mathematics that developed from simple measurements. A theorem is the most important result in all of elementary mathematics. It was the motivation for a wealth of advanced mathematics‚ such as Fermat’s Last Theorem and the theory of Hilbert space. The Pythagorean Theorem asserts that for a right triangle‚ the square of the hypotenuse is equal to the sum of the squares of the other two sides. There are many ways to prove the Pythagorean Theorem. A particularly simple one is the scaling relationship
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1. As the degrees of freedom increase‚ the t distribution approaches the b. normal distribution 2. If the margin of error in an interval estimate of μ is 4.6‚ the interval estimate equals b. [pic] 3. The t distribution is a family of similar probability distributions‚ with each individual distribution depending on a parameter known as the c. degrees of freedom 4. The probability that the interval estimation procedure will generate an interval that does
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a NOR gate. DeMorgan’s theorems state the same equivalence in "backward" form: that inverting the output of any gate results in the same function as the opposite type of gate (AND vs. OR) with inverted inputs De Morgan’s theorem is used to simplify a lot expression of complicated logic gates. For example‚ (A + (BC)’)’. The parentheses symbol is used in the example. _ The answer is A BC. Let’s apply the principles of DeMorgan’s theorems to the simplification of
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Descriptive statistics information Descriptive statistics organize‚ summarize‚ and communicate a group of numerical observations and describe large amounts of data in a single number or in just a few numbers Inferential statistics Use samples to draw conclusions about a population Inferential statistical use sample data to make general estimates about the larger population‚ and infer or make an intelligence guess about‚ the population Sample: a set of observations drawn from the population
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vital statistics of populations studied probability through games of chance‚ gambling | 18th Century | Laplace‚ Gauss | normal curve‚ regression through study of astronomy | 19th Century | Quetelet Galton | astronomer who first applied statistical analyses to human biologystudied genetic variation in humans(used regression and correlation) | 20th Century (early) | PearsonGossett (Student) Fisher | studied natural selection using correlation‚ formed first academic department of statistics‚ Biometrika
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Theology 100 Father O’Leary 6/5/08 Final Exam Questions 1. Is Religion important? Why or why not? 2. Would anything change if the Tomb of Jesus was discovered and the bones within were proven to be his? 3. Think a bit about your talents and abilities. Do you think that one of more of these talents you possess could serve the common good of the society in which you live? 4. Think a bit about the talents or skills that either you have not yet developed or do not think you possess
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Chapter 2: Descriptive Statistics CHAPTER 2: Descriptive Statistics 2.3 [LO 1] 28 2007 #1 28 71‚273.93 58‚069‚987.70 7‚620.37 59490 87970 28480 Distribution is skewed right. Descriptive statistics count mean sample variance sample standard deviation minimum maximum range Stem and Leaf plot for stem unit = leaf unit = Frequency 2 9 13 4 28 #1 10000 1000 Stem 5 6 7 8 Leaf 99 123446677 0000112444447 1377 Distribution is more normally shaped in 2007. 2.5 [LO 2] a. We have 2
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very common throughout the world and it causes deaths every day. So what exactly is asthma and how does it affect your lungs? Asthma is a chronic condition which causes inflammation that narrows your bronchial tubes. The bronchial tubes are very important to us in breathing because it is the passageways to allow air to enter
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How Much Protein Do You Really Need? Why is protein important? Protein is part of an important food group that you will need in order for your body to be able to function properly. As a macronutrient‚ protein allows your body to undergo proper growth and development‚ as well as to strengthen its immunity against various sicknesses and diseases. Protein is also responsible for acting as the main building block that repairs your tissues‚ organs‚ tendons‚ muscles‚ and even your bones‚ skin‚ and eyes
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LIMITS AND CONTINUITY 1. The concept of limit x2 − 4 . Examine the behavior of f (x) as x approaches 2. Example 1.1. Let f (x) = x−2 Solution. Let us compute some values of f (x) for x close to 2‚ as in the tables below. We see from the first table that f (x) is getting closer and closer to 4 as x approaches 2 from the left side. We express this by saying that “the limit of f (x) as x approaches 2 from left is 4”‚ and write x→2− lim f (x) = 4. Similarly‚ by looking at the second table
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