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Let O be the set of odd numbers and O’ = {1, 5, 9, 13, 17, ...} be its subset. Define
the bijections, f and g as:
f : O "\\to" O’, f(d) = 2d - 1, "\\forall" d "\\in" O.
g : "\\Nu" "\\to" O, g(n) = 2n + 1, "\\forall" n "\\isin" "\\Nu" .
Using only the concept of function composition, can there be a bijective map from "\\Nu"
to O’? If so, compute it. If not, explain in details why not.
Programming Problem 4: Caffeine Absorption
(Note: Programming Problem 4 draws directly on Chapter 6, Programming Project 1, page 285.)
Nutritional Associates of New Jersey stresses to their patients the effects of caffeine on the body. After caffeine is absorbed into the body, 13% is eliminated from the body each hour. Assume a person drinks an 8-ounce cup of brewed coffee containing 130 mg of caffeine, and the caffeine is absorbed immediately into the body. See Figure 6.77 in the Visual Basic text, and write a program to compute the following values:
- The number of hours required until 65 mg (one-half the original amount) remain in the body
- The amount of caffeine in the body 24 hours after the person drinks the coffee
Suppose the person drinks a cup of coffee at 7:00 a.m. and then drinks a cup of coffee at the end of each hour until 7:00 a.m. the next day. How much caffeine will be in the body at the end of the 24 hours?
Consider the statement form (P↓Q)↓R.
Now, find a restricted statement form logically equivalent to it, in
a) Disjunctive normal form (DNF).
b) Conjunctive normal form (CNF).
5. In a particular industry, labor supply is L
S = 10+W and labor demand is L
D = 40−4W,
where L is the level of employment and W is the hourly wage.
(a) What are the equilibrium wage and employment if the labor market is competitive?
What is the unemployment rate? [7]
(b) Suppose the government sets a minimum hourly wage of M8.
(i) How many workers would lose their jobs? [4]
(ii) How many additional workers would want a job at the minimum wage? [2]
(iii) What is the unemployment rate? [2]
(c) Suppose the hourly wage is M10 and the price of each unit of capital is M25. The
price of output is constant at M50 per unit. The production function is
f(L, K) = L
1/2K1/2
so that the marginal product of labor is
MPL = (1/2)(K/L)
1/2
If the current capital stock is fixed at 1,600 units, how much labor should the firm
employ in the short run? How much profit will the firm earn?
Consider the statement form
(P \downarrow Q) \downarrow RNow, find a restricted statement form logically equivalent to it, in
a) Disjunctive normal form (DNF).
b) Conjunctive normal form (CNF).
The density of concentrated ammonia, which is 28.0% w/w NH3, is 0.899 g/mL. What volume of this reagent should be diluted to 1.0 × 103 mL to make a solution that is 0.036 M in NH3?
Consider an individual with M5000 of annual nonlabour income. She has total available
time (T) of 80 hours per week, for 52 × 80 = 54160 hours per year. Her current wage
rate is M15.00 per hour, and she currently chooses to work 2000 hours in a year.
(a) Draw a labour-leisure diagram, carefully illustrating her current labour supply
decision. [10]
(b) The wage rate rises to M18.00 per hour, and she decides to work 2040 hours.
At M18.00 per hour, if she worked 2200 hours per year, she would have been
indifferent to her original work decision (in part (a)). Show her new choice on
a diagram, and calculate the income and substitution effects associated with the
wage change. Calculate the compensated and uncompensated elasticities of labour
supply implied by her response to the wage increase.
Create a Python script which will compute the TOTAL Sales in a Grapes Store. The grapes is sold at 235.75 per kilo. 5% discount is given to customers that will buy 5 kilos and above. Compute also the CHANGE after the customer tendered their money. Format the display with two decimal digits.
Sample Output 1:
GRAPE STORE
No. of Kilos: 3
Total Price: 707.25
Discount: 0.00
Discounted Price: 707.25
CASH: 1000
Change: 292.75
I need the complete coding of this. Thank you
Create a Python script that will accept three integers and will check each input number. If the input number is EVEN it will display the square of cube of the number and if the number is ODD it will display the square of the number.
Sample Output
Number 1: 5
Number 2: 8
Number 3: 3 The square of 5 is 25
The cube of 8 is 512 The square of 3 is 9.
I need the complete coding of this. Thank you
A container holds 5grams of ccl4 vapour, calculate the volume of ccl4 present
#340153 on Dec 2023