An ideal gas is contained in a piston-cylinder device and undergoes a power cycle as follows: 1-2 isentropic compression from an initial temperature T1 5 208C with a compression ratio r 5 5 2-3 constant pressure heat addition 3-1 constant volume heat rejection The gas has constant specific heats with cv 5 0.7 kJ/kg·K and R 5 0.3 kJ/kg·K. (a) Sketch the P-v and T-s diagrams for the cycle. (b) Determine the heat and work interactions for each pro- cess, in kJ/kg. (c) Determine the cycle thermal efficiency. (d) Obtain the expression for the cycle thermal efficiency as a function of the compression ratio r and ratio of specific heats k.

Part A) A chemical reaction occurring in a cylinder equipped with a moveable piston produces 0.621 mol of a gaseous product. If the cylinder contained 0.260 mol of gas before the reaction and had an initial volume of 2.09 L , what was its volume after the reaction? (Assume that pressure and temperature are constant and that the initial amount of gas completely reacts.) Express the volume to thee significant figures and include the appropriate units.

PartB) A syringe containing 1.49 mL of oxygen gas is cooled from 92.5 ∘C to 0.7 ∘C. What is the final volume Vf of oxygen gas? (Assume that the pressure is constant.)

PartC) A sample of gas has an initial volume of 14.4 L at a pressure of 1.07 atm. If the sample is compressed to a volume of 10.5 L , what is its pressure? Express the pressure in atmospheres to three significant figures.

Part D) A sample of nitrogen gas in a 1.61-L container exerts a pressure of 1.52 atm at 19 ∘C. What is the pressure if the volume of the container is maintained constant and the temperature is raised to 361 ∘C? Express the pressure in atmospheres to three significant figures.

18-54. Have you ever heard someone repeat the contradictory statement, "The place is so crowded no one goes there any more"? This statement can be interpreted as saying that the opportunity for balking increases with the increase in the number of customers seeking service. A possible platform for modeling this situation is to say that the arrival rate at the system decreases as the number of customers in the system increases. More specifically, we consider the simplified case of M&M Pool Club, where customers usually arrive in pairs to "shoot pool." The normal arrival rate is 6 pairs (of people) per hour. However, once the number of pairs in the pool hall exceeds 8, the arrival rate drops to 5 pairs per hour. The arrival process is assumed to follow the Poisson distribution. Each pair shoots pool for an exponential time with mean 30 minutes. The pool hall has a total of 5 tables and can accommodate no more than 12 pairs at any one time. Determine the following:

(a) The probability that customers will balk.

(b) The probability that all tables are in use.

(c) The average number of tables in use.

(d) The average number of pairs waiting for a pool table to be available.

Consider a situation where you are picking a number from [0, 4]. The software you are using randomly selects a number following the percentage breakdown below.

[0, 1) [1,2) [2,3) [3,4]

20% 10% 30% 40%

(a) What is the random variable? Is it continuous or finite?

(b) Write the probability distribution

(c) Find P(X ? 2.7)

f(x,y) = 2/7(2x + 5y) for 0 < x < 1, 0 < y < 1

given X is the number of students who get an A on test 1

given Y is the number of students who get an A on test 2

find the probability that more then 90% students got an A test 2 given that 85 % got an A on test 1

The average number of graduates for a school district has been 250 per year with a standard deviation of 30. What is the probability that the number of graduates next year will be:

a. Less than 220

b. Less than 325

c. Less than 285

d. More than 238

e. More than 300

f. More than 325

The mean weight of 500 students at a certain college is 151 lb and the standard deviation is 15 lb. Assume that the weights are normally distributed.
a.) How many students weigh between 120 and 155 lb? (ANSWER IN WHOLE NUMBER)

b.) What is the probability that randomly selected male students to weigh less than 128 lb? (ANSWER IN 4 DECIMAL NUMBER)

Assignment #2*: Build A Report Purpose: Exercise, use, Inputs, Outputs, and perform conditional evaluation Requirements: (Multiple classes/Multiple types of input) • Input: Report Owner’s full name and 7 numbers (at least one double and one integer) o The owner’s name cannot contain any special characters, blank spaces, or numbers • You must use an if statement and at least one switch statement in your program • You are not allowed to have static variables or methods in any class except for the class with the main method. • You have to have at least 2 classes • You are not allowed to use ArrayLists or Vectors, only primitive arrays or string arrays if you want. Application Operation: 1.) Input, via a question in the console, the report owner’s first name as a string and build the last name via input, one character at a time. a. Check, conditionally, to make sure the first name and last name don’t contain any numeric characters, numbers between 0 – 9. If it does you must remove it. The names can not contain any white space either or special characters. 2.) Input report name via a request from the console. 3.) Input, and display, the total of the numeric input after each input is entered. Average the numeric input, indicate lowest numeric input value and the highest numeric input value for the previous numeric inputs, before the next numeric input is asked for. (Example given in class) 4.) Have a program exit input, condition, value available (i.e. if you type -1 the program exits) 5.) Create and display a final report that should have the report name, owner and the following: Numeric output should appear as a table with the following columns: (columns should be underlined) a. Input Number b. Highest Number c. Lowest Number d. Total (by the row) e. Average Number 6.) At the end of the report you must have a grand total for the numeric entries

Suppose that you have several numbered billiard balls on a pool table. The smallest possible number on the ball is “1”. At each step, you remove a billiard ball from the table. If the ball removed is numbered n, you replace it with n balls randomly numbered less than n. For example, if you remove the “5” ball, you replace it with balls numbered “2”, “1”, “1”, “4”, and “3”, where numbers 2, 1, 1, 4, and 3 were randomly generated. If you remove the “1” ball, no new balls will be added.

Write a program that simulates this process. Start with only one ball on the table with the number on it selected by the user. Use the class ResizableBag in your implementation as defined in the UML diagram below. You only need to finish the Billiard.java class that contains main. Please note the sample run below.

need help with TODO sections

public class Billiard
{
    private BagInterface poolTable;

    /**
     * constructor creates this.poolTable object as ResizableArrayBag
     */
    public Billiard()
    {
        this.poolTable = new ResizableArrayBag<>();
    }

    /**
     * prompts the user for the first numbered ball and adds it to this.poolTable
     */
    public void addFirstElement()
    {
        final int SMALLEST_BALL = 1;
        final int LARGEST_BALL = 6;
        Scanner keyboard = new Scanner(System.in);
        int start;
        do
        {
            System.out.println("What is the first numbered ball to start with? (must be between " + SMALLEST_BALL
                    + " and " + LARGEST_BALL + " inclusive)");
            start = keyboard.nextInt();
        } while (!(start >= SMALLEST_BALL && start <= LARGEST_BALL));

        System.out.println("The first ball is: \"" + start + "\"");
        this.poolTable.add(start);
    }

    /**
     * Removes balls from this.poolTable until all are gone.
     */
    public void removeBallsFromTable()
    {
        System.out.println("\n*** Removing balls from the poolTable ***\n");
        Random random = new Random(17);
        // TODO Project1

        System.out.println("\nThe poolTable is empty!!!");
    } // end removeBallsFromTable

    /**
     * Displays the content of this.poolTable
     */
    private void DisplayContentOfPoolTable()
    {
        Object[] content = this.poolTable.toArray();
        System.out.println(Arrays.toString(content));
        System.out.println();
    } // end DisplayContentOfPoolTable

    public static void main(String args[])
    {
        Billiard billiard = new Billiard();
        billiard.addFirstElement();

        long startTime = Calendar.getInstance().getTime().getTime(); // get current time in miliseconds

        billiard.removeBallsFromTable();

        long stopTime = Calendar.getInstance().getTime().getTime();

        System.out.println("\nThe time required was " + (stopTime - startTime) + " milliseconds");
    } // end main
} // end Billiard

public final class ResizableArrayBag<T> implements BagInterface<T>
{
    private T[] bag; // Cannot be final due to doubling
    private int numberOfEntries;
    private boolean initialized = false;
    private static final int DEFAULT_CAPACITY = 25; // Initial capacity of bag
    private static final int MAX_CAPACITY = 10000;

    /**
     * Creates an empty bag whose initial capacity is 25.
     */
    public ResizableArrayBag()
    {
        this(DEFAULT_CAPACITY);
    } // end default constructor

    /**
     * Creates an empty bag having a given initial capacity.
     *
     * @param initialCapacity The integer capacity desired.
     */
    public ResizableArrayBag(int initialCapacity)
    {
        checkCapacity(initialCapacity);

        // The cast is safe because the new array contains null entries
        @SuppressWarnings("unchecked")
        T[] tempBag = (T[]) new Object[initialCapacity]; // Unchecked cast
        this.bag = tempBag;
        this.numberOfEntries = 0;
        this.initialized = true;
    } // end constructor

    /**
     * Creates a bag containing given entries.
     *
     * @param contents An array of objects.
     */
    public ResizableArrayBag(T[] contents)
    {
        checkCapacity(contents.length);
        this.bag = Arrays.copyOf(contents, contents.length);
        this.numberOfEntries = contents.length;
        this.initialized = true;
    } // end constructor

    /**
     * Adds a new entry to this bag.
     *
     * @param newEntry The object to be added as a new entry.
     * @return True.
     */
    public boolean add(T newEntry)
    {
        checkInitialization();
        if (isArrayFull())
        {
            doubleCapacity();
        } // end if

        this.bag[this.numberOfEntries] = newEntry;
        this.numberOfEntries++;

        return true;
    } // end add

    /**
     * Retrieves all entries that are in this bag.
     *
     * @return A newly allocated array of all the entries in this bag.
     */
    public T[] toArray()
    {
        checkInitialization();

        // The cast is safe because the new array contains null entries.
        @SuppressWarnings("unchecked")
        T[] result = (T[]) new Object[this.numberOfEntries]; // Unchecked cast
        for (int index = 0; index < this.numberOfEntries; index++)
        {
            result[index] = this.bag[index];
        } // end for

        return result;
    } // end toArray

    /**
     * Sees whether this bag is empty.
     *
     * @return True if this bag is empty, or false if not.
     */
    public boolean isEmpty()
    {
        return this.numberOfEntries == 0;
    } // end isEmpty

    /**
     * Gets the current number of entries in this bag.
     *
     * @return The integer number of entries currently in this bag.
     */
    public int getCurrentSize()
    {
        return this.numberOfEntries;
    } // end getCurrentSize

    /**
     * Counts the number of times a given entry appears in this bag.
     *
     * @param anEntry The entry to be counted.
     * @return The number of times anEntry appears in this ba.
     */
    public int getFrequencyOf(T anEntry)
    {
        checkInitialization();
        int counter = 0;

        for (int index = 0; index < this.numberOfEntries; index++)
        {
            if (anEntry.equals(this.bag[index]))
            {
                counter++;
            } // end if
        } // end for

        return counter;
    } // end getFrequencyOf

    /**
     * Tests whether this bag contains a given entry.
     *
     * @param anEntry The entry to locate.
     * @return True if this bag contains anEntry, or false otherwise.
     */
    public boolean contains(T anEntry)
    {
        checkInitialization();
        return getIndexOf(anEntry) > -1; // or >= 0
    } // end contains

    /**
     * Removes all entries from this bag.
     */
    public void clear()
    {
        while (!isEmpty())
            remove();
    } // end clear

    /**
     * Removes one unspecified entry from this bag, if possible.
     *
     * @return Either the removed entry, if the removal
     * was successful, or null.
     */
    public T remove()
    {
        checkInitialization();
        T result = removeEntry(this.numberOfEntries - 1);
        return result;
    } // end remove

    /**
     * Removes one occurrence of a given entry from this bag.
     *
     * @param anEntry The entry to be removed.
     * @return True if the removal was successful, or false if not.
     */
    public boolean remove(T anEntry)
    {
        checkInitialization();
        int index = getIndexOf(anEntry);
        T result = removeEntry(index);
        return anEntry.equals(result);
    } // end remove

    // Locates a given entry within the array bag.
    // Returns the index of the entry, if located,
    // or -1 otherwise.
    // Precondition: checkInitialization has been called.
    private int getIndexOf(T anEntry)
    {
        int where = -1;
        boolean found = false;
        int index = 0;

        while (!found && (index < this.numberOfEntries))
        {
            if (anEntry.equals(this.bag[index]))
            {
                found = true;
                where = index;
            } // end if
            index++;
        } // end while

        // Assertion: If where > -1, anEntry is in the array bag, and it
        // equals bag[where]; otherwise, anEntry is not in the array.

        return where;
    } // end getIndexOf

    // Removes and returns the entry at a given index within the array.
    // If no such entry exists, returns null.
    // Precondition: 0 <= givenIndex < numberOfEntries.
    // Precondition: checkInitialization has been called.
    private T removeEntry(int givenIndex)
    {
        T result = null;

        if (!isEmpty() && (givenIndex >= 0))
        {
            result = this.bag[givenIndex];          // Entry to remove
            int lastIndex = this.numberOfEntries - 1;
            this.bag[givenIndex] = this.bag[lastIndex];  // Replace entry to remove with last entry
            this.bag[lastIndex] = null;             // Remove reference to last entry
            this.numberOfEntries--;
        } // end if

        return result;
    } // end removeEntry

    // Returns true if the array bag is full, or false if not.
    private boolean isArrayFull()
    {
        return this.numberOfEntries >= this.bag.length;
    } // end isArrayFull

    // Doubles the size of the array bag.
    // Precondition: checkInitialization has been called.
    private void doubleCapacity()
    {
        int newLength = 2 * this.bag.length;
        checkCapacity(newLength);
        this.bag = Arrays.copyOf(this.bag, newLength);
    } // end doubleCapacity

    // Throws an exception if the client requests a capacity that is too large.
    private void checkCapacity(int capacity)
    {
        if (capacity > MAX_CAPACITY)
            throw new IllegalStateException("Attempt to create a bag whose capacity exceeds " +
                    "allowed maximum of " + MAX_CAPACITY);
    } // end checkCapacity

    // Throws an exception if receiving object is not initialized.
    private void checkInitialization()
    {
        if (!this.initialized)
            throw new SecurityException("Uninitialized object used " +
                    "to call an ArrayBag method.");
    } // end checkInitialization
} // end ResizableArrayBag

Roulette is a casino game that involves spinning a ball on a wheel that is marked with numbered squares that are red, black, or green. Half of the numbers 1-36 are red and half are black, 0 and 00 are green. Each number occurs only once on the wheel.

The most common bets are to bet on a single number or to bet on a color (red or black). The pocket in which the ball lands on the wheel determines the winning number and color. The ball can land on only one color and number at a time.

We begin by placing a bet on a number between 1 and 36. This bet pays 36 to 1 in most casinos, which means we will be paid $36 for each $1 we bet on the winning number. If we lose, we simply lose whatever amount of money we bet.

Calculate the probability that we will win on a single spin of the wheel.

Calculate the probability that we will lose.

What is the expected value of a bet on a single number if we bet $1?

What is the expected value of a bet on a single number if we bet $5?

What is the expected value of a bet on a single number if we bet $10?

Can you explain your responses to the three expected value questions?

We decide that we can certainly increase our chances of winning if we bet on a color instead of a number. This bet pays even money in most casinos. This means that for each dollar we bet, we will win $1 for choosing the winning color. So, if we bet $5 and win, we would keep our $5 and win $5 more. If we lose, we lose whatever amount of money we bet, just as before.

What is the probability that we will win on a single spin?

If we bet $60 on the winning color, will we win more or less than if we bet $8 on the winning number?

What is the expected value of a $1 bet on red?

What is the expected value of a $5 bet on red?

What is the expected value of a $10 bet on red?

How does the expected value of betting on a number compare to the expected value of betting on a color?

Are casinos really gambling when we place a bet against them? Explain.