1. All the ramps below are identical, smooth and 5 m high except for the shape of their inclines. The crates at the top of each ramp are identical, with a mass of 2 kg. Initially, stationary crates are released from the top of the ramps. What is the initial GPE of the crates in each case? Show and explain your work.

The frequencies refer to the sample data collected from a population of interest when performing a hypothesis test comparing two or more population proportions.

The star betelgeuse is about 600 light-years away. if it explodes tonight, a. we'll know because debris from the explosion will rain down on us from space.b. we'll know it immediately because it will be brighter than the full moon in the sky.c. we won't know about it until 600 years from now.d. none of the above.

Water is siphoned from a large tank and discharges into the atmosphere through a 50-mm diameter tube. the end of the tube is b = 2.1 m below the tank bottom which is a = 7.4 m deep, and viscous effects are negligible. determine the maximum height h over which the water can be siphoned without cavitation occurring. atmospheric pressure is 101.4 kpa, and the water vapor pressure is 1.79 kpa (absolute)