ \tt{ \: S \: O \:L\: V \: I \: N\: G}}}} ..... [/tex]
[tex] \large {\tt{i. \: n(u) = n_{o}(s) + n_{o}(m) + n(s ∩ \: m) \: + n( \overline{s \:∪ \: m)} }}[/tex]
⟶ [tex] \large{ \tt{23000 = 9200 + 8050 + n(s∩m) + 1150}}[/tex]
⟶ [tex] \large \tt \: 23000 = 18400 + n(s ∩ m)[/tex]
⟶ [tex] \large \tt \: 23000 - 18400 = n(s \: ∩ \: m \: )[/tex]
⟶ [tex] \large \boxed{ \tt {4600} = n(s ∩ m)}[/tex]
Therefore , 4600 students failed in both subjects.
[tex] \large{ \sf{ii. \: Please \:see \: the \: attached \: picture \: for \: venn - diagram!}}[/tex]
☪ Hope I helped! ♡
♕ Have a wonderful day / night ! ツ
☆ [tex] \underbrace{ \overbrace{ \mathfrak{Carry \: On \: Learning}}}[/tex] !
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