Is it safe to drive your 1600-kgkg car at speed 27 m/sm/s around a level highway curve of radius 150 mm if the effective coefficient of static friction between the car and the road is 0.40?

It isn't safe for the car to drive on this road.

The radial acceleration of the car exceeds the maximum radial acceleration the road can support.

Explanation:

For the road to be safe for the car, frictional force of the road on the car must always exceed or match the force keeping the car in circular motion

Frictional force of the road on the car = μmg = 0.4 × 1600 × 9.8 = 6272 N

Force keeping the car in circular motion = mv²/r = 1600×27²/150 = 7776 N

The force keeping the car in circular motion > Frictional force that the road can support the car with.

Maximum radial acceleration the road can support = Frictional force/mass of the car = 6272/1600 = 3.92 m/s²

Radial acceleration of the car currently = 7776/1600 = 4.86 m/s²

which evidently exceeds the maximum allowable radial acceleration

This means the road isn't safe for the car.

it takes about 30 days for it to break down

because if the tool that you are using is not balanced it there would be false mass.