7) The mean of 18. 14, 24, 2x + 1 and 12 is 33. Find the value of x.
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7) The mean of 18. 14, 24, 2x + 1 and 12 is 33. Find the value of x.
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Answer:
x=48
Step-by-step explanation:
you add the 18,14,24 and 12
the answer is 68.
You need to multipy the 33 by 5.
the answer is 165.
subtract the 165 and 68
165-68= 97
subtract 1 from 97 and divide it by 2.
97-1=96
96÷2=48
x=48
[tex]\large\underline{\frak{\qquad Given :\qquad}} \\ \\ \\ [/tex]
[tex]\qquad\bullet\:\:\textsf{Mean and observation} \\ \\ [/tex]
[tex]\large\underline{\frak{\qquad To\:Find :\qquad}} \\ \\ \\ [/tex]
[tex]\qquad\bullet\:\:\textsf{The value of x = ?} \\ \\ [/tex]
[tex]\large\underline{\frak{\qquad Solution :\qquad}} \\ [/tex]
☯ [tex]\underline{\boldsymbol{According\: to \:the\: Question\:now :}}\\[/tex]
[tex]:\implies \sf Mean = \dfrac{Sum \: of \: observations}{Total \: number \: of \: observations}\\ \\ \\ [/tex]
[tex]:\implies \sf 33= \dfrac{69 + 2x}{5}\\ \\ \\ [/tex]
[tex]:\implies \sf 33 \times 5= 69 + 2x\\ \\ \\ [/tex]
[tex]:\implies \sf 165= 69 + 2x\\ \\ \\ [/tex]
[tex]:\implies \sf 165 - 69 = 2x\\ \\ \\ [/tex]
[tex]:\implies \sf 96 = 2x\\ \\ \\ [/tex]
[tex]:\implies \sf 2x = 96\\ \\ \\ [/tex]
[tex]:\implies \sf x = \dfrac{96}{2}\\ \\ \\ [/tex]
[tex]:\implies \underline{ \boxed{\textsf{\textbf{x = 48}}}}\\ \\ \\ [/tex]
[tex]\therefore\:\underline{\textsf{The value of x is \textbf{48}}}. \\ \\ [/tex]
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[tex]\large\underline{\frak{\qquad Verification :\qquad}} \\ \\ [/tex]
[tex]\dashrightarrow\:\:\sf 33 = \dfrac{69 + 2x}{5}\\ \\ \\ [/tex]
[tex]\dashrightarrow\:\:\sf 33 = \dfrac{69 + 2(48)}{5}\\ \\ \\ [/tex]
[tex]\dashrightarrow\:\:\sf 33 = \dfrac{69 + 96}{5}\\ \\ \\ [/tex]
[tex]\dashrightarrow\:\:\sf 33 = \dfrac{165}{5}\\ \\ \\ [/tex]
[tex]\dashrightarrow\:\:\underline{\boxed{\sf 33 = 33}}\\ \\ \\ [/tex]
[tex]\large\underline{\frak{\qquad Hence\: Verified \qquad}} \\ \\ [/tex]
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