1)A realtor has been told that 46 % of homeowners in a city prefer to have a finished basement. She surveys a group of 200 homeowners randomly chosen from her client list. Find the standard deviation of the proportion of homeowners in this sample who prefer a finished basement.

a) 0.46% b) 46% c) 3.5% d)0.5% e)1.8%

2)the number of games won by a minor league baseball team and the average attendance at their home game is analyzed. A regression analysis to predict the average attendance from the number of games won gives the model attendance = -2800 +197 wins. Predict the average attendance of a team with 55 wins.

a) 10,835 b)-2548 c)13,635 d)14 e)8,035

3)In a large class, the professor has each person toss a coin several times and calculate the proportion of his or her tosses that were heads. The students then report their results, and the professor plots a histogram of these several proportions. Use the 68-95-99.7 Rule to provide the appropriate response. If the students toss the coin 80 times each, about 95% should have proportions between what two numbers?

4)The average composite ACT score for Ohio students who took the test in 2003 was 21.4. Assume that the standard deviation is 1.05. In a random sample of 64 students who took the exam in 2003, what is the probability that the average composite ACT score is 22.5 or more? Make sure to identify the sampling distribution you use and check all necessary conditions.

JAVA code

Create a new class called BetterDiGraph that implements the EditableDiGraph interface See the interface below for details.

EditableDigraph below:

import java.util.NoSuchElementException;

/**
* Implements an editable graph with sparse vertex support.
*
*
*/
public interface EditableDiGraph {
  
/**
* Adds an edge between two vertices, v and w. If vertices do not exist,
* adds them first.
*
* @param v source vertex
* @param w destination vertex
*/
void addEdge(int v, int w);

/**
* Adds a vertex to the graph. Does not allow duplicate vertices.
*
* @param v vertex number
*/
void addVertex(int v);

/**
* Returns the direct successors of a vertex v.
*
* @param v vertex
* @return successors of v
*/
Iterable getAdj(int v);
  
/**
* Number of edges.
*
* @return edge count
*/
int getEdgeCount();
  
/**
* Returns the in-degree of a vertex.
* @param v vertex
* @return in-degree.
* @throws NoSuchElementException exception thrown if vertex does not exist.
*/
int getIndegree(int v) throws NoSuchElementException;
  
/**
* Returns number of vertices.
* @return vertex count
*/
int getVertexCount();
  
/**
* Removes edge from graph. If vertices do not exist, does not remove edge.
*
* @param v source vertex
* @param w destination vertex
*/
void removeEdge(int v, int w);

/**
* Removes vertex from graph. If vertex does not exist, does not try to
* remove it.
*
* @param v vertex
*/
void removeVertex(int v);

/**
* Returns iterable object containing all vertices in graph.
*
* @return iterable object of vertices
*/
Iterable vertices();

/**
* Returns true if the graph contains at least one vertex.
*
* @return boolean
*/
boolean isEmpty();
  
/**
* Returns true if the graph contains a specific vertex.
*
* @param v vertex
* @return boolean
*/
boolean containsVertex(int v);
}

(a) Starting from entropy as a function of pressure and volume, S(P, V), show that

d S = C V T ( ∂ T ∂ P ) V d P + C P T ( ∂ T ∂ V ) P d V

For a certain gas that follows the following equation of state:

P(V-b) = RT

Where b is a constant

(b) Starting from the above relationship show that P(V-b)^γ=constant for the reversible adiabatic process. Assume constant heat capacity and γ=C_P/C_V as that for the ideal gas.

GRAPH THEORY

Prove/Show that a connected Graph G is not separable if and only if it is nonseparable.

Definitions for Reference: A connected Graph G is called nonseparable if it has no cut vertices (A vertex v in a connected graph G is caled a cut vertex if G-v is disconnected)

A connected graph G is called separable if there exist subgraphs H1, H2 ⊂ G. with E(H1) ∪ E(H2) = E(G) and E(H1) ∩ E(H2) = ∅. V (H1) ∪ V (H2) =V (G) and V (H1) ∩ V (H2) containing a single vertex.

P = Power, V = Voltage, I = Current, and R = Resistance. Which of the following relations is incorrect?

Choices:

V = I R

P = V R

P = VI

I = V/R

Given two sets S and T, the direct product of S and T is the set of ordered pairs S × T = {(s, t)|s ∈ S, t ∈ T}.Let V, W be two vector spaces over F.

(a) Prove that V × W is a vector space over F under componentwise addition and scalar multiplication (i.e. if (v1, w1),(v2, w2) ∈ V × W, then (v1, w1) + (v2, w2) = (v1+w1, v2+w2) and a(v, w) = (av, aw) for any (v, w) ∈ V ×W, a ∈ F).

(b) If dim V = n and dim W = m, prove that dim V × W = n + m by constructing a basis.

1.) Translate the following C code to MIPS assembly code. Assume that the variables f, g, h, i, and j are assigned to registers $s0, $s1, $s2, $s3, and $s4, respectively. Assume that the base address of the arrays A and B are in registers $s6 and $s7, respectively

  B[8] = A[i-j];

2.Translate the following C code to MIPS assembly code. Assume that the values of v in $a0, k in $a1, temp in $t0.

// leaf procedure that swaps v[k] and v[k+1]

void swap(int v[], int k)

{
int temp;
temp = v[k];
v[k] = v[k+1];
v[k+1] = temp;
}

1. A random sample of BMI from college students were collected as follows:

23 32 34 26 23 28 38 33 25 29 28

1. Find sample size.
2. Find sample median.
3. Find sample mean.
4. Find IQR.
5. Construct a box plot.
6. Mention one reason that box plot is useful
7. What aspect of the data are both the sample standard deviation and IQR measuring? List an advantage and disadvantage of each.
8. If each person’s BMI in the sample increase the same amount, 5, how the median and IQR will change?

A franchise is when an owner of a trademark, trade name, or copyright licensees it to a separate party to use to sell goods and/or services. Many websites are dedicated to franchise opportunities, and the Small Business Administration (SBA) also provides information on franchises (www.sba.gov). Identify a franchise business and list the requirements needed to purchase franchise. What are the costs of franchising this business? Do you feel the franchise fee is reasonable? Why or why not? Look at the businesses your fellow students have identified, which ones have the greatest risk vs. reward? Which are the safest? Why?