Let T be an operator on a finite-dimensional complex vector space V, and suppose that dim Null T = 3, dimNullT2 =6. Prove that T does not have a square root; i.e. there does not exist any S ∈ L (V) such that S2 = T.

14. From the half-reactions below, calculate the solubility product of Mg(OH)₂.

          Mg²⁺ + 2e º Mg(s)                        E° = -2.360 V

          Mg(OH)₂(s) + 2e º Mg(s) + 2OH^- E° = -2.690 V

Find V(X) of the geometric distribution (Hint for the problem: Use the interchange derivative and summation, Find E(X^2), and then use the formula V(X) = E(X^2) - E(X)^2). Please show all work and all steps.

Cost can be classified in 5 categories-behavior, traceability, controllability, relevance and function. Briefly explain each category.

these videos will help you: https://www.youtube.com/watch?v=NqC0hgdcPuM&feature=youtu.be

https://www.youtube.com/watch?v=0y4cLVZQdOE&feature=youtu.be

A voltaic cell consists of an Al/Al3+ half-cell and a Cd/Cd2+ half-cell. Calculate Ecell when [Cd2+] = 0.00303 M and [Al3+] = 0.47 M. You should use the reduction potentials for Al3+ is -1.66 V and for Cd2+ is -0.40 V.

How large is the content of ethanol expressed in mass percent and in mole percent in hand spirit?

Hand spirit contains 70 vol% ethanol.

Subjects density in (g/cm^3)

Ethanol 0.78934  

Water 0.99823

70% v / v ethanol 0.88650

About 58% of students go to a college within 100 miles of their home. If you choose a random sample of 10 students, what is the probability that at least four students go to a college within 100 miles of their home?

1. Describe the personal qualities of teachers who increase students’ motivation to learn.
2. Identify the learning climate variables that increase students’ motivation to learn.
3. Explain how different Instructional variables increase students’ motivation to learn.

At LIU, they wish to test whether the mean working hours/week of students in LIU Beirut is
higher than the mean working hours/week of students in Bekaa campus. A sample was taken
from each campus and the details were reported in the table below.

Beirut students (1) Bekaa students (2)

Population standard deviation σ1 = 6 σ2 =5
Sample Mean x̄1 = 35 x̄2 = 30
Sample size n1 = 40 n2 = 40
a. Can you conclude, at α = 0.1(10%), that students in Beirut have a higher mean working
hours/week than that of the students in Bekaa? (Use the 5-step hypothesis testing)
b. Confirm your answer using the P-value method