The figure shows the boundary temperatures (in degrees Celsius) of an insulated thin metal plate. The steady-state temperature at an interior junction is approximately equal to the mean of the temperatures at the four surrounding junctions. Use a system of linear equations to approximate the interior temperatures T₁, T2, T3, and T4. (T₁, T2, T3, T4) =( °C (20 (20 60 X 60 (50° (50%

Data on alcohol content and wine quality was collected from variants of a particular wine. From a sample of 50 ​wines, a model was created using the percentages of alcohol to predict wine quality. The data are modeled by Yi=−0.384+0.5332Xi​, where Xi is the alcohol content​ (%) and Yi is the rated quality of the wine. For these​ data, SYX=0.9431​, X=10.19​, and hi=0.029612 when X=11.   a. Construct a 90​% confidence interval estimate of the mean wine quality rating for all wines that have 11​% alcohol.   _____≤μY|X=11≤_______ ​(Type integers or decimals. Round to three decimal places as needed. Use ascending​ order.)

b. Find the equilibrium quantity.

Determine the linearization of y = 4 – 2x at (1,2). Then use it to approximate the value of y %3D - when x = 1.15.