The length of the fourth piece of wood carpenter cut is equals to
[tex]35\frac{7}{8}[/tex] inches.
" Length is defined as one of the dimension which represents the distance between two points as how long an object be."
Formula used
mean = [tex]\frac{sum of all the given numbers}{total number of numbers}[/tex]
According to the question,
Number of pieces of wood cut by carpenter = 4
length of four pieces =[tex]36\frac{3}{4} ,36\frac{3}{8}, 37\frac{1}{2}[/tex] and z inches
mean of given lengths = [tex]36\frac{5}{8}[/tex]
Substitute the value in the formula of mean we get,
[tex]\frac{36\frac{3}{4} +36\frac{3}{8}+37\frac{1}{2}+z}{4} =36 \frac{5}{8}[/tex]
[tex]\implies \frac{294+ 291+300+ 8z}{(8)(4)} = \frac{293}{8}\\\\\implies \frac{885+8z }{4}= 293\\ \\\implies 885 +8z = 1172\\\\\implies 8z = 287\\\\\implies z = 35.875\\\\\implies z = 35\frac{7}{8}[/tex]
Hence, the length of the fourth piece of wood carpenter cut is equals to
[tex]35\frac{7}{8}[/tex] inches .
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