Choose the correct simplification of the expression a to the 6th power times b to the 3rd power all over a to the 4th power times b to the second power.

a to the second power over b
a^10b^5
a to the 10th power over b to the 5th power
a^2b

Successful implementation of a new system is based on three independent modules. module 1 works properly with probability 0.96. for modules 2 and 3, these probabilities equal 0.95 and 0.90. compute the probability that at least one of these three modules fails to work properly.

In each of the cases that follow, the magnitude of a vector is given along with the counterclockwise angle it makes with the +x axis. use trigonometry to find the x and y components of the vector. also, sketch each vector approximately to scale to see if your calculated answers seem reasonable. (a) 50.0 n at 60.0°, (b) 75 m/ s at 5π/ 6 rad, (c) 254 lb at 325°, (d) 69 km at 1.1π rad.

Solve the system of equations. y=3x-1 and y=-2x+9. show work