2329 lines
107 KiB
HTML
2329 lines
107 KiB
HTML
<html>
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|
||
<head>
|
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<!-- saved from url=(0014)about:internet --><!-- MSIE Mark of the Web -->
|
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<meta http-equiv="Content-Type" content="text/html; charset=utf-8"/>
|
||
<meta name="keywords" content="MathPageGen"/>
|
||
<meta name="Generator" content="MathPage 1.0.1"/>
|
||
<meta name="Originator" content="Microsoft Word 12"/>
|
||
|
||
|
||
<script type="text/javascript"
|
||
src="http://cdn.mathjax.org/mathjax/latest/MathJax.js?config=MML_HTMLorMML"><!-- empty -->
|
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</script>
|
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<title>Test Set for MathML Cloud</title>
|
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</head>
|
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<body lang="EN-US" >
|
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|
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<h1>Test Set for MathML Cloud</h1>
|
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<p>Last updated: September 18, 2014</p>
|
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<h2>Source: Carnegie Learning Math Series Level 2</h2>
|
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<ol><li>
|
||
|
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<math xmlns="http://www.w3.org/1998/Math/MathML">
|
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<semantics>
|
||
<mrow>
|
||
<mo>−</mo><mn>5</mn><mfrac>
|
||
<mn>1</mn>
|
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<mn>5</mn>
|
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</mfrac>
|
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<mo>−</mo><mn>6</mn><mfrac>
|
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<mn>2</mn>
|
||
<mn>3</mn>
|
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</mfrac>
|
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<mo>=</mo>
|
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</mrow>
|
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<annotation encoding='MathType-MTEF'>MathType@MTEF@5@5@+=feaaguart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHXgarmWu51MyVXgaruWqVvNCPvMCG4uz3bqefqvATv2CG4uz3bIuV1wyUbqee0evGueE0jxyaibaieYlf9irVeeu0dXdh9vqqj=hEeea0dXdcba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9q8qqaq=dir=f0=yqaiVgFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaaeaqbaaGcbaGaeyOeI0IaaGynamaalaaabaGaaGymaaqaaiaaiwdaaaGaeyOeI0IaaGOnamaalaaabaGaaGOmaaqaaiaaiodaaaGaeyypa0daaa@3F7C@</annotation>
|
||
</semantics>
|
||
</math>
|
||
</li>
|
||
<li>
|
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<math xmlns="http://www.w3.org/1998/Math/MathML">
|
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<semantics>
|
||
<mrow>
|
||
<mo>−</mo><mn>7</mn><mfrac>
|
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<mn>3</mn>
|
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<mn>4</mn>
|
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</mfrac>
|
||
<mo>−</mo><mrow><mo>(</mo>
|
||
<mrow>
|
||
<mo>−</mo><mn>4</mn><mfrac>
|
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<mn>7</mn>
|
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<mn>8</mn>
|
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</mfrac>
|
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|
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</mrow>
|
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<mo>)</mo></mrow><mo>=</mo>
|
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</mrow>
|
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<annotation encoding='MathType-MTEF'>MathType@MTEF@5@5@+=feaaguart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHXgarmWu51MyVXgaruWqVvNCPvMCG4uz3bqefqvATv2CG4uz3bIuV1wyUbqee0evGueE0jxyaibaieYlf9irVeeu0dXdh9vqqj=hEeea0dXdcba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9q8qqaq=dir=f0=yqaiVgFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaaeaqbaaGcbaGaeyOeI0IaaG4namaalaaabaGaaG4maaqaaiaaisdaaaGaeyOeI0YaaeWaaeaacqGHsislcaaI0aWaaSaaaeaacaaI3aaabaGaaGioaaaaaiaawIcacaGLPaaacqGH9aqpaaa@41FD@</annotation>
|
||
</semantics>
|
||
</math>
|
||
</li><li>
|
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<math xmlns="http://www.w3.org/1998/Math/MathML">
|
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<semantics>
|
||
<mrow>
|
||
<mo>−</mo><mn>24.15</mn><mo>−</mo><mrow><mo>(</mo>
|
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<mrow>
|
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<mn>13.7</mn>
|
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</mrow>
|
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<mo>)</mo></mrow><mo>=</mo>
|
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</mrow>
|
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<annotation encoding='MathType-MTEF'>MathType@MTEF@5@5@+=feaaguart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHXgarmWu51MyVXgaruWqVvNCPvMCG4uz3bqefqvATv2CG4uz3bIuV1wyUbqee0evGueE0jxyaibaieYlf9irVeeu0dXdh9vqqj=hEeea0dXdcba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9q8qqaq=dir=f0=yqaiVgFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaaeaqbaaGcbaGaeyOeI0IaaGOmaiaaisdacaGGUaGaaGymaiaaiwdacqGHsisldaqadaqaaiaaigdacaaIZaGaaiOlaiaaiEdaaiaawIcacaGLPaaacqGH9aqpaaa@4304@</annotation>
|
||
</semantics>
|
||
</math>
|
||
</li><li>
|
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<math xmlns="http://www.w3.org/1998/Math/MathML">
|
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<semantics>
|
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<mrow>
|
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<mrow><mo>(</mo>
|
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<mrow>
|
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<mo>−</mo><mn>4</mn>
|
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</mrow>
|
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<mo>)</mo></mrow><mo>×</mo><mn>3</mn><mo>=</mo><mo>−</mo><mn>12</mn>
|
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</mrow>
|
||
<annotation encoding='MathType-MTEF'>MathType@MTEF@5@5@+=feaaguart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHXgarmWu51MyVXgaruWqVvNCPvMCG4uz3bqefqvATv2CG4uz3bIuV1wyUbqee0evGueE0jxyaibaieYlf9irVeeu0dXdh9vqqj=hEeea0dXdcba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9q8qqaq=dir=f0=yqaiVgFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaaeaqbaaGcbaWaaeWaaeaacqGHsislcaaI0aaacaGLOaGaayzkaaGaey41aqRaaG4maiabg2da9iabgkHiTiaaigdacaaIYaaaaa@417C@</annotation>
|
||
</semantics>
|
||
</math>
|
||
</li><li>
|
||
<math xmlns="http://www.w3.org/1998/Math/MathML">
|
||
<semantics>
|
||
<mrow>
|
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<mo>−</mo><mn>12</mn><mo>÷</mo><mn>3</mn><mo>=</mo><mo>−</mo><mn>4</mn>
|
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</mrow>
|
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<annotation encoding='MathType-MTEF'>MathType@MTEF@5@5@+=feaaguart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHXgarmWu51MyVXgaruWqVvNCPvMCG4uz3bqefqvATv2CG4uz3bIuV1wyUbqee0evGueE0jxyaibaieYlf9irVeeu0dXdh9vqqj=hEeea0dXdcba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9q8qqaq=dir=f0=yqaiVgFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaaeaqbaaGcbaGaeyOeI0IaaGymaiaaikdacqGH3daUcaaIZaGaeyypa0JaeyOeI0IaaGinaaaa@4017@</annotation>
|
||
</semantics>
|
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</math>
|
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</li><li>
|
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<math xmlns="http://www.w3.org/1998/Math/MathML">
|
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<semantics>
|
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<mrow>
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<mo>−</mo><mn>12</mn><mo>÷</mo><mrow><mo>(</mo>
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<mrow>
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<mo>−</mo><mn>4</mn>
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</mrow>
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<mo>)</mo></mrow><mo>=</mo><mn>3</mn>
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</mrow>
|
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<annotation encoding='MathType-MTEF'>MathType@MTEF@5@5@+=feaaguart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHXgarmWu51MyVXgaruWqVvNCPvMCG4uz3bqefqvATv2CG4uz3bIuV1wyUbqee0evGueE0jxyaibaieYlf9irVeeu0dXdh9vqqj=hEeea0dXdcba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9q8qqaq=dir=f0=yqaiVgFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaaeaqbaaGcbaGaeyOeI0IaaGymaiaaikdacqGH3daUdaqadaqaaiabgkHiTiaaisdaaiaawIcacaGLPaaacqGH9aqpcaaIZaaaaa@41A0@</annotation>
|
||
</semantics>
|
||
</math>
|
||
</li>
|
||
<li>
|
||
<math>
|
||
<semantics>
|
||
<mrow>
|
||
<mn>6</mn><mo>×</mo><mn>5</mn>
|
||
</mrow>
|
||
<annotation encoding='MathType-MTEF'>MathType@MTEF@5@5@+=feaaguart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHXgarmWu51MyVXgaruavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqiVy0xe9vqqrpepeYlI8qiW7rqaqpepiea0xe9Lq=Jc9vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9Fve9Ff0dmeaabaqaciaacaGaaeqabaqaamaaeaaakeaacaaI2aGaey41aqRaaGynaaaa@36AC@</annotation>
|
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</semantics>
|
||
</math></li>
|
||
<li>
|
||
<math>
|
||
<semantics>
|
||
<mrow>
|
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<mn>6</mn><mo>×</mo><mrow><mo>(</mo>
|
||
<mrow>
|
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<mo>−</mo><mn>5</mn>
|
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</mrow>
|
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<mo>)</mo></mrow>
|
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</mrow>
|
||
<annotation encoding='MathType-MTEF'>MathType@MTEF@5@5@+=feaaguart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHXgarmWu51MyVXgaruavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqiVy0xe9vqqrpepeYlI8qiW7rqaqpepiea0xe9Lq=Jc9vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9Fve9Ff0dmeaabaqaciaacaGaaeqabaqaamaaeaaakeaacaaI2aGaey41aq7aaeWaaeaacqGHsislcaaI1aaacaGLOaGaayzkaaaaaa@3922@</annotation>
|
||
</semantics>
|
||
</math>
|
||
</li>
|
||
<li>
|
||
<math>
|
||
<semantics>
|
||
<mrow>
|
||
<mo>−</mo><mn>6</mn><mo>×</mo><mn>5</mn>
|
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</mrow>
|
||
<annotation encoding='MathType-MTEF'>MathType@MTEF@5@5@+=feaaguart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHXgarmWu51MyVXgaruavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqiVy0xe9vqqrpepeYlI8qiW7rqaqpepiea0xe9Lq=Jc9vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9Fve9Ff0dmeaabaqaciaacaGaaeqabaqaamaaeaaakeaacqGHsislcaaI2aGaey41aqRaaGynaaaa@3799@</annotation>
|
||
</semantics>
|
||
</math>
|
||
</li>
|
||
<li>
|
||
<math>
|
||
<semantics>
|
||
<mrow>
|
||
<mo>−</mo><mn>6</mn><mo>×</mo><mrow><mo>(</mo>
|
||
<mrow>
|
||
<mo>−</mo><mn>5</mn>
|
||
</mrow>
|
||
<mo>)</mo></mrow>
|
||
</mrow>
|
||
<annotation encoding='MathType-MTEF'>MathType@MTEF@5@5@+=feaaguart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHXgarmWu51MyVXgaruavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqiVy0xe9vqqrpepeYlI8qiW7rqaqpepiea0xe9Lq=Jc9vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9Fve9Ff0dmeaabaqaciaacaGaaeqabaqaamaaeaaakeaacqGHsislcaaI2aGaey41aq7aaeWaaeaacqGHsislcaaI1aaacaGLOaGaayzkaaaaaa@3A0F@</annotation>
|
||
</semantics>
|
||
</math>
|
||
</li>
|
||
<li>
|
||
<math>
|
||
<semantics>
|
||
<mrow>
|
||
<mo>−</mo><mn>8</mn><mo>×</mo><mn>7</mn>
|
||
</mrow>
|
||
<annotation encoding='MathType-MTEF'>MathType@MTEF@5@5@+=feaaguart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHXgarmWu51MyVXgaruavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqiVy0xe9vqqrpepeYlI8qiW7rqaqpepiea0xe9Lq=Jc9vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9Fve9Ff0dmeaabaqaciaacaGaaeqabaqaamaaeaaakeaacqGHsislcaaI4aGaey41aqRaaG4naaaa@379D@</annotation>
|
||
</semantics>
|
||
</math> </li>
|
||
<li>
|
||
<math>
|
||
<semantics>
|
||
<mrow>
|
||
<mo>−</mo><mn>8</mn><mo>×</mo><mrow><mo>(</mo>
|
||
<mrow>
|
||
<mo>−</mo><mn>7</mn>
|
||
</mrow>
|
||
<mo>)</mo></mrow>
|
||
</mrow>
|
||
<annotation encoding='MathType-MTEF'>MathType@MTEF@5@5@+=feaaguart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHXgarmWu51MyVXgaruavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqiVy0xe9vqqrpepeYlI8qiW7rqaqpepiea0xe9Lq=Jc9vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9Fve9Ff0dmeaabaqaciaacaGaaeqabaqaamaaeaaakeaacqGHsislcaaI4aGaey41aq7aaeWaaeaacqGHsislcaaI3aaacaGLOaGaayzkaaaaaa@3A13@</annotation>
|
||
</semantics>
|
||
</math>
|
||
</li>
|
||
<li>
|
||
<math>
|
||
<semantics>
|
||
<mrow>
|
||
<mn>8</mn><mo>×</mo><mrow><mo>(</mo>
|
||
<mrow>
|
||
<mo>−</mo><mn>7</mn>
|
||
</mrow>
|
||
<mo>)</mo></mrow>
|
||
</mrow>
|
||
<annotation encoding='MathType-MTEF'>MathType@MTEF@5@5@+=feaaguart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHXgarmWu51MyVXgaruavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqiVy0xe9vqqrpepeYlI8qiW7rqaqpepiea0xe9Lq=Jc9vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9Fve9Ff0dmeaabaqaciaacaGaaeqabaqaamaaeaaakeaacaaI4aGaey41aq7aaeWaaeaacqGHsislcaaI3aaacaGLOaGaayzkaaaaaa@3926@</annotation>
|
||
</semantics>
|
||
</math>
|
||
</li>
|
||
<li>
|
||
<math>
|
||
<semantics>
|
||
<mrow>
|
||
<mn>8</mn><mo>×</mo><mn>7</mn>
|
||
</mrow>
|
||
<annotation encoding='MathType-MTEF'>MathType@MTEF@5@5@+=feaaguart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHXgarmWu51MyVXgaruavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqiVy0xe9vqqrpepeYlI8qiW7rqaqpepiea0xe9Lq=Jc9vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9Fve9Ff0dmeaabaqaciaacaGaaeqabaqaamaaeaaakeaacaaI4aGaey41aqRaaG4naaaa@36B0@</annotation>
|
||
</semantics>
|
||
</math>
|
||
</li>
|
||
|
||
|
||
<h2>Source: Glencoe/McGraw-Hill Mathematics: Applications and Concepts Course 1</h2>
|
||
|
||
<li>
|
||
<p><math xmlns="http://www.w3.org/1998/Math/MathML">
|
||
<semantics>
|
||
<mrow>
|
||
<mi>m</mi><mo>∠</mo><mn>1</mn><mo>=</mo><mi>30°</mi>
|
||
</mrow>
|
||
<annotation encoding='MathType-MTEF'>MathType@MTEF@5@5@+=feaaguart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHXgarmWu51MyVXgaruavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqiVy0xe9vqqrpepeYlI8qiW7rqaqpepiea0xe9Lq=Jc9vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9Fve9Ff0dmeaabaqaciaacaGaaeqabaqaamaaeaaakeaacaWGTbGaeyiiIaTaaGymaiabg2da9aaa@3767@</annotation>
|
||
</semantics>
|
||
</math> , <math xmlns="http://www.w3.org/1998/Math/MathML">
|
||
<semantics>
|
||
<mrow>
|
||
<mi>m</mi><mo>∠</mo><mn>2</mn><mo>=</mo>
|
||
<mi>60°</mi> </mrow>
|
||
<annotation encoding='MathType-MTEF'>MathType@MTEF@5@5@+=feaaguart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHXgarmWu51MyVXgaruavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqiVy0xe9vqqrpepeYlI8qiW7rqaqpepiea0xe9Lq=Jc9vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9Fve9Ff0dmeaabaqaciaacaGaaeqabaqaamaaeaaakeaacaWGTbGaeyiiIaTaaGOmaiabg2da9aaa@3768@</annotation>
|
||
</semantics>
|
||
</math> , <math xmlns="http://www.w3.org/1998/Math/MathML">
|
||
<semantics>
|
||
<mrow>
|
||
<mi>m</mi><mo>∠</mo><mn>1</mn><mo>+</mo><mi>m</mi><mo>∠</mo><mn>2</mn><mo>=</mo>
|
||
<mi>90°</mi> </mrow>
|
||
<annotation encoding='MathType-MTEF'>MathType@MTEF@5@5@+=feaaguart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHXgarmWu51MyVXgaruavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqiVy0xe9vqqrpepeYlI8qiW7rqaqpepiea0xe9Lq=Jc9vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9Fve9Ff0dmeaabaqaciaacaGaaeqabaqaamaaeaaakeaacaWGTbGaeyiiIaTaaGymaiabgUcaRiaad2gacqGHGic0caaIYaGaeyypa0daaa@3B95@</annotation>
|
||
</semantics>
|
||
</math> </p>
|
||
</li>
|
||
<li><math xmlns="http://www.w3.org/1998/Math/MathML">
|
||
<semantics>
|
||
<mrow>
|
||
<mi>m</mi><mo>∠</mo><mi>M</mi><mo>+</mo><mi>m</mi><mo>∠</mo><mi>N</mi><mo>=</mo>
|
||
<mi>180°</mi> </mrow>
|
||
<annotation encoding='MathType-MTEF'>MathType@MTEF@5@5@+=feaaguart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHXgarmWu51MyVXgaruavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqiVy0xe9vqqrpepeYlI8qiW7rqaqpepiea0xe9Lq=Jc9vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9Fve9Ff0dmeaabaqaciaacaGaaeqabaqaamaaeaaakeaacaWGTbGaeyiiIaTaamytaiabgUcaRiaad2gacqGHGic0caWGobGaeyypa0daaa@3BC3@</annotation>
|
||
</semantics>
|
||
</math><span style='font-size:12.0pt;
|
||
font-family:"Formata-Regular","sans-serif"'>.</span>
|
||
</li><li>
|
||
<math xmlns="http://www.w3.org/1998/Math/MathML">
|
||
<semantics>
|
||
<mrow>
|
||
<mi>A</mi><mo>=</mo><mfrac>
|
||
<mn>1</mn>
|
||
<mn>2</mn>
|
||
</mfrac>
|
||
<mi>b</mi><mi>h</mi>
|
||
</mrow>
|
||
<annotation encoding='MathType-MTEF'>MathType@MTEF@5@5@+=feaaguart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHXgarmWu51MyVXgaruavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqiVy0xe9vqqrpepeYlI8qiW7rqaqpepiea0xe9Lq=Jc9vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9Fve9Ff0dmeaabaqaciaacaGaaeqabaqaamaaeaaakeaacaWGbbGaeyypa0ZaaSaaaeaacaaIXaaabaGaaGOmaaaacaWGIbGaamiAaaaa@383D@</annotation>
|
||
</semantics>
|
||
</math>
|
||
</li>
|
||
<li>
|
||
<math xmlns="http://www.w3.org/1998/Math/MathML">
|
||
<semantics>
|
||
<mrow>
|
||
<mfrac>
|
||
<mrow>
|
||
<mtext>area of triangle</mtext>
|
||
</mrow>
|
||
<mrow>
|
||
<mtext>area of square</mtext>
|
||
</mrow>
|
||
</mfrac>
|
||
<mo>=</mo><mfrac>
|
||
<mrow>
|
||
<msup>
|
||
<mrow>
|
||
<mtext>1 unit</mtext>
|
||
</mrow>
|
||
<mn>2</mn>
|
||
</msup>
|
||
|
||
</mrow>
|
||
<mrow>
|
||
<msup>
|
||
<mrow>
|
||
<mtext>16 units</mtext>
|
||
</mrow>
|
||
<mn>2</mn>
|
||
</msup>
|
||
|
||
</mrow>
|
||
</mfrac>
|
||
|
||
</mrow>
|
||
<annotation encoding='MathType-MTEF'>MathType@MTEF@5@5@+=feaaguart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHXgarmWu51MyVXgaruavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqiVy0xe9vqqrpepeYlI8qiW7rqaqpepiea0xe9Lq=Jc9vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9Fve9Ff0dmeaabaqaciaacaGaaeqabaqaamaaeaaakeaadaWcaaqaaiaabggacaqGYbGaaeyzaiaabggacaqGGaGaae4BaiaabAgacaqGGaGaaeiDaiaabkhacaqGPbGaaeyyaiaab6gacaqGNbGaaeiBaiaabwgaaeaacaqGHbGaaeOCaiaabwgacaqGHbGaaeiiaiaab+gacaqGMbGaaeiiaiaabohacaqGXbGaaeyDaiaabggacaqGYbGaaeyzaaaacqGH9aqpdaWcaaqaaiaabgdacaqGGaGaaeyDaiaab6gacaqGPbGaaeiDamaaCaaaleqabaGaaGOmaaaaaOqaaiaabgdacaqG2aGaaeiiaiaabwhacaqGUbGaaeyAaiaabshacaqGZbWaaWbaaSqabeaacaaIYaaaaaaaaaa@5CAA@</annotation>
|
||
</semantics>
|
||
</math>
|
||
</li>
|
||
<li>
|
||
<math xmlns="http://www.w3.org/1998/Math/MathML">
|
||
<semantics>
|
||
<mrow>
|
||
<msup>
|
||
<mrow>
|
||
<mn>0.6</mn>
|
||
</mrow>
|
||
<mn>2</mn>
|
||
</msup>
|
||
|
||
</mrow>
|
||
<annotation encoding='MathType-MTEF'>MathType@MTEF@5@5@+=feaaguart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHXgarmWu51MyVXgaruavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqiVy0xe9vqqrpepeYlI8qiW7rqaqpepiea0xe9Lq=Jc9vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9Fve9Ff0dmeaabaqaciaacaGaaeqabaqaamaaeaaakeaacaaIWaGaaiOlaiaaiAdadaahaaWcbeqaaiaaikdaaaaaaa@362B@</annotation>
|
||
</semantics>
|
||
</math>
|
||
</li>
|
||
<li><math xmlns="http://www.w3.org/1998/Math/MathML">
|
||
<semantics>
|
||
<mrow>
|
||
<msup>
|
||
<mrow>
|
||
<mn>1.5</mn>
|
||
</mrow>
|
||
<mn>2</mn>
|
||
</msup>
|
||
|
||
</mrow>
|
||
<annotation encoding='MathType-MTEF'>MathType@MTEF@5@5@+=feaaguart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHXgarmWu51MyVXgaruavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqiVy0xe9vqqrpepeYlI8qiW7rqaqpepiea0xe9Lq=Jc9vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9Fve9Ff0dmeaabaqaciaacaGaaeqabaqaamaaeaaakeaacaaIXaGaaiOlaiaaiwdadaahaaWcbeqaaiaaikdaaaaaaa@362B@</annotation>
|
||
</semantics>
|
||
</math>
|
||
</li>
|
||
|
||
<h2>Source: Teacher Created</h2>
|
||
|
||
<li>
|
||
<math xmlns="http://www.w3.org/1998/Math/MathML">
|
||
<semantics>
|
||
<mrow>
|
||
<mn>4</mn><mrow><mo>(</mo>
|
||
<mrow>
|
||
<mn>2</mn><mi>x</mi><mo>+</mo><mn>3</mn><mi>x</mi>
|
||
</mrow>
|
||
<mo>)</mo></mrow>
|
||
</mrow>
|
||
<annotation encoding='MathType-MTEF'>MathType@MTEF@5@5@+=feaaguart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHXgarmWu51MyVXgaruWqVvNCPvMCG4uz3bqefqvATv2CG4uz3bIuV1wyUbqee0evGueE0jxyaibaieYlf9irVeeu0dXdh9vqqj=hEeea0dXdcba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9q8qqaq=dir=f0=yqaiVgFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaaeaqbaaGcbaGaaGinamaabmaabaGaaGOmaiaadIhacqGHRaWkcaaIZaGaamiEaaGaayjkaiaawMcaaaaa@3EA6@</annotation>
|
||
</semantics>
|
||
</math>
|
||
</li>
|
||
<li>
|
||
<math xmlns="http://www.w3.org/1998/Math/MathML">
|
||
<semantics>
|
||
<mrow>
|
||
<mn>36</mn><mo>+</mo><mn>4</mn><mi>y</mi><mo>−</mo><mn>1</mn><msup>
|
||
<mi>y</mi>
|
||
<mn>2</mn>
|
||
</msup>
|
||
<mo>+</mo><mn>5</mn><msup>
|
||
<mi>y</mi>
|
||
<mn>2</mn>
|
||
</msup>
|
||
<mo>−</mo><mn>2</mn>
|
||
</mrow>
|
||
<annotation encoding='MathType-MTEF'>MathType@MTEF@5@5@+=feaaguart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHXgarmWu51MyVXgaruWqVvNCPvMCG4uz3bqefqvATv2CG4uz3bIuV1wyUbqee0evGueE0jxyaibaieYlf9irVeeu0dXdh9vqqj=hEeea0dXdcba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9q8qqaq=dir=f0=yqaiVgFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaaeaqbaaGcbaGaaG4maiaaiAdacqGHRaWkcaaI0aGaamyEaiabgkHiTiaaigdacaWG5bWaaWbaaSqabeaacaaIYaaaaOGaey4kaSIaaGynaiaadMhadaahaaWcbeqaaiaaikdaaaGccqGHsislcaaIYaaaaa@44F9@</annotation>
|
||
</semantics>
|
||
</math>
|
||
</li>
|
||
<li>
|
||
<math xmlns="http://www.w3.org/1998/Math/MathML">
|
||
<semantics>
|
||
<mrow>
|
||
<mrow><mo>(</mo>
|
||
<mrow>
|
||
<mn>5</mn><mo>+</mo><mn>9</mn>
|
||
</mrow>
|
||
<mo>)</mo></mrow><mo>−</mo><mn>4</mn><mo>+</mo><mn>3</mn><mo>=</mo>
|
||
</mrow>
|
||
<annotation encoding='MathType-MTEF'>MathType@MTEF@5@5@+=feaaguart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHXgarmWu51MyVXgaruWqVvNCPvMCG4uz3bqefqvATv2CG4uz3bIuV1wyUbqee0evGueE0jxyaibaieYlf9irVeeu0dXdh9vqqj=hEeea0dXdcba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9q8qqaq=dir=f0=yqaiVgFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaaeaqbaaGcbaWaaeWaaeaacaaI1aGaey4kaSIaaGyoaaGaayjkaiaawMcaaiabgkHiTiaaisdacqGHRaWkcaaIZaGaeyypa0daaa@4047@</annotation>
|
||
</semantics>
|
||
</math>
|
||
</li>
|
||
<h2>Source: Holt McDougal Mathematics</h2>
|
||
<li>
|
||
<p class="MsoNormal" style='text-autospace:none'><span
|
||
style='font-size:12.0pt;font-family:"Helvetica","sans-serif";color:black'>Line </span><i><span
|
||
style='font-size:12.0pt;font-family:"Helvetica-Oblique","sans-serif";
|
||
color:black'>BC</span></i><span
|
||
style='font-size:12.0pt;font-family:"Helvetica","sans-serif";color:black'>, or </span><math xmlns="http://www.w3.org/1998/Math/MathML">
|
||
<semantics>
|
||
<mrow>
|
||
<mover accent='true'>
|
||
<mrow>
|
||
<mi>B</mi><mi>C</mi>
|
||
</mrow>
|
||
<mo stretchy='true'>↔</mo>
|
||
</mover>
|
||
|
||
</mrow>
|
||
<annotation encoding='MathType-MTEF'>MathType@MTEF@5@5@+=feaaguart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHXgarmWu51MyVXgaruavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqiVy0xe9vqqrpepeYlI8qiW7rqaqpepiea0xe9Lq=Jc9vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9Fve9Ff0dmeaabaqaciaacaGaaeqabaqaamaaeaaakeaadaWhdaqaaiaadkeacaWGdbaacaGLHdcaaaa@3664@</annotation>
|
||
</semantics>
|
||
</math></p>
|
||
</li>
|
||
<li>
|
||
<math xmlns="http://www.w3.org/1998/Math/MathML">
|
||
<semantics>
|
||
<mrow>
|
||
<mover accent='true'>
|
||
<mrow>
|
||
<mi>P</mi><mi>Q</mi>
|
||
</mrow>
|
||
<mo stretchy='true'>→</mo>
|
||
</mover>
|
||
|
||
</mrow>
|
||
<annotation encoding='MathType-MTEF'>MathType@MTEF@5@5@+=feaaguart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHXgarmWu51MyVXgaruavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqiVy0xe9vqqrpepeYlI8qiW7rqaqpepiea0xe9Lq=Jc9vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9Fve9Ff0dmeaabaqaciaacaGaaeqabaqaamaaeaaakeaadaWhcaqaaiaadcfacaWGrbaacaGLxdcaaaa@3675@</annotation>
|
||
</semantics>
|
||
</math>
|
||
</li><li>
|
||
<math xmlns="http://www.w3.org/1998/Math/MathML">
|
||
<semantics>
|
||
<mrow>
|
||
<mover accent='true'>
|
||
<mrow>
|
||
<mi>G</mi><mi>H</mi>
|
||
</mrow>
|
||
<mo stretchy='true'>¯</mo>
|
||
</mover>
|
||
</mrow>
|
||
<annotation encoding='MathType-MTEF'>MathType@MTEF@5@5@+=feaaguart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHXgarmWu51MyVXgaruavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqiVy0xe9vqqrpepeYlI8qiW7rqaqpepiea0xe9Lq=Jc9vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9Fve9Ff0dmeaabaqaciaacaGaaeqabaqaamaaeaaakeaadaqdaaqaaiaadEeacaWGibaaaaaa@34C0@</annotation>
|
||
</semantics>
|
||
</math>
|
||
</li>
|
||
<li>
|
||
<math xmlns="http://www.w3.org/1998/Math/MathML">
|
||
<semantics>
|
||
<mrow>
|
||
<mover accent='true'>
|
||
<mrow>
|
||
<mi>W</mi><mi>X</mi>
|
||
</mrow>
|
||
<mo stretchy='true'>¯</mo>
|
||
</mover>
|
||
<mo>≅</mo><mover accent='true'>
|
||
<mrow>
|
||
<mi>Y</mi><mi>Z</mi>
|
||
</mrow>
|
||
<mo stretchy='true'>¯</mo>
|
||
</mover>
|
||
|
||
</mrow>
|
||
<annotation encoding='MathType-MTEF'>MathType@MTEF@5@5@+=feaaguart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHXgarmWu51MyVXgaruavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqiVy0xe9vqqrpepeYlI8qiW7rqaqpepiea0xe9Lq=Jc9vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9Fve9Ff0dmeaabaqaciaacaGaaeqabaqaamaaeaaakeaadaqdaaqaaiaadEfacaWGybaaaiabgwKianaanaaabaGaamywaiaadQfaaaaaaa@37E1@</annotation>
|
||
</semantics>
|
||
</math>
|
||
</li>
|
||
<li>
|
||
<p class="MsoNormal" style='text-autospace:none'><span
|
||
style='font-family:"Arial","sans-serif";color:black'>Some angles are contained
|
||
within other, larger angles. For instance, <i><math xmlns="http://www.w3.org/1998/Math/MathML">
|
||
<semantics>
|
||
<mrow>
|
||
<mo>∠</mo><mi>B</mi><mi>E</mi><mi>F</mi>
|
||
</mrow>
|
||
<annotation encoding='MathType-MTEF'>MathType@MTEF@5@5@+=feaaguart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHXgarmWu51MyVXgaruavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqiVy0xe9vqqrpepeYlI8qiW7rqaqpepiea0xe9Lq=Jc9vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9Fve9Ff0dmeaabaqaciaacaGaaeqabaqaamaaeaaakeaacqGHGic0caWGcbGaamyraiaadAeaaaa@3710@</annotation>
|
||
</semantics>
|
||
</math> </i>includes <i><math xmlns="http://www.w3.org/1998/Math/MathML">
|
||
<semantics>
|
||
<mrow>
|
||
<mo>∠</mo><mi>B</mi><mi>E</mi><mi>D</mi>
|
||
</mrow>
|
||
<annotation encoding='MathType-MTEF'>MathType@MTEF@5@5@+=feaaguart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHXgarmWu51MyVXgaruavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqiVy0xe9vqqrpepeYlI8qiW7rqaqpepiea0xe9Lq=Jc9vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9Fve9Ff0dmeaabaqaciaacaGaaeqabaqaamaaeaaakeaacqGHGic0caWGcbGaamyraiaadseaaaa@370E@</annotation>
|
||
</semantics>
|
||
</math> </i>and <i><math xmlns="http://www.w3.org/1998/Math/MathML">
|
||
<semantics>
|
||
<mrow>
|
||
<mo>∠</mo><mi>D</mi><mi>E</mi><mi>F</mi>
|
||
</mrow>
|
||
<annotation encoding='MathType-MTEF'>MathType@MTEF@5@5@+=feaaguart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHXgarmWu51MyVXgaruavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqiVy0xe9vqqrpepeYlI8qiW7rqaqpepiea0xe9Lq=Jc9vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9Fve9Ff0dmeaabaqaciaacaGaaeqabaqaamaaeaaakeaacqGHGic0caWGebGaamyraiaadAeaaaa@3712@</annotation>
|
||
</semantics>
|
||
</math></i>.</span></p>
|
||
</li>
|
||
|
||
|
||
<h2>Source: Say It With Symbols: Making Sense of Symbols (Pearson)</h2>
|
||
|
||
|
||
|
||
<li><math xmlns:m="http://www.w3.org/1999/xhtml" id="EQp044-010" alttext="x equals negative b +/- square root of b squared - 4 a c over 2 a" overflow="scroll">
|
||
<mrow>
|
||
<mi>x</mi>
|
||
<mo>=</mo>
|
||
<mfrac>
|
||
<mrow>
|
||
<mo>−</mo>
|
||
<mi>b</mi>
|
||
<mo>±</mo>
|
||
<msqrt>
|
||
<mrow>
|
||
<msup>
|
||
<mrow>
|
||
<mi>b</mi>
|
||
</mrow>
|
||
<mrow>
|
||
<mn>2</mn>
|
||
</mrow>
|
||
</msup>
|
||
<mo>−</mo>
|
||
<mn>4</mn>
|
||
<mi>a</mi>
|
||
<mi>c</mi>
|
||
</mrow>
|
||
</msqrt>
|
||
</mrow>
|
||
<mrow>
|
||
<mn>2</mn>
|
||
<mi>a</mi>
|
||
</mrow>
|
||
</mfrac>
|
||
</mrow>
|
||
</math>
|
||
|
||
|
||
<li>
|
||
<math xmlns:m="http://www.w3.org/1999/xhtml" id="EQp059-006" alttext=" " overflow="scroll"><mrow><mi>y</mi><mo>=</mo><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>+</mo><mn>8</mn><mi>x</mi><mo>+</mo><mn>16</mn></mrow></math></li>
|
||
<li>
|
||
<math xmlns:m="http://www.w3.org/1999/xhtml" id="EQp059-007" alttext="y = 1 over 3 left parenthesis 3 to the power x right parenthesis" overflow="scroll"><mrow><mi>y</mi><mo>=</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>3</mn></mrow></mfrac><mrow><mo>(</mo><msup><mrow><mn>3</mn></mrow><mrow><mi>x</mi></mrow></msup><mo>)</mo></mrow></mrow></math></li>
|
||
<li>
|
||
<math xmlns:m="http://www.w3.org/1999/xhtml" id="EQp059-008" alttext=" " overflow="scroll"><mrow><mi>y</mi><mo>=</mo><mn>10</mn><mo>−</mo><mn>2</mn><mi>x</mi></mrow></math></li>
|
||
<li>
|
||
<math xmlns:m="http://www.w3.org/1999/xhtml" id="EQp059-009" alttext=" " overflow="scroll"><mrow><mi>y</mi><mo>=</mo><mn>2</mn><msup><mrow><mi>x</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>+</mo><mn>5</mn></mrow></math></li>
|
||
<li>
|
||
<math xmlns:m="http://www.w3.org/1999/xhtml" id="EQp059-010" alttext=" " overflow="scroll"><mrow><mi>y</mi><mo>=</mo><mo>(</mo><msup><mrow><mo/><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>+</mo><mn>1</mn><mrow><mo>)</mo><mo>(</mo><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow><mo>+</mo><mn>3</mn><mo>)</mo></mrow></math></li>
|
||
<li>
|
||
<math xmlns:m="http://www.w3.org/1999/xhtml" id="EQp059-011" alttext=" " overflow="scroll"><mrow><mi>y</mi><mo>=</mo><msup><mrow><mn>0.5</mn></mrow><mrow><mi>x</mi></mrow></msup></mrow></math></li>
|
||
<li>
|
||
<math xmlns:m="http://www.w3.org/1999/xhtml" id="EQp059-012" alttext=" " overflow="scroll"><mrow><mi>y</mi><mo>=</mo><mn>22</mn><mo>−</mo><mn>2</mn><mi>x</mi></mrow></math></li>
|
||
<li>
|
||
<math xmlns:m="http://www.w3.org/1999/xhtml" id="EQp059-013" alttext="y = 3 over x" overflow="scroll"><mrow><mi>y</mi><mo>=</mo><mfrac><mrow><mn>3</mn></mrow><mrow><mi>x</mi></mrow></mfrac></mrow></math></li>
|
||
<li>
|
||
<math xmlns:m="http://www.w3.org/1999/xhtml" id="EQp059-014" alttext=" " overflow="scroll"><mrow><mi>y</mi><mo>=</mo><mo>(</mo><mi>x</mi><mo>+</mo><mn>4</mn><mo>)</mo><mo>(</mo><mi>x</mi><mo>+</mo><mn>4</mn><mo>)</mo></mrow></math></li>
|
||
<li>
|
||
<math xmlns:m="http://www.w3.org/1999/xhtml" id="EQp059-015" alttext=" " overflow="scroll"><mrow><mi>y</mi><mo>=</mo><mo>(</mo><mn>4</mn><mi>x</mi><mo>−</mo><mn>3</mn><mo>)</mo><mo>(</mo><mi>x</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow></math></li>
|
||
<li>
|
||
<math xmlns:m="http://www.w3.org/1999/xhtml" id="EQp059-016" alttext=" " overflow="scroll"><mrow><mi>y</mi><mo>=</mo><mn>20</mn><mi>x</mi><mo>−</mo><mn>4</mn><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></math></li>
|
||
<li>
|
||
<math xmlns:m="http://www.w3.org/1999/xhtml" id="EQp059-017" alttext=" " overflow="scroll"><mrow><mi>y</mi><mo>=</mo><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></math></li>
|
||
<li>
|
||
<math xmlns:m="http://www.w3.org/1999/xhtml" id="EQp059-018" alttext=" " overflow="scroll"><mrow><mi>y</mi><mo>=</mo><msup><mrow><mn>3</mn></mrow><mrow><mi>x</mi><mo>−</mo><mn>1</mn></mrow></msup></mrow></math></li>
|
||
<li>
|
||
<math xmlns:m="http://www.w3.org/1999/xhtml" id="EQp059-019" alttext=" " overflow="scroll"><mrow><mi>y</mi><mo>=</mo><mn>16</mn><mo>−</mo><mn>2</mn><mo>(</mo><mi>x</mi><mo>+</mo><mn>3</mn><mo>)</mo></mrow></math></li>
|
||
<li>
|
||
<math xmlns:m="http://www.w3.org/1999/xhtml" id="EQp059-020" alttext=" " overflow="scroll"><mrow><mi>y</mi><mo>=</mo><mn>4</mn><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>−</mo><mi>x</mi><mo>−</mo><mn>3</mn></mrow></math></li>
|
||
<li>
|
||
<math xmlns:m="http://www.w3.org/1999/xhtml" id="EQp056-021" alttext="y = x + 1 over x" overflow="scroll"><mrow><mi>y</mi><mo>=</mo><mi>x</mi><mo>+</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mi>x</mi></mrow></mfrac></mrow></math></li>
|
||
<li>
|
||
<math xmlns:m="http://www.w3.org/1999/xhtml" id="EQp059-021" alttext=" " overflow="scroll"><mrow><mi>y</mi><mo>=</mo><mn>4</mn><mi>x</mi><mo>(</mo><mn>5</mn><mo>−</mo><mi>x</mi><mo>)</mo></mrow></math></li>
|
||
<li>
|
||
<math xmlns:m="http://www.w3.org/1999/xhtml" id="EQp056-023" alttext=" " overflow="scroll"><mrow><mi>y</mi><mo>=</mo><mn>2</mn><mo>(</mo><mi>x</mi><mo>−</mo><mn>3</mn><mo>)</mo><mo>+</mo><mn>6</mn><mo>(</mo><mn>1</mn><mo>−</mo><mi>x</mi><mo>)</mo></mrow></math>
|
||
</li>
|
||
|
||
|
||
|
||
<h2>Source: Kentucky KCCT Practice Test</h2>
|
||
|
||
<li>
|
||
<math xmlns="http://www.w3.org/1998/Math/MathML">
|
||
<semantics>
|
||
<mrow>
|
||
<mn>0.25</mn><mo>></mo><mfrac>
|
||
<mn>5</mn>
|
||
<mrow>
|
||
<mn>16</mn>
|
||
</mrow>
|
||
</mfrac>
|
||
|
||
</mrow>
|
||
<annotation encoding='MathType-MTEF'>MathType@MTEF@5@5@+=feaaguart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHXgarmWu51MyVXgaruavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqiVy0xe9vqqrpepeYlI8qiW7rqaqpepiea0xe9Lq=Jc9vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9Fve9Ff0dmeaabaqaciaacaGaaeqabaqaamaaeaaakeaacaaIWaGaaiOlaiaaikdacaaI1aGaeyOpa4ZaaSaaaeaacaaI1aaabaGaaGymaiaaiAdaaaaaaa@394F@</annotation>
|
||
</semantics>
|
||
</math>
|
||
</li><li>
|
||
<math xmlns="http://www.w3.org/1998/Math/MathML">
|
||
<semantics>
|
||
<mrow>
|
||
<mn>32</mn><mo>⋅</mo><mrow><mo>(</mo>
|
||
<mrow>
|
||
<mn>5</mn><mo>⋅</mo><mn>7</mn>
|
||
</mrow>
|
||
<mo>)</mo></mrow>
|
||
</mrow>
|
||
<annotation encoding='MathType-MTEF'>MathType@MTEF@5@5@+=feaaguart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHXgarmWu51MyVXgaruavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqiVy0xe9vqqrpepeYlI8qiW7rqaqpepiea0xe9Lq=Jc9vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9Fve9Ff0dmeaabaqaciaacaGaaeqabaqaamaaeaaakeaacaaIZaGaaGOmaiabgwSixpaabmaabaGaaGynaiabgwSixlaaiEdaaiaawIcacaGLPaaaaaa@3C2C@</annotation>
|
||
</semantics>
|
||
</math>
|
||
</li>
|
||
<h2>Source: Pearson Filling and Wrapping Three-Dimensional Measurement</h2>
|
||
<li>
|
||
<math id="EQp039-001" alttext=" " overflow="scroll"><mrow><mrow><mo>(</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac><mo>×</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac><mo>×</mo><mi>π</mi><mo>×</mo><mn>2</mn><mo>)</mo></mrow><mo>+</mo><mrow><mo>(</mo><mn>2</mn><mo>×</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac><mo>×</mo><mi>π</mi><mo>×</mo><mn>5</mn><mo>)</mo></mrow></mrow></math>
|
||
</li>
|
||
|
||
|
||
<h2>Source: Examples and Problems in Mathematical Statistics (Wiley)</h2>
|
||
|
||
<li>
|
||
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mrow><munder><mtext>liminf</mtext><mrow><mi>n</mi><mo>→</mo><mi>∞</mi></mrow></munder><msub><mi>E</mi><mrow><mi>n</mi></mrow></msub><mo>=</mo><munder><mo>⋃</mo><mrow><mi>n</mi><mo>≥</mo><mn>1</mn></mrow></munder><munder><mo>⋂</mo><mrow><mi>k</mi><mo>≥</mo><mi>n</mi></mrow></munder><msub><mi>E</mi><mrow><mi>k</mi></mrow></msub><mo>,</mo><mspace width="0.2em" /><munder><mtext>limsup</mtext><mrow><mi>n</mi><mo>→</mo><mi>∞</mi></mrow></munder><msub><mi>E</mi><mrow><mi>n</mi></mrow></msub><mo>=</mo><munder><mo>⋂</mo><mrow><mi>n</mi><mo>≥</mo><mn>1</mn></mrow></munder><munder><mo>⋃</mo><mrow><mi>k</mi><mo>≥</mo><mi>n</mi></mrow></munder><msub><mi>E</mi><mrow><mi>k</mi></mrow></msub><mo>.</mo></mrow></math>
|
||
</li>
|
||
<li>
|
||
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mrow><mtable columnalign="left"><mtr><mtd columnalign="left"><mrow><mtext>(i)</mtext></mrow></mtd><mtd columnalign="left"><mrow><mspace width="0.2em" /><mi>𝒮</mi><mo>∈</mo><mi>𝒜</mi><mo>;</mo></mrow></mtd></mtr><mtr><mtd columnalign="right" columnspan="1"><mrow><mtext>(ii)</mtext></mrow></mtd><mtd columnalign="left"><mrow><mspace width="0.2em" /><mtext>if</mtext><mi>E</mi><mo>∈</mo><mi>𝒜</mi><mspace width="0.2em" /><mtext>then</mtext><mspace width="0.2em" /><mover><mrow><mi>E</mi></mrow><mrow><mrow /><mo>‾</mo></mrow></mover><mo>∈</mo><mi>𝒜</mi><mo>;</mo></mrow></mtd></mtr><mtr><mtd columnalign="right" columnspan="1"><mrow><mtext>(iii)</mtext></mrow></mtd><mtd columnalign="left"><mrow><mspace width="0.2em" /><mtext>if</mtext><msub><mi>E</mi><mrow><mn>1</mn></mrow></msub><mo>,</mo><msub><mi>E</mi><mrow><mn>2</mn></mrow></msub><mo>∈</mo><mi>𝒜</mi><mspace width="0.2em" /><mtext>then</mtext><mspace width="0.2em" /><msub><mi>E</mi><mrow><mn>1</mn></mrow></msub><mo>∪</mo><msub><mi>E</mi><mrow><mn>2</mn></mrow></msub><mo>∈</mo><mi>𝒜</mi><mo>.</mo></mrow></mtd></mtr></mtable></mrow></math>
|
||
</li>
|
||
<li>
|
||
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mrow><mtable columnalign="left"><mtr><mtd columnalign="left"><mrow /></mtd><mtd columnalign="left"><mrow /></mtd><mtd columnalign="left"><mrow><mo stretchy="false">(</mo><mi mathvariant="normal">A</mi><mo mathvariant="normal">.</mo><mn>1</mn><mo stretchy="false">)</mo><mspace width="0.2em" /><mi mathvariant="normal">If</mi><mspace width="0.2em" /><mi>A</mi><mo>∈</mo><mrow><mi>ℱ</mi></mrow><mspace width="0.2em" /><mi mathvariant="normal">then</mi><mspace width="0.2em" /><mn>0</mn><mo>≤</mo><mi>P</mi><mo stretchy="false">{</mo><mi>A</mi><mo stretchy="false">}</mo><mo>≤</mo><mn>1</mn><mo>.</mo></mrow></mtd><mtd columnalign="left"><mo stretchy="false">(</mo><mn>1</mn><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd columnalign="right" columnspan="1"><mrow /></mtd><mtd columnalign="left"><mrow /></mtd><mtd columnalign="left"><mrow><mo stretchy="false">(</mo><mi mathvariant="normal">A</mi><mo mathvariant="normal">.</mo><mn>2</mn><mo stretchy="false">)</mo><mspace width="0.2em" /><mi>P</mi><mo stretchy="false">{</mo><mrow><mi>𝒮</mi></mrow><mo stretchy="false">}</mo><mo>=</mo><mn>1</mn><mo>.</mo></mrow></mtd><mtd columnalign="left"><mo stretchy="false">(</mo><mn>2</mn><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd columnalign="right" columnspan="1"><mrow /></mtd><mtd columnalign="left"><mrow /></mtd><mtd columnalign="left"><mrow><mo stretchy="false">(</mo><mi mathvariant="normal">A</mi><mo mathvariant="normal">.</mo><mn>3</mn><mo stretchy="false">)</mo><mspace width="0.2em" /><mi mathvariant="normal">If</mi><mspace width="0.2em" /><mo stretchy="false">{</mo><msub><mi>E</mi><mrow><mi>n</mi></mrow></msub><mo>,</mo><mi>n</mi><mo>≥</mo><mn>1</mn><mo stretchy="false">}</mo><mo>∈</mo><mrow><mi>ℱ</mi></mrow><mspace width="0.2em" /><mtext>is a sequence of</mtext><mspace width="0.2em" /><mtext>disjoint</mtext></mrow></mtd><mtd columnalign="left"><mo stretchy="false">(</mo><mn>3</mn><mo stretchy="false">)</mo></mtd></mtr></mtable></mrow></math>
|
||
</li>
|
||
<li>
|
||
<mathStatement xml:id="c01-mthst-0010">
|
||
<title type="mathStatementName">Theorem</title>
|
||
<p><b>(Bayes)</b>
|
||
<displayedItem xml:id="c01-disp-0015" type="mathematics">
|
||
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mrow><mi>P</mi><mo stretchy="false">{</mo><msub><mi>B</mi><mrow><mi>j</mi></mrow></msub><mi>|</mi><mi>A</mi><mo stretchy="false">}</mo><mo>=</mo><mfrac><mrow><mi>P</mi><mo stretchy="false">{</mo><msub><mi>B</mi><mrow><mi>j</mi></mrow></msub><mo stretchy="false">}</mo><mi>P</mi><mo stretchy="false">{</mo><mi>A</mi><mi>|</mi><msub><mi>B</mi><mrow><mi>j</mi></mrow></msub><mo stretchy="false">}</mo></mrow><mrow><munder><mo>∑</mo><mrow><mi>j</mi><mo>′</mo><mo>∈</mo><mi>J</mi></mrow></munder><mi>P</mi><mo stretchy="false">{</mo><msub><mi>B</mi><mrow><mi>j</mi><mo>′</mo></mrow></msub><mo stretchy="false">}</mo><mi>P</mi><mo stretchy="false">{</mo><mi>A</mi><mi>|</mi><msub><mi>B</mi><mrow><mi>j</mi><mo>′</mo></mrow></msub><mo stretchy="false">}</mo></mrow></mfrac><mo>.</mo></mrow></math></displayedItem></p>
|
||
</mathStatement>
|
||
</li>
|
||
<li>
|
||
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mrow><msub><mi>μ</mi><mrow><mn>1</mn></mrow></msub><mo stretchy="false">(</mo><mi>B</mi><mo stretchy="false">)</mo><mo>=</mo><msub><mo>∫</mo><mrow><mi>B</mi></mrow></msub><mi>f</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mi>d</mi><msub><mi>μ</mi><mrow><mn>2</mn></mrow></msub><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo></mrow></math>
|
||
</li>
|
||
<li>
|
||
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mrow><munder><mtext>lim</mtext><mrow><mi>n</mi><mo>→</mo><mi>∞</mi></mrow></munder><mi>E</mi><mo stretchy="false">{</mo><mo>|</mo><msub><mi>X</mi><mrow><mi>n</mi></mrow></msub><mo>−</mo><mi>X</mi><mo>|</mo><mo stretchy="false">}</mo><mo>=</mo><mi>E</mi><mrow><mo>{</mo><munder><mtext>lim</mtext><mrow><mi>n</mi><mo>→</mo><mi>∞</mi></mrow></munder><mo>|</mo><msub><mi>X</mi><mrow><mi>n</mi></mrow></msub><mo>−</mo><mi>X</mi><mo>|</mo><mo>}</mo></mrow><mo>=</mo><mn>0</mn><mo>.</mo></mrow></math>
|
||
</li>
|
||
<li>
|
||
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mrow><mtable columnalign="left"><mtr><mtd columnalign="left"><mrow><msub><mi>P</mi><mrow><mi>μ</mi><mo>,</mo><mi>σ</mi></mrow></msub><mo stretchy="false">{</mo><mi>Y</mi><mo>≥</mo><msub><mi>l</mi><mrow><mi>β</mi></mrow></msub><mo stretchy="false">(</mo><msub><mover><mrow><mi>Y</mi></mrow><mrow><mrow /><mo>‾</mo></mrow></mover><mrow><mi>n</mi></mrow></msub><mo>,</mo><msub><mi>S</mi><mrow><mi>n</mi></mrow></msub><mo stretchy="false">)</mo><mo stretchy="false">}</mo><mo>=</mo><msub><mi>P</mi><mrow><mi>μ</mi><mo>,</mo><mi>σ</mi></mrow></msub><mo stretchy="false">{</mo><mo stretchy="false">(</mo><mi>Y</mi><mo>−</mo><msub><mover><mrow><mi>Y</mi></mrow><mrow><mrow /><mo>‾</mo></mrow></mover><mrow><mi>n</mi></mrow></msub><mo stretchy="false">)</mo><mo>/</mo><mrow><mo>(</mo><mi>S</mi><mo>·</mo><msup><mrow><mo>(</mo><mn>1</mn><mo>+</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mi>n</mi></mrow></mfrac><mo>)</mo></mrow><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></msup><mo>)</mo></mrow><mo>≥</mo><mo>−</mo><msub><mi>t</mi><mrow><mi>β</mi></mrow></msub><mo stretchy="false">[</mo><mi>n</mi><mo>−</mo><mn>1</mn><mo stretchy="false">]</mo><mo stretchy="false">}</mo><mo>=</mo><mi>β</mi><mo>,</mo></mrow></mtd></mtr><mtr><mtd columnalign="right" columnspan="1"><mrow /></mtd><mtd columnalign="left"><mo stretchy="false">(</mo><mn>1</mn><mo stretchy="false">)</mo></mtd></mtr></mtable></mrow></math>
|
||
</li>
|
||
<li>
|
||
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mrow><mi>L</mi><mo>=</mo><mrow><mo>(</mo><mtable><mtr><mtd columnalign="center"><mrow><mn>1</mn></mrow></mtd><mtd columnalign="center"><mrow><mspace width="0.2em" /><mo>−</mo><mn>1</mn></mrow></mtd><mtd columnalign="center"><mrow><mspace width="0.2em" /></mrow></mtd><mtd columnalign="center"><mrow><mspace width="0.2em" /></mrow></mtd><mtd columnalign="center"><mrow><mspace width="0.2em" /></mrow></mtd><mtd columnalign="center"><mrow><mspace width="0.2em" /></mrow></mtd></mtr><mtr><mtd columnalign="center"><mrow /></mtd><mtd columnalign="center"><mrow><mspace width="0.2em" /><mn>1</mn></mrow></mtd><mtd columnalign="center"><mrow><mspace width="0.2em" /><mo>−</mo><mn>1</mn></mrow></mtd><mtd columnalign="center"><mrow><mspace width="0.2em" /></mrow></mtd><mtd columnalign="center"><mrow><mspace width="0.2em" /><mn>0</mn></mrow></mtd><mtd columnalign="center"><mrow><mspace width="0.2em" /></mrow></mtd></mtr><mtr><mtd columnalign="center"><mrow /></mtd><mtd columnalign="center"><mrow><mspace width="0.2em" /></mrow></mtd><mtd columnalign="center"><mrow><mspace width="0.2em" /></mrow></mtd><mtd columnalign="center"><mrow><mspace width="0.2em" /></mrow></mtd><mtd columnalign="center"><mrow><mspace width="0.2em" /></mrow></mtd><mtd columnalign="center"><mrow><mspace width="0.2em" /></mrow></mtd></mtr><mtr><mtd columnalign="center"><mrow /></mtd><mtd columnalign="center"><mrow><mspace width="0.2em" /><mn>0</mn></mrow></mtd><mtd columnalign="center"><mrow><mspace width="0.2em" /></mrow></mtd><mtd columnalign="center"><mrow><mspace width="0.2em" /></mrow></mtd><mtd columnalign="center"><mrow><mspace width="0.2em" /></mrow></mtd><mtd columnalign="center"><mrow><mspace width="0.2em" /></mrow></mtd></mtr><mtr><mtd columnalign="center"><mrow /></mtd><mtd columnalign="center"><mrow><mspace width="0.2em" /></mrow></mtd><mtd columnalign="center"><mrow><mspace width="0.2em" /></mrow></mtd><mtd columnalign="center"><mrow><mspace width="0.2em" /></mrow></mtd><mtd columnalign="center"><mrow><mspace width="0.2em" /><mn>1</mn></mrow></mtd><mtd columnalign="center"><mrow><mspace width="0.2em" /><mo>−</mo><mn>1</mn></mrow></mtd></mtr></mtable><mo>)</mo></mrow><mo>.</mo></mrow></math>
|
||
</li><li>
|
||
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mrow><msqrt><mrow><mi>n</mi></mrow></msqrt><mo stretchy="false">[</mo><msub><mover><mrow><mi>Y</mi></mrow><mrow><mrow /><mo>‾</mo></mrow></mover><mrow><mi>n</mi></mrow></msub><mo>−</mo><mo stretchy="false">(</mo><mi>μ</mi><mo>+</mo><msub><mi>z</mi><mrow><mi>β</mi></mrow></msub><mi>σ</mi><mo stretchy="false">)</mo><mo stretchy="false">]</mo><mo>/</mo><msub><mi>S</mi><mrow><mi>n</mi></mrow></msub><mo>~</mo><mfrac><mrow><mi>U</mi><mo>+</mo><msqrt><mrow><mi>n</mi></mrow></msqrt><mspace width="0.2em" /><msub><mi>z</mi><mrow><mn>1</mn><mo>−</mo><mi>β</mi></mrow></msub></mrow><mrow><mo stretchy="false">(</mo><msup><mi>χ</mi><mrow><mn>2</mn></mrow></msup><mo stretchy="false">[</mo><mi>n</mi><mo>−</mo><mn>1</mn><mo stretchy="false">]</mo><mo>/</mo><mo stretchy="false">(</mo><mi>n</mi><mo>−</mo><mn>1</mn><mo stretchy="false">)</mo><mo stretchy="false">)</mo><msup><mi /><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></msup></mrow></mfrac><mo>~</mo><mi>t</mi><mo stretchy="false">[</mo><mi>n</mi><mo>−</mo><mn>1</mn><mo>;</mo><msqrt><mrow><mi>n</mi></mrow></msqrt><mspace width="0.2em" /><msub><mi>z</mi><mrow><mn>1</mn><mo>−</mo><mi>β</mi></mrow></msub><mo stretchy="false">]</mo><mo>,</mo></mrow></math>
|
||
</li><li>
|
||
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mrow><mtable columnalign="left"><mtr><mtd columnalign="left"><mrow><mi>γ</mi></mrow></mtd><mtd columnalign="left"><mrow><mo>=</mo><mi>P</mi><mo stretchy="false">{</mo><msub><mi>E</mi><mrow><mi>p</mi><mo>,</mo><mi>q</mi></mrow></msub><mo>⊂</mo><mo stretchy="false">(</mo><msub><mi>X</mi><mrow><mo stretchy="false">(</mo><mi>r</mi><mo stretchy="false">)</mo></mrow></msub><mo>,</mo><msub><mi>X</mi><mrow><mo stretchy="false">(</mo><mi>s</mi><mo stretchy="false">)</mo></mrow></msub><mo stretchy="false">}</mo></mrow></mtd></mtr><mtr><mtd columnalign="right" columnspan="1"><mrow /></mtd><mtd columnalign="left"><mrow><mo>=</mo><mfrac><mrow><mi>n</mi><mo>!</mo></mrow><mrow><mo stretchy="false">(</mo><mi>r</mi><mo>−</mo><mn>1</mn><mo stretchy="false">)</mo><mo>!</mo></mrow></mfrac><munderover><mo>∑</mo><mrow><mi>j</mi><mo>=</mo><mn>0</mn> </mrow><mrow><mi>s</mi><mo>−</mo><mi>r</mi><mo>−</mo><mn>1</mn></mrow></munderover><mo stretchy="false">(</mo><mo>−</mo><mn>1</mn><mo stretchy="false">)</mo><msup><mi /><mrow><mi>j</mi></mrow></msup><mfrac><mrow><msup><mi>p</mi><mrow><mi>r</mi><mo>+</mo><mi>j</mi></mrow></msup></mrow><mrow><mo stretchy="false">(</mo><mi>n</mi><mo>−</mo><mi>r</mi><mo>−</mo><mi>j</mi><mo stretchy="false">)</mo><mo>!</mo><mi>j</mi><mo>!</mo></mrow></mfrac><msub><mi>I</mi><mrow><mn>1</mn><mo>−</mo><mi>q</mi></mrow></msub><mo stretchy="false">(</mo><mi>n</mi><mo>−</mo><mi>s</mi><mo>+</mo><mn>1</mn><mo>,</mo><mi>s</mi><mo>−</mo><mi>r</mi><mo>−</mo><mi>j</mi><mo stretchy="false">)</mo><mo>.</mo></mrow></mtd></mtr></mtable></mrow></math>
|
||
</li>
|
||
<h2>Source: Fractal Geometry</h2>
|
||
<li>
|
||
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mrow><msub><mrow><mi>S</mi></mrow><mrow><mi>i</mi></mrow></msub><mfenced open="[" close="]"><mrow><mtable><mtr><mtd><mi>t</mi></mtd></mtr><mtr><mtd><mi>x</mi></mtd></mtr></mtable></mrow></mfenced><mo>=</mo><mfenced open="[" close="]"><mrow><mtable><mtr><mtd><mn>1</mn><mo stretchy="false">/</mo><mi>m</mi></mtd><mtd><mn>0</mn></mtd></mtr><mtr><mtd><msub><mrow><mi>a</mi></mrow><mrow><mi>i</mi></mrow></msub></mtd><mtd><msub><mrow><mi>r</mi></mrow><mrow><mi>i</mi></mrow></msub></mtd></mtr></mtable></mrow></mfenced><mfenced open="[" close="]"><mrow><mtable><mtr><mtd><mi>t</mi></mtd></mtr><mtr><mtd><mi>x</mi></mtd></mtr></mtable></mrow></mfenced><mo>+</mo><mfenced open="[" close="]"><mrow><mtable><mtr><mtd><mo stretchy="false">(</mo><mi>i</mi><mo>−</mo><mn>1</mn><mo stretchy="false">)</mo><mo stretchy="false">/</mo><mi>m</mi></mtd></mtr><mtr><mtd><msub><mrow><mi>b</mi></mrow><mrow><mi>i</mi></mrow></msub></mtd></mtr></mtable></mrow></mfenced><mo>,</mo></mrow></math>
|
||
</li><li>
|
||
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mrow><msub><mrow><mi>c</mi></mrow><mrow><mn>1</mn></mrow></msub><msup><mrow><mi>h</mi></mrow><mrow><mn>4</mn><mo>−</mo><mn>2</mn><mi>s</mi></mrow></msup><mo>≤</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn><mi>T</mi></mrow></mfrac><msubsup><mrow><mo>∫</mo></mrow><mrow><mo>−</mo><mi>T</mi></mrow><mrow><mi>T</mi></mrow></msubsup><msup><mrow><mo stretchy="false">(</mo><mi>f</mi><mo stretchy="false">(</mo><mi>t</mi><mo>+</mo><mi>h</mi><mo stretchy="false">)</mo><mo>−</mo><mi>f</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">)</mo></mrow><mrow><mn>2</mn></mrow></msup><mi mathvariant="normal">d</mi><mi>t</mi><mo>≤</mo><msub><mrow><mi>c</mi></mrow><mrow><mn>2</mn></mrow></msub><msup><mrow><mi>h</mi></mrow><mrow><mn>4</mn><mo>−</mo><mn>2</mn><mi>s</mi></mrow></msup></mrow></math>
|
||
</li><li>
|
||
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mrow><mi>C</mi><mo stretchy="false">(</mo><mn>0</mn><mo stretchy="false">)</mo><mo>−</mo><mi>C</mi><mo stretchy="false">(</mo><mi>h</mi><mo stretchy="false">)</mo><mo>≃</mo><mi>c</mi><msup><mrow><mi>h</mi></mrow><mrow><mn>4</mn><mo>−</mo><mn>2</mn><mi>s</mi></mrow></msup></mrow></math>
|
||
</li><li>
|
||
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mrow><mi>S</mi><mo stretchy="false">(</mo><mi>ω</mi><mo stretchy="false">)</mo><mo>=</mo><munder><mrow><mi>lim</mi></mrow><mrow><mi>T</mi><mo>→</mo><mi>∞</mi></mrow></munder><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn><mi>T</mi></mrow></mfrac><msup><mrow><mfenced open="|" close="|"><msubsup><mrow><mo>∫</mo></mrow><mrow><mo>−</mo><mi>T</mi></mrow><mrow><mi>T</mi></mrow></msubsup><mi>f</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><msup><mrow><mi mathvariant="normal">e</mi></mrow><mrow><mi mathvariant="italic">it</mi><mi>ω</mi></mrow></msup><mi mathvariant="normal">d</mi><mi>t</mi></mfenced></mrow><mrow><mn>2</mn></mrow></msup><mo>.</mo></mrow></math>
|
||
</li><li>
|
||
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mrow><msubsup><mrow><mo>∫</mo></mrow><mrow><mn>0</mn></mrow><mrow><mn>1</mn></mrow></msubsup><mspace width="-0.2em" /><msubsup><mrow><mo>∫</mo></mrow><mrow><mn>0</mn></mrow><mrow><mn>1</mn></mrow></msubsup><msup><mrow><mrow><mo stretchy="false">[</mo><mrow><mo>|</mo><mi>f</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><mo>−</mo><mi>f</mi><mo stretchy="false">(</mo><mi>u</mi><mo stretchy="false">)</mo><msup><mrow><mo>|</mo></mrow><mrow><mn>2</mn></mrow></msup><mo>+</mo><mo>|</mo><mi>t</mi><mo>−</mo><mi>u</mi><msup><mrow><mo>|</mo></mrow><mrow><mn>2</mn></mrow></msup></mrow><mo stretchy="false">]</mo></mrow></mrow><mrow><mo>−</mo><mi>s</mi><mo stretchy="false">/</mo><mn>2</mn></mrow></msup><mi mathvariant="normal">d</mi><mi>t</mi><mi mathvariant="normal">d</mi><mi>u</mi><mo><</mo><mi>∞</mi></mrow></math>
|
||
</li><li>
|
||
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mrow><mi mathvariant="sans-serif">E</mi><mfenced open="(" close=")"><mrow><munder><mrow><mo stretchy="true">∑</mo></mrow><mrow><mi>I</mi><mo>∈</mo><msub><mrow><mi>E</mi></mrow><mrow><mi>k</mi><mo>+</mo><mn>1</mn></mrow></msub></mrow></munder><mo>|</mo><mi>I</mi><msup><mrow><mo>|</mo></mrow><mrow><mi>s</mi></mrow></msup></mrow></mfenced><mo>=</mo><mi mathvariant="sans-serif">E</mi><mfenced open="(" close=")"><mrow><munder><mrow><mo stretchy="true">∑</mo></mrow><mrow><mi>I</mi><mo>∈</mo><msub><mrow><mi>E</mi></mrow><mrow><mi>k</mi></mrow></msub></mrow></munder><mo>|</mo><mi>I</mi><msup><mrow><mo>|</mo></mrow><mrow><mi>s</mi></mrow></msup></mrow></mfenced><mi mathvariant="sans-serif">E</mi><mo stretchy="false">(</mo><msubsup><mrow><mi>R</mi></mrow><mrow><mn>1</mn></mrow><mrow><mi>s</mi></mrow></msubsup><mo>+</mo><msubsup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow><mrow><mi>s</mi></mrow></msubsup><mo stretchy="false">)</mo><mo>.</mo></mrow></math>
|
||
</li>
|
||
|
||
|
||
<h2>Source: Miscellaneous Demostration Examples</h2>
|
||
|
||
<li>
|
||
<p class="MsoNormal">The Distance Formula: The distance between points <math xmlns="http://www.w3.org/1998/Math/MathML">
|
||
<semantics>
|
||
<mrow>
|
||
<mo stretchy='false'>(</mo><msub>
|
||
<mi>x</mi>
|
||
<mn>1</mn>
|
||
</msub>
|
||
<mo>,</mo><msub>
|
||
<mi>y</mi>
|
||
<mn>1</mn>
|
||
</msub>
|
||
<mo stretchy='false'>)</mo></mrow>
|
||
<annotation encoding='MathType-MTEF'>MathType@MTEF@5@5@+=
|
||
feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX
|
||
garmWu51MyVXgaruWqVvNCPvMCG4uz3bqefqvATv2CG4uz3bIuV1wy
|
||
Ubqee0evGueE0jxyGqvANvMCaibaieYlf9irVeeu0dXdh9vqqj=hEe
|
||
ea0dXdcba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9q8qqaq=d
|
||
ir=f0=yqaiVgFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaaea
|
||
qbaaGcbaaeaaaaaaaaa8qacaGGOaGaamiEa8aadaWgaaWcbaWdbiaa
|
||
igdaa8aabeaak8qacaGGSaGaamyEa8aadaWgaaWcbaWdbiaaigdaa8
|
||
aabeaak8qacaGGPaaaaa@40AB@
|
||
</annotation>
|
||
</semantics>
|
||
</math> and <math xmlns="http://www.w3.org/1998/Math/MathML">
|
||
<semantics>
|
||
<mrow>
|
||
<mo stretchy='false'>(</mo><msub>
|
||
<mi>x</mi>
|
||
<mn>2</mn>
|
||
</msub>
|
||
<mo>,</mo><msub>
|
||
<mi>y</mi>
|
||
<mn>2</mn>
|
||
</msub>
|
||
<mo stretchy='false'>)</mo></mrow>
|
||
<annotation encoding='MathType-MTEF'>MathType@MTEF@5@5@+=
|
||
feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX
|
||
garmWu51MyVXgaruWqVvNCPvMCG4uz3bqefqvATv2CG4uz3bIuV1wy
|
||
Ubqee0evGueE0jxyGqvANvMCaibaieYlf9irVeeu0dXdh9vqqj=hEe
|
||
ea0dXdcba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9q8qqaq=d
|
||
ir=f0=yqaiVgFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaaea
|
||
qbaaGcbaaeaaaaaaaaa8qacaGGOaGaamiEa8aadaWgaaWcbaWdbiaa
|
||
ikdaa8aabeaak8qacaGGSaGaamyEa8aadaWgaaWcbaWdbiaaikdaa8
|
||
aabeaak8qacaGGPaaaaa@40AD@
|
||
</annotation>
|
||
</semantics>
|
||
</math> is
|
||
given by the formula: </p>
|
||
|
||
<p class="MsoNormal"><math xmlns="http://www.w3.org/1998/Math/MathML">
|
||
<semantics>
|
||
<mrow>
|
||
<mi>d</mi><mo>=</mo><msqrt>
|
||
<mrow>
|
||
<msup>
|
||
<mrow>
|
||
<mo stretchy='false'>(</mo><msub>
|
||
<mi>x</mi>
|
||
<mn>2</mn>
|
||
</msub>
|
||
<mo>−</mo><msub>
|
||
<mi>x</mi>
|
||
<mn>1</mn>
|
||
</msub>
|
||
<mo stretchy='false'>)</mo></mrow>
|
||
<mn>2</mn>
|
||
</msup>
|
||
<mo>+</mo><msup>
|
||
<mrow>
|
||
<mo stretchy='false'>(</mo><msub>
|
||
<mi>y</mi>
|
||
<mn>2</mn>
|
||
</msub>
|
||
<mo>−</mo><msub>
|
||
<mi>y</mi>
|
||
<mn>1</mn>
|
||
</msub>
|
||
<mo stretchy='false'>)</mo></mrow>
|
||
<mn>2</mn>
|
||
</msup>
|
||
</mrow>
|
||
</msqrt>
|
||
</mrow>
|
||
<annotation encoding='MathType-MTEF'>MathType@MTEF@5@5@+=
|
||
feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX
|
||
garmWu51MyVXgaruWqVvNCPvMCG4uz3bqefqvATv2CG4uz3bIuV1wy
|
||
Ubqee0evGueE0jxyGqvANvMCaibaieYlf9irVeeu0dXdh9vqqj=hEe
|
||
ea0dXdcba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9q8qqaq=d
|
||
ir=f0=yqaiVgFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaaea
|
||
qbaaGcbaaeaaaaaaaaa8qacaWGKbGaeyypa0ZaaOaaa8aabaWdbiaa
|
||
cIcacaWG4bWdamaaBaaaleaapeGaaGOmaaWdaeqaaOWdbiabgkHiTi
|
||
aadIhapaWaaSbaaSqaa8qacaaIXaaapaqabaGcpeGaaiyka8aadaah
|
||
aaWcbeqaa8qacaaIYaaaaOGaey4kaSIaaiikaiaadMhapaWaaSbaaS
|
||
qaa8qacaaIYaaapaqabaGcpeGaeyOeI0IaamyEa8aadaWgaaWcbaWd
|
||
biaaigdaa8aabeaak8qacaGGPaWdamaaCaaaleqabaWdbiaaikdaaa
|
||
aabeaaaaa@4CA2@
|
||
</annotation>
|
||
</semantics>
|
||
</math></p>
|
||
</li><li>
|
||
|
||
<p class="MsoNormal"><span lang="EN"> </span><math xmlns="http://www.w3.org/1998/Math/MathML">
|
||
<semantics>
|
||
<mi>ℝ</mi>
|
||
<annotation encoding='MathType-MTEF'>MathType@MTEF@5@5@+=
|
||
feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX
|
||
garmWu51MyVXgaruWqVvNCPvMCG4uz3bqefqvATv2CG4uz3bIuV1wy
|
||
Ubqee0evGueE0jxyGqvANvMCaibaieYlf9irVeeu0dXdh9vqqj=hEe
|
||
ea0dXdcba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9q8qqaq=d
|
||
ir=f0=yqaiVgFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaaea
|
||
qbaaGcbaGaeSyhHekaaa@3B99@
|
||
</annotation>
|
||
</semantics>
|
||
</math> is the
|
||
set of all real numbers: <math xmlns="http://www.w3.org/1998/Math/MathML">
|
||
<semantics>
|
||
<mrow>
|
||
<mi>ℝ</mi><mo>=</mo><mrow><mo>(</mo>
|
||
<mrow>
|
||
<mo>−</mo><mi>∞</mi><mo>,</mo><mi>∞</mi></mrow>
|
||
<mo>)</mo></mrow></mrow>
|
||
<annotation encoding='MathType-MTEF'>MathType@MTEF@5@5@+=
|
||
feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX
|
||
garmWu51MyVXgaruWqVvNCPvMCG4uz3bqefqvATv2CG4uz3bIuV1wy
|
||
Ubqee0evGueE0jxyGqvANvMCaibaieYlf9irVeeu0dXdh9vqqj=hEe
|
||
ea0dXdcba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9q8qqaq=d
|
||
ir=f0=yqaiVgFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaaea
|
||
qbaaGcbaGaeSyhHeQaeyypa0ZaaeWaaeaacqGHsislcqGHEisPcaGG
|
||
SaGaeyOhIukacaGLOaGaayzkaaaaaa@42A7@
|
||
</annotation>
|
||
</semantics>
|
||
</math></p>
|
||
</li><li>
|
||
<p class="MsoNormal">If <i >S</i> is the set <math xmlns="http://www.w3.org/1998/Math/MathML">
|
||
<semantics>
|
||
<mrow>
|
||
<mrow><mo>{</mo> <mrow>
|
||
<mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn></mrow> <mo>}</mo></mrow></mrow>
|
||
<annotation encoding='MathType-MTEF'>MathType@MTEF@5@5@+=
|
||
feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX
|
||
garmWu51MyVXgaruWqVvNCPvMCG4uz3bqefqvATv2CG4uz3bIuV1wy
|
||
Ubqee0evGueE0jxyGqvANvMCaibaieYlf9irVeeu0dXdh9vqqj=hEe
|
||
ea0dXdcba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9q8qqaq=d
|
||
ir=f0=yqaiVgFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaaea
|
||
qbaaGcbaWaaiWaaeaacaaIXaGaaiilaiaaikdacaGGSaGaaG4maaGa
|
||
ay5Eaiaaw2haaaaa@3FEE@
|
||
</annotation>
|
||
</semantics>
|
||
</math> then
|
||
all of the following statements are true: <math xmlns="http://www.w3.org/1998/Math/MathML">
|
||
<semantics>
|
||
<mrow>
|
||
<mn>1</mn><mo>∈</mo><mi>S</mi></mrow>
|
||
<annotation encoding='MathType-MTEF'>MathType@MTEF@5@5@+=
|
||
feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX
|
||
garmWu51MyVXgaruWqVvNCPvMCG4uz3bqefqvATv2CG4uz3bIuV1wy
|
||
Ubqee0evGueE0jxyGqvANvMCaibaieYlf9irVeeu0dXdh9vqqj=hEe
|
||
ea0dXdcba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9q8qqaq=d
|
||
ir=f0=yqaiVgFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaaea
|
||
qbaaGcbaGaaGymaiabgIGiolaadofaaaa@3D40@
|
||
</annotation>
|
||
</semantics>
|
||
</math>, <math xmlns="http://www.w3.org/1998/Math/MathML">
|
||
<semantics>
|
||
<mrow>
|
||
<mn>3</mn><mo>∈</mo><mi>S</mi></mrow>
|
||
<annotation encoding='MathType-MTEF'>MathType@MTEF@5@5@+=
|
||
feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX
|
||
garmWu51MyVXgaruWqVvNCPvMCG4uz3bqefqvATv2CG4uz3bIuV1wy
|
||
Ubqee0evGueE0jxyGqvANvMCaibaieYlf9irVeeu0dXdh9vqqj=hEe
|
||
ea0dXdcba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9q8qqaq=d
|
||
ir=f0=yqaiVgFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaaea
|
||
qbaaGcbaGaaG4maiabgIGiolaadofaaaa@3D42@
|
||
</annotation>
|
||
</semantics>
|
||
</math> and <math xmlns="http://www.w3.org/1998/Math/MathML">
|
||
<semantics>
|
||
<mrow>
|
||
<mn>4</mn><mo>∉</mo><mi>S</mi></mrow>
|
||
<annotation encoding='MathType-MTEF'>MathType@MTEF@5@5@+=
|
||
feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX
|
||
garmWu51MyVXgaruWqVvNCPvMCG4uz3bqefqvATv2CG4uz3bIuV1wy
|
||
Ubqee0evGueE0jxyGqvANvMCaibaieYlf9irVeeu0dXdh9vqqj=hEe
|
||
ea0dXdcba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9q8qqaq=d
|
||
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|
||
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|
||
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|
||
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|
||
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|
||
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|
||
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|
||
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|
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|
||
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|
||
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|
||
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|
||
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|
||
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|
||
<mn>2</mn>
|
||
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|
||
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|
||
</msqrt>
|
||
</mrow>
|
||
<mrow>
|
||
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|
||
</mfrac>
|
||
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|
||
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|
||
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|
||
garmWu51MyVXgaruWqVvNCPvMCG4uz3bqefqvATv2CG4uz3bIuV1wy
|
||
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||
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||
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|
||
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|
||
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|
||
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|
||
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||
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||
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|
||
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|
||
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||
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||
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||
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|
||
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|
||
aaigdaaaaaaaaa@4109@
|
||
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|
||
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|
||
</math> </p>
|
||
</li><li>
|
||
<p class=MsoNormal><math xmlns="http://www.w3.org/1998/Math/MathML">
|
||
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|
||
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|
||
<munder>
|
||
<mrow>
|
||
<mi>lim</mi></mrow>
|
||
<mrow>
|
||
<mi>x</mi><mo>→</mo><mn>0</mn></mrow>
|
||
</munder>
|
||
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|
||
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|
||
<mi>sin</mi><mi>x</mi></mrow>
|
||
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|
||
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|
||
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|
||
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||
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||
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|
||
qbaaGcbaWaaCbeaeaaqaaaaaaaaaWdbiGacYgacaGGPbGaaiyBaaWc
|
||
paqaa8qacaWG4bGaeyOKH4QaaGimaaWdaeqaaOWdbmaalaaapaqaa8
|
||
qaciGGZbGaaiyAaiaac6gacaWG4baapaqaa8qacaWG4baaaiabg2da
|
||
9iaaigdaaaa@481F@
|
||
</annotation>
|
||
</semantics>
|
||
</math> </p>
|
||
</li><li>
|
||
<p class=MsoNormal><math xmlns="http://www.w3.org/1998/Math/MathML">
|
||
<semantics>
|
||
<mrow>
|
||
<mi>d</mi><mo>=</mo><msqrt>
|
||
<mrow>
|
||
<msup>
|
||
<mrow>
|
||
<mo stretchy='false'>(</mo><msub>
|
||
<mi>x</mi>
|
||
<mn>2</mn>
|
||
</msub>
|
||
<mo>−</mo><msub>
|
||
<mi>x</mi>
|
||
<mn>1</mn>
|
||
</msub>
|
||
<mo stretchy='false'>)</mo></mrow>
|
||
<mn>2</mn>
|
||
</msup>
|
||
<mo>+</mo><msup>
|
||
<mrow>
|
||
<mo stretchy='false'>(</mo><msub>
|
||
<mi>y</mi>
|
||
<mn>2</mn>
|
||
</msub>
|
||
<mo>−</mo><msub>
|
||
<mi>y</mi>
|
||
<mn>1</mn>
|
||
</msub>
|
||
<mo stretchy='false'>)</mo></mrow>
|
||
<mn>2</mn>
|
||
</msup>
|
||
</mrow>
|
||
</msqrt>
|
||
</mrow>
|
||
<annotation encoding='MathType-MTEF'>MathType@MTEF@5@5@+=
|
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||
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||
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||
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||
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||
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||
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||
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||
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|
||
biaaigdaa8aabeaak8qacaGGPaWdamaaCaaaleqabaWdbiaaikdaaa
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||
aabeaaaaa@4CA2@
|
||
</annotation>
|
||
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|
||
</math></p>
|
||
</li><li>
|
||
<p class=MsoNormal><math xmlns="http://www.w3.org/1998/Math/MathML">
|
||
<semantics>
|
||
<mrow>
|
||
<msub>
|
||
<mi>F</mi>
|
||
<mi>n</mi>
|
||
</msub>
|
||
<mo>=</mo><msub>
|
||
<mi>F</mi>
|
||
<mrow>
|
||
<mi>n</mi><mo>−</mo><mn>1</mn></mrow>
|
||
</msub>
|
||
<mo>+</mo><msub>
|
||
<mi>F</mi>
|
||
<mrow>
|
||
<mi>n</mi><mo>−</mo><mn>2</mn></mrow>
|
||
</msub>
|
||
</mrow>
|
||
<annotation encoding='MathType-MTEF'>MathType@MTEF@5@5@+=
|
||
feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX
|
||
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|
||
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|
||
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|
||
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|
||
qbaaGcbaGaamOramaaBaaaleaacaWGUbaabeaakiabg2da9iaadAea
|
||
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||
aaBaaaleaacaWGUbGaeyOeI0IaaGOmaaqabaaaaa@4534@
|
||
</annotation>
|
||
</semantics>
|
||
</math></p>
|
||
</li>
|
||
<h2>Source: Silicon and Related Materials (Elsevier)</h2>
|
||
<li>
|
||
<math xmlns="http://www.w3.org/1998/Math/MathML"
|
||
altimg="si16.gif"
|
||
overflow="scroll">
|
||
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|
||
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|
||
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|
||
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|
||
<mtable>
|
||
<mtr>
|
||
<mtd columnalign="right">
|
||
<msub>
|
||
<mi>π</mi>
|
||
<mn>11</mn>
|
||
</msub>
|
||
</mtd>
|
||
<mtd columnalign="center">
|
||
<msub>
|
||
<mi>π</mi>
|
||
<mn>12</mn>
|
||
</msub>
|
||
</mtd>
|
||
<mtd columnalign="left">
|
||
<msub>
|
||
<mi>π</mi>
|
||
<mn>12</mn>
|
||
</msub>
|
||
</mtd>
|
||
<mtd columnalign="center">
|
||
<mn>0</mn>
|
||
</mtd>
|
||
<mtd columnalign="center">
|
||
<mn>0</mn>
|
||
</mtd>
|
||
<mtd columnalign="center">
|
||
<mn>0</mn>
|
||
</mtd>
|
||
</mtr>
|
||
<mtr>
|
||
<mtd columnalign="right">
|
||
<msub>
|
||
<mi>π</mi>
|
||
<mn>12</mn>
|
||
</msub>
|
||
</mtd>
|
||
<mtd columnalign="center">
|
||
<msub>
|
||
<mi>π</mi>
|
||
<mn>11</mn>
|
||
</msub>
|
||
</mtd>
|
||
<mtd columnalign="left">
|
||
<msub>
|
||
<mi>π</mi>
|
||
<mn>12</mn>
|
||
</msub>
|
||
</mtd>
|
||
<mtd columnalign="center">
|
||
<mn>0</mn>
|
||
</mtd>
|
||
<mtd columnalign="center">
|
||
<mn>0</mn>
|
||
</mtd>
|
||
<mtd columnalign="center">
|
||
<mn>0</mn>
|
||
</mtd>
|
||
</mtr>
|
||
<mtr>
|
||
<mtd columnalign="right">
|
||
<msub>
|
||
<mi>π</mi>
|
||
<mn>12</mn>
|
||
</msub>
|
||
</mtd>
|
||
<mtd columnalign="center">
|
||
<msub>
|
||
<mi>π</mi>
|
||
<mn>12</mn>
|
||
</msub>
|
||
</mtd>
|
||
<mtd columnalign="left">
|
||
<msub>
|
||
<mi>π</mi>
|
||
<mn>11</mn>
|
||
</msub>
|
||
</mtd>
|
||
<mtd columnalign="center">
|
||
<mn>0</mn>
|
||
</mtd>
|
||
<mtd columnalign="center">
|
||
<mn>0</mn>
|
||
</mtd>
|
||
<mtd columnalign="center">
|
||
<mn>0</mn>
|
||
</mtd>
|
||
</mtr>
|
||
<mtr>
|
||
<mtd columnalign="right">
|
||
<mn>0</mn>
|
||
</mtd>
|
||
<mtd columnalign="center">
|
||
<mn>0</mn>
|
||
</mtd>
|
||
<mtd columnalign="left">
|
||
<mn>0</mn>
|
||
</mtd>
|
||
<mtd columnalign="center">
|
||
<msub>
|
||
<mi>π</mi>
|
||
<mn>44</mn>
|
||
</msub>
|
||
</mtd>
|
||
<mtd columnalign="center">
|
||
<mn>0</mn>
|
||
</mtd>
|
||
<mtd columnalign="center">
|
||
<mn>0</mn>
|
||
</mtd>
|
||
</mtr>
|
||
<mtr>
|
||
<mtd columnalign="right">
|
||
<mn>0</mn>
|
||
</mtd>
|
||
<mtd columnalign="center">
|
||
<mn>0</mn>
|
||
</mtd>
|
||
<mtd columnalign="left">
|
||
<mn>0</mn>
|
||
</mtd>
|
||
<mtd columnalign="center">
|
||
<mn>0</mn>
|
||
</mtd>
|
||
<mtd columnalign="center">
|
||
<msub>
|
||
<mi>π</mi>
|
||
<mn>44</mn>
|
||
</msub>
|
||
</mtd>
|
||
<mtd columnalign="center">
|
||
<mn>0</mn>
|
||
</mtd>
|
||
</mtr>
|
||
<mtr>
|
||
<mtd columnalign="right">
|
||
<mn>0</mn>
|
||
</mtd>
|
||
<mtd columnalign="center">
|
||
<mn>0</mn>
|
||
</mtd>
|
||
<mtd columnalign="left">
|
||
<mn>0</mn>
|
||
</mtd>
|
||
<mtd columnalign="center">
|
||
<mn>0</mn>
|
||
</mtd>
|
||
<mtd columnalign="center">
|
||
<mn>0</mn>
|
||
</mtd>
|
||
<mtd columnalign="center">
|
||
<msub>
|
||
<mi>π</mi>
|
||
<mn>44</mn>
|
||
</msub>
|
||
</mtd>
|
||
</mtr>
|
||
</mtable>
|
||
<mo>)</mo>
|
||
</mrow>
|
||
</math>
|
||
</li><li>
|
||
<math xmlns="http://www.w3.org/1998/Math/MathML"
|
||
altimg="si29.gif"
|
||
overflow="scroll">
|
||
<mrow>
|
||
<msub>
|
||
<mi>s</mi>
|
||
<mn>11</mn>
|
||
</msub>
|
||
<mo>=</mo>
|
||
<mfrac>
|
||
<mrow>
|
||
<msub>
|
||
<mi>c</mi>
|
||
<mn>11</mn>
|
||
</msub>
|
||
<mo>+</mo>
|
||
<msub>
|
||
<mi>c</mi>
|
||
<mn>12</mn>
|
||
</msub>
|
||
</mrow>
|
||
<mrow>
|
||
<mfenced open="(" close=")">
|
||
<mrow>
|
||
<msub>
|
||
<mi>c</mi>
|
||
<mn>11</mn>
|
||
</msub>
|
||
<mo>−</mo>
|
||
<msub>
|
||
<mi>c</mi>
|
||
<mn>12</mn>
|
||
</msub>
|
||
</mrow>
|
||
</mfenced>
|
||
<mfenced open="(" close=")">
|
||
<mrow>
|
||
<msub>
|
||
<mi>c</mi>
|
||
<mn>11</mn>
|
||
</msub>
|
||
<mo>+</mo>
|
||
<mrow>
|
||
<mn>2</mn>
|
||
<msub>
|
||
<mi>c</mi>
|
||
<mn>12</mn>
|
||
</msub>
|
||
</mrow>
|
||
</mrow>
|
||
</mfenced>
|
||
</mrow>
|
||
</mfrac>
|
||
</mrow>
|
||
</math>
|
||
</li>
|
||
<li>
|
||
<math>
|
||
<mrow>
|
||
|
||
<mi mathvariant="normal">Si</mi>
|
||
<msub><mi mathvariant="normal">O</mi>
|
||
<mn>2</mn>
|
||
</msub>
|
||
<mo>+</mo>
|
||
|
||
<mn>6</mn>
|
||
|
||
<mi mathvariant="normal">H</mi>
|
||
<mi mathvariant="normal">F</mi>
|
||
|
||
|
||
<mo>→</mo>
|
||
|
||
|
||
<msub>
|
||
<mi mathvariant="normal">H</mi>
|
||
<mn>2</mn>
|
||
</msub>
|
||
|
||
<mi mathvariant="normal">Si</mi>
|
||
<msub><mi mathvariant="normal">F</mi>
|
||
<mn>6</mn>
|
||
</msub>
|
||
|
||
<mo>+</mo>
|
||
|
||
<mn>2</mn>
|
||
<msub>
|
||
<mi mathvariant="normal">H</mi>
|
||
<mn>2</mn>
|
||
</msub>
|
||
<mi mathvariant="normal">O</mi>
|
||
|
||
</mrow>
|
||
</math>
|
||
</li>
|
||
|
||
|
||
<h2>Source: Systematic Synthesis Methods (Elsevier)</h2>
|
||
|
||
<li>
|
||
<math xmlns="http://www.w3.org/1998/Math/MathML"
|
||
altimg="si2.gif"
|
||
overflow="scroll">
|
||
<mrow>
|
||
<mfrac>
|
||
<mtext>d</mtext>
|
||
<mrow>
|
||
<mtext>d</mtext>
|
||
<mi>x</mi>
|
||
</mrow>
|
||
</mfrac>
|
||
<mrow>
|
||
<mo stretchy="true">(</mo>
|
||
<mrow>
|
||
<mi>E</mi>
|
||
<mo stretchy="false">(</mo>
|
||
<mi>x</mi>
|
||
<mo stretchy="false">)</mo>
|
||
<mi>A</mi>
|
||
<mo stretchy="false">(</mo>
|
||
<mi>x</mi>
|
||
<mo stretchy="false">)</mo>
|
||
<mfrac>
|
||
<mrow>
|
||
<mtext>d</mtext>
|
||
<mi>w</mi>
|
||
<mo stretchy="false">(</mo>
|
||
<mi>x</mi>
|
||
<mo stretchy="false">)</mo>
|
||
</mrow>
|
||
<mrow>
|
||
<mtext>d</mtext>
|
||
<mi>x</mi>
|
||
</mrow>
|
||
</mfrac>
|
||
</mrow>
|
||
<mo stretchy="true">)</mo>
|
||
</mrow>
|
||
<mo>+</mo>
|
||
<mi>p</mi>
|
||
<mo stretchy="false">(</mo>
|
||
<mi>x</mi>
|
||
<mo stretchy="false">)</mo>
|
||
<mo>=</mo>
|
||
<mn>0</mn>
|
||
</mrow>
|
||
</math>
|
||
</li>
|
||
<h2>Source: Pressure Sensors (Elsevier)</h2>
|
||
<li>
|
||
<math xmlns="http://www.w3.org/1998/Math/MathML"
|
||
altimg="si10.gif"
|
||
overflow="scroll">
|
||
<mrow>
|
||
<msub>
|
||
<mtext>TCS</mtext>
|
||
<mtext>gas</mtext>
|
||
</msub>
|
||
<mo>=</mo>
|
||
<mrow>
|
||
<mo>−</mo>
|
||
<mrow>
|
||
<mfrac>
|
||
<mn>1</mn>
|
||
<mn>2</mn>
|
||
</mfrac>
|
||
<mfenced open="(" close=")">
|
||
<mfrac>
|
||
<msub>
|
||
<mi>P</mi>
|
||
<mtext>seal</mtext>
|
||
</msub>
|
||
<msub>
|
||
<mi>P</mi>
|
||
<mtext>max</mtext>
|
||
</msub>
|
||
</mfrac>
|
||
</mfenced>
|
||
<mfenced open="(" close=")">
|
||
<mfrac>
|
||
<mn>1</mn>
|
||
<msub>
|
||
<mi>T</mi>
|
||
<mtext>seal</mtext>
|
||
</msub>
|
||
</mfrac>
|
||
</mfenced>
|
||
</mrow>
|
||
</mrow>
|
||
</mrow>
|
||
</math>
|
||
</li><li>
|
||
<math xmlns="http://www.w3.org/1998/Math/MathML"
|
||
altimg="si20.gif"
|
||
overflow="scroll">
|
||
<mrow>
|
||
<msub>
|
||
<mi>B</mi>
|
||
<mi>p</mi>
|
||
</msub>
|
||
<mo>=</mo>
|
||
<mfrac>
|
||
<mrow>
|
||
<mrow>
|
||
<mfrac>
|
||
<mrow>
|
||
<mn>7</mn>
|
||
<mo>−</mo>
|
||
<msup>
|
||
<mi>v</mi>
|
||
<mn>2</mn>
|
||
</msup>
|
||
</mrow>
|
||
<mn>3</mn>
|
||
</mfrac>
|
||
<mfenced open="(" close=")">
|
||
<mrow>
|
||
<mn>1</mn>
|
||
<mo>+</mo>
|
||
<mfrac>
|
||
<msup>
|
||
<mi>c</mi>
|
||
<mn>2</mn>
|
||
</msup>
|
||
<msup>
|
||
<mi>a</mi>
|
||
<mn>2</mn>
|
||
</msup>
|
||
</mfrac>
|
||
<mo>+</mo>
|
||
<mfrac>
|
||
<msup>
|
||
<mi>c</mi>
|
||
<mn>4</mn>
|
||
</msup>
|
||
<msup>
|
||
<mi>a</mi>
|
||
<mn>4</mn>
|
||
</msup>
|
||
</mfrac>
|
||
</mrow>
|
||
</mfenced>
|
||
</mrow>
|
||
<mo>+</mo>
|
||
<mfrac>
|
||
<mrow>
|
||
<msup>
|
||
<mfenced open="(" close=")">
|
||
<mrow>
|
||
<mn>3</mn>
|
||
<mo>−</mo>
|
||
<mi>v</mi>
|
||
</mrow>
|
||
</mfenced>
|
||
<mn>2</mn>
|
||
</msup>
|
||
<msup>
|
||
<mi>c</mi>
|
||
<mn>2</mn>
|
||
</msup>
|
||
</mrow>
|
||
<mrow>
|
||
<mfenced open="(" close=")">
|
||
<mrow>
|
||
<mn>1</mn>
|
||
<mo>+</mo>
|
||
<mi>v</mi>
|
||
</mrow>
|
||
</mfenced>
|
||
<msup>
|
||
<mi>a</mi>
|
||
<mn>2</mn>
|
||
</msup>
|
||
</mrow>
|
||
</mfrac>
|
||
</mrow>
|
||
<mrow>
|
||
<mfenced open="(" close=")">
|
||
<mrow>
|
||
<mn>1</mn>
|
||
<mo>−</mo>
|
||
<mi>v</mi>
|
||
</mrow>
|
||
</mfenced>
|
||
<mfenced open="(" close=")">
|
||
<mrow>
|
||
<mn>1</mn>
|
||
<mo>−</mo>
|
||
<mfrac>
|
||
<msup>
|
||
<mi>c</mi>
|
||
<mn>4</mn>
|
||
</msup>
|
||
<msup>
|
||
<mi>a</mi>
|
||
<mn>4</mn>
|
||
</msup>
|
||
</mfrac>
|
||
</mrow>
|
||
</mfenced>
|
||
<mfenced open="(" close=")">
|
||
<mrow>
|
||
<mn>1</mn>
|
||
<mo>−</mo>
|
||
<mfrac>
|
||
<msup>
|
||
<mi>c</mi>
|
||
<mn>2</mn>
|
||
</msup>
|
||
<msup>
|
||
<mi>a</mi>
|
||
<mn>2</mn>
|
||
</msup>
|
||
</mfrac>
|
||
</mrow>
|
||
</mfenced>
|
||
</mrow>
|
||
</mfrac>
|
||
</mrow>
|
||
</math>
|
||
</li><li>
|
||
<math xmlns="http://www.w3.org/1998/Math/MathML"
|
||
altimg="si38.gif"
|
||
overflow="scroll">
|
||
<mrow>
|
||
<msubsup>
|
||
<mi>Q</mi>
|
||
<mtext>tank</mtext>
|
||
<mtext>series</mtext>
|
||
</msubsup>
|
||
<mo>=</mo>
|
||
<mrow>
|
||
<mfrac>
|
||
<mn>1</mn>
|
||
<msub>
|
||
<mi>R</mi>
|
||
<mtext>s</mtext>
|
||
</msub>
|
||
</mfrac>
|
||
<msqrt>
|
||
<mfrac>
|
||
<msub>
|
||
<mi>L</mi>
|
||
<mtext>s</mtext>
|
||
</msub>
|
||
<msub>
|
||
<mi>C</mi>
|
||
<mtext>s</mtext>
|
||
</msub>
|
||
</mfrac>
|
||
</msqrt>
|
||
</mrow>
|
||
</mrow>
|
||
</math>
|
||
</li><li>
|
||
<math xmlns="http://www.w3.org/1998/Math/MathML"
|
||
altimg="si37.gif"
|
||
overflow="scroll">
|
||
<mrow>
|
||
<mtext>Δ</mtext>
|
||
<msub>
|
||
<mi>ϕ</mi>
|
||
<mtext>peak</mtext>
|
||
</msub>
|
||
<mo>=</mo>
|
||
<msup>
|
||
<mo>tan</mo>
|
||
<mrow>
|
||
<mo>−</mo>
|
||
<mn>1</mn>
|
||
</mrow>
|
||
</msup>
|
||
<mo>(</mo>
|
||
<msup>
|
||
<mi>k</mi>
|
||
<mn>2</mn>
|
||
</msup>
|
||
<msubsup>
|
||
<mi>Q</mi>
|
||
<mtext>tank</mtext>
|
||
<mtext>series</mtext>
|
||
</msubsup>
|
||
<mo>)</mo>
|
||
</mrow>
|
||
</math>
|
||
</li>
|
||
<h2>Source: Resonators, Oscillators, and Frequency References (Elsevier)</h2>
|
||
<li>
|
||
<math xmlns="http://www.w3.org/1998/Math/MathML"
|
||
altimg="si52.gif"
|
||
overflow="scroll">
|
||
<mrow>
|
||
<mi>f</mi>
|
||
<mo>=</mo>
|
||
<mn>1.013</mn>
|
||
<mfrac>
|
||
<mi>W</mi>
|
||
<msup>
|
||
<mi>L</mi>
|
||
<mn>2</mn>
|
||
</msup>
|
||
</mfrac>
|
||
<msqrt>
|
||
<mfrac>
|
||
<mi>E</mi>
|
||
<mi>ρ</mi>
|
||
</mfrac>
|
||
</msqrt>
|
||
<msqrt>
|
||
<mo>(</mo>
|
||
<mn>1</mn>
|
||
<mo>+</mo>
|
||
<mn>0.293</mn>
|
||
<mfrac>
|
||
<msup>
|
||
<mi>L</mi>
|
||
<mn>2</mn>
|
||
</msup>
|
||
<mrow>
|
||
<msup>
|
||
<mtext>EW</mtext>
|
||
<mn>2</mn>
|
||
</msup>
|
||
</mrow>
|
||
</mfrac>
|
||
<mi>σ</mi>
|
||
<mo>)</mo>
|
||
</msqrt>
|
||
</mrow>
|
||
</math>
|
||
</li>
|
||
<li>
|
||
<math xmlns="http://www.w3.org/1998/Math/MathML"
|
||
altimg="si6.gif"
|
||
overflow="scroll">
|
||
<mrow>
|
||
<mrow>
|
||
<msub>
|
||
<mi>u</mi>
|
||
<mi>n</mi>
|
||
</msub>
|
||
<mfenced open="(" close=")">
|
||
<mi>x</mi>
|
||
</mfenced>
|
||
</mrow>
|
||
<mo>=</mo>
|
||
<mrow>
|
||
<mrow>
|
||
<msub>
|
||
<mi>γ</mi>
|
||
<mi>n</mi>
|
||
</msub>
|
||
<mfenced open="(" close=")">
|
||
<mrow>
|
||
<mrow>
|
||
<mi>cosh</mi>
|
||
<msub>
|
||
<mi>k</mi>
|
||
<mi>n</mi>
|
||
</msub>
|
||
<mi>x</mi>
|
||
</mrow>
|
||
<mo>−</mo>
|
||
<mrow>
|
||
<mi>cos</mi>
|
||
<msub>
|
||
<mi>k</mi>
|
||
<mi>n</mi>
|
||
</msub>
|
||
<mi>x</mi>
|
||
</mrow>
|
||
</mrow>
|
||
</mfenced>
|
||
</mrow>
|
||
<mo>+</mo>
|
||
<mfenced open="(" close=")">
|
||
<mrow>
|
||
<mrow>
|
||
<mi>sinh</mi>
|
||
<msub>
|
||
<mi>k</mi>
|
||
<mi>n</mi>
|
||
</msub>
|
||
<mi>x</mi>
|
||
</mrow>
|
||
<mo>−</mo>
|
||
<mrow>
|
||
<mi>sin</mi>
|
||
<msub>
|
||
<mi>k</mi>
|
||
<mi>n</mi>
|
||
</msub>
|
||
<mi>x</mi>
|
||
</mrow>
|
||
</mrow>
|
||
</mfenced>
|
||
</mrow>
|
||
</mrow>
|
||
</math>
|
||
</li>
|
||
<li>
|
||
<math xmlns="http://www.w3.org/1998/Math/MathML"
|
||
altimg="si17.gif"
|
||
overflow="scroll">
|
||
<mtable>
|
||
<mtr>
|
||
<mtd columnalign="left">
|
||
<mi>B</mi>
|
||
</mtd>
|
||
<mtd columnalign="left">
|
||
<mo>=</mo>
|
||
<mfrac>
|
||
<mfrac>
|
||
<msub>
|
||
<mi>F</mi>
|
||
<mn>0</mn>
|
||
</msub>
|
||
<mi>m</mi>
|
||
</mfrac>
|
||
<mrow>
|
||
<msqrt>
|
||
<mo stretchy="false">(</mo>
|
||
<msubsup>
|
||
<mi>ω</mi>
|
||
<mn>0</mn>
|
||
<mn>2</mn>
|
||
</msubsup>
|
||
<mo>−</mo>
|
||
<msup>
|
||
<mi>ω</mi>
|
||
<mn>2</mn>
|
||
</msup>
|
||
<msup>
|
||
<mo stretchy="false">)</mo>
|
||
<mn>2</mn>
|
||
</msup>
|
||
<mo>+</mo>
|
||
<mn>4</mn>
|
||
<msup>
|
||
<mi>n</mi>
|
||
<mn>2</mn>
|
||
</msup>
|
||
<msup>
|
||
<mi>ω</mi>
|
||
<mn>2</mn>
|
||
</msup>
|
||
</msqrt>
|
||
</mrow>
|
||
</mfrac>
|
||
</mtd>
|
||
</mtr>
|
||
<mtr>
|
||
<mtd/>
|
||
<mtd columnalign="left">
|
||
<mo>=</mo>
|
||
<mfrac>
|
||
<mfrac>
|
||
<mrow>
|
||
<msub>
|
||
<mi>F</mi>
|
||
<mn>0</mn>
|
||
</msub>
|
||
</mrow>
|
||
<mi>k</mi>
|
||
</mfrac>
|
||
<mrow>
|
||
<msqrt>
|
||
<mo>(</mo>
|
||
<mn>1</mn>
|
||
<mo>−</mo>
|
||
<mo stretchy="false">(</mo>
|
||
<mi>ω</mi>
|
||
<mo stretchy="true">/</mo>
|
||
<msubsup>
|
||
<mi>ω</mi>
|
||
<mn>0</mn>
|
||
<mn>2</mn>
|
||
</msubsup>
|
||
<msup>
|
||
<mo stretchy="false">)</mo>
|
||
<mn>2</mn>
|
||
</msup>
|
||
<msup>
|
||
<mo>)</mo>
|
||
<mn>2</mn>
|
||
</msup>
|
||
<mo>+</mo>
|
||
<mn>4</mn>
|
||
<mo stretchy="false">(</mo>
|
||
<mi>n</mi>
|
||
<mo stretchy="true">/</mo>
|
||
<msub>
|
||
<mi>ω</mi>
|
||
<mn>0</mn>
|
||
</msub>
|
||
<msup>
|
||
<mo stretchy="false">)</mo>
|
||
<mn>2</mn>
|
||
</msup>
|
||
<mo stretchy="false">(</mo>
|
||
<mi>ω</mi>
|
||
<mo stretchy="true">/</mo>
|
||
<msub>
|
||
<mi>ω</mi>
|
||
<mn>0</mn>
|
||
</msub>
|
||
<msup>
|
||
<mo stretchy="false">)</mo>
|
||
<mn>2</mn>
|
||
</msup>
|
||
</msqrt>
|
||
</mrow>
|
||
</mfrac>
|
||
</mtd>
|
||
</mtr>
|
||
</mtable>
|
||
</math>
|
||
</li>
|
||
|
||
<h2>Source: Doing Data Science (O'Reilly)</h2>
|
||
|
||
<li>
|
||
<math xmlns:mml="http://www.w3.org/1998/Math/MathML" mode="display" overflow="scroll">
|
||
<mrow>
|
||
<mi mathvariant="normal">p</mi>
|
||
|
||
<mo>(</mo>
|
||
|
||
<mi>A</mi>
|
||
|
||
<mspace width="3.33333pt"/>
|
||
|
||
<mi>and</mi>
|
||
|
||
<mspace width="3.33333pt"/>
|
||
|
||
<mi>B</mi>
|
||
|
||
<mo>)</mo>
|
||
|
||
<mo>=</mo>
|
||
|
||
<mi mathvariant="normal">p</mi>
|
||
|
||
<mo>(</mo>
|
||
|
||
<mi>A</mi>
|
||
|
||
<mo>)</mo>
|
||
|
||
<mspace width="3.33333pt"/>
|
||
|
||
<mi mathvariant="normal">p</mi>
|
||
|
||
<mo>(</mo>
|
||
|
||
<mi>B</mi>
|
||
|
||
<mo>|</mo>
|
||
|
||
<mi>A</mi>
|
||
|
||
<mo>)</mo>
|
||
</mrow>
|
||
</math>
|
||
</li>
|
||
<li>
|
||
<math xmlns:mml="http://www.w3.org/1998/Math/MathML" mode="display" overflow="scroll">
|
||
<mrow>
|
||
<mi>PMF</mi>
|
||
|
||
<mrow>
|
||
<mo>(</mo>
|
||
|
||
<mi>x</mi>
|
||
|
||
<mo>)</mo>
|
||
</mrow>
|
||
|
||
<mo>∝</mo>
|
||
|
||
<msup>
|
||
<mfenced close=")" open="(" separators="">
|
||
<mfrac>
|
||
<mn>1</mn>
|
||
|
||
<mi>x</mi>
|
||
</mfrac>
|
||
</mfenced>
|
||
|
||
<mi>α</mi>
|
||
</msup>
|
||
</mrow>
|
||
</math>
|
||
</li>
|
||
<li>
|
||
<math xmlns:mml="http://www.w3.org/1998/Math/MathML" mode="display" overflow="scroll">
|
||
<mrow>
|
||
<mi>f</mi>
|
||
|
||
<mrow>
|
||
<mo>(</mo>
|
||
|
||
<mi>x</mi>
|
||
|
||
<mo>)</mo>
|
||
</mrow>
|
||
|
||
<mo>=</mo>
|
||
|
||
<mfrac>
|
||
<mn>1</mn>
|
||
|
||
<msqrt>
|
||
<mrow>
|
||
<mn>2</mn>
|
||
|
||
<mi>π</mi>
|
||
</mrow>
|
||
</msqrt>
|
||
</mfrac>
|
||
|
||
<mo form="prefix">exp</mo>
|
||
|
||
<mrow>
|
||
<mo>(</mo>
|
||
|
||
<mo>-</mo>
|
||
|
||
<msup>
|
||
<mi>x</mi>
|
||
|
||
<mn>2</mn>
|
||
</msup>
|
||
|
||
<mo>/2)</mo>
|
||
</mrow>
|
||
</mrow>
|
||
</math>
|
||
<li>
|
||
<math xmlns:mml="http://www.w3.org/1998/Math/MathML" mode="display" overflow="scroll">
|
||
<mrow>
|
||
<mfrac>
|
||
<mrow>
|
||
<mi>d</mi>
|
||
|
||
<mi>x</mi>
|
||
</mrow>
|
||
|
||
<mrow>
|
||
<mi>d</mi>
|
||
|
||
<mi>θ</mi>
|
||
</mrow>
|
||
</mfrac>
|
||
|
||
<mo>=</mo>
|
||
|
||
<mfrac>
|
||
<mi>β</mi>
|
||
|
||
<mrow>
|
||
<msup>
|
||
<mo form="prefix">cos</mo>
|
||
|
||
<mn>2</mn>
|
||
</msup>
|
||
|
||
<mi>θ</mi>
|
||
</mrow>
|
||
</mfrac>
|
||
</mrow>
|
||
</math>
|
||
</li>
|
||
<li>
|
||
<math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll">
|
||
<mrow>
|
||
<mi>s</mi>
|
||
|
||
<mo>/</mo>
|
||
|
||
<msqrt>
|
||
<mrow>
|
||
<mn>2</mn>
|
||
|
||
<mo>(</mo>
|
||
|
||
<mi>n</mi>
|
||
|
||
<mo>-</mo>
|
||
|
||
<mn>1</mn>
|
||
|
||
<mo>)</mo>
|
||
</mrow>
|
||
</msqrt>
|
||
</mrow>
|
||
</math>
|
||
</li>
|
||
</ol>
|
||
</body>
|
||
</html>
|