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What is the correlation coefficient and what does it indicate?

Back

The correlation coefficient (r) is a statistical measure that describes the strength and direction of a relationship between two variables. Values range from -1 to 1, where 1 indicates a strong positive correlation, -1 indicates a strong negative correlation, and 0 indicates no correlation.

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How do you simplify the expression (4a^3 - 8a - 4a^2) + (7a^3 - 7 - 6a)?

Back

Combine like terms: 4a^3 + 7a^3 = 11a^3, -4a^2 remains, -8a - 6a = -14a, and -7 remains. Final result: 11a^3 - 4a^2 - 14a - 7.

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Back

Front

What does the system of inequalities 2x - y > 4 and 4x + 2y < 6 represent graphically?

Back

The graph represents the region where both inequalities are satisfied, typically shown as a shaded area on a coordinate plane.

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What does a negative correlation in a scatterplot indicate?

Back

A negative correlation indicates that as one variable increases, the other variable tends to decrease.

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What is a strong positive correlation?

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A strong positive correlation occurs when the correlation coefficient is close to 1, indicating that both variables increase together.

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What is the difference between a positive correlation and a negative correlation?

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In a positive correlation, both variables increase together, while in a negative correlation, one variable increases as the other decreases.

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How do you identify like terms in an algebraic expression?

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Like terms are terms that have the same variable raised to the same power. For example, 3a^2 and 5a^2 are like terms.

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What is the significance of the correlation coefficient value of r = 0.956?

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An r value of 0.956 indicates a very strong positive correlation between the two variables being analyzed.

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What is the process for simplifying algebraic expressions?

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To simplify an algebraic expression, combine like terms, apply the distributive property, and reduce fractions if possible.