Use the Binomial Theorem to Expand the Binomial $$\left( \frac { a } { 2 } + t \right) ^ { 4 }$$

question 150

Multiple Choice

Use the binomial theorem to expand the binomial. $$\left( \frac { a } { 2 } + t \right) ^ { 4 }$$

• A) \(\quad a ^ { 4 } + a ^ { 3 } t + a ^ { 2 } t ^ { 2 } + a t ^ { 3 } + t ^ { 4 }\)
• B) \(\quad \frac { 1 } { 8 } a ^ { 4 } + \frac { 1 } { 2 } a ^ { 3 } t + \frac { 3 } { 2 } a ^ { 2 } t ^ { 2 } + 2 a t ^ { 3 } + t ^ { 4 }\)
• C) \(\quad \frac { 1 } { 2 } a ^ { 4 } + t ^ { 4 }\)
• D) \(\quad \frac { 1 } { 16 } a ^ { 4 } + \frac { 1 } { 2 } a ^ { 3 } t + \frac { 3 } { 2 } a ^ { 2 } t ^ { 2 } + 2 a t ^ { 3 } + t ^ { 4 }\)
• E) \(\quad \frac { 1 } { 16 } a ^ { 4 } + \frac { 1 } { 8 } a ^ { 3 } t + \frac { 1 } { 4 } a ^ { 2 } t ^ { 2 } + \frac { 1 } { 2 } a t ^ { 3 } + t ^ { 4 }\)

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Definitions:

Perfect Relationship

Refers to a situation where two variables move together in either 100% positive or 100% negative linear correlation, indicating a direct relationship without any variation.

Variance

Variance is a statistical measurement that describes the spread of numbers in a data set, indicating how far each number in the set is from the mean.

T-statistics

A measure used in statistical analysis to determine the difference between a sample statistic and its hypothesized population parameter, scaled by the standard error.

Within-group Variability

Refers to variations in observations within individual groups or categories in a dataset.