Somebody please help me in solving the following..

1.Determine the transfer function of a system where its response t>0 is c(t)=1-e^-2t and it is subject to r(t)=1-e^-t when at rest.

2.What determines the transfer function in regenerating the feedback?

3.What is the name given to a set that contains all the assemblage of subsets?

4.How many subsets are there in an empty set? Explain.

5.Determine the difference equation and its conditions when the system is at rest that result to 6.3(0.5)ⁿu(n) as being the transient response.

6.When the system is at rest, the steady state response is given by 13.56cos(n/4 -28.7^o)u(n), determine the difference equation and the necessary conditions.

7.Given that (X²= 11.7), conduct a hypothesis test to determine whether the dice is unbiased. Determine also the frequency that is observed in the distribution of chi-square.

8.There are 5 green, 15 blue, 8 red and 12 orange balls in a kindergarten. Given that each color occurs with equal frequency, test for the null hypothesis. What is the value of chi square?

9.Taking a case study of monic polynomial, the Q^th degree derivative is given by p. Both p and q are positive integers. What will 2p⁴+ 3pq³₂= 3q³₂+ 2qp³ result in?

10. Find value of f(1) - f(0) in a quadratic polynomial where x =1 is 1 and 2 (first and second derivative)