Q.1a Suppose you go into an ice cream shop every day. Every day, you ask them for a uniformly random flavor of ice cream, independent of those chosen on previous days. Since you are such a regular customer, they are willing to abide your strange request. The ice cream parlor has 30 different flavors of ice cream, and each of the 30 flavors are offered every day. What is the probability that after 8 days, you have tried at least 7 unique flavors of ice cream?

It is fine to leave your answer in mathematical notation.

Q.A. B, C are playing a game. They each roll a 6-sided die. A player wins the game if the value of their die roll lies strictly in between the other two players. What is the probability that B wins the game?

Python program that simulates playing a game where a US penny (radius of 3/8 inches) is tossed into a board with a 1-inch by 1-inch square. The player wins only if the penny lands entirely within the square. Estimate the probability of winning by repeating the game 1,000 times. Record the estimate of the winning chance as a comment. Also, find the winning probability.

Please use comments to better explain :)

An insulated cylinder is initially divided into halves by a frictionless, thermally conducting piston. On one side of the piston is 1 m³ of a gas at 300 K, 2 bar. On the other side is 1 m³ of the same gas at 300 K, 1 bar.The piston is released and equilibrium is attained, with the piston experiencing no change of state. Employing the ideal gas model for the gas, determine

(a) the final temperature, in K.

(b) the final pressure, in bar.

(c) the amount of entropy produced, in kJ/K.

1.

The input and output pistons of a hydraulic lift have circular tops. The radius of the output piston is 74.3 times the radius of the input piston. Neglecting friction: find the minimum force, in N, that must be applied to the input piston so the output piston raises a trash bin of mass 25,547 kg.    

2.

A cube of mass 9.36 kg floats in a liquid of specific gravity 1.31 with 22.4% of its volume submerged. Find the length of one side of the cube, in m.

Two kilograms of CO₂ gas is contained in a piston-cylinder assembly at a pressure of 6.5 bar and a temperature of 300 K. The piston has a mass of 5000 kg and surface area of 1m². The friction of the piston on the walls is significant and cannot be ignored. The atmospheric pressure is 1.01325 bar. The latch holding the piston in position is suddenly removed and the gas is allowed to expand. The expansion is arrested when the volume is double the original volume. Determine the work appearing in the surroundings. Will it be the same as the work done by the gas?

An insulated cylinder is initially divided into halves by a frictionless, thermally conducting piston. On one side of the piston is 1 m3 of a gas at 300 K, 2 bar. On the other side is 1 m3 of the same gas at 300 K, 1 bar.The piston is released and equilibrium is attained, with the piston experiencing no change of state. Employing the ideal gas model for the gas, determine

(a) the final temperature, in K.

(b) the final pressure, in bar.

(c) the amount of entropy produced, in kJ/K.

I am in need of a great elevator pitch for a nursing portfolio. I am presenting this via video and I am at a loss on where to even begin for an elevator pitch while introducing myself.

Consider a 80.0-kg man standing on a spring scale in an elevator. Starting from rest, the elevator ascends, attaining its maximum speed of 1.36 m/s in 0.700 s. It travels with this constant speed for the next 5.00 s. The elevator then undergoes a uniform acceleration in the negative y direction for 1.70 s and comes to rest.

I can't seem to get the right answer on this one. Please help. Can someone show me the steps?

An elevator (1500 kg mass, with passengers) is attached to a 1000 kg counterweight by a cable that is wrapped over a pulley. It is also attached (by a second cable) to a motor. The elevator is moving down at a constant speed of 5 m/s.

a) Determine the force that the motor must apply to the second cable.

b) Determine the force that the motor must exert to lower the elevator with a constant downward acceleration of 1 m/s^2.

c) Determine the Force that the motor must exert to lower the elvator with a constant upward acceleration of 1 m/s^2.

d) Draw a graph of the acceleration of the elevator as a function of the force exerted by the motor. Fill in imoprtant numbers on each axis.

I know this is alot, but thank you!

Describe the general types of interactions that contribute to the collision stop- ping power, (dTl&),.