Find the​ range, variance, and standard deviation for the given sample​ data, if possible. If the measures of variation can be obtained for these​ values, do the results make​ sense?

Biologists conducted experiments to determine whether a deficiency of carbon dioxide in the soil affects the phenotypes of peas. Listed below are the phenotype​ codes, where 1=​smooth-yellow, 2=​smooth-green, 3=wrinkled yellow, and 4=​wrinkled-green.

2 1 3 2 3 1 4 3 2 2 2 3 2 2 2 2 1 2 2 2

1. Can the range of the sample data be obtained for these​ values? Choose the correct answer below​ and, if​ necessary, fill in the answer box within your choice.

2. Can the standard deviation of the sample data be obtained for these​ values? Choose the correct answer below​ and, if​ necessary, fill in the answer box within your choice. The standard deviation of the sample data is

3.Can the variance of the sample data be obtained for these​ values? Choose the correct answer below​ and, if​ necessary, fill in the answer box within your choice. The variance of the sample data is

4. Do the results make​ sense?

A. The measures of variation do not make sense because the standard deviation cannot be greater than the variance.

B. The measures of variation make sense because the data is​ numeric, so the spread between the values is meaningful.

C. While the measures of variation can be​ found, they do not make sense because the data are​ nominal; they​ don't measure or count anything.

D. It makes sense that the measures of variation cannot be calculated because there is not a large enough sample size to calculate the measures of variation.

A negative Rational could either be represented by a negative value stored in __numerator or a negative value stored in __denominator. If negative values are stored in both, the reduce() method that is provided for you will make them both positive.

If a Rational happens to reduce to a whole number, it will still be saved in Rational form. In other words, if the result of an add() call creates a fraction 6/2, it should reduce to 3/1 but will remain 3/1 rather than turning into 3.

Before moving into the methods that you will create, here is a quick overview of methods that are provided for you (don't change the functionality of these methods):

__init__(self, iNum, iDen): Initializes a new Rational object with value iNum/iDen stored in hidden __numerator and __denominator variables. These are the only instance variables that you should need to define as a part of your Rational class. This method also calls the reduce() method, described next.

reduce(self): Reduces a Rational object to its lowest terms, e.g., 2/4 is reduced to 1/2. If both the numerator and denominator are negative, this method makes them both positive. After that, it repeatedly calls the gcf() method (defined next) to find common factors between the numerator and denominator, which are used to reduce the Rational.

gcf(self): Determines the greatest common factor between the numerator and denominator. When it finds a number divisible by both, it breaks the search loop and returns that number. The smallest factor that can be returned is 1.

__str__(self): Returns a string representation of the Rational object, e.g., "1/8". This is a "dunder" method that will be useful for you in debugging. You can call print(r1) on Rational object r1 to use this method.

__eq__(self, r2): Determines if two Rationals are exactly equal to each other (same numerator and same denominator, no consideration of reducing the numbers). This method is necessary for the grading code, but you can also use it to test your methods by checking r1==r2 for Rational objects r1 and r2.

Next, the methods that you will write. In the method descriptions and usage cases below, you can assume that r1 and r2 are Rational objects with __numerator and __denominator instance variables initialized with values.

Accessors and mutators: You should create accessors and mutators (or "getters" and "setters") for both the __numerator and __denominator instance variables. There are thus four required methods here: getNumerator(self), getDenominator(self), setNumerator(self, n), and setDenominator(self, d). Additionally, the mutators should call the reduce() method to put the updated Rational in lowest terms, e.g., calling setDenominator(4) on the Rational 2/7 should update the Rational to 2/4 and then reduce it to 1/2. Only the accessors should return a value.Usage: n = r1.getNumerator(). If r1 is 3/4, returns 3.Usage: d = r1.getDenominator(). If r1 is 3/4, returns 4. Usage: r1.setNumerator(7) If r1 is 3/14, updates r1 to 7/14 and then reduces to ½. Usage: r1.setDenominator(-4). If r1 is 3/4, updates r1 to 3/-4

isValid(self): Rational numbers cannot have a 0 in the denominator. This method should return True if the Rational is valid, and should return False if the Rational has a 0 denominator. Usage: val = r1.isValid(). If r1 is 7/4, returns True. If r1 is -7/0, returns False

add(self, num2): Given input Rational num2, you should add num2 to the current Rational, updating the self.__numerator and self.__denominator instance variables to the sum of self and num2. You should also call the reduce() method to put the Rational in lowest terms. Nothing is returned by this method. Usage: r1.add(r2). If r1 is 1/4 and r2 is 1/8, updates r1 to ⅜. sub(self, num2): Same as the add() method, but subtracting num2 from self. Usage: r1.sub(r2). If r1 is 1/4 and r2 is 1/8, updates r1 to ⅛. mult(self, num2): Same as the add() method, but multiplying num2 by self. Usage: r1.mult(r2). If r1 is 1/4 and r2 is 1/8, updates r1 to 1/32

div(self, num2): Same as the add() method, but dividing num2 out of self. Usage: r1.div(r2). If r1 is 1/4 and r2 is 1/8, updates r1 to 2/1.

Ross and Rachel produce clay pots and garden gnomes. The first table shows Ross’s production possibilities and the second table shows Rachel’s production possibilities. Each week, Ross produces 4 clay pots and 32 garden gnomes and Rachel produces 8 clay pots and 4 garden gnomes.

Ross’s Production Possibilities

Rachel’s Production Possibilities

INTRODUCTION TO MICROECONOMICS ECON 101 ONLINE

6. Using FACT #1, what is Ross’s opportunity cost of producing 1 clay pot? What is Ross’sopportunity cost of producing 1 garden gnome?

A) 8 garden gnomes; 18 clay pots. B) 18 garden gnomes; 8 clay pots. C) 2 garden gnomes; 12 clay pots. D) 12 garden gnomes; 2 clay pots.

7. Using FACT #1, what is Rachel’s opportunity cost of producing 1 clay pot? What is Rachel’sopportunity cost of producing 1 garden gnome?

A) 8 garden gnomes; 18 clay pots. B) 18 garden gnomes; 8 clay pots. C) 2 garden gnomes; 12 clay pots. D) 12 garden gnomes; 2 clay pots.

8. Using FACT #1, who has the comparative advantage in producing garden gnomes? Who has the comparative advantage in producing clay pots?

A) Ross; Rachel. B) Ross; Ross.
C) Rachel; Ross. D) Rachel; Rachel.

9. Using FACT #1, what are the overall net gains from specialization and trade?

A) 16 clay pots and 40 garden gnomes. B) 4 clay pots and 4 garden gnomes. C) 8 clay pots and 4 garden gnomes. D) 8 clay pots and 20 garden gnomes.

In year 1 and year 2, there are two products produced in a given economy: apples and oranges. Suppose that there are no intermediate goods. In year 1, 10 apples are produced and sold at $4 each, and in year 2, 8 apples are produced and sold at $5 each. In year 1, 2 oranges are sold for $12 each, and in year 2, 5 oranges are sold for $6 each.

What is the CPI for year 2 using year 1 as a base year?

LP Output Question

Consider the following LP formulation of the Dog Food example. The objective coefficients represent unit costs ($ per 16 oz) for the gruels. The RHS’s represent the nutrition requirements (measured in oz).

  MIN     4 G1 + 6 G2 + 3 G3 + 2 G4 + 5 G5

  SUBJECT TO

  2)   3 G1 + 5 G2 + 2 G3 + 3 G4 + 4 G5 >=   3   (Protein Req.)

  3)   7 G1 + 4 G2 + 2 G3 + 8 G4 + 2 G5 >=   5   (Carbohydrate Req.)

  4)   5 G1 + 6 G2 + 6 G3 + 2 G4 + 4 G5 >=   4   (Fat Req.)

  5)   G1 + G2 + G3 + G4 + G5 =    1            (Total %)

  END

Below is the LINDO output of the problem.

        OBJECTIVE FUNCTION VALUE

        1)         (1)

  VARIABLE        VALUE          REDUCED COST

        G1         0.000000          0.500000

        G2         0.166667          0.000000

        G3         0.333333          0.000000

        G4         0.500000          0.000000

        G5          (2)             1.000000

       ROW  SLACK OR SURPLUS     DUAL PRICES

        2)         0.000000         -1.000000

        3)           (3)             (4)

        4)         0.000000         -0.500000

        5)         0.000000          2.000000

RANGES IN WHICH THE BASIS IS UNCHANGED:

                           OBJ COEFFICIENT RANGES

VARIABLE         CURRENT        ALLOWABLE        ALLOWABLE

                   COEF          INCREASE         DECREASE

       G1       4.000000           (5)            (6)

       G2       6.000000         2.000000         3.000000

       G3       3.000000         1.000000         3.000000

       G4       2.000000         2.000000         INFINITY

       G5       5.000000         INFINITY         1.000000

                           RIGHTHAND SIDE RANGES

      ROW         CURRENT        ALLOWABLE        ALLOWABLE

                    RHS          INCREASE         DECREASE

        2       3.000000         1.000000         0.500000

        3       5.000000         0.333333           (7)

        4       4.000000         0.250000         2.000000

        5       1.000000         0.142857         0.038462

Consider yourself as the dog food producer. Answer the following questions based on the partial LP output:

Complete the LP output by filling in the missing numbers. Provide either calculations or explanations for your answers:

(1)

(2)

(3)

(4)

(5)

(6)

(7)

The dog food buyer asks for a 20% discount (of the minimum dog food cost in LINDO solution, i.e. (1) ) in exchange for a reduction of protein by 0.6oz. Do you want to take the offer? Why?

​​​​​​​

What would the attractive price for you to use Gruel 5? Explain.

If the unit price (cost) of gruel 3, and gruel 5 increase by $0.5, respectively, and that of gruel 4 decreases by $0.5, do you want to change the current dog food mix? With the price changes, what will be the minimum cost for the dog food? Show your calculations.

A new gruel supplier wants to sell you its new gruel mix which contains, in a 16 oz of gruel, 3 oz of protein, 4 oz of carbohydrate, and 5 oz of fat. What is the maximum price you are willing to pay for the new gruel? Show your calculations.

If a dog food buyer requests to increase the protein level by 0.5 oz in exchange for a reduction of the fat level. What would you recommend the minimum reduction to keep the same dog food price? Explain and show your calculation.

4. Find the Discounted Payback period for the following projects.

The discount rate is 7%.

Initial Outlay 17,827

Year 1 5917

Year 2 5484

Year 3 5968

Year 4 8405

Verifica si las ecuaciones diferenciales son exactas, de no serlo calcula el factor integrante. En ambos casos resuélvelas:

(5t^4 y-15t^2-y)dt+(t^5+3y^2-t)dy=0, y(1)=-2

cos⁡〖(x)〗 dx+(1+2/y) sin⁡x dy=0

• Write a program for Bob’s Bus Company that allows a user check on ticket prices following the guidelines below:

                     Zones Crossed
             ---------------------------
Passengers     0      1      2      3
----------------------------------------
1             7.50  10.00  12.00  12.75
2            14.00  18.50  22.00  23.00
3            20.00  21.00  32.00  33.00
4            25.00  27.50  36.00  37.00

• The user enters ticket data (number of passengers and number of zones crossed) continuously until a sentinel value, -1 for passengers, is entered. When -1 is entered for number of passengers, there is no prompt for number of zones.
• After each set of ticket data is entered, display the price or the ticket(s).

Sample Run #1 (bold, underlined text is what the user types):

Passengers? 2

Zones? 3

$23
Passengers? 4

Zones? 0

$25
Passengers? -1

Done

c++

RACKET

a) Write a recursive function (gen-list start end). This function will generate a list of consecutive integers, from start to end. If start > end then an empty list is generated. For example: (gen-list 1 5) ---> (1 2 3 4 5)

b) write a recursive function pair-sum? that takes an integer sequence as generated by the gen-list function in exercise 4 above. This function tests whether any two adjacent values in the given list sum to the given val. For example,

   (pair-sum? '(1 2 3) 3) ---> #t since 1+2=3. Similarly,

   (pair-sum? (gen-list 1 100) 1000) ---> #f since no two adjacent integers in the range 1 to 100 can sum to 1000.

You must use recursion, and not iteration. Please include explanation thanks.

[ RACKET]

a) Write a recursive function (gen-list start end). This function will generate a list of consecutive integers, from start to end. If start > end then an empty list is generated.

For example: (gen-list 1 5) ---> (1 2 3 4 5)

b) write a recursive function pair-sum? that takes an integer sequence as generated by the gen-list function in exercise 4 above. This function tests whether any two adjacent values in the given list sum to the given val.

For example,

   (pair-sum? '(1 2 3) 3) ---> #t since 1+2=3. Similarly,

   (pair-sum? (gen-list 1 100) 1000) ---> #f since no two adjacent integers in the range 1 to 100 can sum to 1000.

You must use recursion, and not iteration. Please include explanation thanks.