1. If you apply the potential difference V to a parallel plate capacitor, it is charged to the charge value Q. Now you double the separation between the plates keeping the same V. As a result, charge on the plates will be equal to:

A. 2Q;

B. 4Q;

C. Q;

D. Q/2;

E. Q/4;

2. You have several capacitors of different capacitances. Which statement is correct?

A. If the capacitors connected to a battery in series, charges on all capacitors are the same, but potential differences are different;

B. If the capacitors connected to a battery in series, charges on all capacitors are different, but potential differences are the same;

C. If the capacitors connected to a battery in parallel, charges on all capacitors are different, but potential differences are the same;

D. If the capacitors connected to a battery in parallel, charges on all capacitors are the same, but potential differences are different;

E. A and C;

F. B and D.

3. If you apply voltage V to a long aluminum wire, the power P is dissipated in the wire. If you apply the same voltage V to another aluminum wire which has the same diameter, but is 2 times longer, the dissipated power will be equal to:

A. 4P;

B. 2P;

C. P;

D. P/2;

E. P/4.

1) Determine the angle between vectors:

U = <2, -3, 4> and V= <-1, 3, -2>

2) determine the distance between line and point

P: -2x+3y-4z =2

L: 3x – 5y+z =1

3) Determine the distance between the line L and the point A given by

L; (x-1)/2 = (y+2)/5 = (z-3)/4 and A (1, -1,1)

4) Find an equation of the line given by the points A, B and C.

A (2, -1,0), B (-2,4,-1) and C ( 3,-4,1)

5) Determine whether the lines are parallel, perpendicular or neither.

(x-1)/2 = (y+2)/5 = (z-3)/4 and (x-2)/4 = (y-1)/3 = (z-2)/6

6) A) Find the line intersection of vector planes given by the equations

-2x+3y-z+4=0 and 3x-2y+z=-2

B) Given U = <2, -3, 4> and V= <-1, 3, -2>

Find

a. U . V

b. U x V

7) Find the angle between the planes:

3x -5y+7z -4=0 and 3x -2y+5z +3 =0

Numeric responses must be either an integer (if exact) or a real number with three decimal places, with the least significant number rounded. Do not use commas. If there are units, the integer part must be between 1 and 999. Use the following units: Ohm, kOhm, mOhm resistors, etc. Conductances: S, mS, MS, etc. Voltage: V, kV, mV, MV, etc. Current: A, mA, kA, uA, nA, etc. Power: W, mW, kW, uA, pW, etc. Time: s, hrs, ks, ms, etc.

1. Voltage amplifiers are available with Avoc = 8 V / V, Rin = 1.8 kΩ, Ro = 850 Ω. With a 12 V DC power source, each amplifier consumes 1.5 mA average current.

a. How many amplifiers do you need to cascade to get at least a 1000 voltage gain with a load resistance of 1.0 kΩ?

b.What is the voltage gain Av obtained? (Respond with a rounded whole number)

c. For the cascade connection, find the open circuit voltage gain. (Respond with a rounded whole number)

d. If you have a 1.5 mV input, how efficient is the equivalent amplifier?

e. Find the transconductance of the entire circuit.

-- Consider a concentration cell. Two Ag-electrodes are immersed in AgNO3 solutions of different concentrations. When the two compartments have an AgNO3-concentration of 1 M and 0.1 M, respectively, the measured voltage is 0.065 V (note: T in not necessarily = 25°C ).

The electrochemical behavior of silver nanoclusters (Agn, with n the number of Ag atoms in the cluster) is investigated using the following electrochemical cells at 298 K:

I. Ag(s) | AgCl (saturated) || Ag+(aq, 0.01M) | Ag(s), E=0.170

II. (Pt electrode) Agn (s, nanocluster) | Ag+(aq, 0.01M) || AgCl (saturated) | Ag(s), with E = +1.030 V for Ag5 nanocluster and E = +0.430 V for Ag10 nanocluster

The standard reduction potential for Ag+ + e- → Ag, is E0 = +0.800 V.

The two nanoclusters Ag5 and Ag10-nanoclusters have standard potentials different from the potential of metallic bulk silver.

c. Calculate the standard potentials of Ag5 and of Ag10 nanoclusters. [for this part use Ksp(AgCl)=1.800·10-5;]

d. What happens, if you put the Ag10 nanoclusters and – in a second experiment – the Ag5 nanoclusters into an aqueous solution of pH=5? Estimate the consequences using the reduction potentials you calculated.

Assume that the following relationship holds:

Maintenance Costs = (v * Machine Hours) + f

REQUIRED

Estimate the values of v and f and the cost equation, using,

1. The Linear Regression method.

Note, to use the linear regression method, you MUST use the Microsoft Excel program.

Make sure to report

1. The values of v and f;

2. A scatter plot of the data points, and

3. The adjusted R-square; explain what the adjusted R-square means.

4. The cost equation in the form of Y = vx + f, substituting the values for v and f from the regression output.

YOUR SUBMISSION MUST BE IN EXCEL.

Three resistors with resistances R₁, R₂, R₃ are connected in parallel across a battery with voltage V. By Ohm’s law, the current (amps) is

I = V* [ (1/R₁) + (1/R₂) + (1/R₃) ]

Assume that R₁, R₂, R_3, and V are independent random variables

where R₁ ~ Normal (m = 10 ohms, s = 1.5 ohm)

            R₂ ~ Normal (m = 15 ohms, s = 1.5 ohm)

            R₃ ~ Normal (m =20 ohms, s = 1.0 ohms)

            V ~ Normal (m = 120 volts, s = 2.0 volts

(a) Use Monte Carlo Simulation (10,000 random draws from each input random variable) to estimate the mean and standard deviation of the output variable current. (b) Assess whether the output variable current is normally distributed. (c) Assess whether the inverse of current squared (1/ I2 ) is normally distributed. (d) Estimate the probability that the current is less than 25 amps assuming that the inverse of current squared is normally distributed. (e) Compare your answer to (d) with your simulation results – how many of the 10,000 random results for current are below 25 amps via the Stat > Tables > Tally command?

A Java question. You are given a Student class. A Student has a name and an ArrayList of grades (Doubles) as instance variables.

Write a class named Classroom which manages Student objects.

You will provide the following:

1. public Classroom() a no-argument constructor.
2. public void add(Student s) adds the student to this Classroom (to an ArrayList
3. public String hasAverageGreaterThan(double target) gets the name of the first student in the Classroom who has an average greater than the target or the empty string. Do not use break. Do not return from the middle of the loop. Use a boolean flag if you need to terminate early.
4. public ArrayList<String> getStudents() gets an ArrayList<String> containing the names of all the Students in this Classroom.
5. public Student bestStudent() gets the Student with the highest average in this classroom or null there are no students
6. public String toString() gets a string represent ion using ArrayList's toString method

Provide Javadoc

-------------------------------------------------------------------------------------------------

ClassroomTester.java

import java.util.ArrayList;

public class ClassroomTester
{
public static void main(String[] args)
    {
       ArrayList<Double> grades1 = new ArrayList<>();
       grades1.add(82.0);
       grades1.add(91.5);
       grades1.add(85.0);
       Student student1 = new Student("Srivani", grades1);
      
       ArrayList<Double> grades2 = new ArrayList<>();
       grades2.add(95.0);
       grades2.add(87.0);
       grades2.add(99.0);
       grades2.add(100.0);
       Student student2 = new Student("Carlos", grades2);
       
       ArrayList<Double> grades3 = new ArrayList<>();
       grades3.add(100.0);
       grades3.add(98.0);
       grades3.add(100.0);
       grades3.add(97.0);
       Student student3 = new Student("Maria", grades3);
       
       ArrayList<Double> grades4 = new ArrayList<>();
       grades4.add(80.0);
       grades4.add(70.0);
       grades4.add(82.0);
       grades4.add(75.0);
       Student student4 = new Student("Fred", grades4);
       
       Classroom myClass = new Classroom();
       myClass.add(student1);
       myClass.add(student2);
       myClass.add(student3);
       myClass.add(student4);
       
       System.out.println(myClass);
       System.out.println("Expected: [[Student:name=Srivani,grades=[82.0, 91.5, 85.0]], [Student:name=Carlos,grades=[95.0, 87.0, 99.0, 100.0]], [Student:name=Maria,grades=[100.0, 98.0, 100.0, 97.0]], [Student:name=Fred,grades=[80.0, 70.0, 82.0, 75.0]]]");
       
       System.out.println(">90 GPA: " + myClass.hasAverageGreaterThan(90.0));
       System.out.println("Expected: Carlos");
       
       System.out.println(">99 GPA: " + myClass.hasAverageGreaterThan(99));
       System.out.println("Expected: ");
       
       Student best = myClass.bestStudent();
       if (best != null)
       {
          System.out.println(best.getName());
          System.out.println("Expected: Maria");
       }
       
       System.out.println(myClass.getStudents());
       System.out.println("Expected: [Srivani, Carlos, Maria, Fred]");
       
       //test with an empty classroom
       myClass = new Classroom();
       System.out.println(myClass);
       System.out.println("Expected: []");
       
       System.out.println(">90 GPA: " + myClass.hasAverageGreaterThan(90.0));
       System.out.println("Expected: ");
       
      
       best = myClass.bestStudent();
       if (best != null)
       {
          System.out.println(best.getName());
          
       }
       
       System.out.println(myClass.getStudents());
       System.out.println("Expected: []");
        
    }
}

Student.java

import java.util.ArrayList;
/**
 * Models a student with a name and collection
 * pf grades
 */
public class Student
{
    private String name;
    private ArrayList<Double> grades;

    /**
     * Constructor for Student with name 
     * and list of grades
     * @param name the name of the student
     * @param list the list of grades
     */
    public Student(String name, ArrayList<Double> list)
    {
        this.name = name;
        this.grades = list;
    }
    
    /**
     * Gets the name of the student
     * @return the student's name
     */
    public String getName()
    {
        return name;
    }
    
    /**
     * Gets the average of this student's grades
     * @return the average or 0 if there are no grades
     */
    public double getAverage()
    {
        double sum = 0;
        for ( double g : grades)
        {
            sum = sum + g;
        }
        
        double average = 0;
        if (grades.size() > 0)
        {
            average = sum / grades.size();
        }
        
        return average;
    }
    
    /**
     * @overrides
     */
    public String toString()
    {
        String s = "[Student:name=" + name 
           + ",grades=" + grades.toString() +"]";

        return s;
    }

}

Many high school students take the AP tests in different subject areas. In 2007, of the 143044 students who took the AP biology exam 76712 of them were female. In that same year, of the 211993 students who took the AP calculus AB exam 100106 of them were female. Is there enough evidence to show that the proportion of AP biology exam takers who are female is higher than the proportion of AP calculus AB exam takers who are female?

a) Test at the 5% level

b) Compute a 90% confidence interval for the difference in proportions.

Use the steps of PHANTOMS for the hypothesis test.

For the confidence interval you do not need to do all the steps of PANIC since you did some of them already in PHANTOMS.

You just need to do the NIC of PANIC.

Part a.) HYPOTHESIS TEST

P: Parameter

What is the correct parameter symbol and wording for population 1?

     Select an answer p̂₁ N₁ n₁ p₁ μ? X̄ μ₁  = Select an answer A randomly selected student who took the AP biology test that is female The percentage of all students who took the AP biology test that are female A randomly selected student who took the AP biology test 143044 randomly selected students who took the AP biology test All students who took the AP biology test The percentage of 143044 randomly selected students who took the AP biology test that are female All students who took the AP biology test that are female Whether or not a randomly selected student who took the AP biology test is female

     What is the correct parameter symbol and wording for population 2?

     Select an answer μ? p̂₂ N₂ μ₂ p₂ X̄₂ n₂  = Select an answer All students who took the AP calculus AB test that are female The percentage of all students who took the AP calculus AB test that are female All students who took the AP calculus AB test A randomly selected student who took the AP calculus AB test The percentage of 211993 randomly selected students who took the AP calculus AB test that are female A randomly selected student who took the AP calculus AB test that is female Whether or not a randomly selected student who took the AP calculus AB test is female 211993 randomly selected students who took the AP calculus AB test

H: Hypotheses

Fill in the correct null and alternative hypotheses:

H0:H0: Select an answer μ₁ - μ₂ p₁ - p₂ X̄₁ - X̄₂ N₁ - N₂ p̂₁ - p̂₂ n₁ - n₂ μ?  ? > ≥ = ≠ ≤ <  

HA:HA: Select an answer μ₁ - μ₂ n₁ - n₂ X̄₁ - X̄₂ p̂₁ - p̂₂ N₁ - N₂ p₁ - p₂ μ?  ? ≠ ≥ = > < ≤  

A: Assumptions

Since Select an answer quantitative qualitative  information was collected from each object, we need to check the following conditions:

Check all that apply.

    

• Normal population or at least 30 pairs of data with no outliers in the differences
• σσ is unknown for each group.
• The samples are dependent.
• n1−x1≥10n1-x1≥10 and n2−x2≥10n2-x2≥10
• The samples are independent.
• x1≥10x1≥10 and x2≥10x2≥10
• Normal population or n1≥30n1≥30 and n2≥30n2≥30 with no outliers for each group.
• N1≥20n1N1≥20n1 and N2≥20n2N2≥20n2

     Check those assumptions:

x1x1 =  which is ? ≥ ≠ = < > ≤  

x2x2 =  which is ? > ≥ < ≤ = ≠  

n1−x1n1-x1 =  which is ? ≥ = < ≠ > ≤  

n2−x2n2-x2 =  which is ? = ≤ > < ≠ ≥  

Population sizes are not given.

We will assume that N1N1 >= 20(n1)n1) and N2N2 >= 20(n2)n2)

N: Name the test

The conditions are met to use a Select an answer T-Test Paired T-Test 2-Proportion Z-Test 2-Sample T-Test 1-Proportion Z-Test  .

T: Test Statistic

The symbol and value of the random variable (to 4 decimal places) on this problem are as follows:

     Select an answer n₁ - n₂ N₁ - N₂ μ₁ - μ₂ p₁ - p₂ μ? p̂₁ - p̂₂ X̄₁ - X̄₂  =

Pooled Sample proportion of ˆpp^ is as follows:

     (Leave your answer in FRACTION form and use this fraction form in the set up of the test statistic)

ˆpp^ = x1+x2n1+n2x1+x2n1+n2 =

(( ++  )) /(/(  ++  )=)=

Set up the formula for the test statistic with EXACT FRACTIONS or given decimal values for each box:
z=ˆp1−ˆp2√ˆp(1−ˆp)(1n1+1n2)=z=p^1-p^2p^(1-p^)(1n1+1n2)=

((  −-  ) / √(( ⋅⋅ (1−(1- )⋅ (1)⋅ (1/  +1+1/  ))=))=

Round final answer from technology to 2 decimal places.

     z =

O: Obtain the P-value

Report the final answer to 4 decimal places. It is possible when rounded that a p-value is 0.0000

     P-value =

M: Make a decision

Since the p-value ? = ≤ ≠ ≥ < >   , we Select an answer accept H₀ reject Hₐ fail to reject H₀ fail to reject Hₐ reject H₀  .

S: State a conclusion

• There Select an answer is not is  significant evidence to conclude Select an answer All students who took the AP biology test that are female Whether or not a randomly selected student who took the AP biology test is female 143044 randomly selected students who took the AP biology test The percentage of all students who took the AP biology test that are female A randomly selected student who took the AP biology test The percentage of 143044 randomly selected students who took the AP biology test that are female All students who took the AP biology test A randomly selected student who took the AP biology test that is female  Select an answer is more than is less than is equal to differs from  Select an answer 211993 randomly selected students who took the AP calculus AB test The percentage of all students who took the AP calculus AB test that are female The percentage of 211993 randomly selected students who took the AP calculus AB test that are female All students who took the AP calculus AB test that are female A randomly selected student who took the AP calculus AB test Whether or not a randomly selected student who took the AP calculus AB test is female All students who took the AP calculus AB test A randomly selected student who took the AP calculus AB test that is female
  

Part b.) CONFIDENCE INTERVAL

N: Name the procedure

   The conditions are met to use a Select an answer Paired T-Interval 2-Sample T-Interval T-Interval 2-Proportion Z-Interval 1-Proportion Z-Interval

I: Interval estimate (round endpoints to 3 decimal places)

A  % confidence interval for Select an answer p₁ - p₂ μ? μ₁ - μ₂ n₁ - n₂ X̄₁ - X̄₂ p̂₁ - p̂₂ N₁ - N₂  is (  ,   )

C: Conclusion in context

• We are  % confident that Select an answer All students who took the AP biology test that are female Whether or not a randomly selected student who took the AP biology test is female 143044 randomly selected students who took the AP biology test All students who took the AP biology test The percentage of 143044 randomly selected students who took the AP biology test that are female A randomly selected student who took the AP biology test A randomly selected student who took the AP biology test that is female The percentage of all students who took the AP biology test that are female  is between  % and  % Select an answer more than less than  Select an answer A randomly selected student who took the AP calculus AB test that is female Whether or not a randomly selected student who took the AP calculus AB test is female All students who took the AP calculus AB test that are female All students who took the AP calculus AB test The percentage of all students who took the AP calculus AB test that are female A randomly selected student who took the AP calculus AB test 211993 randomly selected students who took the AP calculus AB test The percentage of 211993 randomly selected students who took the AP calculus AB test that are female

LicensePoints possible: 58
This is attempt 1 of 2.

The mean salary of professors in the US is $52,000.

The standard deviation of finishing times for runners in a marathon is at least 106 minutes.

At most 8% of college students cheat on exams.

The mean GPA of Students is less than 2.8.