Problem 6.
1. If X N(9; 4), nd Pr(jX ? 2j < 4).
2. If X N(0; 1), nd Pr(jX + 3j > 5).
3. If X N(?2; 9), nd the number c such that Pr(jX + 2j < c) = 0:5.

Solve this differential equation

y''+(-4-2-2)y'+(4+4+4+4)y=x

y(0)=3-2

y'(0)=2-3

Answer it as y(x)=... and motivate all the steps of the calculation

1. a. Evaluate the following limit: lim ?→4 ( 2? 3−128 √?−2 ) b. Find the number ? ???ℎ ?ℎ?? lim ?→−2 ( 3? 2+??+?+3 ? 2+?−2 ) exists, then find the limit

given the sequences 
x1 = [2, 6, -4, 1]
x2 = [8, 0, 2, 0, -9, 0, 1, 0]
x3 = [2, 0, -8, -8, 2]
x4 = [0, 1, 5i, 0, 6i, 0]
x5 = [9, 3, 7]
plot the
1. DFT magnitude of the computed sequences in MATLAB 
2. phase responses in degrees and radians against frequency and number of samples
3. comment on the plots

2) An ideal gas cycle operates via the following 4 stages:
1→2 The gas is compressed adiabatically
2→3 The gas is ignited and heated at constant pressure
3→4 The gas expands adiabatically
4→1 Heat is removed from the gas at constant pressure
a) Draw the cycle on a pressure-volume diagram, labelling the states
1, 2, 3, and 4 and showing where heat enters the cycle and where
heat is removed from the cycle. Identify the highest pressure phigh
and lowest pressure plow in the cycle on the diagram.
[4 marks]
b) Calculate Qin, Qout, and Wnet of the cycle per unit mole of a
monoatomic working-fluid gas if T1 = 300 K, T2 = 600 K, T3 = 800 K,
and T4 = 400 K.
[6 marks]
c) Derive the following expression for the efficiency of the cycle in
terms of pressure ratio rp = phigh/plow.
?௧௛ = 1 − ?௣
ቀ
ଵିఊ
ఊ
ቁ
[10 marks]
d) Briefly explain three ways by which the efficiency of the cycle can
be improved.
[3 marks]
e) For fixed values of T1 and T3, prove that the net amount of work
produced is maximum at the pressure ratio given below:
?௣ = ቀ
்య
்భ
ቁ
ം
మ(ംషభ)
[7 marks]

Find the modulus of:

(a) (3 – j4) (-5 + j12)

(b) (2+?)/(4?+(1+?)^2)

Express (6 – ?8)^−3 in the standard form ? + ??. Find its conjugate.

If ? + ?? = (?+?)/ (?−?) ,where a, b and c are real, prove that ?^2 + ?^2 = 1 and ?/?= (2?)/ (?^2−1)

Please show all your steps so I can understand

Thank you

1. (a) Evaluate the integral: ∫0 to 2 16 /x^2+4 dx
Your answer should be in the form kπkπ, where k is an integer. What is the value of k?
Hint: d/dx arctan(x)=1/x^2+1
k=
(b) What is the upper bound for your error of your estimate if you use the first 11 terms? (Use the alternating series estimation.) =

2.

The function f(x)=8xln(1+x) is represented as a power series
f(x)=∞∑n=0 cn x^n.
Find the specified coefficients in the power series.
c2=   
c3=   
c4=   
c5=   
c6=   
Find the radius of convergence R of the series.
R=

For the following data set [ 1, 4, 3, 6, 2, 7, 18, 3, 7, 2, 4, 3, 5, 3, 7] please compute the following

1. measures of central tendency (3 points)

2. standard deviation ( 5 points)

3. is 18 an outlier? (5 points)

4. describe the shape of the distribution (2 points)

• Introduction (1 to 2 paragraphs maximum)
• Purpose Statement (2 to 3 sentences)
• Analysis (3.5 to 4 pages maximum)
  • What purpose does an ethical climate serve, and why is it important to an organization?
  • How do biases impact our moral decision making? (Pick 2) (Please note: The biases that are required for this paper, are located in the Values, Ethics, and Character Chapter).
  • Provide an example of an ethical issue. Why is this issue unethical? What behaviors are occurring that are unethical?
  • How could the ethical issue have been avoided? In other words, what are some of the leadership actions that should have been implemented to establish an ethical climate? (Note: think about the 5 components that help leaders “create and sustain an ethical climate,” that we examined in the week 2 discussion post. Just pick 1, from the list of 5 on p. 198).
  • Conclusion (1 to 2 paragraphs maximum)

• Reference pag

Required information

Foundational [LO 2-1, LO 2-2, LO 2-3, LO 2-4, LO 2-6, LO 2-7]

Foundational 2-1