Find the Center, Foci, and Asymptotes of the Hyperbola $$\frac { y ^ { 2 } } { 256 } - \frac { x ^ { 2 } } { 144 } = 1$$

question 3

Multiple Choice

Find the center, foci, and asymptotes of the hyperbola.
- $$\frac { y ^ { 2 } } { 256 } - \frac { x ^ { 2 } } { 144 } = 1$$

• A) C: \(( 0,0 ) ; F : ( 0 , - 20 ) , ( 0,20 ) ; A : y = \frac { 4 } { 3 } x , y = - \frac { 4 } { 3 } x\)
• B) C: \(( 0,0 ) ; \mathrm { F } : ( - 12,0 ) , ( 12,0 ) ; \mathrm { A } : \mathrm { y } = \frac { 3 } { 4 } \mathrm { x } , \mathrm { y } = - \frac { 3 } { 4 } \mathrm { x }\)
• C) C: \(( 0,0 ) ; F : ( - 20,0 ) , ( 20,0 ) ; A : y = \frac { 3 } { 4 } x , y = - \frac { 3 } { 4 } x\)
• D) C: \(( 0,0 ) ; F : ( 0 , - 12 ) , ( 0,12 ) ; A : y = \frac { 4 } { 3 } x , y = - \frac { 4 } { 3 } x\)

Determine appropriate statistical tests for analyzing the relationship between two qualitative variables.

Comprehend the concept of expected frequency in the context of contingency tables.

Apply chi-square tests to real-world research scenarios to assess independence between variables.

Interpret results from chi-square tests to draw meaningful conclusions.

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Definitions:

Rousseau

Jean-Jacques Rousseau, an 18th-century philosopher who focused on the importance of nature, the critique of modernity, and the concept of the social contract influencing political theory.

General Will

A concept in political philosophy referring to what is in the best interest of the public or society as a whole, famously discussed by Rousseau.

Positive Freedom

The possession of the power and resources to fulfill one's own potential, as opposed to merely being free from restraint.

Determinism

The philosophical idea that all events, including moral choices, are completely determined by previously existing causes.