The properties of equality (or axioms of equality) are used to solve equations. It is important to note that these properties are NOT for simplifying expressions; they describe various things one can do to an equation, while maintaining the validity of the equal sign throughout the entire process. There are four basic properties of equality: Substitution property, Reflexive property, Symmetric property and Transitive property. In addition to these four basic properties, the Addition property of equality and Multiplication property of equality are essential for solving equations. Research more about the properties of equality; introduce and explain each property textually and mathematically.

Your response should include the following:
A clear Introduction including the history of the basic properties of equality (Hint: Peano axioms).
A mathematical definition of each of the properties.
A discussion on which properties are mainly used for solving the equations and which are primarily used for various proofs.
In-text citations for any sources that you use to support evidence/examples as well as a complete and properly formatted citations in the Works Cited page at the end.

Weekly wages at a certain factory are normally distributed with a mean of $400 and a standard deviation of $50. find the probability that a worker selected at random makes between $450 and $500

Name and describe the three most important measures of central tendency. choose the correct answer below. a. the mean, sample size, and mode are the most important measures of central tendency. the mean of a data set is the sum of the observations divided by the middle value in its ordered list. the sample size of a data set is the number of observations. the mode of a data set is its highest value in its ordered list. b. the sample size, median, and mode are the most important measures of central tendency. the sample size of a data set is the difference between the highest value and lowest value in its ordered list. the median of a data set is its most frequently occurring value. the mode of a data set is sum of the observations divided by the number of observations. c. the mean, median, and mode are the most important measures of central tendency. the mean of a data set is the product of the observations divided by the number of observations. the median of a data set is the lowest value in its ordered list. the mode of a data set is its least frequently occurring value. d. the mean, median, and mode are the most important measures of central tendency. the mean of a data set is its arithmetic average. the median of a data set is the middle value in its ordered list. the mode of a data set is its most frequently occurring value.

Solve these problems: 1.what is the perimeter of an equilateral triangle with sides measuring 6cm? 2. a regular pentagon has sides measuring 3.2 cm. what is its perimeter? 3. a regular decagon has sides of 3.5mm . what is it’s perimeter? 4. a regular octagon has a perimeter of 64cm. what is the length of one of the sides? 5. a regular hexagon has a perimeter of 72mm . what is the length of one of the sides? 6. what is the perimeter of a rhombus with sides measuring 11m?