Notes, summaries, assignments, exams, and problems for Mathematics

Worksheet: Revisiting Calculating Probabilities from a Table

1. Goals

P(F) = 251/478 = 0.525

The probability that a randomly selected student is a girl is 0.525.

P(P^C) = (247 + 90)/478 = (478 – 141)/478 = 337/478 = 0.705

The probability that a randomly selected student did not indicate being popular as a primary goal is 0.705.

P(B or S) = (227 + 90 – 60)/478 = 257/478 = 0.538

The probability that a randomly selected student is a boy or indicated a primary goal is to excel at sports or both is 0.538.

P(B and S) = 60/478 = 0.126

The probability that a randomly selected student is a boy and indicated a primary goal is to excel at sports is 0.126.

P(S|B) = 60/227 =... Continue reading "Calculating Probabilities from a Table" »

Operating Segments & Disclosures

Revenue Test Criteria

Both external and intersegment revenue are included in the revenue test.

Profit & Loss (P&L) Test

The P&L test includes 10% of the higher absolute value of intersegment revenue and expenses.

Management's Business Evaluation

Management evaluates business results along product, customer, or geographic lines, not based on legal entity results.

Defining an Operating Segment

• Includes state
• Reviewed by the chief decision maker
• Discrete information available
• Product is the primary breakdown, with geographic and customer as secondary.

Operating Segment Disclosure Rules

• Must reconcile to GAAP.
• For immaterial operating segments, revenue, P&L, and assets must be disclosed.

Non-Operating Segment

In the examples C = {1,2,3,4} and D = {3,4,5}

SymbolMeaningExample{ }Set: a collection of elements{1,2,3,4}A ∪ BUnion: in A or B (or both)C ∪ D = {1,2,3,4,5}A ∩ BIntersection: in both A and BC ∩ D = {3,4}A ⊆ BSubset: A has some (or all) elements of B{3,4,5} ⊆ DA ⊂ BProper Subset: A has some elements of B{3,5} ⊂ DA ⊄ BNot a Subset: A is not a subset of B{1,6} ⊄ CA ⊇ BSuperset: A has same elements as B, or more{1,2,3} ⊇ {1,2,3}A ⊃ BProper Superset: A has B's elements and more{1,2,3,4} ⊃ {1,2,3}A ⊅ BNot a Superset: A is not a superset of B{1,2,6} ⊅ {1,9}A^cComplement: elements not in AD^c = {1,2,6,7}
When  = {1,2,3,4,5,6,7}A − BDifference: in A but not in B{1,2,3,4} − {3,4} =

Unit 7: Scheduling and Time Management

• Date: A numbered day in a month. *What's the date today?
• Schedule: To plan your tasks. *We have to schedule the flight.
• Paper Diary: A traditional notebook to write down tasks and important dates. *I use the diary more than the electronic planner.
• Electronic Planner: A digital device used to store information.
• Wall Calendar: A paper display showing 12 months divided into weeks and days. *I have to erase an appointment on the wall calendar.
• Up to Date: Containing the latest information. *I bought a diary to stay up to date.
• Appointment: A formal arrangement to meet or visit.
• Erase: To remove something. *I have to erase an appointment on the wall calendar.
• Deadline: A specific time or day by which something must

Understanding Prefixes and Suffixes

A prefix is a letter or a group of letters that appears at the beginning of a word and changes the word’s original meaning.

A suffix is a letter or a group of letters that is usually added onto the end of words to change the way a word fits into a sentence grammatically.

Nouns, verbs, adjectives, and adverbs all tend to use different suffixes, which makes them easier to remember. Collectively, prefixes and suffixes are known as affixes.

What Are Affixes?

An affix is added to the root of a word to change its meaning.

• An affix added to the front of a word is known as a prefix.
• One added to the back is known as a suffix.

Sometimes, prefixes are hyphenated. Read more about hyphens in prefixes.

Examples of Affixes

Here... Continue reading "Understanding Prefixes, Suffixes, and Root Words" »

Inventory Costing Methods: Situational Analysis

For each of the following situations, determine whether FIFO, LIFO, or Weighted Average would apply:

• FIFO would produce the highest amount of net income in an inflationary environment.
• FIFO would produce the highest amount of assets in an inflationary environment.
• FIFO would produce the lowest amount of net income in a deflationary environment.
• Weighted Average would produce the same unit cost for assets and cost of goods sold in an inflationary environment.
• LIFO would produce the lowest amount of net income in an inflationary environment.
• Weighted Average would produce an asset value that was the same regardless of whether the environment was inflationary or deflationary.
• LIFO would produce the lowest

Statistics Problems and Solutions

Great! Let's continue with providing solutions to the questions:

Question 1: Empirical Rule Name

The Empirical Rule is also known as:

• E. The 68–95–99.7 Rule

Question 2: Normal Distribution Interval (95%)

For a normally distributed data set with a mean of 70 and a standard deviation of 13, approximately 95% of the data lie within about two standard deviations of the mean.

• Calculate: 70 ± 2 × 13 = 70 ± 26
• Result: 44 and 96

Question 3: Mean and Median for the Set

For the set of numbers: 27, 83, 55, 61, 102, 17:

• a) Mean — Add all the numbers together and divide by the count (6):
• Sum = 27 + 83 + 55 + 61 + 102 + 17 = 345
• Mean = 345 / 6 = 57.5
• b) Median — Arrange in ascending order and take the middle value (or average

Chapter 3: Key Concepts

Missing Variable

x = given Median * 2 - ((1 of 2) median numbers if even): ascending order

Unreadable Score

(U * N of unreadable) - (U * N of readable)

Degrees of Freedom

1 # of freedom is lost

Chebyshev's Theorem

K = Deviation

Calculate time % within K Dev of mean - (1 - 1/k^2) * 100 = %

Finding Values

Find x K devs from mean - (mean - K * given standard dev) = XLow...(mean + k * given standard dev) = XHigh

Finding % Within Times Xlow-Xhigh

K = (XHigh - Mean) / Given Standard dev....then do Chebyshev's - (1 - 1/k^2) * 100 = %

Z-Score Simplified

(Mean - Given Mean) / Given Standard Dev = ZScore

Finding Minimum Score Accepted

(Min devs) * (Given Devs) + (Mean) = Min Score

Weighted Mean

Chart Xi / Wi /XiWi

Use Empirical Rule if distribution