Answer
$20$
$20+\frac{15}{2\pi} \approx 22.39$
Work Step by Step
$$T_{ave}=\frac{1}{24-0}\int_{0}^{24}(20+5\cos(\frac{\pi}{12}\cdot t))dt=\frac{1}{24}[20t+5\cdot \frac{12}{\pi}\sin(\frac{\pi}{12}\cdot t)]_{0}^{24}=\frac{1}{24}[20\cdot 24+5\cdot \frac{12}{\pi}\sin(\frac{\pi}{12}\cdot 24)-(20\cdot 0+5\cdot \frac{12}{\pi}\sin(\frac{\pi}{12}\cdot 0))]=20$$
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$$T_{ave}=\frac{1}{6-2}\int_{2}^{6}(20+5\cos(\frac{\pi}{12}\cdot t))dt=\frac{1}{4}[20t+5\cdot \frac{12}{\pi}\sin(\frac{\pi}{12}\cdot t)]_{2}^{6}=\frac{1}{4}[20\cdot 6+5\cdot \frac{12}{\pi}\sin(\frac{\pi}{12}\cdot 6)-(20\cdot 2+5\cdot \frac{12}{\pi}\sin(\frac{\pi}{12}\cdot 2))]=20+\frac{15}{2\pi} \approx 22.39$$
