Answered

IDNLearn.com: Your reliable source for finding precise answers. Ask your questions and get detailed, reliable answers from our community of experienced experts.

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 :

GinnyAnsweridn
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]
Your presence in our community is highly appreciated. Keep sharing your insights and solutions. Together, we can build a rich and valuable knowledge resource for everyone. IDNLearn.com is your reliable source for accurate answers. Thank you for visiting, and we hope to assist you again.