Two bells ring at intervals of 9, 15, and 21 minutes. If they last rang together at 11:00 p.m., when did they last ring together?

The intervals are 9 minutes, 15 minutes, and 21 minutes.

The LCM represents the time in minutes after which all bells will ring together again.

To find when they last rang together, subtract the LCM from 11:00 p.m.

Converting back to 12-hour format:

The bells had last rang together at $\boxed{\text{5:45 p.m.}}$.

:

Length $L = 15 \text{ cm}$
Width $W = 10 \text{ cm}$
Nominal Area $A_0 = L \times W = 15 \text{ cm} \times 10 \text{ cm} = 150 \text{ cm}^2$.

The error in each measurement is 5%.
Maximum length $L_{max} = L + (0.05 \times L) = 15 \text{ cm} + (0.05 \times 15 \text{ cm}) = 15 \text{ cm} + 0.75 \text{ cm} = 15.75 \text{ cm}$.
Maximum width $W_{max} = W + (0.05 \times W) = 10 \text{ cm} + (0.05 \times 10 \text{ cm}) = 10 \text{ cm} + 0.5 \text{ cm} = 10.5 \text{ cm}$.

The maximum percentage error in the area of the rectangle is $\boxed{10.25\%}$.

:

Given interior angle $= 3x^\circ$
Given exterior angle $= (x-20)^\circ$

Exterior angle $= (x-20)^\circ = (50-20)^\circ = 30^\circ$.

For a regular polygon, the sum of the exterior angles is $360^\circ$, and each exterior angle is $\frac{360^\circ}{n}$.

The number of sides of the polygon is $\boxed{12}$.