Problem 6. The set (Z19 − {0}, ·19) is a group with the indicated operation; see the attached table. a.) Show that H = {1, 7, 8, 11, 12, 18} is a subgroup. b.) List all the right cosets of H. c.) Show that if Hy = Hx then xy−1 ∈ H. [Make sure to give a reason for each step.] d.) Show that φ : H → Hx defined by φ(h) = hx is one-to-one and onto. [Use the fact that H is a group and the property of inverses to do this. Part (c) may also come in handy.] e.) Show that the operation ⊗ defined by (Ha) ⊗ (Hb) ≡ Hab is well-defined.
Problem 6. The set (Z19 − {0}, ·19) is a group with the indicated operation; see...
Review the 6 karyotypes in Figure 10 and determine the chromosomal disorder. Record the chromosomal disorder in Data Table 3. Describe the genotype of each chromosomal disorder and record in Data Table 3. Describe the phenotype of each chromosomal disorder and record in Data Table 3. Data Table 3: Karyotype to Genotype to Phenotype # Chromosomal Disorder Genotype Phenotype 1 2 3 4 5 6 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7...
Cork price: 16 10 15 10 17 11 14 13 11 14 11 16 18 16 10 17 14 14 16 7 10 12 19 15 16 14 9 12 21 13 10 16 12 16 13 17 17 13 14 18 11 12 15 16 13 18 16 17 12 12 14 9 11 14 19 13 11 17 11 13 15 14 18 18 18 12 10 11 13 14 11 14 18 13 13 19 17 14...
Suppose there are 100 identical firms in the market and the luggage industry is perfectly competitive. What does the market supply curve look like? 20 19 18 17 16 15 14 13 12 11 A 10 9 8 7 6 5 4 20 19 18 17 16 15 14 13 12 11 A 10 8 7 6 2 1 0 0 0 1 2 3 4 5 6 7 8 9 10 11 12 0 1 2 3 4 5...
Suppose there are 100 identical firms in the market and the luggage industry is perfectly competitive. What does the market supply curve look like? 20 19 18 17 16 15 14 13 12 11 A 10 20 19 18 17 16 15 14 13 12 11 A 10 8 7 5 2 1 0 1 0 0 1 2 3 4 5 6 7 8 9 10 11 12 4 5 6 7 8 9 10 11 12 0 1...
Given the following array of integers (of capacity 20) with 12 items: 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 8 4 10 15 5 7 11 3 9 13 1 6 Index of last element = 11 Does this array represent a min heap? If not, convert it to a min heap (i.e., “heapify” it). Please show all steps.
Are all disciplines in the University equally boring or there are some more boring than others? To answer that question, a study performed at Columbia University counted the number of times per 5-minute interval when professors from three different departments said “uh” or “ah” during lectures to fill gaps between words. These counts were used as a proxy (approximation) for the measure of class boredom. The data from observing one hundred of 5-minute intervals from each of three departments’ professors were recorded in...
Problem 3 Professor Bell suspected that there might be a relationship between shyness and loneliness. For 40 participants he measured shyness using the Ottawa Shyness Questionnaire and measured loneliness using the Carleton Loneliness scale. For both measures, a higher value indicates more shyness or more loneliness. The data are on the right. Did he find support for his hypothesis? Person Shyness Loneliness 1 12 6 2 6 8 3 4 8 4 13 7 5 7 5 6 13 7...
Problem 3 Professor Bell suspected that there might be a relationship between shyness and loneliness. For 40 participants he measured shyness using the Ottawa Shyness Questionnaire and measured loneliness using the Carleton Loneliness scale. For both measures, a higher value indicates more shyness or more loneliness. The data are on the right. Did he find support for his hypothesis? Person Shyness Loneliness 1 12 6 2 6 8 3 4 8 4 13 7 5 7 5 6 13 7...
Calculate the mean, median, and standard deviation for the total number of candies (per bag). Construct a histogram of the total number of candies (per bag). Use the z-score method to identify any potential outliers and outliers. Assume the total number of candies is normally distributed, calculate the probability that a randomly sampled bag has at least 55 candies in a bag. If a random sample of 50 bags is selected, find the probability that the mean number of candies...
The following frequency table represents the ages of children living in one apartment complex for 56 children. What is the 3rd quartile of the data? 1 1 2 2 3 3 3 3 4 4 5 5 5 5 6 6 6 8 8 8 9 9 9 9 9 9 10 10 11 11 11 11 11 11 12 12 12 13 13 13 14 15 15 16 16 16 17 17 18 18 18 18 18 18 18...