Too Cold, Too Hot

A smart thermostat uses a tiny network to decide whether the room temperature $x$ (in °C) is comfortable. The network has one input, a hidden layer of three neurons, and one output neuron.

Each hidden neuron computes its weighted sum of $x$ plus its bias, then applies ReLU, which replaces a negative sum with $0$ and passes a positive one through unchanged.

hidden neuron	weight on $x$	bias
A	$-2$	$36$
B	$1$	$-22$
C	$2$	$-56$

The output neuron reads the three hidden outputs and has no activation. Its weights are $-0.5$ on A's output, $-0.4$ on B's output and $-0.3$ on C's output, and its bias is $2$ . Its weighted sum plus bias is $z$ .

A temperature is flagged as comfortable when $z > 0$ . The input $x$ can be any real number.

What is the total width, in °C, of the set of temperatures the network flags as comfortable?

Round your answer to 2 decimal places.

Too Cold, Too Hot

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