Given that events A and B are independent with P(A)=0.34P(A)=0.34 and P(A\text{ and }B)=0.034P(A and B)=0.034, determine the value of P(B)P(B), rounding to the nearest thousandth, if necessary.

Abouncy ball is released from a certain height. on the first bounce, it travels 32cm. with each subsequent bounce, it travels 9/10 the distance of the previous bounce. what is the total distance that the ball has traveled when it completes its 25th bounce?

Afactory makes propeller drive shafts for ships. a quality assurance engineer at the factory needs to estimate the true mean length of the shafts. she randomly selects four drive shafts made at the factory, measures their lengths, and finds their sample mean to be 1000 mm. the lengths are known to follow a normal distribution whose standard deviation is 2 mm. calculate a 95% confidence interval for the true mean length of the shafts. input your answers for the margin of error, lower bound, and upper bound.

Find the vertex for the parabola given by the function ƒ(x) = −3x2 − 6x.