(Part 2) M4 Review for FINALS (Fall 2024)

Front

What is the Law of Sines?

Back

The Law of Sines states that in any triangle, the ratio of the length of a side to the sine of its opposite angle is constant. It can be expressed as: \( \frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C} \.

Front

How do you find the length of a side in a triangle using the Law of Sines?

Back

To find the length of a side using the Law of Sines, rearrange the formula: \( a = \frac{b \cdot \sin A}{\sin B} \) where \( A \) and \( B \) are the angles opposite sides \( a \) and \( b \) respectively.

Front

What is the Law of Cosines?

Back

The Law of Cosines relates the lengths of the sides of a triangle to the cosine of one of its angles. It is expressed as: \( c^2 = a^2 + b^2 - 2ab \cdot \cos(C) \.

Front

How do you find an angle in a triangle using the Law of Cosines?

Back

To find an angle using the Law of Cosines, rearrange the formula: \( C = \cos^{-1}\left(\frac{a^2 + b^2 - c^2}{2ab}\right) \.

Front

What is the empirical rule in statistics?

Back

The empirical rule states that for a normal distribution: about 68% of data falls within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations.

Front

How do you calculate the percentage of data within a certain range using the empirical rule?

Back

To calculate the percentage of data within a certain range, determine how many standard deviations the range is from the mean and apply the empirical rule accordingly.

Front

What is a normal distribution?

Back

A normal distribution is a probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean.

Front

What is the mean in a normal distribution?

Back

The mean is the average of all data points in a distribution and is the center point of a normal distribution curve.

Front

What is standard deviation?

Back

Standard deviation is a measure of the amount of variation or dispersion in a set of values. A low standard deviation means that the values tend to be close to the mean, while a high standard deviation means that the values are spread out over a wider range.

Front

How do you find the number of occurrences below the mean in a normal distribution?

Back

In a normal distribution, approximately 50% of the data falls below the mean. To find the number of occurrences below the mean, multiply the total number of observations by 0.5.