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In the map below, the path from the whales to the sharks is parallel to the path from the penguins to the fish tanks. Set up and solve the proportion to find the distance between the penguins and the fish tank. (3 points) Set up the proportion: 3054= NOTE: Type the correct fraction into the box to receive credit. Cross Multiply: 30x= NOTE: Type the correct numerical answer into the box to receive credit. Solve for x: x= feet NOTE: Type the correct numerical answer into the box to receive credit. Skip to navigation

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To solve this problem, we'll set up the proportion based on the information that the path from the whales to the sharks is parallel to the path from the penguins to the fish tanks.

Let's denote:

  • Distance from whales to sharks as \( d_1 = 3054 \) feet
  • Distance from penguins to fish tanks as \( d_2 \)

According to the problem, the paths are parallel, so we can establish a ratio:

\[ \frac{d_1}{d_2} = \frac{\text{distance from whales to sharks}}{\text{distance from penguins to fish tanks}} \]

Assuming we have the distance between the whales and the sharks is \( 3054 \) feet and some other value \( x \) that is equivalent to \( d_2 \), we can express the proportion as:

\[ \frac{3054}{x} = \frac{\text{(other corresponding distances)}}{\text{(another corresponding distance)}} \]

Since the problem does not provide specifics about the other distances, we can work with a placeholder. Let's assume the other corresponding distance is provided as \( k \) for clarity:

\[ \frac{3054}{x} = \frac{k_1}{k_2} \]

Let’s say the numerical values for \( k_1 \) and \( k_2 \) yield a relation we can solve (if they have known distances).

Cross multiplying gives:

\[ 3054 \cdot k_2 = k_1 \cdot x \]

Now solving for \( x \) gives:

\[ x = \frac{3054 \cdot k_2}{k_1} \]

To provide concrete numbers for the second part of your request, I would need those corresponding distances for the penguins and fish tanks (which are not specified). If you have those values, plug them in for \( k_1 \) and \( k_2 \).

However, assuming \( k_1 = 30 \) and \( k_2 = 1 \) based on your hints (perhaps distance units), we can substitute and find \( x \):

If you provide actual numbers for \( k_1 \) and \( k_2 \), we can finalize this with:

\[ x = \frac{3054 \cdot 1}{30} = 101.8 \]

So, for your setup:

  • Set up the proportion:
    \( \frac{3054}{x} = \frac{30}{1} \)

  • Cross Multiply:
    \( 3054 = 30x \)

  • Solve for \( x \):
    \( x = \frac{3054}{30} \)

If we compute:

\[ x \approx 101.8 \text{ feet} \]

So, please confirm if you have different \( k_1 \) and \( k_2 \) values or any distance that relates to your problem.