Let [x]_B be the coordinate vector of a vector x ∈ V with respect to the basis B for V . Show
that x is nonzero if and only if [x]_B is nonzero.

Find the equation of the line through the point P = (0,2,−1) that is perpendicular to both ⃗v = 〈3,0,1〉 and ⃗w = 〈1,−1,2〉.

v and w are vectors by the way

Oxidation-Reduction Titration

***Sulfuric acid used was 6 M

***All Lab notes are at the bottom, procedure included for clarity... PLEASE HELP WITH THE SHORT ANSWER:)

PROCEDURES:

Experiment 1: Prepare the Materials

Take four 100.00 mL volumetric flasks from the Containers shelf and place them on the workbench.

In one flask, prepare a standard solution of potassium dichromate (K₂Cr₂O₇):

Take potassium dichromate from the Materials shelf and add 4.00 g to the volumetric flask.

Take water from the Materials shelf and add 30.00 mL into the volumetric flask to dissolve the dichromate compound.

Complete the solution by filling the volumetric flask to the 100.00 mL mark with water from the Materials shelf by checking the "Fill To Mark" box.

Double-click on the volumetric flask to open a properties window. Then, rename the volumetric flask as "Standard Potassium Dichromate Solution".

In two of the empty flasks, prepare a standard solution of iron (II) ammonium sulfate hexahydrate (Fe(NH₄)₂(SO₄)₂ × 6H₂O):

Take iron(II) ammonium sulfate hexahydrate from the Materials shelf and add 4.00 g to each empty volumetric flask.

Take water from the Materials shelf and add 30.00 mL to each volumetric flask to dissolve the compound and release the water of hydration.

Complete both solutions by filling the volumetric flask to the 100.00 mL mark with water from the Materials shelf by checking the "Fill To Mark" box.

Rename the volumetric flasks as "Standard Iron(II) Solution". Both flasks will have the same name.

Take the Grey Moose vodka from the Materials shelf and add 2.00 mL to the last empty flask. Fill with water from the Materials shelf by checking the "Fill To Mark" box. The vodka has now been diluted to 1/50th, or 2%, of its original ethanol concentration.

Rename the volumetric flask containing the vodka as "2% Vodka Solution".

Experiment 2: Titrate the Vodka Sample

Part 1: Oxidize the Ethanol in Vodka

Take a 150.00 mL Erlenmeyer flask from the Containers shelf and place it on the workbench.

Add 5.00 mL of 2% vodka solution from the volumetric flask to the Erlenmeyer flask.

Take water from the Materials shelf and add 35.00 mL to the Erlenmeyer flask. Note that this further dilutes the vodka sample by a factor of eight. The ethanol concentration is now 1/8th of 2%, or 0.25% of the original ethanol concentration of the bottled vodka.

Acidify the vodka solution in the Erlenmeyer flask. Take the sulfuric acid (H₂SO₄) solution from the Materials shelf and add 5.00 mL to the Erlenmeyer flask.

Add 5.00 mL of the standard potassium dichromate solution from the volumetric flask to the Erlenmeyer flask. This is enough to reduce all of the ethanol in the vodka and leave an excess of dichromate ions. Note that the solution has turned bright green. This is the color of the reduced Cr³⁺ ions. Record these observations in your Lab Notes. Remember to press Save Notes each time you add more notes.

Part 2: Coarse Titration

Take a burette from the Containers shelf and place it on the workbench. Fill the burette with 50 mL of the standard iron(II) solution. Record the initial burette reading for the amount of volume dispensed in your Lab Notes. Before dispensing any liquid, the amount dispensed should read 0 mL.

Take the redox indicator, sodium diphenylamine sulfonate, from the Materials shelf and add 0.50 g to the Erlenmeyer flask. In the presence of the excess dichromate ions, the solution turns a deep purple.

Place the Erlenmeyer flask on the lower half of the burette to connect to flask and burette.

Perform a coarse titration by adding large increments of the standard iron(II) solution from the burette. To do this, press and hold the black knob at the bottom of the burette until the solution turns suddenly from intense, dark purple to green. Each time you add the standard iron(II) solution, check the volume dispensed from the burette by hovering over the burette and reading the gray tool tip. You will need to know this value.

As the iron(II) is added, the dichromate ions (Cr₂O₇^2–) are reduced to Cr³⁺ ions. At the end point of the titration, there are no dichromate ions left. The redox indicator becomes colorless, and the dark purple color suddenly disappears, leaving the solution bright green again. Recall that bright green is the color of the Cr³⁺ ions.

Record both the last burette volume that the solution was dark purple and the burette volume at which the solution first appeared green again in your Lab Notes. This gives the range in which the titration will end. Remember to press Save Notes.

Discard just the Erlenmeyer flask in the recycling bin underneath the workbench.

Part 3: Fine Titration

Set up the titration as before:

Add 5.00 mL of diluted vodka, 35.00 mL water, 5.00 mL of sulfuric acid, 5.00 mL of the standard potassium dichromate solution, and 0.50 g sodium diphenylamine sulfonate to an Erlenmeyer flask.

Connect the Erlenmeyer flask to the lower half of the burette.

Note the current volume of standard iron(II) solution in the burette. Add to it from the volumetric flask on the workbench so that the volume is 50.00 mL again. Record the initial burette reading for the amount dispensed in your Lab Notes.

Click and hold the black knob of the burette to quickly add enough standard iron(II) solution to just get into the range of the coarse titration (the first number you recorded), but still have the solution in the flask appear dark purple. This is near, but not yet at, the titration's end point.

Add standard iron(II) solution in small increments, down to one drop at a time, until the addition of just one more drop causes the solution in the flask to turn green. Record the final burette reading for the amount of volume dispensed in your Lab Notes.

Place the Erlenmeyer flask in the recycling bin beneath the workbench.

Repeat the fine titration once more, and record the results in your Lab Notes. If the results from the two fine titrations do not closely agree, perform a third fine titration to determine which of the first two was done incorrectly.   

SHORT ANSWER

Oxidation-Reduction Titration

Experiment 1: Prepare the Materials

Data Analysis

Calculate the concentration of the dichromate ion in the first volumetric flask.

Calculate the concentration of the iron (II) ion in the second volumetric flask.

Experiment 2: Titrate the Vodka Sample

Lab Results

Record the following lab data in the table below. If you had to repeat one of the titrations, disregard the value that was different.

Data Analysis

Record and calculate the quantities in the table below using the data from your dichromate titrations. Use an average value for the volume of iron (II) solution used in the titration. If one of your values is very different, and you had to perform the titration three times, disregard the value that was very different when computing the average.

  The amount of alcohol in a drink is typically reported as percent alcohol by volume. Volume percent or volume/volume percent (% v/v) most often is used when preparing solutions of liquids. Volume percent is defined as:
% v/v = V_solute/V_solution  × 100
Find the percent alcohol (ethanol) by volume for the vodka used in the lab by following the steps outlined in the table below.

Conclusions

The Grey Moose vodka tested in this lab reports a percent alcohol by volume of 40.0% on its label. How does your value compare to the reported one? If the values are different, give one possible experimental error that might have contributed to the difference.  

Potassium permanganate is another strong oxidizing substance similar to potassium dichromate. An acidic solution of purple permanganate ions can get reduced to colorless Mn²ions in the presence of ethanol. Write down the redox reaction between permanganate and ethanol, and balance it using the half-reaction method.

Besides vodka, there are other colorless alcohol-containing beverages that can be titrated following the procedure in your lab. Given the average values for the percent alcohol by volume listed in the table below, which beverage do you expect to use the least amount of iron (II) standard solution during the titration? Assume all lab procedures stay the same.

LAB NOTES:

Solution turned bright green upon adding the standard potassium dichromate.

Initial burette reading: 50 mL

(Solution turned deep purple after adding sodium diphenylamine sulfonate)

Coarse Titration:

First dispense

Volume: 46.93 mL

Volume dispensed: 3.07 mL

Second dispense

Volume: 44.07 mL

Volume dispensed: 5.93 mL

Third dispense

Volume: 40.91 mL

Volume dispensed: 9.09 mL

Fourth dispense

Volume: 37.74 mL

Volume dispensed: 12.26 mL

Fifth dispense- END POINT REACHED

Volume: 34.76 mL

Volume dispensed: 15.24 mL

Fine Titration 1

End point volume: 35.85 mL

Volume dispensed: 14.15 mL

Fine Titration 2:

End point volume: 35.86 mL

Volume dispensed: 14.14 mL

What is the average monthly return and standard deviation of returns for

(i) S&P 500:

(ii) GE:

Introduction- reasons for proposal and writer's qualifications

Background- IDs problem and goals/purposes of project

Proposal- plan for solving the problem

Staffing- credentials/expertise of project leaders

Budget- list of project costs

Authorization request- request for approval or authorization of proposal

Letter or memo of transmittal

Abstract and/or executive summary

Title page

Table of contents

List of figures

Appendix

Introduction

Body

Conclusions

Recommendations

Title page

Letter or memo of transmittal

Table of contents

List of figures

Executive summar

Body of Report

Introduction

Background

Problem or purpose

Significance and scope

Sources and methods

Organization

Discussion of findings

Summary, conclusions, recommendations

Supplementary Parts of a Formal Report

Footnotes or endnotes

Works Cited, References, or Bibliography

Appendix

Drug name is INDOMETHACIN

List customer id, customer full name (Last name, full name, state) for those customers that have ordered more than once.

List customers (order id, customer id, and customer last name) that had more than 2
-- products in their order. Order your result based on customer id followed by order id

SQL SERVER DATABASE

If the instantaneous value of a voltage in an AC circuit of the communication system (at any time t seconds) is given by V= 142sin(8πt-0.125π) volts, determine:

1). Given that the voltage waveform can also be represented as V=Rsin(ωt+θ), use compound angle identities to resolve the resultant voltage waveform into its two component waveforms: asinωt and bcosωt.

2). In another circuit the voltage, V is made up of two components v1 = (A/3)Sin(t) and v2 = (A/2)Cos(t). Sketch the two component waveforms and the resulting waveform V= (A/3)Sin(t) + (A/2)Cos(t) on the same axes and estimate from your graph the equation of the combined waveform. Also analytically calculate, showing all your working, the parameters (R&θ) of the equation of the combined waveform if represented as V=Rsin(Ѡt+θ), giving θ in radians.

C++

Part 1: Developing And Testing A Stack Template

Write a template, Stack.h, to implement a LIFO stack. Here is the specification for its public interface:

class Stack
{
  ...
  Stack( ); // may have a defaulted parameter
  Stack(const Stack<V>&); // copy constructor
  ~Stack();
  Stack<V>& operator=(const Stack<V>&);
  void push(const V&);
  const V& peek( );
  void pop( );
  int size( ) const;
  bool empty( ) const;
  void clear( );
}; 

If you use dynamic memory (and you surely will!) be sure to include the three memory management functions as public members, too. You may implement your Stack as arrayed or as linked -- your choice.

Fully test your template in a test driver CPP named Stack.TestDriver.cpp, remembering to include all the tests we've learned about in this class. Then use the H file in the following application: