A hollow sphere and the solid sphere have the same mass and radius. They both start from rest and roll, without slipping down a 5.00 m long 3.00 m high ramp.  What is the speed of each at the bottom of the incline?   vhollow =                                                    vsolidl= How long will each take to reach the bottom of the incline?   thollow =                                                   tsolidl=  

A person pulling a wagon holding a child pulls on the handle with a 50 N force. The child and wagon have a mass of 80 kg and are pulled a distance of 25 m at a constant velocity. There is friction between the wagon’s tires and the grass.a. What is the work done by the normal force?b. What is the work done by the gravitational force?c. Calculate the work done by the applied force.d. What is the work done by the frictional force? e. What is the coefficient of friction between the wagon’s tires and the grass?

Extra credit (las frases de la semana) – What is the Spanish equivalent of the phrase “to be as mad as a hornet” in English?

The joint probability mass function for discrete random variables X and Y is given in the table below: X\Y 1 2 0 0.20 0.30 1 0.10 0.40 What is the conditional probability P(Y=2|X=1)?

The joint probability mass function for discrete random variables X and Y is given in the table below: X\Y 1 2 0 0.20 0.30 1 0.10 0.40 What is the marginal probability P(X=1) and P(Y=2)?

Identify the intervals where the function is changing as requested.Increasing, Decreasing, and/or Constant

Determine whether the relation is a function.{(-6, 4), (-6, -8), (1, -8), (3, 6), (10, 4)}

Find the inverse of the one-to-one function.f(x) = -7x + 2

The inferior alveolar artery exits the mandible through the mental foramen and immediately becomes the mental artery.

In an experiment to develop a self-inflating balloon, citric acid and baking soda (sodium bicarbonate) are mixed to generate carbon dioxide gas.  The gas inflates the balloon. 25.0 mL of 0.50 M citric acid solution was placed into seven identical bottles.  The volume of sodium bicarbonate solution was varied as shown in the plot below. The volume of CO2 generated in the balloon was measured and plotted versus the volume of 0.50 M sodium bicarbonate solution used in each trial. Based on the graph, complete the following statements: Between 0 and 20 mL, increasing the volume of sodium bicarbonate solution causes the CO2 volume to [drop1] The maximum volume of CO2 generated is [drop2] The limiting reactant at 25 mL is [drop3]. At 25 mL, there is leftover [drop4] when the reaction is complete.