Final answer:
The minimum tension that the cable must be able to support without having the sign come crashing down is 600.0 N..
Step-by-step explanation:
In order to determine the minimum tension that the cable must be able to support without having the sign come crashing down, we need to consider the forces acting on the sign.
The weight of the sign acts downwards, exerting a force of 200.0 N.
The weight of the strut also needs to be taken into account, which is 400.0 N.
To calculate the tension in the cable, we need to find the sum of these forces acting upwards.
200.0 N + 400.0 N = 600.0 N
By applying Newton's second law, we can find that the total force acting upwards is 600.0 N. Therefore, the minimum tension that the cable must be able to support is 600.0 N.