Could you show me how to form PLAs for the following question? Thanks.

7. Draw a PLA for the following functions, given in S notation, using variables x₀, x₁, x₂, x₃.

1. f₁ = S (0, 3, 5, 7, 8, 11, 13)
2. f₂ = S (1, 2, 3, 6, 11, 13, 14, 15)
3. f₃ = S (0, 2, 4, 6, 7, 12, 13, 15)
4. f₄ = S (1, 4, 5, 6, 9, 10, 12)
5. f₅ = S (2, 3, 4, 5, 8, 9, 10, 11, 14)

The figure above shows four very thin parallel planes of charge with equal separation between them.  
The charge density on plate 1 is 3 nC/m₂.
The charge density on plate 2 is 4 nC/m₂.
The charge density on plate 3 is 2 nC/m₂.
The charge density on plate 4 is -4 nC/m₂.
Your answers for the electric field must include the correct sign. We choose positive electric field along the positive x-direction.

I am unable to put the image but it is point A then plate 1- point B then plate 2 and so forth..

Two profit maximizing oligopolists produce electricity. They set their productions levels,y1 and y2, simultaneously. p(y) = 10−y, where y=y1+y2. Assume the cost curve for firm 1 and firm 2 are C(y1) = 2y1 and C(y2) = 2y2 respectively. Marginal cost for each firm is constant at 2.

Suppose firm 1 is the leader and sets the quantity first. Firm 2 is the follower.

(Stackelberg)

1. Write down each firm’s profit maximization problem

2. Determine the optimal (equilibrium ) levels of production y^S_1 and y^S_2.

3. Determine the Consumer Surplus, Producer Surplus and Dead weight loss.

4. In a diagram compare the equilibrium output in Problem 3 and 4 by using the best response for firm 1 and firm 2.

#######################################################################
#####################################
###############python#################

# RQ1
def merge(dict1, dict2):
    """Merges two Dictionaries. Returns a new dictionary that combines both. You may assume all keys are unique.

    >>> new =  merge({1: 'one', 3:'three', 5:'five'}, {2: 'two', 4: 'four'})
    >>> new == {1: 'one', 2: 'two', 3: 'three', 4: 'four', 5: 'five'}
    True
    """
    "*** YOUR CODE HERE ***"


# RQ2
def counter(message):
    """ Returns a dictionary where the keys are the words in the message, and each
    key is mapped (has associated value) equal 
    to the number of times the word appears in the message.
    >>> x = counter('to be or not to be')
    >>> x['to']
    2
    >>> x['be']
    2
    >>> x['not']
    1
    >>> y = counter('run forrest run')
    >>> y['run']
    2
    >>> y['forrest']
    1
    """
    "*** YOUR CODE HERE ***"

Linearize by hand y = a(x₁)^b(x₂)^c and determine the coefficients a, b and c, and the coefficient of determination using the data below.

Instructions:

1. Your answers should be precise. Do not give information not directly relevant for answering the questions. Show all your work in numerical problems to receive full credits. The assignment will be graded on a scale of 0-5. Clarity and grammatical correctness will carry some weights in the evaluation of this assignment. Please refer to the scoring rubric. You must submit your answers to Q.1 – 2. You are not required to submit your answers to Q.3 - 7. 1. Consider a bond with a 5% annual coupon and a face value of $1,000. Complete the following table. What relationships do you observe between years to maturity, yield to maturity, and the current price? Show all your work.

2. “The Federal Reserve System resembles the U. S. Constitution in that it was designed with many checks and balances.” Do you agree? If so, discuss at least three distinctive features of the structure and organization of the Fed that provide with these checks and balances. If not, explain why. (3 points)

1. Each value in the data set is called a ? .

1. Variables whose values are determined by chance are called ? .

1. A Blank 1 consists of all subjects (human or otherwise) that are being studied.

1. A Blank 1 is a circle that is divided into sections or wedges according to the percentage of frequencies in each category of the distribution.

1. Tell whether Descriptive or Inferential Statistics has been used. In the upcoming election, it is predicted that candidate Murphy will get 52% of the votes and candidate Patterson will receive 46% of the votes.

   	1.	Descriptive
   	2.	Inferential

1. Tell whether Descriptive or Inferential Statistics has been used. Results of the election last week showed that candidate Patterson received 53% of the votes and candidate Murphy received 44% of the votes.

   	1.	Descriptive
   	2.	Inferential

1. Classify as nominal-level, ordinal-level, interval-level, or ratio-level data. Salaries of employees of the United Nations.

   	1.	Nominal
   	2.	Ordinal
   	3.	Interval
   	4.	Ratio

1. Classify as nominal-level, ordinal-level, interval-level, or ratio-level data. Temperatures of automobile engines.

   	1.	Nominal
   	2.	Ordinal
   	3.	Interval
   	4.	Ratio

1. Classify each variable as discrete or continuous. Capacity of water in automobile engines.

   	1.	Discrete
   	2.	Continuous

1. Classify each variable as discrete or continuous. Temperatures of airplane interiors at a given airport.

   	1.	Discrete
   	2.	Continuous

1. Classify each variable as qualitative or quantitative. Classification of a speaker as Excellent, Good, Fair, Poor, Very Poor.

   	1.	Qualitative
   	2.	Quantitative

1. Classify each variable as qualitative or quantitative. Number of cups of coffee sold by McDonald's in a day.

   	1.	Qualitative
   	2.	Quantitative

1. Identify which sampling technique was used to select the given sample. On a large University campus, students attending classes in 3 buildings on a Tuesday during the hours of 10am and 5PM were selected to complete a survey.

   	1.	Random
   	2.	Systematic
   	3.	Stratified
   	4.	Cluster

1. Identify which sampling technique was used to select the given sample. On a large college campus, faculty were selected using random numbers to determine annual salaries.

   	1.	Random
   	2.	Systematic
   	3.	Stratified
   	4.	Cluster

Calculate an approximate value of the area of the place inside the curve. (So if you sketch it up (by using WolframAlpha or something else) then you will see that what is sought after is the calculated value of the area that is inside the curve

1 = (40+43)x^2y^2 + y^4 + (1+1)x^4

5. Suppose the index model for stocks 1 and 2 has the following results ?1 = 0.5% + 0.95?? + ?1, ?2 = −1.2% + 1.25?? + ?2, ?? = 25%. The standard deviations of ?1 and ?2 are 20% and 22% respectively. (

1) Calculate the standard deviation of stock 1 and stock 2.

(2) What is the covariance between each stock and the market index.

(3) What are the covariance and correlation coefficient between these two stocks?

(4) Break down the variance of each stock into its systematic and firm-specific component.

when the diaphragm relaxes, it moves_____, compressing the lungs and pushing waste gases out.
1. outward
2. inward
3. downward
4. upward

2. How does the vast majority of oxygen travel in the blood?
1. as oxygen associated with hemoglobin
2. as bicarbonate
3. as dissolved oxygen in the plasma
4. as carbaminohemoglobin

3. what occurs when air moves from the atmosphere of high pressure into the lower pressure of the lungs?
1. gas exchange
2. exhalation
3. expiration
4. inspiration

4. in your own words, describe the process of inspiration

5. In pneumonia, fluid collects in the alveoli. What conclusion can you draw regarding the efficiency of gas exchange in this state?

6. for a person who has or is currently hyperventilating, why does breathing into a paper bag restore normal blood chemistry more rapidly than continued breathing into the atmosphere?

7. identify the separate volumes that make up the total lung capacity.