Two players play each other in a pool tournament of "Solids and Stripes". The first player to win two games wins the tournament. In the game of "Solids and Stripes", it is equally likely that a player will be assigned solid balls or striped balls. Assume that 1) one-half of the balls are solids and the other half are stripes, 2) the two players have the same skill: each with a 0.5 probability of winning, 3) there are no ties, and 4) the tournament is concluded once a player has won two games. In a tournament, what is the probability that a player is assigned the same ball design (i.e., solids or stripes) throughout the tournament?

You are in a skyscraper and you are currently in floor s, where you see an elevator. Upon entering the elvator, you learn that it has only two buttons, marked "UP u" and "DOWN d". The UP-button takes the elevator u floors up (if there aren't enough floors, pressing the UP-botton does nothing), whereas the DOWN-button takes you d stories down (or none if there aren't enough). If you want to go to floor g, and that there are only f floors in the building, write a program that gives you the amount of button pushes you need to perform. If you simply cannot reach the correct floor, your program halts with the message "use the stairs".

Given input f, s, g, u and d (floors, start, goal, up, down), find the shortest sequence of button presses you must press in order to get from s to g, given a building of floors, or output "use the stairs" if you cannot get from s to g by the given elevator.

Use Breadth First Search

Input

The input will consist of one line, namely f s g u d, where 1 <= s, g <= f <= 100 and 0 <= u, d <= 100. The floors are one-indexed, i.e. if there are 10 stories, s and g be in [1; 10].

Output

Write the sequence with the minimum number of pushes you must make in order to get from s to g, or output "use the stairs" if it is impossible given the conguration of the elevator.

Example 1:

Input:

99 1 10 2 1

Output:

1 -> 3 -> 5 -> 7 -> 9 -> 11 -> 10

Example 2:

Input:

70 2 1 1 0

Output:

use the stairs

• Your program should compile using gcc on a unix/lunix machine. Using a makefile is encouraged but not required. You can also provide a readme file if needed.

• You may not use g++ for a C++ code. Only C

A fitness company is building a 20-story high-rise. Architects building the high-rise know that women working for the company have weights that are normally distributed with a mean of 143 lb and a standard deviation of 29 lb, and men working for the company have weights that are normally distributed with a mean of 165 lb and a standard deviation or 32 lb. You need to design an elevator that will safely carry 15 people. Assuming a worst case scenario of 15 male passengers, find the maximum total allowable weight if we want to a 0.98 probability that this maximum will not be exceeded when 15 males are randomly selected.

maximum weight =

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Suppose that two teams (for fun, let’s call them the Domestic Shorthairs and Cache Cows) play a series of games to determine a winner. In a best-of-three series, the games end as soon as one team has won two games. In a best-of-five series, the games end as soon as one team has won three games, and so on. Assume that the Domestic Shorthair’s probability of winning any one game is p, where .5 < p < 1. (Notice that this means that the Domestic Shorthairs are the better team.) Also assume that the outcomes are independent from game to game.

We will compare different series configurations/rules on two criteria: the probability that the better team wins the series, and the expected value of the number of games needed to complete the series.

Best-of-Three Series

1. Determine (exactly) the probability that the Domestic Shorthairs win a best-of-three series, as a function of p. (Show your work. Also note that you solved this for a particular value of p in Quiz 4, so you might want to review that quiz.)

2. Graph this function for values of .5 < p < 1 (include good axis labels), and comment on its behavior. [Hint: As with Investigation 2, you could use Excel or RStudio or Wolfram Alpha to produce the graph.]

3.Let the random variable X3 = number of games played in a best-of-three series. Determine the probability distribution (pmf) of X3, as a function of p. (Show your work.)

Two gaseous systems in a cylinder are separated by a frictionless movable piston. The cylinder and piston are diathermal. Which of the following statements are true?

The systems are in equilibrium with respect to pressure only.

The systems are in equilibrium with respect to temperature only.

The systems are in equilibrium with respect to pressure and temperature.

The systems are in equilibrium with respect to pressure, temperature and composition.

A rigid container whose volume can be varied with the use of a piston contains 2.53 mol H₂ gas at STP.

(a) What is the volume of the gas?
_____L

(b) The container is cooled to 209 K. The piston is held fixed so the volume does not change. What is the new pressure inside the container?
____atm

(c) The temperature of the container is held at 209 K and 1.55 mol He gas is added to the container. The pressure inside the container is held constant, but the piston is released so the volume of the container can vary. What is the final volume of the container?
_____ L

(d) What are the partial pressures of H₂ and He in the container in part (c)?

(e) The piston on the container in part (c) is set to maintain a constant pressure of 1 atm. The container is then heated from 209 K to 380 K.What is the minimum amount of heat that must be added to the container for it to reach 380 K?
______ J

You burn 12.3 mL of octane (C8H18, a liquid with a density of 0.703 g/mL and a molar mass of 114.23 g/mol, which is a major component of gasoline) in a piston. Initial conditions of the piston:

Initial volume of 1.6 L (ignore the small volume contribution of liquid octane).

Initial pressure of 1.00 atm (which is also this system’s ambient pressure).

Initial temperature of 0.00 °C (which is also this system’s ambient temperature).

Initial content is air, 20.0% O2 and 80.0% N2.

You then perform a complete combustion reaction (hydrocarbon reacting with molecular gaseous oxygen to yield carbon dioxide gas and water VAPOR gas).

Final conditions of the piston:

Final pressure of 1.00 atm (it was allowed to equilibrate to ambient pressure)

Final temperature of 0.00 °C (it was allowed to equilibrate to ambient temperature).

Final contents contains the combustion products, leftover oxygen (if any), and unreacted nitrogen.

Calculate the final volume of the piston

For the following process, use a calculation to predict whether or not it will occur spontaneously.

A piston with radius of 10.0 cm containing 4.00 L of an ideal gas (Cv,m = 3/2 R) at 1.03 atm, 298.15 K undergoes isothermal expansion when a 4.63 kg weight that was sitting on the piston was quickly removed.