Semester Review Pt. 2

Front

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.

Front

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.

Front

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.

Front

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.

Front

What is a strong positive correlation?

Back

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

Front

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

Back

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

Front

How do you identify like terms in an algebraic expression?

Back

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

Front

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

Back

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

Front

What is the process for simplifying algebraic expressions?

Back

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