Discuss in detail the constitutional disagreement between North and South going into the Civil War. Note, both sides argued that the union was either a compact of sovereign states or an indivisible nation. Who do your think had the better argument and why?

In the 1860s and 1870s while the Civil War and Reconstruction were still going on Americans were trying to settle the west. Discuss the efforts made to settle out on the Great Plains, and the rise of key economic developments such as the building of the Transcontinental Railroad and the rise of the mining industry and cattle kingdoms. How successful were these efforts in settling the west and how long did it take to do so?

In the years after the Civil War southerners tried to put their lives back together. An example of this was the New South movement. What was this idea of the “New South”? Who were its leaders and what did it hope to accomplish? How successful was the New South movement? 4. What was American culture like in the period during and after the Civil War? How did life in the East differ from that of those who lived out in the West? Why did the West hold such fascination for Easterners and in what ways did Americans demonstrate their curiosity about the areas of the country being settled in places like western Kansas, west Texas, Montana, etc.

The ANOVA infrequently alluded to as the F test (named after the analyst Sir Roland Fisher, the creator of this test) is an arrangement of systems for testing the hugeness of contrasts among in excess of two autonomous means. This strategy decides the degree to which there are noteworthy contrasts between the methods for at least three examples with a solitary level of essentialness. Since this technique and others like it center around fluctuations, they are alluded to as the examination of difference or ANOVA One Way Analysis of Variance The progression in ANOVA can be outlined by a case Case 5.1.1 The quantity of wrongdoings submitted in 4 months in different parts of a town are list underneath: Month Craftsman quarters Ghettos CDB GRA January February Walk April 20 16 32 16 52 44 56 36 36 40 36 40 16 20 32 20 At 0.05 level of certainty, are wrongdoing frequencies identified with urban morphology or month of the year? To begin with set up an invalid theory of equity of the methods Let Ho be: "There is no noteworthy distinction between the violations frequencies and urban morphology or month of the year. Next, locate the aggregate of the four zones as recorded beneath then their methods Add up to =Artesan SlumsCBDGRA 8418815288 Mean Next, figure the Grand mean Next, figure the entirety of squares for every populace. Note that in ANOVA the quantity of tests don't need to be same Table 4.1.1: Means and totals of squares of wrongdoings submitted In ANOVA, we decide contrasts between implies by figuring their fluctuation. Three sorts of changeability are evaluated: The variety inside each example result The variety between the example comes about The aggregate variety of the examples, paying little respect to the example gathering to which they have a place (Anyadike, 2009) Next, ascertain the totals of the whole of squares for every section (i.e Variable): SSW = ∑∑(Xij - X)2 = 172+236+16+144 =568 Figure whole of square between = ? N (X — X)2 =4(21-3 2)2+4(473 2)2+4 (3832)2 + 4(2232)2 = 484 +900+144+400 =1928 Figure the inside gathering whole of square. MSW = SSW n-rn Where n=no of perceptions M=no of gatherings Thus, the mean s square between will be MSb =SSb M-l In this way MSW =SSb=568=568 n-m 16-4 12 = 47.33 The proportion between the difference assess is known as the Snedecor's fluctuation proportion test or Snedecor's F Presently set up an ANOVA table: At long last, test for essentialness: The degrees of flexibility, V are: V-numerator = M-1=4-1=3 V-denominator = n-m= 16—4=12 From the Table of the F-Distribution, basic estimation of F at 0.05 3 and 12 =3.49 Computed esteem is 13.18 Since the computed F of 13.58 is more noteworthy (>) 3.49, Ho is rejected. Consequently, "There is a noteworthy contrast between wrongdoing frequencies with respect to urban morphology or month of the year. THE STUDENT 'T TEST The most intense test for the examination of test implies is the understudy 't' test. It is a parametric test and is utilized to decide if the contrasts between two example implies are adequately incredible as to legitimize a conclusion that the methods for their populaces likewise vary essentially. It is likewise utilized for little examples The understudy 't' is communicated as: T = x1-x1 vS12/N1 + S22/N2 Where X1 and X2 are the methods for the two arrangements of information; S1 and S2 their standard deviations; and N1 and N2 the quantity of perceptions. The level of opportunity, V is communicated as takes after: V = N+N,- 2 Level of Freedom There is regularly perplexity among understudies about the idea of "level of flexibility". Fundamentally, if the aggregate of an arrangement of components and the total of everything except one is of its components are both known, at that point the estimation of the last component should likewise be known, i.e. it isn't, not at all like the others, allowed to differ (Ayandike, 2009). For instance, if the entirety of 8 components is 30 and the estimations of 7 of the components differently signify 28, at that point the esteem ofthe last (i.e. the 8") component must be (30-28) = 2, i.e. on the off chance that isn't allowed to receive some other esteem. The level of flexibility for this situation is along these lines (8-1) = 7, i.e. in the arrangement of 8 component, 7 of them are allowed to go up against any qualities to entirety up to 28, leaving esteem untouched Components OF MATRIX ALGEBRA Presentation The lattice is a rectangular cluster of number organized in lines n and segments, m i.e Every one of the numbers is called a components. The situation of every component is controlled by its situation in the line and in addition in the The extent of the grid is given by the quantity of lines (n) and number of segment (m) for instance. A network which has a similar number of lines and segments is known as a square lattice. In the case over, an and c are square grids. A lattice with a solitary line is known as a line vector, while a framework of a solitary segment is known as a segment vector. Case of a line vector is {3 5 7 8} case of section vector is Grid can be included, subtracted, duplicated and modified however can't be separated. Be that as it may, they must be isolated by a scalar (i.e a conventional number). Expansion of Matrix Grids to be included must be of an indistinguishable size from each other. That is they should have a similar number of sections and line s. This is on the grounds that every component of one lattice must be added to a similar component of the other network e.g. assuming we are including two framework [A] ± [B] [A] + [BI =[C] i.e you include component by component N.B:The number of segments and lines must be the same before it can be included Framework Subtraction An indistinguishable administer from expansion is connected e.g to subtract [BI from [A] [A] [B] Lattice Multiplication There are two part of lattice augmentation specifically: a.Multiplication of lattice by a scaler b.Multiplication of lattice by two grids By Scaler Assuming we are duplicating the grid beneath by 4 Augmentation by Two Matrices At the point when two networks are to be duplicated, the quantity of sections in the main framework must be equivalent the quantity of columns in the second grid e.g. 2x3 grid can be duplicated by 3x2 lattice. Be that as it may, a 2x3 lattice can't be duplicated by another 2x3 grid in light of the fact that the quantity of lines there isn't equivalent to the quantity of segments in the second e.g. The outcome will have the same number of lines as the first and as may segments as the second. Duplication of a grid by vector, case A personality or solidarity framework 1, is where the askew comprise of l's and whatever is left of the components are zero e.g.: Framework Inversion In framework, variable based math capacity of division is changed to that of reversal. The reverse of the framework is it's corresponding i.e. Just square frameworks have inverses. A network that can't be altered is known as a particular grid. A few strategies exists for finding the backwards of a lattice. They incorporates 1.The traditional strategy This is to set the framework adjacent to a personality network, and to play out all activities at the same time in the two grids, for instance, on the off chance that you are to rearrange this lattice [A], you ahead of all comers it alongside a character network You have Stage 1 Subtract push 2 from 3, duplicate line 1 Column 2(3xrow 1) Stage 3 2.By Determinants This is the more present day one. A determinant is a solitary number removed from a square grid by arrangement of activities. It is spoken to by either det An or/A/ The way toward getting a determinant from a grid is called assessing the determinant. Utilizing determinant, the converse of grid [A] moves toward becoming>

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