Apply the Axioms Test whether you understand each of Euclid's axíoms by matching each of these statements with the axiom that applies. 1. The population of California is greater than the population of San Francisco. 2. If a + b = 6 and x a+ b, then x 6. 3. If 3x + 8= 10, then 3x = 2. 4. A carton and a bottle each contain the same volume of milk. If one more cup of milk is poured into each container, then the volume of milk in the carton will still equal the volume of milk in the bottle. 5. If one triangle can be placed on top of another triangle and they match perfectly, then the two triangles must have the same area. The Vertical Angles Theorem In mathematics, a statement that is proven is called a theorem. Our first theorem deals with the picture of intersecting lines from What Do We Already Know? and the fill-in-the blank statement that went with it. The pair Zb and Zd, and the pair Za and Zc, are angles. One possible word that fills the blank is "vertical." When two lines intersect, the non-adjacent angle pairs are called vertical angles. 6. Suppose mZa = 50°. What is the measure of Lb? What are the measures of Lc and Ld? Why? 7. Suppose mZa = x°. What is the measure of Lb in terms of x? What are the measures of Lc and Ld? Why? Looking at your answers to Questions 1 and 2, you can probably guess our first theorem, the Vertical Angles Theorem: When two lines intersect, the vertical angles are equal. сontinued Geometry by Design: Do In Lil
Addition Rule of Probability
It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.
Expected Value
When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known as the expectation, is denoted by: E(X).
Probability Distributions
Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosing a card. Each of these events has multiple possibilities. Every such possibility is measured with the help of probability. To be more precise, the probability is used for calculating the occurrence of events that may or may not happen. Probability does not give sure results. Unless the probability of any event is 1, the different outcomes may or may not happen in real life, regardless of how less or how more their probability is.
Basic Probability
The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the probability value 1 indicates that the event will occur. Sum of the probability value must be 1. The probability value is never a negative number. If it happens, then recheck the calculation.
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