To find the net change in the elevator's position after these movements, we can break down the problem into several steps:
1. The elevator initially goes up 15 floors.
- Net Change: [tex]\( +15 \)[/tex] floors
2. It then goes down 9 floors.
- Net Change: [tex]\( +15 - 9 = +6 \)[/tex] floors
3. After that, the elevator goes up 11 floors.
- Net Change: [tex]\( +6 + 11 = +17 \)[/tex] floors
4. Finally, the elevator goes down 19 floors.
- Net Change: [tex]\( +17 - 19 = -2 \)[/tex] floors
The net change in the elevator's position after all these movements is [tex]\( -2 \)[/tex] floors.
