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A study conducted Dy the Urban Energy Commission in a large metropolitan area indicates the probabilities that homeowners within the area will use certain heating fuels or solar energy during the neat 10 years as the major source of heat for their homes. The following transition matrix represents the transition probabilities from one state to another.
Finchioty \( \quad\left[\begin{array}{llll}0.00 & 0.05 & 0.10 & 0 \\ 0.15 & 0.85 & 0.10 & 0.01 \\ 0.10 & 0.02 & 0.75 & 0.01 \\ 0.15 & 0.08 & 0.05 & 0.98\end{array}\right] \)
Among homeswhers whthin the area, \( 20 \% \) carrently une electricity, \( 35 \% \) use natural gas, \( 40 \% \) use oil, and \( 5 \% \) use solar energy as the major source of heat for their homes. In the long nin, mhat percentage of homeowners nithin the area will be using solar energy as their major source of heating fuel? (Round your answer to one decimal place. Assume the trend cortinues.) \% \( \square \)
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