Mastering Essential Math Concepts: Algebra to Statistics
Multiplying Binomials
Multiply (3r – 1)(2r + 3).
Use the FOIL method, keeping the largest exponent on the left. Multiply each number on the left by both numbers on the right.
This gives you 6r2 + 9r – 2r – 3. Combine like terms, 9r – 2r = 7r. This gives you (6r2 + 7r – 3). This is the answer.
Dividing Fractions and Exponents
Divide:
When dividing two fractions, cross-multiply. When dividing exponents, subtract them. So:
Adding and Simplifying Algebraic Fractions
Add and simplify:
Finding X and Y Intercepts
Find
Read MoreSolved Problems in Probability and Statistics
Probability and Statistics Problems: Solutions
1. FSU Volleyball Team: Probability of Losing Both Games
The probability that the FSU volleyball team wins a game is 0.8. If the team has two games this weekend, assuming independence of events, what is the probability that the team will lose both games?
P(A) = (1 – 0.8) = 0.2
P(B) = (1 – 0.8) = 0.2
P(losing both games) = 0.2 x 0.2 = 0.04
2. Probability of at Least Two Female Babies
If a girl gives birth to 3 babies, what is the probability that she would
Read MoreSampling Plans and Data Preparation in Market Research
Topic 5: Sampling Plan and Data Collection
Sample or Census
Differences: A census is a complete enumeration of all individuals and asks them what their opinion is. The problem is that it is impossible to survey the entire population. Sampling involves choosing people to learn something about the population.
Sampling Design Process
- Determine the Target Population
- Determine the Sampling Frame (how to identify them)
- Select a Sampling Technique
Sampling Techniques
Non-Probability Sampling Techniques
- Convenience
Ecology and Population Dynamics: Key Concepts
Ecology and Population Dynamics
Ecology: A discipline of biology that studies the interrelations among living things and their environments.
Ecosystem
The interacting system that encompasses a community and its nonliving, physical environment. Compare with community.
Community
An association of populations of different species living together in a defined habitat with some degree of interdependence. Compare with ecosystem.
Population
A group of organisms of the same species that live in a defined geographic
Mathematical Models of Disease Spread: A Curriculum Unit
Contents:
- Overview of the Unit
- Rationale and Objectives
- Section I
- The Origins of Microbes
- How Diseases Spread
- Cholera
- Malaria
- Immunity
- The Mathematical Connections
- Lesson Plan I
- Lesson II
- Lesson Plan III
- Lesson Plan IV
- Bibliography
- Web Sites
- Appendix: Connecting to the Mathematics Standards
- Endnotes
To Guide Entry
Overview of the Unit
In today’s society, there is an increasing demand for understanding how mathematics is relevant to everyday activities. As this demand for the application of mathematics increases, teachers
Read MoreProbability and Statistics: Formulas and Concepts
Counting
- Multiplication Rule: There are n1n2 . . . nr possible outcomes if an experiment has r steps and the ith step has ni outcomes.
- Ordered, Without Replacement: There are n(n−1)(n−2)…(n−k + 1) = n! / (n−k)! ways to choose k items out of n without replacement if the order in which the k items are chosen matters (e.g., out of 10 people, choose a president, vice president, and treasurer).
- Unordered, Without Replacement: There are n! / (n−k)!k! ways to choose k items out of n without replacement