Lecture Review - Math Applications & Set Theory Concept Flashcards

Vocabulary flashcards covering mathematical estimation, sequence analysis, budgeting calculations, exam average problems, and fundamental set theory concepts from the lecture material.

Set

A collection of objects called elements or members.

Roster Method

A method of writing a set by listing its elements inside braces, such as $A = \{1, 2, 3, 4\}$.

Word Description

A method of defining a set using descriptive language, such as "first four letters of alphabet".

Natural or Counting Numbers

The set of basic counting numbers defined as $N = \{1, 2, 3, 4\}$.

Kim's Exam Average Calculation

The required score of $91$ on a $5\text{th}$ exam needed to reach a $90$ average ($90 \times 5 = 450$ total points) after scoring $87$, $91$, $86$, and $95$ (summing to $359$) on the first four exams.

Dishwasher Down Payment Savings

The amount saved ($21$) by paying a total price of $550$ upfront instead of paying a $55$ down payment plus $43$ per month for $12$ months ($43 \times 12 + 55 = 571$).

Entertainment vs. Food Budget Difference

The dollar difference ($124.80$) between entertainment expenditures ($19.1\%$ or $372.45$) and food expenditures ($12.7\%$ or $247.65$) given a monthly income of $1950$.

Housing vs. Transportation Budget Difference

The dollar difference ($358.80$) between housing expenses ($34.4\%$ or $670.80$) and transportation expenses ($16\%$ or $312$) on a monthly income of $1950$.

Geometric Sequence ($1, -2, 4, -8\dots$)

A number pattern generated by multiplying the preceding term by $-2$, yielding the next three numbers: $16$, $-32$, and $64$.

Tip Estimation Method

An estimation technique for calculating a $15\%$ tip on a $26.32$ bill using the simplified formula $0.15 \times 26 = 3.9$.

Savings Duration Calculation

The calculation used to find the number of months required to save $400$ when saving $23$ per month ($400 / 23 = 17.39$), which rounds up to $18$ months.

Four Exam Total Score

The sum of four individual exam scores $80$, $74$, $81$, and $74$, which totals $309$.