Show That $\int _ { C } 2 x d x + 2 y d y + 2 z d z = \mathbf { a } \cdot \mathbf { a }$

question 15

Essay

Show that $\int _ { C } 2 x d x + 2 y d y + 2 z d z = \mathbf { a } \cdot \mathbf { a }$ , where $\mathbf { a } = a _ { 1 } \mathbf { i } + a _ { 2 } \mathbf { j } + a _ { 3 } \mathbf { k }$ , and C is any path from $( 0,0,0 )$ to $\left( a _ { 1 } , a _ { 2 } , a _ { 3 } \right)$ .

Understand the distribution of the test statistic used in linear regression hypothesis testing.

Determine the appropriate sample size for a linear regression analysis based on given information.

Differentiate between confidence intervals and prediction intervals in the context of linear regression.

Understand the influence of physical attractiveness on person perception and performance evaluations.

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Definitions:

Ad Valorem Tariff

A tax placed on goods based on a percentage of the goods' value.

Import Quota

An import quota is a government-imposed limit on the quantity or monetary value of a particular good that can be imported into a country within a specified time frame.

World Price

The global market price of a good or service, determined by worldwide supply and demand.

Market Equilibrium

A condition or point where market supply and demand balance each other, and as a result, prices become stable.