The town of Ferndale has four candidates running for mayor: the town barber, Darrell; the fire chief, Clough;the grocer, Abel; and a homemaker, Belle. A poll of 1000 of the voters shows the following results:

DABC = 225

CABD = 190

CADB = 210

BADC = 375

Is there a winner using the plurality method?

1. D

2. A

3. B

4. C

The seniors at Weseltown High School are voting on where to go for their senior trip. They are deciding on Angel Falls(A), Bend Canyon(B), Cedar Lake(C), or Danger Gap(D). The results of the preferences are:

DABC = 120

ACBD = 100

BCAD = 90

CBDA = 80

CBAD = 45

Who wins using the Borda count method?

1. Danger Gap(D)

2. Bend Canyon(B)

3. Cedar Lake(C)

4. Angel Falls(A

Show that a subset of R is open if an only if it can be expressed as a union of open intervals

Find a singular value decomposition for the matrix A = [ 1 0 -1, -1 1 0] (that means 1 0 -1 is the first row and -1 1 0 is the second)

If you could provide a step-by-step tutorial on how to complete this I'd greatly appreciate it.

Curve-fitting Project - Linear Model

Instructions

For this assignment, collect data exhibiting a relatively linear trend, find the line of best fit, plot the data and the line, interpret the slope, and use the linear equation to make a prediction. Also, find r² (coefficient of determination) and r (correlation coefficient). Discuss your findings. Your topic may be that is related to sports, your work, a hobby, or something you find interesting. If you choose, you may use the suggestions described below.

A Linear Model Example and Technology Tips are provided in separate documents.

Tasks for Linear Regression Model (LR)

(LR-1) Describe your topic, provide your data, and cite your source. Collect at least 8 data points. Label appropriately.  (Highly recommended: Post this information in the Linear Model Project discussion as well as in your completed project. Include a brief informative description in the title of your posting. Each student must use different data.)

The idea with the discussion posting is two-fold: (1) To share your interesting project idea with your classmates, and (2) To give me a chance to give you a brief thumbs-up or thumbs-down about your proposed topic and data. Sometimes students get off on the wrong foot or misunderstand the intent of the project, and your posting provides an opportunity for some feedback. Remark: Students may choose similar topics, but must have different data sets. For example, several students may be interested in a particular Olympic sport, and that is fine, but they must collect different data, perhaps from different events or different gender.

(LR-2) Plot the points (x, y) to obtain a scatterplot. Use an appropriate scale on the horizontal and vertical axes and be sure to label carefully. Visually judge whether the data points exhibit a relatively linear trend. (If so, proceed. If not, try a different topic or data set.)

(LR-3) Find the line of best fit (regression line) and graph it on the scatterplot. State the equation of the line.

(LR-4) State the slope of the line of best fit. Carefully interpret the meaning of the slope in a sentence or two.

(LR-5) Find and state the value of r², the coefficient of determination, and r, the correlation coefficient. Discuss your findings in a few sentences. Is r positive or negative? Why? Is a line a good curve to fit to this data? Why or why not? Is the linear relationship very strong, moderately strong, weak, or nonexistent?

(LR-6) Choose a value of interest and use the line of best fit to make an estimate or prediction. Show calculation work.

(LR-7) Write a brief narrative of a paragraph or two. Summarize your findings and be sure to mention any aspect of the linear model project (topic, data, scatterplot, line, r, or estimate, etc.) that you found particularly important or interesting.

You may submit all of your project in one document or a combination of documents, which may consist of word processing documents or spreadsheets or scanned handwritten work, provided it is clearly labeled where each task can be found. Be sure to include your name. Projects are graded on the basis of completeness, correctness, ease in locating all of the checklist items, and strength of the narrative portions.

A sequence (xn) converges quadratically to x if there is some Q ∈ R such that |xn − x| ≤ Q/n^2

for all n ∈ N. Prove directly that if (xn) converges quadratically, then it is also Cauchy.

Suppose you are climbing a hill whose shape is given by the equation

z = 1400 − 0.005x² − 0.01y²,

where x, y, and z are measured in meters, and you are standing at a point with coordinates (60, 40, 1366). The positive x-axis points east and the positive y-axis points north.

(a) If you walk due south, will you start to ascend or descend?

At what rate?

vertical meters per horizontal meter

(b) If you walk northwest, will you start to ascend or descend?

At what rate? (Round your answer to two decimal places.)

vertical meters per horizontal meter

(c) In which direction is the slope largest?

What is the rate of ascent in that direction?

vertical meters per horizontal meter

At what angle above the horizontal does the path in that direction begin? (Round your answer to two decimal places.)

°

Obtain a spectral decomposition for the symmetric matrix A = [0 2 2, 2 0 2, 2 2 0] (that means the first row is 022, then below that 202, etc.) , whose characteristic polynomial is −(λ + 2)^2 (λ − 4)

If you could provide a step-by-step way to solve this I'd greatly appreciate it.

1. Perform two iterations of the gradient search method on f(x,y)= x^2+4xy+2y^2+2x+2y. Use (0,0) as a starting point. Please find the optimal λ* by taking the derivative and setting it equal to 0.

4(a)Verify that the equation y=lnx-lny is an implicit solution of the IVP,

                  ydx=x(y+1)dy    

                            y(e)=1                                          

   (b) Consider the IVP, test whether it is exact and solve it.    

             x(x-y)dy=-(3xy-y^2)dx                   

                      y(-1)=1                                        

(c) Determine the degree of the following homogeneous function                                                 

       (i) f(x,y)=4x^2+2y^4 ,                                     

       (ii) f(x,y)=√5x^6-3y^6+4x^2y^4 ,           

Using a real world example, state the domain and range of the function or relationship. What are the practical things to consider when limiting the domain and range of a real world function?

If u(t) = < sin(5t), cos(5t), t > and v(t) = < t, cos(5t), sin(5t) >, use the formula below to find the given derivative.

d/dt[ u(t) * v(t)] = u'(t) * v(t) + u(t)* v'(t)

d/dt [ u(t) x v(t)] = ?

olve the linear programming problem by sketching the region and labeling the vertices, deciding whether a solution exists, and then finding it if it does exist. (If an answer does not exist, enter DNE.) Maximize P = 20x + 30y Subject to 2x + y ≤ 16 x + y ≤ 10 x ≥ 0, y ≥ 0

A biologist must make a medium to grow a type of bacteria. The percentage of salt in the medium is given by S=0.01x2y2zS=0.01x2y2z , where SS is the percentage expressed as a decimal. And where xx, yy, and zz are the amounts in liters of 3 different nutrients mixed together to create the medium. The ideal salt percentage for this type of bacteria is 34.7%. The costs of the xx, yy, and zz nutrient solutions are respectively 10 , 4, and 10 dollars per liter. Determine the minimum cost that can be achieved.

(Round your answers to the nearest 4 decimal places.)