Summary: Review

Key Concepts

Translating Word Problems Into Expressions

Addition	$+$	sum, total, together, more than, increased by, …
Subtraction	$-$	difference, less than, decreased by, …
Multiplication	$\times$	product, double, half, percent of, …
Equality	$=$	is, is the same as, is not different from, …

Inequality Symbols

Symbol	In Words	Example
$\neq$	Not equal to	$3 \neq 5$
$>$	Greater than	$5>3$
$<$	Less than	$2<7$
$\geq$	Greater than or equal to	$5 \geq 5$
$\leq$	Less than or equal to	$4 \leq 7$

The inequality [latex]aa[/latex].

Graphing an Inequality

Locate the endpoint of the inequality on the number line. Draw a closed (shaded) circle if the inequality includes the endpoint $(\geq \mathrm{or} \leq)$ . Draw an open circle for a strict inequality ( $< \mathrm{or} >$ ).
Shade the portion of the number line which satisfies the stated inequality.

Translating Verbal Statements Involving Inequalities

Verbal Statement: x is…	Mathematical Statement
greater than or equal to $k$ at least $k$ not more than $k$	$x \geq k$
less than or equal to $k$ at most $k$ not more than $k$	$x \leq k$
less than $k$ below $k$ fewer than $k$	[latex]x
greater than $k$ more than $k$ above $k$	$x>k$
equal to $k$ is $k$ exactly $k$ the same as $k$	$x=k$
not equal to $k$ not $k$ different from $k$	$x \neq k$

To convert a number in scientific notation to standard notation, move the decimal point $n$ places to the write if $n$ is positive, or $|n|$ places to the left if $n$ is negative. Add zeros as needed.

To write a number in scientific notation, move the decimal point to the right of the first nonzero digit in the number. Write the digits as a decimal number between 1 and 10. Count the number of places $n$ that you moved the decimal point. Multiply the decimal number by 10 raised to a power of $n$ . If you moved the decimal left as in a very large number, $n$ is positive. If you moved the decimal right as in a small large number, $n$ is negative.

Glossary

constant: number whose value does not change

inequality: compares two expressions, identifying one as more, less, or simply different than the other

inference: drawing reliable conclusions about the population on the basis of what we’ve discovered in our sample

probability: a number between zero and one, inclusive, that gives the likelihood that a specific event will occur; also described as long-term relative frequency. Probabilities are between 0 and 1, inclusive.

real number line: a horizontal line used to represent the real numbers. An arbitrary fixed point is chosen to represent 0; positive numbers lie to the right of 0 and negative numbers to the left.

scientific notation: number is written in the form $a \times 10^{n}$ where $1 \leq |a| < 10$ solution set: values of a variable which make a statement true

variable: a quantity that may change value, or whose value we don’t know

Module 4: Discrete Random Variables

Key Concepts

Translating Word Problems Into Expressions

Inequality Symbols

Symbol

In Words

Example

Graphing an Inequality

Translating Verbal Statements Involving Inequalities

Verbal Statement: x is…

Mathematical Statement

Glossary

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