To find the value of \( t \) in the proportion \( t : 42.2 = 7.3 : 0.4 \), we can set up the equation based on the cross multiplication of the ratios.
So, we have: \[ t \cdot 0.4 = 42.2 \cdot 7.3 \]
Now, let's calculate \( 42.2 \cdot 7.3 \): \[ 42.2 \cdot 7.3 = 308.06 \]
Now, substituting back into the equation, we get: \[ t \cdot 0.4 = 308.06 \]
To solve for \( t \), divide both sides by \( 0.4 \): \[ t = \frac{308.06}{0.4} \]
Calculating this gives: \[ t = 770.15 \]
Thus, the value of \( t \) is approximately \( 770.15 \).