A thermostat is set so that the temperature T, in degrees Celsius, satisfies -5 ≤ T ≤ 30. If an additional rule requires T > 10, what is…

Intersect the original range, $-5 \leq T \leq 30$, with the new rule, $T > 10$. The temperatures must satisfy both, so the lower bound is the larger of the two lower limits, and 10 is larger than $-5$. Because $T > 10$ is strict, 10 itself is excluded. The upper bound stays at 30, inclusive. The result is $10 < T \leq 30$, choice B. Choice A ignores the new rule. Choice C keeps the region below 10, which the new rule forbids. Choice D includes $T = 10$, but the rule says strictly greater than 10.