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2.1. Solve 2xy + 6x + (x^2 - 4)y'=0


Problem: The program will determine the gross wages of each employee type, salaried and hourly, and output the total gross wages to be paid for each employee type.


Prompt the user to enter the number of employee wages to be calculated.

1.The program will end when the data for all the employees has been entered.


2. For each employee, indicate if the employee is salaried or paid hourly.


3. Define and implement functions for the following:

a) If the employee is salaried, enter the annual salary. The gross for that employee will be determined by dividing the annual salary by 24. Add the result to the total salaried wage. b) If the employee is paid hourly, enter hours worked (40 ≥ hours ≥ 0) and rate per hour. The gross for that employee is determined by multiplying hours worked by rate per hour. Add the result to the total hourly wages.


4. After performing the calculations for each employee, display the total wages for salaried employees, total wages for hourly employees, and total gross wages.


Abebe, who is Maryland International College’s MBA student, wanted to pursue his Master thesis with the title ‘’The effect of service quality on customer satisfaction: Case of Abyssinia Bank”. He wanted to distribute questionnaires and analyze it using statistical methods in a specific branch (Bole Branch).

Assume that Abyssinia bank at Bole Branch has 5,000 customers where there are two types of customers out of the 5,000 (i.e. Current and Saving account holders as 2,000 current account customers and 3,000 as saving account holders).

Questions:

-What is the type of the research based on Outcome, purpose, environment, time and data?

-What is the accurate sample size using the formula you learned in class?

- How many questionnaires are going to be distributed for each type of customers (i.e. current account and saving account holders)?


A drug company is testing a drug intended to increase heart rate. A sample of 100 yielded a mean increase of 1.4 beats per minute, with a population standard deviation known to be 3.6. Since the company wants to avoid marketing an ineffective drug, it proposes a 0.001 significance level.


Let x(s) be a curve with arc length parametrization, and satisfies "||x(s)||\\leq ||x(s_0)||\\leq1" for all s sufficiently close to x0. Prove "\\kappa" (s0) > 1. (Hint: Consider f(s) = ||x(s)|| 2 . Then f(s) has a local maximum at s0. Calculate f''(s0))


Let f be a smooth function. Calculate the curvature and the torsion of the curve that is the intersection of x = y and z = f(x).


Calculate T ; N; B; "\\kappa" ; "\\tau" of the curve x(t) = (t; t 2 ; t 4) at the point (1; 1; 1).


3.10 If U, V are ideals of R, let U + V = {u + v | u ∈ U, v ∈ V }.

Prove that U + V is also an ideal.


3.9 Show that the commutative ring D is an integral domain if

and only if for a, b, c ∈ D with a #= 0 the relation ab = ac implies that

b = c.


3.8 D is an integral domain and D is of finite characteristic,

prove that the characteristic of D is a prime number.


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