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Text Solution:

We can let V, h, and A represent the volume, height, and base area of the pyramid, respectively. Because V varies directly jointly with h and A, we can set up a joint variation equation $V=khA$, where k is some unknown constant. Substituting the initial given values for V, h, and A, we can solve for k.

$\begin{array}{l}\Rightarrow V=khA\\ \Rightarrow 92=k(12)(23)\\ \Rightarrow \frac{92}{276}=k\\ \Rightarrow \frac{1}{3}=k\end{array}$

Now that we know the value of k in a pyramid’s volume equation, we can determine V when h = 13 and A = 24.

$\begin{array}{l}\Rightarrow V=\frac{1}{3}hA\\ \Rightarrow V=\frac{1}{3}(13)(24)\\ \Rightarrow V=104\end{array}$

The volume of the pyramid is 104 cubic feet.

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