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Which equation can Howard use to determine [tex] x [/tex], the height in meters, of the Statue of Liberty?

- The model is 15 inches tall.
- The scale of the model to the actual statue is 1 inch : 6.2 meters.

A. [tex] 15x = 6.2 [/tex]

B. [tex] 6.2x = 15 [/tex]

C. [tex] \frac{1}{6.2} = \frac{x}{15} [/tex]

D. [tex] \frac{1}{6.2} = \frac{15}{x} [/tex]

Answer :

We are given that the model is 15 inches tall and the scale is 1 inch : 6.2 meters. This means that for every 1 inch on the model, the actual statue has a height of 6.2 meters.

Let [tex]$x$[/tex] be the height of the Statue of Liberty in meters. The proportion between the model and the statue is set up as follows:

[tex]$$
\frac{1}{6.2} = \frac{15}{x}.
$$[/tex]

This equation relates 1 inch on the model to 6.2 meters on the statue, and 15 inches on the model to [tex]$x$[/tex] meters on the statue. This corresponds to option D.

To solve for [tex]$x$[/tex], we cross-multiply:

[tex]$$
1 \cdot x = 6.2 \cdot 15.
$$[/tex]

Thus,

[tex]$$
x = 6.2 \times 15.
$$[/tex]

After calculating, we find that

[tex]$$
x = 93 \text{ meters}.
$$[/tex]

Therefore, the correct equation and answer are given in option D, and the height of the statue is 93 meters.

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