Solving Linear Equations and Inequalities to Make Predictions

This flashcard set covers key vocabulary, formulas, and concepts from the lecture on solving linear equations, probability additions for disjoint events, temperature conversions, and summation notation.

Disjoint events

Events that have no members in common, allowing the use of the formula $P(A \text{ OR } H) = P(A) + P(H)$.

Summation formula (Evaluating a sum)

A process of evaluating the sum of terms, for example, $\sum x \cdot P(x)$, by substituting specific values for indices such as $x_1, x_2, ... , x_n$ and their probabilities.

Fahrenheit-Celsius association formula

The exact linear association between Fahrenheit ($F$) and Celsius ($C$) expressed as $C = \frac{5}{9}(F - 32)$.

Celsius to Fahrenheit conversion formula

The formula derived by solving for $F$, resulting in $F = \frac{9}{5}C + 32$.

Rule for Squaring a Principal Square Root

If $x$ is nonnegative, then $(\sqrt{x})^2 = x$; in words, the square of the principal square root of a nonnegative number is the number itself.

Margin of error formula variable ($E$)

A variable in a statistical formula representing the error in making a certain type of estimate.

Sample size variable ($n$)

The variable in the margin of error formula representing the number of individuals who are randomly selected.

Slope-intercept form ($y = a + bx$)

A form of a linear equation used to identify the y-intercept $(0, a)$ and the slope ($b$) to help sketch a graph.

y-intercept

The point where a line crosses the y-axis; for example, in the equation $2x + 3y = 9$ (or $y = 3 - \frac{2}{3}x$), the y-intercept is $(0, 3)$.

Slope

In the linear equation $y = 3 - \frac{2}{3}x$, the value $-\frac{2}{3}$ which represents the steepness and direction of the line.