Perform the addition: 40 + 15 = 55^(°). This is the temperature of the house before the window is opened.

Perform the final subtraction: 55 - 6 = 49^(°). This is the final temperature of the house.

Answer: The house's final temperature is $49^{\circ}$ .

Start with the initial temperature of the house when Marcus wakes up. This is given as $40^{\circ}$ .

Calculate the total temperature increase due to baking. Marcus bakes for 3 hours, and the oven raises the temperature by $5^{\circ}$ each hour.

Multiply the number of hours by the temperature increase per hour to find the total increase. So, $3 \times 5 = 15^{\circ}$ .

Add the temperature increase from baking to the initial temperature to find the house's temperature after baking.

Perform the addition: $40 + 15 = 55^{\circ}$ . This is the temperature of the house before the window is opened.

Determine how many 10-minute cooling intervals are in the 30 minutes the window is open. Each interval causes a $2^{\circ}$ drop.

Divide the total time the window is open by the duration of each cooling interval to find the number of times the temperature drops.

Calculate the total temperature decrease from the window being open. Each interval reduces the temperature by $2^{\circ}$ .

Multiply the number of cooling intervals by the temperature drop per interval: $3 \times 2 = 6^{\circ}$ .

Subtract the total temperature decrease from the temperature after baking to find the house's final temperature.

Perform the final subtraction: $55 - 6 = 49^{\circ}$ . This is the final temperature of the house.