Wai needed a wire with a total length of 14.625 feet.
Step-by-step explanation:
Step 1:
First, we need to know what values Wai has measured.
There are two points on the plot that do not have values.
The value between 0 and [tex]\frac{1}{4}[/tex]. The value between [tex]1\frac{1}{4}[/tex] and [tex]1\frac{1}{2}[/tex].
To determine these values we take the average of the values they are in between.
The value between 0 and [tex]\frac{1}{4}[/tex] [tex]= \frac{0+\frac{1}{4} }{2} = \frac{1}{8} .[/tex]
The value between [tex]1\frac{1}{4}[/tex] and [tex]1\frac{1}{2}[/tex] = [tex]\frac{1\frac{1}{4} + 1\frac{1}{2} }{2} = \frac{2\frac{3}{4} }{2} = 1\frac{3}{8} .[/tex]
[tex]1\frac{3}{8} = \frac{11}{8} .[/tex]
Step 2:
The number of values at each point,
The number of wires measuring [tex]\frac{1}{8}[/tex] that are needed = 1,
The number of wires measuring [tex]\frac{1}{4}[/tex] that are needed = 1,
The number of wires measuring [tex]\frac{1}{2}[/tex] that are needed = 3,
The number of wires measuring [tex]\frac{3}{4}[/tex] that are needed = 8,
The number of wires measuring 1 that are needed = 4,
The number of wires measuring [tex]\frac{11}{8}[/tex] that are needed = 2.
Step 3:
The total length of the wire [tex]= 1(\frac{1}{8}) + 1(\frac{1}{4}) + 3(\frac{1}{2}) + 8(\frac{3}{4}) + 4(1) + 2 (\frac{11}{8}) = \frac{1}{8} + \frac{1}{4} + \frac{3}{2} + 6 + 4 + \frac{22}{8} = 14.625.[/tex]
So Wai needed a wire with a total length of 14.625 feet.
