Answered

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Cherie measures and records the lengths and sizes of the same style of a sandal found at a shoe store.

Sandal Size

\begin{tabular}{|c|c|}
\hline
\begin{tabular}{c}
Foot length (in.) \\
[tex]$(x)$[/tex]
\end{tabular} &
\begin{tabular}{c}
Shoe size \\
[tex]$(S)$[/tex]
\end{tabular} \\
\hline
8 & 6 \\
\hline
8.5 & 7 \\
\hline
9 & 8 \\
\hline
9.5 & 9 \\
\hline
10 & 10 \\
\hline
\end{tabular}

Which equation can be used to determine the approximate shoe size, [tex]$S$[/tex], for a foot length of [tex]$x$[/tex] inches?

A. [tex]$S = x - 2$[/tex]
B. [tex]$S = 2x - 10$[/tex]
C. [tex]$S = x + 6$[/tex]
D. [tex]$S = 2x + 4$[/tex]

Sagot :

GinnyAnswer
To find the equation that best fits the given data relating foot length [tex]\(x\)[/tex] to shoe size [tex]\(S\)[/tex], we need to check which provided formula correctly represents the relationship between these two variables for all given data points.

The data provided are:
- When [tex]\( x = 8 \)[/tex], [tex]\( S = 6 \)[/tex]
- When [tex]\( x = 8.5 \)[/tex], [tex]\( S = 7 \)[/tex]
- When [tex]\( x = 9 \)[/tex], [tex]\( S = 8 \)[/tex]
- When [tex]\( x = 9.5 \)[/tex], [tex]\( S = 9 \)[/tex]
- When [tex]\( x = 10 \)[/tex], [tex]\( S = 10 \)[/tex]

Let's check each equation one by one:

1. [tex]\( S = x - 2 \)[/tex]
- For [tex]\( x = 8 \)[/tex]: [tex]\( S = 8 - 2 = 6 \)[/tex] (matches)
- For [tex]\( x = 8.5 \)[/tex]: [tex]\( S = 8.5 - 2 = 6.5 \)[/tex] (does not match)
- Therefore, [tex]\( S = x - 2 \)[/tex] does not fit all data points.

2. [tex]\( S = 2x - 10 \)[/tex]
- For [tex]\( x = 8 \)[/tex]: [tex]\( S = 2(8) - 10 = 16 - 10 = 6 \)[/tex] (matches)
- For [tex]\( x = 8.5 \)[/tex]: [tex]\( S = 2(8.5) - 10 = 17 - 10 = 7 \)[/tex] (matches)
- For [tex]\( x = 9 \)[/tex]: [tex]\( S = 2(9) - 10 = 18 - 10 = 8 \)[/tex] (matches)
- For [tex]\( x = 9.5 \)[/tex]: [tex]\( S = 2(9.5) - 10 = 19 - 10 = 9 \)[/tex] (matches)
- For [tex]\( x = 10 \)[/tex]: [tex]\( S = 2(10) - 10 = 20 - 10 = 10 \)[/tex] (matches)
- Therefore, [tex]\( S = 2x - 10 \)[/tex] fits all data points.

3. [tex]\( S = x + 6 \)[/tex]
- For [tex]\( x = 8 \)[/tex]: [tex]\( S = 8 + 6 = 14 \)[/tex] (does not match)
- Therefore, [tex]\( S = x + 6 \)[/tex] does not fit all data points.

4. [tex]\( S = 2x + 4 \)[/tex]
- For [tex]\( x = 8 \)[/tex]: [tex]\( S = 2(8) + 4 = 16 + 4 = 20 \)[/tex] (does not match)
- Therefore, [tex]\( S = 2x + 4 \)[/tex] does not fit all data points.

After evaluating all the equations, we find that the equation [tex]\( S = 2x - 10 \)[/tex] is the only one that correctly fits all the provided data points. Therefore, the equation that can be used to determine the approximate shoe size [tex]\( S \)[/tex] for a foot length [tex]\( x \)[/tex] inches is:

[tex]\[ S = 2x - 10 \][/tex]
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