Normal subgroup

Question 1 (i) Mean: ‘’The sum of a series of measurements (or numbers) divided by the number of those measurements.’’ (Open University,2015: S104 Exploring Science Glossary, Milton Keynes, The Open University). Scientific Notation: ‘’ A notation that represents any number by expressing it as a number that is equal to or greater than 1 but less than 10, multiplied by a simple power of ten where the index may be positive or negative. Thus, 1.30 × 103 is in scientific notation (because 1.30 is…

Lemma: If p > 3 is prime, then either p = 1 (mod 6) or p = 5 (mod 6). Proof: The residue classes modulo 6 partition Z, so any z in Z satisfies a congruence z = n (mod 6) where n is in {0,1,...,5}. z is divisible by 6 if n = 0, 2 if n = 2, 3 if n = 3, and 2 if n = 4. These cases cover the primes z = 2 and z = 3; if z > 3 is prime, it follows that n = 1 or n = 5, i.e., z = 1 (mod 6) or z = 5 (mod 6). Now suppose there are only finitely many primes congruent to 5 modulo 6, say p_1, ...,…

Chapters 3 Test MULTIPLE CHOICE Select the answer that best completes the statement or that correctly answers the question. 1. Which of the following is the correct scientific notation for the value 5,545.98? a. 55.4598 x 102 b. 55.4598 x 10-2 c. 5.54598 x 103 d. 5.54598 x 105 2. Which of the following is the correct scientific notation for the value 0.0001023? a. 102.3 x 106 b. 1.023 x 10-3 c. 102.3 x 10-6 d. 1.023 x 10-4 3. The atomic mass of Hydrogen is 1.00797 amu. How many significant…

Reflection 30: Unexcused Absences ANOVA Methods An analysis of variance (ANOVA) test is used to evaluate statistically significant differences between two or more samples (Creighton, 2007). For this assignment, I tested the hypothesis stating there is a difference between the number of unexcused absences for ninth through twelfth grade students at North Panola High School (NPHS). To conduct my ANOVA test, I first obtained monthly absence data for ninth, tenth, eleventh, and twelfth grade…

impressive totals. This leads to the company seeming as if it is exceeding expectations and look good to management and investors. Also, employees could have produced units at a slower rate at the beginning of the year in order to produce units at a normal production rate after the budget is produced. This would enable employees to produce more units than budgeted for and still have idle time. This behavior is not ethical because it does not align with the IMA Statement of Ethical Professional…

Living In Dubuque Iowa My cousin is moving to Dubuque this weekend from Chicago but she doesn’t believe that it is the right thing for her to do. But little do she know their are a lot of good things about this town. Such as all the good history that this town holds. Also there is a lot of fun things to do here as far as going snowboarding at sundown in the winter time. Or even going out enjoying the national parks like going to the Minds Of Spain or the Aubroritom. Dubuque has a lot of great…

1. (a) I would observe the rent of all tenants in 4 areas and then compare the results. (b) I would use the mean value to determine the average amount of rent in all areas. (c) The mean values are: Area A: μ=1005.5; Area B: μ=887.0; Area C: μ=881.0; Area D: μ=945.5. 2. (a) I would use the column chart because we are comparing continuous data. (b) Average Monthly Rent (c) It appears that the monthly rent in Area A is higher than the…

My initial thoughts and feelings walking into the courthouse were one of nervousness, and excitement. I was nervous to be in the presence of criminals, and to go through security. Also, just being around people with such high authority is intimidating. I was really excited though, I have always been interested in the workings of a trial. I was anxious to hear what the case I was sitting in on was all about, and do come up with theories and verdicts of my own. The spatial arrangement in the…

Decription The product that was chosen to be brought back to the future would be the Nike PreCool Vest. The Nike PreCool Vest is simply a vest that allows athletes to cool their working muscles down so that they can improve their performance to a better degree. This vest is used to cool down core body temperature so that athletes can compete at a better rate; with the core cooling, athletes can often last 21% longer than without it (NikeNews, 2008). The vest in general clings to the wearer to…

Homeostasis is defined as the means by which the internal atmosphere of the human body remains balanced regardless of the numerous changes within the environment (Mastrangelo, 2013). One of the most remarkable attributes of homeostatic control is body temperature regulation. Thermoregulation is controlled by the autonomic nervous system (ANS), which is a vastly complex, multifaceted neural system that sustains the internal homeostasis of the human body (Chawla, 2013). Within the ANS, is the…