(Requires Appendix Material)Show That the Two Alternative Formulae for the Slope

question 12

Essay

(Requires Appendix material)Show that the two alternative formulae for the slope given
in your textbook are identical. $$\frac { \frac { 1 } { n } \sum _ { i = 1 } ^ { n } X _ { i } Y _ { i } - \bar { X } \bar { Y } } { \frac { 1 } { n } \sum _ { i = 1 } ^ { n } X _ { i } ^ { 2 } - \bar { X } ^ { 2 } } = \frac { \sum _ { i = 1 } ^ { n } \left( X _ { i } - \bar { X } \right) \left( Y _ { i } - \bar { Y } \right) } { \sum _ { i = 1 } ^ { n } \left( X _ { i } - \bar { X } \right) ^ { 2 } }$$

Describe the concept and implications of bureaucracy in Victorian Britain.

Explain the significance of Benjamin Disraeli's background and political career.

Understand the events and impact of "Bloody Sunday" in Russian history.

Analyze the factors contributing to Russia's defeat in the Russo-Japanese War.

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Definitions:

Government

An organized system that establishes rules and regulations, governs, and provides services to its constituents.

Taxes

Essential fees levied by authorities on personal and corporate income, or added onto the costs of selected merchandise, services, and operations.

Tax Revenue

Income earned by the government from taxing individuals and businesses.

Tax

An obligatory fiscal charge or another form of assessment applied to a taxpayer by a government body to finance government operations and diverse public expenses.