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	<title>Matem&#225;ticas IES</title>
	<link>https://lubrin.cloud/</link>
	<description>Ejercicios resueltos, apuntes y v&#237;deos de Matem&#225;ticas para Secundaria y Bachillerato</description>
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<item xml:lang="es">
		<title>Ecuaci&#243;n de primer grado con denominadores</title>
		<link>https://lubrin.cloud/Ecuacion-de-primer-grado-con-denominadores</link>
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		<dc:date>2026-03-13T18:35:42Z</dc:date>
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		<dc:creator>Dani</dc:creator>



		<description>
&lt;p&gt;Resolver Ecuaci&#243;n de Primer Grado con Denominadores &lt;br class='autobr' /&gt;
Introduce la ecuaci&#243;n con el teclado matem&#225;tico:
&lt;br class='autobr' /&gt; math-field::part(menu-toggle) display: none !important; &lt;br class='autobr' /&gt; Resolver Respuesta animada&lt;/p&gt;


-
&lt;a href="https://lubrin.cloud/Ecuaciones-236" rel="directory"&gt;Ecuaciones&lt;/a&gt;


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&lt;div class=&#034;container-ecuacion&#034;&gt; &lt;h2&gt;Resolver Ecuaci&#243;n de Primer Grado con Denominadores&lt;/h2&gt; &lt;p&gt;Introduce la ecuaci&#243;n con el teclado matem&#225;tico:&lt;/p&gt; &lt;div class=&#034;base64javascript17727806456a09936b1aaa57.28558838&#034; title=&#034;PHNjcmlwdCBkZWZlciBzcmM9Imh0dHBzOi8vdW5wa2cuY29tL21hdGhsaXZlIj48L3NjcmlwdD4=&#034;&gt;&lt;/div&gt; &lt;style&gt; math-field::part(menu-toggle) { display: none !important; } &lt;/style&gt; &lt;math-field id=&#034;ec-input&#034; math-virtual-keyboard-policy=&#034;manual&#034; style=&#034;font-size:1.8rem;width:80%;background:white;border:2px solid #ddd; border-radius:8px;padding:10px;margin:20px 0;display:block;&#034;&gt; &lt;/math-field&gt; &lt;div style=&#034;display:inline-flex;align-items:center;gap:14px;margin-top:4px;&#034;&gt; &lt;button id=&#034;ec-btn&#034; style=&#034;background:#4CAF50;color:#fff;padding:12px 30px;border:none; border-radius:4px;cursor:pointer;font-size:16px;font-weight:bold;&#034;&gt; Resolver &lt;/button&gt; &lt;label style=&#034;display:inline-flex;align-items:center;gap:6px;cursor:pointer;font-size:15px;user-select:none;&#034;&gt; &lt;input type=&#034;checkbox&#034; id=&#034;ec-anim-check&#034; checked style=&#034;width:17px;height:17px;cursor:pointer;accent-color:#4CAF50;&#034;&gt; Respuesta animada &lt;/label&gt; &lt;/div&gt; &lt;div id=&#034;ec-resultado&#034; style=&#034;margin-top:30px;&#034;&gt;&lt;/div&gt;
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<item xml:lang="es">
		<title>Ecuaci&#243;n de primer grado con parr&#233;ntesis</title>
		<link>https://lubrin.cloud/Ecuacion-de-primer-grado-con-parrentesis</link>
		<guid isPermaLink="true">https://lubrin.cloud/Ecuacion-de-primer-grado-con-parrentesis</guid>
		<dc:date>2026-03-13T18:30:58Z</dc:date>
		<dc:format>text/html</dc:format>
		<dc:language>es</dc:language>
		<dc:creator>Dani</dc:creator>



		<description>
&lt;p&gt;Resolver Ecuaci&#243;n de Primer Grado con Par&#233;ntesis &lt;br class='autobr' /&gt;
Introduce una ecuaci&#243;n de primer grado con par&#233;ntesis:
&lt;br class='autobr' /&gt; Resolver Respuesta animada&lt;/p&gt;


-
&lt;a href="https://lubrin.cloud/Ecuaciones-236" rel="directory"&gt;Ecuaciones&lt;/a&gt;


		</description>


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&lt;div class=&#034;container-ecuacion&#034;&gt; &lt;h2&gt;Resolver Ecuaci&#243;n de Primer Grado con Par&#233;ntesis&lt;/h2&gt; &lt;p&gt;Introduce una ecuaci&#243;n de primer grado con par&#233;ntesis:&lt;/p&gt; &lt;input type=&#034;text&#034; id=&#034;ec-input&#034; placeholder=&#034;Ejemplo: 2(3x+4)-5=3(x-2)+1&#034; style=&#034;width:80%;padding:12px;font-size:18px;border:2px solid #ddd; border-radius:4px;text-align:center;margin:20px 0;&#034;&gt; &lt;br&gt; &lt;div style=&#034;display:inline-flex;align-items:center;gap:14px;margin-top:4px;&#034;&gt; &lt;button id=&#034;ec-btn&#034; style=&#034;background:#4CAF50;color:#fff;padding:12px 30px;border:none; border-radius:4px;cursor:pointer;font-size:16px;font-weight:bold;&#034;&gt; Resolver &lt;/button&gt; &lt;label style=&#034;display:inline-flex;align-items:center;gap:6px;cursor:pointer;font-size:15px;user-select:none;&#034;&gt; &lt;input type=&#034;checkbox&#034; id=&#034;ec-anim-check&#034; checked style=&#034;width:17px;height:17px;cursor:pointer;accent-color:#4CAF50;&#034;&gt; Respuesta animada &lt;/label&gt; &lt;/div&gt; &lt;div id=&#034;ec-resultado&#034; style=&#034;margin-top:30px;&#034;&gt;&lt;/div&gt;
&lt;/div&gt; &lt;div class=&#034;base64javascript17727806456a09936b1aaa57.28558838&#034; title=&#034;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&#034;&gt;&lt;/div&gt;&lt;/div&gt;
		
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	</item>
<item xml:lang="es">
		<title>Ejercicio distribuci&#243;n normal 4636</title>
		<link>https://lubrin.cloud/Ejercicio-distribucion-normal-4636</link>
		<guid isPermaLink="true">https://lubrin.cloud/Ejercicio-distribucion-normal-4636</guid>
		<dc:date>2024-02-28T09:23:02Z</dc:date>
		<dc:format>text/html</dc:format>
		<dc:language>es</dc:language>
		<dc:creator>Dani</dc:creator>


		<dc:subject>distribuci&#243;n_normal</dc:subject>
		<dc:subject>Ejercicios_Resueltos</dc:subject>

		<description>
&lt;p&gt;Vemos que &lt;br class='autobr' /&gt;
a) &lt;br class='autobr' /&gt;
b) &lt;br class='autobr' /&gt;
c) &lt;br class='autobr' /&gt; La altura de los alumnos de un instituto se distribuye normalmente con una media de 161 cm y una desviaci&#243;n t&#237;pica de 16 cm. Si elegimos un alumno al azar, calcula la probabilidad de que mida:
&lt;br class='autobr' /&gt;
a) M&#225;s de 180 cm.
&lt;br class='autobr' /&gt;
b) M&#225;s de 2 metros.
&lt;br class='autobr' /&gt;
c) Menos de 140 cm.&lt;/p&gt;


-
&lt;a href="https://lubrin.cloud/Variables-Aleatorias-Unidimensionales" rel="directory"&gt;Variables Aleatorias Unidimensionales&lt;/a&gt;

/ 
&lt;a href="https://lubrin.cloud/distribucion-normal-166" rel="tag"&gt;distribuci&#243;n_normal&lt;/a&gt;, 
&lt;a href="https://lubrin.cloud/Ejercicios_Resueltos" rel="tag"&gt;Ejercicios_Resueltos&lt;/a&gt;

		</description>


 <content:encoded>&lt;div class='rss_chapo'&gt;&lt;p&gt;Vemos que &lt;img src='https://lubrin.cloud/local/cache-TeX/09e65249ce59a825c7933031cbd32621.png' style=&#034;vertical-align:middle;&#034; width=&#034;186&#034; height=&#034;26&#034; alt=&#034;X \longrightarrow N(161, 16)&#034; title=&#034;X \longrightarrow N(161, 16)&#034; /&gt;&lt;/math&gt;&lt;/p&gt;
&lt;p&gt;a) &lt;img src='https://lubrin.cloud/local/cache-TeX/d3052cbbdbbf16eedbc6d94f484df13e.png' style=&#034;vertical-align:middle;&#034; width=&#034;983&#034; height=&#034;60&#034; alt=&#034;P(X \geq 180) = P\left(Z \geq \frac{180-161}{16}\right)=P\geft(Z \geq 1.18\right)= 1- P\left(Z \leq 1.18\right)=1- 0.8810=0.119&#034; title=&#034;P(X \geq 180) = P\left(Z \geq \frac{180-161}{16}\right)=P\geft(Z \geq 1.18\right)= 1- P\left(Z \leq 1.18\right)=1- 0.8810=0.119&#034; /&gt;&lt;/math&gt;&lt;/p&gt;
&lt;p&gt;b) &lt;img src='https://lubrin.cloud/local/cache-TeX/bf1fc6e06bfffade86ecc114b5242e6b.png' style=&#034;vertical-align:middle;&#034; width=&#034;995&#034; height=&#034;60&#034; alt=&#034;P(X \geq 200) = P\left(Z \geq \frac{200-161}{16}\right)=P\geft(Z \geq 2.44\right)= 1- P\left(Z \leq 2.44\right)=1- 0.9927=0.0073&#034; title=&#034;P(X \geq 200) = P\left(Z \geq \frac{200-161}{16}\right)=P\geft(Z \geq 2.44\right)= 1- P\left(Z \leq 2.44\right)=1- 0.9927=0.0073&#034; /&gt;&lt;/math&gt;&lt;/p&gt;
&lt;p&gt;c) &lt;img src='https://lubrin.cloud/local/cache-TeX/805a7f719a7418af270ca8022c7faf5f.png' style=&#034;vertical-align:middle;&#034; width=&#034;1013&#034; height=&#034;60&#034; alt=&#034;P(X \leq 140) = P\left(Z \leq \frac{140-161}{16}\right)=P\geft(Z \leq -1.31\right)= 1- P\left(Z \leq 1.31\right)=1- 0.9049=0.0951&#034; title=&#034;P(X \leq 140) = P\left(Z \leq \frac{140-161}{16}\right)=P\geft(Z \leq -1.31\right)= 1- P\left(Z \leq 1.31\right)=1- 0.9049=0.0951&#034; /&gt;&lt;/math&gt;&lt;/p&gt;&lt;/div&gt;
		&lt;div class='rss_texte'&gt;&lt;p&gt;La altura de los alumnos de un instituto se distribuye normalmente con una media de 161 cm y una desviaci&#243;n t&#237;pica de 16 cm. Si elegimos un alumno al azar, calcula la probabilidad de que mida:&lt;br class='autobr' /&gt;
a) M&#225;s de 180 cm.&lt;br class='autobr' /&gt;
b) M&#225;s de 2 metros.&lt;br class='autobr' /&gt;
c) Menos de 140 cm.&lt;/p&gt;&lt;/div&gt;
		
		</content:encoded>


		

	</item>
<item xml:lang="es">
		<title>Ejercicio binomial 4635</title>
		<link>https://lubrin.cloud/Ejercicio-binomial-4635</link>
		<guid isPermaLink="true">https://lubrin.cloud/Ejercicio-binomial-4635</guid>
		<dc:date>2024-02-28T09:21:49Z</dc:date>
		<dc:format>text/html</dc:format>
		<dc:language>es</dc:language>
		<dc:creator>Dani</dc:creator>


		<dc:subject>binomial</dc:subject>
		<dc:subject>Ejercicios_Resueltos</dc:subject>

		<description>
&lt;p&gt;Se trata de una Binomial con n=14 y probabilidad de &#233;xito 1/6 &lt;br class='autobr' /&gt; &lt;br class='autobr' /&gt; Lanzamos un dado de quinielas (111xx2)(6 caras: 3 unos, dos equis y un dos) 14 veces. Calcula la probabilidad de obtener 14 doses.&lt;/p&gt;


-
&lt;a href="https://lubrin.cloud/Variables-Aleatorias-Unidimensionales" rel="directory"&gt;Variables Aleatorias Unidimensionales&lt;/a&gt;

/ 
&lt;a href="https://lubrin.cloud/binomial" rel="tag"&gt;binomial&lt;/a&gt;, 
&lt;a href="https://lubrin.cloud/Ejercicios_Resueltos" rel="tag"&gt;Ejercicios_Resueltos&lt;/a&gt;

		</description>


 <content:encoded>&lt;div class='rss_chapo'&gt;&lt;p&gt;Se trata de una Binomial con n=14 y probabilidad de &#233;xito 1/6&lt;/p&gt;
&lt;p&gt;&lt;img src='https://lubrin.cloud/local/cache-TeX/ccd5dece199afbe8a4f2086125e6484c.png' style=&#034;vertical-align:middle;&#034; width=&#034;184&#034; height=&#034;26&#034; alt=&#034;X \longrightarrow B(14,1/2)&#034; title=&#034;X \longrightarrow B(14,1/2)&#034; /&gt;&lt;/math&gt;&lt;/p&gt;
&lt;p&gt;&lt;img src='https://lubrin.cloud/local/cache-TeX/70a22c61182b70ca2aad7b546c1d8cf5.png' style=&#034;vertical-align:middle;&#034; width=&#034;700&#034; height=&#034;65&#034; alt=&#034;P(X=14)= \left( \begin{array}{c} 14 \\ 14 \end{array} \right) \cdot \left(\frac{1}{6}\right)^{14} \cdot \left(\frac{1}{6}\right)^{0}= 0.00000000001276093494&#034; title=&#034;P(X=14)= \left( \begin{array}{c} 14 \\ 14 \end{array} \right) \cdot \left(\frac{1}{6}\right)^{14} \cdot \left(\frac{1}{6}\right)^{0}= 0.00000000001276093494&#034; /&gt;&lt;/math&gt;&lt;/p&gt;&lt;/div&gt;
		&lt;div class='rss_texte'&gt;&lt;p&gt;Lanzamos un dado de quinielas (111xx2)(6 caras: 3 unos, dos equis y un dos) 14 veces. Calcula la probabilidad de obtener 14 doses.&lt;/p&gt;&lt;/div&gt;
		
		</content:encoded>


		

	</item>
<item xml:lang="es">
		<title>Ejercicio binomial 4634</title>
		<link>https://lubrin.cloud/Ejercicio-binomial-4634</link>
		<guid isPermaLink="true">https://lubrin.cloud/Ejercicio-binomial-4634</guid>
		<dc:date>2024-02-28T09:20:44Z</dc:date>
		<dc:format>text/html</dc:format>
		<dc:language>es</dc:language>
		<dc:creator>Dani</dc:creator>


		<dc:subject>binomial</dc:subject>
		<dc:subject>Ejercicios_Resueltos</dc:subject>

		<description>
&lt;p&gt;Se trata de una Binomial con n=20 y probabilidad de &#233;xito 1/2=0.5
&lt;br class='autobr' /&gt; &#8211; a) &lt;br class='autobr' /&gt;
&#8211; b) &lt;br class='autobr' /&gt; &lt;br class='autobr' /&gt; &lt;br class='autobr' /&gt; Lanzamos una moneda 20 veces. Calcula la probabilidad de:
&lt;br class='autobr' /&gt;
a) Obtener 11 caras
&lt;br class='autobr' /&gt;
b) Obtener al menos 18 caras&lt;/p&gt;


-
&lt;a href="https://lubrin.cloud/Variables-Aleatorias-Unidimensionales" rel="directory"&gt;Variables Aleatorias Unidimensionales&lt;/a&gt;

/ 
&lt;a href="https://lubrin.cloud/binomial" rel="tag"&gt;binomial&lt;/a&gt;, 
&lt;a href="https://lubrin.cloud/Ejercicios_Resueltos" rel="tag"&gt;Ejercicios_Resueltos&lt;/a&gt;

		</description>


 <content:encoded>&lt;div class='rss_chapo'&gt;&lt;p&gt;Se trata de una Binomial con n=20 y probabilidad de &#233;xito 1/2=0.5&lt;br class='autobr' /&gt;
&lt;img src='https://lubrin.cloud/local/cache-TeX/c05dab8871f1d575755c06b51d3f009c.png' style=&#034;vertical-align:middle;&#034; width=&#034;178&#034; height=&#034;26&#034; alt=&#034;X \longrightarrow B(20,0.5)&#034; title=&#034;X \longrightarrow B(20,0.5)&#034; /&gt;&lt;/math&gt;&lt;/p&gt;
&lt;p&gt;&lt;span class=&#034;spip-puce ltr&#034;&gt;&lt;b&gt;&#8211;&lt;/b&gt;&lt;/span&gt; a) &lt;img src='https://lubrin.cloud/local/cache-TeX/184737320153f458d40ead47a9508c36.png' style=&#034;vertical-align:middle;&#034; width=&#034;524&#034; height=&#034;60&#034; alt=&#034;P(X=11)= \left( \begin{array}{c} 20 \\ 11 \end{array} \right) \cdot 0.5^{11} \cdot 0.5 ^{9} = 0,160179138&#034; title=&#034;P(X=11)= \left( \begin{array}{c} 20 \\ 11 \end{array} \right) \cdot 0.5^{11} \cdot 0.5 ^{9} = 0,160179138&#034; /&gt;&lt;/math&gt;&lt;/p&gt;
&lt;p&gt;&lt;span class=&#034;spip-puce ltr&#034;&gt;&lt;b&gt;&#8211;&lt;/b&gt;&lt;/span&gt; b) &lt;img src='https://lubrin.cloud/local/cache-TeX/9b4fa95af28f962eceeed6f591f24d30.png' style=&#034;vertical-align:middle;&#034; width=&#034;559&#034; height=&#034;26&#034; alt=&#034;P(X \geq 18)= P(X = 18) + P(X = 19) + P(X = 20) &#034; title=&#034;P(X \geq 18)= P(X = 18) + P(X = 19) + P(X = 20) &#034; /&gt;&lt;/math&gt;&lt;/p&gt;
&lt;p&gt;&lt;img src='https://lubrin.cloud/local/cache-TeX/5db104f510f223345704a89e1a958ee0.png' style=&#034;vertical-align:middle;&#034; width=&#034;519&#034; height=&#034;60&#034; alt=&#034;P(X=18)=\left( \begin{array}{c} 20 \\ 18 \end{array} \right) \cdot 0.5^{18} \cdot 0.5 ^{2} = 0.000181198&#034; title=&#034;P(X=18)=\left( \begin{array}{c} 20 \\ 18 \end{array} \right) \cdot 0.5^{18} \cdot 0.5 ^{2} = 0.000181198&#034; /&gt;&lt;/math&gt;&lt;/p&gt;
&lt;p&gt;&lt;img src='https://lubrin.cloud/local/cache-TeX/d6c30b341949060f954c11ab93fe4129.png' style=&#034;vertical-align:middle;&#034; width=&#034;519&#034; height=&#034;60&#034; alt=&#034;P(X=19)=\left( \begin{array}{c} 20 \\ 19 \end{array} \right) \cdot 0.5^{19} \cdot 0.5 ^{1} = 0.000019073&#034; title=&#034;P(X=19)=\left( \begin{array}{c} 20 \\ 19 \end{array} \right) \cdot 0.5^{19} \cdot 0.5 ^{1} = 0.000019073&#034; /&gt;&lt;/math&gt;&lt;/p&gt;
&lt;p&gt;&lt;img src='https://lubrin.cloud/local/cache-TeX/1415c123b2d28a5a66859171aae7c4e2.png' style=&#034;vertical-align:middle;&#034; width=&#034;524&#034; height=&#034;60&#034; alt=&#034;P(X=20)=\left( \begin{array}{c} 20 \\ 20 \end{array} \right) \cdot 0.5^{20} \cdot 0.5 ^{0} = 0,000000954&#034; title=&#034;P(X=20)=\left( \begin{array}{c} 20 \\ 20 \end{array} \right) \cdot 0.5^{20} \cdot 0.5 ^{0} = 0,000000954&#034; /&gt;&lt;/math&gt;&lt;/p&gt;
&lt;p&gt;&lt;img src='https://lubrin.cloud/local/cache-TeX/0de8f768231ec4d78b99f4442e269682.png' style=&#034;vertical-align:middle;&#034; width=&#034;760&#034; height=&#034;26&#034; alt=&#034;P(X \geq 18)= 0.000181198 + 0.000019073 + 0,000000954=0.000201225&#034; title=&#034;P(X \geq 18)= 0.000181198 + 0.000019073 + 0,000000954=0.000201225&#034; /&gt;&lt;/math&gt;&lt;/p&gt;&lt;/div&gt;
		&lt;div class='rss_texte'&gt;&lt;p&gt;Lanzamos una moneda 20 veces. Calcula la probabilidad de:&lt;br class='autobr' /&gt;
a) Obtener 11 caras&lt;br class='autobr' /&gt;
b) Obtener al menos 18 caras&lt;/p&gt;&lt;/div&gt;
		
		</content:encoded>


		

	</item>
<item xml:lang="es">
		<title>Ejercicio distribuci&#243;n normal 4633</title>
		<link>https://lubrin.cloud/Ejercicio-distribucion-normal-4633</link>
		<guid isPermaLink="true">https://lubrin.cloud/Ejercicio-distribucion-normal-4633</guid>
		<dc:date>2024-02-28T09:11:46Z</dc:date>
		<dc:format>text/html</dc:format>
		<dc:language>es</dc:language>
		<dc:creator>Dani</dc:creator>


		<dc:subject>distribuci&#243;n_normal</dc:subject>
		<dc:subject>Ejercicios_Resueltos</dc:subject>

		<description>
&lt;p&gt;Vemos que &lt;br class='autobr' /&gt;
a) &lt;br class='autobr' /&gt;
b) &lt;br class='autobr' /&gt;
c) &lt;br class='autobr' /&gt; Las cebollas de un agricultor siguen una distribuci&#243;n normal de media 150 gramos y desviaci&#243;n t&#237;pica 30 gramos. Si elegimos una cebolla al azar calcula la probabilidad de que:
&lt;br class='autobr' /&gt;
a) Pese menos de 130 gramos
&lt;br class='autobr' /&gt;
b) Pese m&#225;s de 190 gramos
&lt;br class='autobr' /&gt;
c) Pese entre 140 y 160 gramos&lt;/p&gt;


-
&lt;a href="https://lubrin.cloud/Variables-Aleatorias-Unidimensionales" rel="directory"&gt;Variables Aleatorias Unidimensionales&lt;/a&gt;

/ 
&lt;a href="https://lubrin.cloud/distribucion-normal-166" rel="tag"&gt;distribuci&#243;n_normal&lt;/a&gt;, 
&lt;a href="https://lubrin.cloud/Ejercicios_Resueltos" rel="tag"&gt;Ejercicios_Resueltos&lt;/a&gt;

		</description>


 <content:encoded>&lt;div class='rss_chapo'&gt;&lt;p&gt;Vemos que &lt;img src='https://lubrin.cloud/local/cache-TeX/990880019b2bdc055a2c2addd0c3dd91.png' style=&#034;vertical-align:middle;&#034; width=&#034;186&#034; height=&#034;26&#034; alt=&#034;X \longrightarrow N(150, 30)&#034; title=&#034;X \longrightarrow N(150, 30)&#034; /&gt;&lt;/math&gt;&lt;/p&gt;
&lt;p&gt;a) &lt;img src='https://lubrin.cloud/local/cache-TeX/86455ae128989db9fb3a442190234660.png' style=&#034;vertical-align:middle;&#034; width=&#034;1028&#034; height=&#034;60&#034; alt=&#034;P(X \leq 130) = P\left(Z \leq \frac{130-150}{30}\right)=P\left(Z \leq -0.67\right)= 1- P\left(Z \leq 0.67\right)=1- 0.7486=0.2514&#034; title=&#034;P(X \leq 130) = P\left(Z \leq \frac{130-150}{30}\right)=P\left(Z \leq -0.67\right)= 1- P\left(Z \leq 0.67\right)=1- 0.7486=0.2514&#034; /&gt;&lt;/math&gt;&lt;/p&gt;
&lt;p&gt;b) &lt;img src='https://lubrin.cloud/local/cache-TeX/b1e7afe1cb4ab519bbe9ab619f8fd846.png' style=&#034;vertical-align:middle;&#034; width=&#034;1009&#034; height=&#034;60&#034; alt=&#034;P(X \geq 190) = P\left(Z \geq \frac{190-150}{30}\right)=P\left(Z \geq 1.33\right)= 1- P\left(Z \leq 1.33\right)=1- 0.9082=0.0918&#034; title=&#034;P(X \geq 190) = P\left(Z \geq \frac{190-150}{30}\right)=P\left(Z \geq 1.33\right)= 1- P\left(Z \leq 1.33\right)=1- 0.9082=0.0918&#034; /&gt;&lt;/math&gt;&lt;/p&gt;
&lt;p&gt;c) &lt;img src='https://lubrin.cloud/local/cache-TeX/ced9d15927e3ff0fb919f5e88681c352.png' style=&#034;vertical-align:middle;&#034; width=&#034;880&#034; height=&#034;60&#034; alt=&#034;P(140 \leq X \leq 160) =P\left(\frac{140-150}{30} \leq Z \leq \frac{160-150}{30} \right) = P(-0.33 \leq Z \leq 0.33) = &#034; title=&#034;P(140 \leq X \leq 160) =P\left(\frac{140-150}{30} \leq Z \leq \frac{160-150}{30} \right) = P(-0.33 \leq Z \leq 0.33) = &#034; /&gt;&lt;/math&gt;&lt;br class='autobr' /&gt;
&lt;img src='https://lubrin.cloud/local/cache-TeX/8e7d739ec1c2ed8824f404fb800063d9.png' style=&#034;vertical-align:middle;&#034; width=&#034;730&#034; height=&#034;26&#034; alt=&#034;P(Z \leq 0.33) - P(Z \leq -0.33) =P(Z \leq 0.33) - (1-P(Z \leq 0.33)) =&#034; title=&#034;P(Z \leq 0.33) - P(Z \leq -0.33) =P(Z \leq 0.33) - (1-P(Z \leq 0.33)) =&#034; /&gt;&lt;/math&gt;&lt;br class='autobr' /&gt;
&lt;img src='https://lubrin.cloud/local/cache-TeX/ded78e444028bf877731379ffcd087ac.png' style=&#034;vertical-align:middle;&#034; width=&#034;353&#034; height=&#034;26&#034; alt=&#034; =0.6293 - (1-0.6293) = 0.2586&#034; title=&#034; =0.6293 - (1-0.6293) = 0.2586&#034; /&gt;&lt;/math&gt;&lt;/p&gt;&lt;/div&gt;
		&lt;div class='rss_texte'&gt;&lt;p&gt;Las cebollas de un agricultor siguen una distribuci&#243;n normal de media 150 gramos y desviaci&#243;n t&#237;pica 30 gramos. Si elegimos una cebolla al azar calcula la probabilidad de que:&lt;br class='autobr' /&gt;
a) Pese menos de 130 gramos&lt;br class='autobr' /&gt;
b) Pese m&#225;s de 190 gramos&lt;br class='autobr' /&gt;
c) Pese entre 140 y 160 gramos&lt;/p&gt;&lt;/div&gt;
		
		</content:encoded>


		

	</item>
<item xml:lang="es">
		<title>Pr&#233;stamos y Dep&#243;sitos. Matem&#225;tica Financiera</title>
		<link>https://lubrin.cloud/Prestamos-y-Depositos-Matematica-Financiera</link>
		<guid isPermaLink="true">https://lubrin.cloud/Prestamos-y-Depositos-Matematica-Financiera</guid>
		<dc:date>2023-11-26T12:04:26Z</dc:date>
		<dc:format>text/html</dc:format>
		<dc:language>es</dc:language>
		<dc:creator>Dani</dc:creator>


		<dc:subject>matem&#225;tica_financiera</dc:subject>
		<dc:subject>Ejercicios_Resueltos</dc:subject>

		<description>
&lt;p&gt;Debemos usar las f&#243;rmulas de Financiaci&#243;n Para el primer banco aplicamos la f&#243;rmula $m = C \cdot \frac\left( 1+\fracr1200 \right)^t\left( 1+\fracr1200 \right)^t -1 \cdot \fracr1200$ &lt;br class='autobr' /&gt;
Que aplicada a nuestros datos ser&#237;a: &lt;br class='autobr' /&gt;
$m = 70000 \cdot \frac\left( 1+\frac21200 \right)^11 \cdot 12\left( 1+\frac21200 \right)^20 \cdot 12 -1 \cdot \frac21200$ &lt;br class='autobr' /&gt;
$m = 70000 \cdot \frac\left( 1+\frac21200 \right)^240\left( 1+\frac21200 \right)^240 -1 \cdot \frac21200$ &lt;br class='autobr' /&gt;
$m = 70000 \cdot (&#8230;)&lt;/p&gt;


-
&lt;a href="https://lubrin.cloud/Matematica-Financiera,217" rel="directory"&gt;Matem&#225;tica Financiera&lt;/a&gt;

/ 
&lt;a href="https://lubrin.cloud/matematica-financiera-32" rel="tag"&gt;matem&#225;tica_financiera&lt;/a&gt;, 
&lt;a href="https://lubrin.cloud/Ejercicios_Resueltos" rel="tag"&gt;Ejercicios_Resueltos&lt;/a&gt;

		</description>


 <content:encoded>&lt;div class='rss_chapo'&gt;&lt;p&gt;Debemos usar las f&#243;rmulas de &lt;a href='https://lubrin.cloud/Financiacion' class=&#034;spip_in&#034;&gt;Financiaci&#243;n&lt;/a&gt;&lt;/p&gt;
&lt;p&gt;Para el primer banco aplicamos la f&#243;rmula&lt;br class='autobr' /&gt;
&lt;img src='https://lubrin.cloud/local/cache-TeX/d1baf1c0e2b60c4bc9019ba851069bae.png' style=&#034;vertical-align:middle;&#034; width=&#034;262&#034; height=&#034;93&#034; alt=&#034;m = C \cdot \frac{\left( 1+\frac{r}{1200} \right)^t}{\left( 1+\frac{r}{1200} \right)^t -1} \cdot \frac{r}{1200}&#034; title=&#034;m = C \cdot \frac{\left( 1+\frac{r}{1200} \right)^t}{\left( 1+\frac{r}{1200} \right)^t -1} \cdot \frac{r}{1200}&#034; /&gt;&lt;/p&gt;
&lt;p&gt;Que aplicada a nuestros datos ser&#237;a:&lt;/p&gt;
&lt;p&gt;&lt;img src='https://lubrin.cloud/local/cache-TeX/32ba9aa69b8cc63a963077fa53c69392.png' style=&#034;vertical-align:middle;&#034; width=&#034;396&#034; height=&#034;76&#034; alt=&#034;m = 70000 \cdot \frac{\left( 1+\frac{2}{1200} \right)^{11 \cdot 12}}{\left( 1+\frac{2}{1200} \right)^{20 \cdot 12} -1} \cdot \frac{2}{1200}&#034; title=&#034;m = 70000 \cdot \frac{\left( 1+\frac{2}{1200} \right)^{11 \cdot 12}}{\left( 1+\frac{2}{1200} \right)^{20 \cdot 12} -1} \cdot \frac{2}{1200}&#034; /&gt;&lt;/p&gt;
&lt;p&gt;&lt;img src='https://lubrin.cloud/local/cache-TeX/fc920ddea2db61a98e3a2e3abe49e19a.png' style=&#034;vertical-align:middle;&#034; width=&#034;382&#034; height=&#034;77&#034; alt=&#034;m = 70000 \cdot \frac{\left( 1+\frac{2}{1200} \right)^{240}}{\left( 1+\frac{2}{1200} \right)^{240} -1} \cdot \frac{2}{1200}&#034; title=&#034;m = 70000 \cdot \frac{\left( 1+\frac{2}{1200} \right)^{240}}{\left( 1+\frac{2}{1200} \right)^{240} -1} \cdot \frac{2}{1200}&#034; /&gt;&lt;/p&gt;
&lt;p&gt;&lt;img src='https://lubrin.cloud/local/cache-TeX/a8c9563ab6d80097d1e377616cf2c8e5.png' style=&#034;vertical-align:middle;&#034; width=&#034;382&#034; height=&#034;56&#034; alt=&#034;m = 70000 \cdot \frac{1.491328057}{1,491328057-1} \cdot \frac{2}{1200}&#034; title=&#034;m = 70000 \cdot \frac{1.491328057}{1,491328057-1} \cdot \frac{2}{1200}&#034; /&gt;&lt;/p&gt;
&lt;p&gt;&lt;img src='https://lubrin.cloud/local/cache-TeX/659a94e447c304656554ae5933d05274.png' style=&#034;vertical-align:middle;&#034; width=&#034;299&#034; height=&#034;56&#034; alt=&#034;m = \frac{70000 \cdot 1,491328057 \cdot 2}{0,491328057 \cdot 1200}&#034; title=&#034;m = \frac{70000 \cdot 1,491328057 \cdot 2}{0,491328057 \cdot 1200}&#034; /&gt;&lt;/p&gt;
&lt;p&gt;&lt;img src='https://lubrin.cloud/local/cache-TeX/2ea4675b4eb183e064bee8af65ea0a92.png' style=&#034;vertical-align:middle;&#034; width=&#034;368&#034; height=&#034;56&#034; alt=&#034;m = \frac{208785,928017256}{589,5936684} = \fbox{354,12}&#034; title=&#034;m = \frac{208785,928017256}{589,5936684} = \fbox{354,12}&#034; /&gt; &#8364; mensuales&lt;/p&gt;
&lt;p&gt;Para el segundo banco aplicamos la f&#243;rmula:&lt;/p&gt;
&lt;p&gt;&lt;img src='https://lubrin.cloud/local/cache-TeX/e94b199d75b67b0f910710c0ae8c24e1.png' style=&#034;vertical-align:middle;&#034; width=&#034;238&#034; height=&#034;93&#034; alt=&#034;a = C \cdot \frac{\left( 1+\frac{r}{100} \right)^t}{\left( 1+\frac{r}{100} \right)^t -1} \cdot \frac{r}{100}&#034; title=&#034;a = C \cdot \frac{\left( 1+\frac{r}{100} \right)^t}{\left( 1+\frac{r}{100} \right)^t -1} \cdot \frac{r}{100}&#034; /&gt;&lt;/p&gt;
&lt;p&gt;Con nuestros datos ser&#225;:&lt;/p&gt;
&lt;p&gt;&lt;img src='https://lubrin.cloud/local/cache-TeX/03fc5d88bf2475f5c3ff8ae333610437.png' style=&#034;vertical-align:middle;&#034; width=&#034;343&#034; height=&#034;76&#034; alt=&#034;a = 70000 \cdot \frac{\left( 1+\frac{4}{100} \right)^{15}}{\left( 1+\frac{4}{100} \right)^{15} -1} \cdot \frac{4}{100}&#034; title=&#034;a = 70000 \cdot \frac{\left( 1+\frac{4}{100} \right)^{15}}{\left( 1+\frac{4}{100} \right)^{15} -1} \cdot \frac{4}{100}&#034; /&gt;&lt;/p&gt;
&lt;p&gt;&lt;img src='https://lubrin.cloud/local/cache-TeX/50ebadf2b1d6c6552fce8eb76d6d14c4.png' style=&#034;vertical-align:middle;&#034; width=&#034;420&#034; height=&#034;56&#034; alt=&#034;a = \frac{70000 \cdot 1,800943506 \cdot 4}{0,800943506 \cdot 100} = \fbox{6295.88}&#034; title=&#034;a = \frac{70000 \cdot 1,800943506 \cdot 4}{0,800943506 \cdot 100} = \fbox{6295.88}&#034; /&gt; &#8364; anuales&lt;/p&gt;
&lt;p&gt;Con el primer banco pagamos &lt;img src='https://lubrin.cloud/local/cache-TeX/a172eac83f6306bc4cc58c59f3caca21.png' style=&#034;vertical-align:middle;&#034; width=&#034;325&#034; height=&#034;19&#034; alt=&#034;354.12 \cdot 240 + 2000 =86988.80&#034; title=&#034;354.12 \cdot 240 + 2000 =86988.80&#034; /&gt;&lt;br class='autobr' /&gt;
Con el segundo banco pagamos &lt;img src='https://lubrin.cloud/local/cache-TeX/9979fb73a192705a5948fa97506caa26.png' style=&#034;vertical-align:middle;&#034; width=&#034;329&#034; height=&#034;22&#034; alt=&#034;6295.88 \cdot 15 + 1500 = 94588,20&#034; title=&#034;6295.88 \cdot 15 + 1500 = 94588,20&#034; /&gt;&lt;/p&gt;
&lt;p&gt;Por lo que el primer banco es mucho m&#225;s rentable (aparte de pagar menos, tenemos m&#225;s tiempo para pagarlo)&lt;/p&gt;
&lt;p&gt;Si queremos pagar lo m&#237;nimo al a&#241;o, nos saldr&#237;a mejor el banco 1 (independientemente de las comisiones)&lt;/p&gt;
&lt;p&gt;Banco 1: &lt;img src='https://lubrin.cloud/local/cache-TeX/e3cc06da8aa871947d0a2f94ba1a9014.png' style=&#034;vertical-align:middle;&#034; width=&#034;221&#034; height=&#034;18&#034; alt=&#034;354.12 \cdot 12 = 4249.44&#034; title=&#034;354.12 \cdot 12 = 4249.44&#034; /&gt;&lt;br class='autobr' /&gt;
Banco 2: &lt;img src='https://lubrin.cloud/local/cache-TeX/5e066f01adc34abe77f0f10bce137a30.png' style=&#034;vertical-align:middle;&#034; width=&#034;79&#034; height=&#034;18&#034; alt=&#034;6295.88&#034; title=&#034;6295.88&#034; /&gt;&lt;/p&gt;
&lt;p&gt;Para el dep&#243;sito usaremos las &lt;a href='https://lubrin.cloud/Interes-compuesto-Formulas' class=&#034;spip_in&#034;&gt;f&#243;rmulas de inter&#233;s compuesto&lt;/a&gt;&lt;/p&gt;
&lt;p&gt;Para nuestro caso, como los periodos son mensuales usar&#237;amos la f&#243;rmula:&lt;/p&gt;
&lt;p&gt;&lt;img src='https://lubrin.cloud/local/cache-TeX/915c9e80101bf959249c258ecbb25fa4.png' style=&#034;vertical-align:middle;&#034; width=&#034;141&#034; height=&#034;34&#034; alt=&#034;C = c \cdot \left( 1 + \frac{r}{1200} \right)^t&#034; title=&#034;C = c \cdot \left( 1 + \frac{r}{1200} \right)^t&#034; /&gt;&lt;/p&gt;
&lt;p&gt;&lt;img src='https://lubrin.cloud/local/cache-TeX/96087ec4e2c13989872720684cf1caed.png' style=&#034;vertical-align:middle;&#034; width=&#034;420&#034; height=&#034;64&#034; alt=&#034;C = 10000 \cdot \left( 1 + \frac{4}{1200} \right)^{5 \cdot 12} = 12209.97&#034; title=&#034;C = 10000 \cdot \left( 1 + \frac{4}{1200} \right)^{5 \cdot 12} = 12209.97&#034; /&gt;&lt;/p&gt;
&lt;p&gt;Para calcular la TAE usamos las &lt;a href='https://lubrin.cloud/TAE-Tasa-Anual-Equivalente' class=&#034;spip_in&#034;&gt;f&#243;mulas de TAE&lt;/a&gt;&lt;/p&gt;
&lt;p&gt;En nuestro caso ser&#225;:&lt;/p&gt;
&lt;p&gt;
&lt;p class=&#034;spip&#034; style=&#034;text-align: center;&#034;&gt;&lt;img src='https://lubrin.cloud/local/cache-TeX/d38162c5fbf478305068e0b9332e8873.png' style=&#034;vertical-align:middle;&#034; width=&#034;292&#034; height=&#034;43&#034; alt=&#034;TAE = \left( 1 + \frac{0.04}{12} \right) ^{12} -1 = 0.040741543&#034; title=&#034;TAE = \left( 1 + \frac{0.04}{12} \right) ^{12} -1 = 0.040741543&#034; /&gt;&lt;/p&gt;
&lt;/p&gt;
&lt;p&gt;La TAE es del &lt;img src='https://lubrin.cloud/local/cache-TeX/bbec005f505e204b8d9e8a1ea714ba89.png' style=&#034;vertical-align:middle;&#034; width=&#034;44&#034; height=&#034;14&#034; alt=&#034;4.07 \%&#034; title=&#034;4.07 \%&#034; /&gt;&lt;/p&gt;
&lt;/math&gt;&lt;/div&gt;
		&lt;div class='rss_texte'&gt;&lt;p&gt;Queremos pedir un pr&#233;stamo y tenemos las ofertas de dos bancos:&lt;/p&gt;
&lt;p&gt;Banco 1
&lt;br /&gt;&lt;span class=&#034;spip-puce ltr&#034;&gt;&lt;b&gt;&#8211;&lt;/b&gt;&lt;/span&gt; Capital pr&#233;stamo: &lt;img src='https://lubrin.cloud/local/cache-vignettes/L59xH18/3078a255aee86ecc4ac1eb36b69af2f0-5557e.png?1773428661' style='vertical-align:middle;' width='59' height='18' alt=&#034;70000&#034; title=&#034;70000&#034; /&gt; &#8364;
&lt;br /&gt;&lt;span class=&#034;spip-puce ltr&#034;&gt;&lt;b&gt;&#8211;&lt;/b&gt;&lt;/span&gt; Inter&#233;s anual: &lt;img src='https://lubrin.cloud/local/cache-vignettes/L30xH42/4785f87bc2dc0d46b2736b0148f16627-bf698.png?1773428661' style='vertical-align:middle;' width='30' height='42' alt=&#034;2 \%&#034; title=&#034;2 \%&#034; /&gt;
&lt;br /&gt;&lt;span class=&#034;spip-puce ltr&#034;&gt;&lt;b&gt;&#8211;&lt;/b&gt;&lt;/span&gt; Periodo de pago: Mensual
&lt;br /&gt;&lt;span class=&#034;spip-puce ltr&#034;&gt;&lt;b&gt;&#8211;&lt;/b&gt;&lt;/span&gt; Tiempo: 20 a&#241;os
&lt;br /&gt;&lt;span class=&#034;spip-puce ltr&#034;&gt;&lt;b&gt;&#8211;&lt;/b&gt;&lt;/span&gt; Gastos y comisiones: &lt;img src='https://lubrin.cloud/local/cache-vignettes/L43xH38/08f90c1a417155361a5c4b8d297e0d78-7f3b0.png?1773428661' style='vertical-align:middle;' width='43' height='38' alt=&#034;2000&#034; title=&#034;2000&#034; /&gt; &#8364;&lt;/p&gt;
&lt;p&gt;Banco 2
&lt;br /&gt;&lt;span class=&#034;spip-puce ltr&#034;&gt;&lt;b&gt;&#8211;&lt;/b&gt;&lt;/span&gt; Capital pr&#233;stamo: &lt;img src='https://lubrin.cloud/local/cache-vignettes/L59xH18/3078a255aee86ecc4ac1eb36b69af2f0-5557e.png?1773428661' style='vertical-align:middle;' width='59' height='18' alt=&#034;70000&#034; title=&#034;70000&#034; /&gt; &#8364;
&lt;br /&gt;&lt;span class=&#034;spip-puce ltr&#034;&gt;&lt;b&gt;&#8211;&lt;/b&gt;&lt;/span&gt; Inter&#233;s anual: &lt;img src='https://lubrin.cloud/local/cache-vignettes/L30xH42/416f965acc1f38b3d2244f6f0ab7d0e0-54807.png?1773428661' style='vertical-align:middle;' width='30' height='42' alt=&#034;4 \%&#034; title=&#034;4 \%&#034; /&gt;
&lt;br /&gt;&lt;span class=&#034;spip-puce ltr&#034;&gt;&lt;b&gt;&#8211;&lt;/b&gt;&lt;/span&gt; Periodo de pago: Anual
&lt;br /&gt;&lt;span class=&#034;spip-puce ltr&#034;&gt;&lt;b&gt;&#8211;&lt;/b&gt;&lt;/span&gt; Tiempo: 15 a&#241;os
&lt;br /&gt;&lt;span class=&#034;spip-puce ltr&#034;&gt;&lt;b&gt;&#8211;&lt;/b&gt;&lt;/span&gt; Gastos y comisiones: &lt;img src='https://lubrin.cloud/local/cache-vignettes/L31xH12/cfa5301358b9fcbe7aa45b1ceea088c6-29f14.png?1773428661' style='vertical-align:middle;' width='31' height='12' alt=&#034;1500&#034; title=&#034;1500&#034; /&gt; &#8364;&lt;/p&gt;
&lt;p&gt;&lt;span class=&#034;spip-puce ltr&#034;&gt;&lt;b&gt;&#8211;&lt;/b&gt;&lt;/span&gt; &#191;Qu&#233; cuota tendr&#237;amos que pagar en cada caso? Recuerda que en el primer banco el pago ser&#225; mensual y en el segundo banco la cuota ser&#225; anual.&lt;/p&gt;
&lt;p&gt;&lt;span class=&#034;spip-puce ltr&#034;&gt;&lt;b&gt;&#8211;&lt;/b&gt;&lt;/span&gt; Cuando terminamos de pagar todo el pr&#233;stamo, &#191;qu&#233; banco nos ha ofrecido el producto m&#225;s rentable?&lt;/p&gt;
&lt;p&gt;&lt;span class=&#034;spip-puce ltr&#034;&gt;&lt;b&gt;&#8211;&lt;/b&gt;&lt;/span&gt; Si lo que nos interesa es pagar cada a&#241;o lo menos posible, &#191;qu&#233; opci&#243;n elegiremos?&lt;/p&gt;
&lt;p&gt;Aparte del pr&#233;stamo que queremos pedir, disponemos de &lt;img src='https://lubrin.cloud/local/cache-vignettes/L58xH18/b7a782741f667201b54880c925faec4b-d424e.png?1773428661' style='vertical-align:middle;' width='58' height='18' alt=&#034;10000&#034; title=&#034;10000&#034; /&gt; &#8364; para posibles imprevistos que colocamos en un dep&#243;sito que nos ofrece un inter&#233;s compuesto del &lt;img src='https://lubrin.cloud/local/cache-vignettes/L30xH42/1c8f6a6fe2a2a2eae3f4910f61c34890-e5871.png?1773428661' style='vertical-align:middle;' width='30' height='42' alt=&#034;4\%&#034; title=&#034;4\%&#034; /&gt;, en periodos mensuales. Despu&#233;s de 5 a&#241;os, &#191;qu&#233; capital final obtendremos? Calcula la tasa anual equivalente (TAE).&lt;/p&gt;
&lt;/math&gt;&lt;/div&gt;
		
		</content:encoded>


		

	</item>
<item xml:lang="es">
		<title>Potencias y Ra&#237;ces. Ejercicio 4631</title>
		<link>https://lubrin.cloud/Potencias-y-Raices-Ejercicio-4631</link>
		<guid isPermaLink="true">https://lubrin.cloud/Potencias-y-Raices-Ejercicio-4631</guid>
		<dc:date>2023-11-23T09:44:05Z</dc:date>
		<dc:format>text/html</dc:format>
		<dc:language>es</dc:language>
		<dc:creator>Dani</dc:creator>


		<dc:subject>potencias</dc:subject>
		<dc:subject>Ejercicios_Resueltos</dc:subject>

		<description>
&lt;p&gt;a) &lt;br class='autobr' /&gt;
b) &lt;br class='autobr' /&gt;
c) &lt;br class='autobr' /&gt;
d) &lt;br class='autobr' /&gt;
e) &lt;br class='autobr' /&gt;
f) sin soluci&#243;n Real
&lt;br class='autobr' /&gt; Calcula el resultado de las siguientes potencias y ra&#237;ces: &lt;br class='autobr' /&gt;
a) &lt;br class='autobr' /&gt;
b) &lt;br class='autobr' /&gt;
c) &lt;br class='autobr' /&gt;
d) &lt;br class='autobr' /&gt;
e) &lt;br class='autobr' /&gt;
f)&lt;/p&gt;


-
&lt;a href="https://lubrin.cloud/Potencias-3-ESO" rel="directory"&gt;Potencias&lt;/a&gt;

/ 
&lt;a href="https://lubrin.cloud/potencias,68" rel="tag"&gt;potencias&lt;/a&gt;, 
&lt;a href="https://lubrin.cloud/Ejercicios_Resueltos" rel="tag"&gt;Ejercicios_Resueltos&lt;/a&gt;

		</description>


 <content:encoded>&lt;div class='rss_chapo'&gt;&lt;p&gt;a) &lt;img src='https://lubrin.cloud/local/cache-TeX/cfddd945dd04a877c4e38abe0f8f0176.png' style=&#034;vertical-align:middle;&#034; width=&#034;78&#034; height=&#034;22&#034; alt=&#034;4^2 = 16&#034; title=&#034;4^2 = 16&#034; /&gt;&lt;/p&gt;
&lt;p&gt;b) &lt;img src='https://lubrin.cloud/local/cache-TeX/cff7fc7bb0a2d70f10992ae83acb71ef.png' style=&#034;vertical-align:middle;&#034; width=&#034;133&#034; height=&#034;25&#034; alt=&#034;\sqrt{100} = \pm 10&#034; title=&#034;\sqrt{100} = \pm 10&#034; /&gt;&lt;/p&gt;
&lt;p&gt;c) &lt;img src='https://lubrin.cloud/local/cache-TeX/6bcad1825083cd225a2a52acc6602c74.png' style=&#034;vertical-align:middle;&#034; width=&#034;116&#034; height=&#034;28&#034; alt=&#034;(-4)^2 = 16&#034; title=&#034;(-4)^2 = 16&#034; /&gt;&lt;/p&gt;
&lt;p&gt;d) &lt;img src='https://lubrin.cloud/local/cache-TeX/57e75f4a3d61e5ca45783fa03ea59eae.png' style=&#034;vertical-align:middle;&#034; width=&#034;152&#034; height=&#034;25&#034; alt=&#034;\sqrt{8} = 2.828 \cdots&#034; title=&#034;\sqrt{8} = 2.828 \cdots&#034; /&gt;&lt;/p&gt;
&lt;p&gt;e) &lt;img src='https://lubrin.cloud/local/cache-TeX/caae60aa260d0df72eedc39bfba85417.png' style=&#034;vertical-align:middle;&#034; width=&#034;116&#034; height=&#034;22&#034; alt=&#034;-4^2 = -16&#034; title=&#034;-4^2 = -16&#034; /&gt;&lt;/p&gt;
&lt;p&gt;f) &lt;img src='https://lubrin.cloud/local/cache-TeX/4156a010a1b423e83f3deb9a5d74fc72.png' style=&#034;vertical-align:middle;&#034; width=&#034;88&#034; height=&#034;25&#034; alt=&#034; \sqrt{-25} = &#034; title=&#034; \sqrt{-25} = &#034; /&gt; sin soluci&#243;n Real&lt;br class='autobr' /&gt;
&lt;/math&gt;&lt;/p&gt;&lt;/div&gt;
		&lt;div class='rss_texte'&gt;&lt;p&gt;Calcula el resultado de las siguientes potencias y ra&#237;ces:&lt;/p&gt;
&lt;p&gt;a) &lt;img src='https://lubrin.cloud/local/cache-vignettes/L20xH21/1a7328941efc55b48f19cf1acc7e3d4e-d6231.png?1773428661' style='vertical-align:middle;' width='20' height='21' alt=&#034;4^2&#034; title=&#034;4^2&#034; /&gt;&lt;/p&gt;
&lt;p&gt;b) &lt;img src='https://lubrin.cloud/local/cache-vignettes/L53xH50/e0dc985c7ae8d98342e49009cff4a747-9e492.png?1773428661' style='vertical-align:middle;' width='53' height='50' alt=&#034;\sqrt{100}&#034; title=&#034;\sqrt{100}&#034; /&gt;&lt;/p&gt;
&lt;p&gt;c) &lt;img src='https://lubrin.cloud/local/cache-vignettes/L56xH28/6adf737ee45bdf92ebe527a811de828b-2dd1d.png?1773428661' style='vertical-align:middle;' width='56' height='28' alt=&#034;(-4)^2&#034; title=&#034;(-4)^2&#034; /&gt;&lt;/p&gt;
&lt;p&gt;d) &lt;img src='https://lubrin.cloud/local/cache-vignettes/L35xH50/23119775abd0f5e44d5d6d464dc9c5b5-22b37.png?1773428661' style='vertical-align:middle;' width='35' height='50' alt=&#034;\sqrt{8}&#034; title=&#034;\sqrt{8}&#034; /&gt;&lt;/p&gt;
&lt;p&gt;e) &lt;img src='https://lubrin.cloud/local/cache-vignettes/L38xH21/59121ed1a664db605b56879504706e5e-4380a.png?1773428661' style='vertical-align:middle;' width='38' height='21' alt=&#034;-4^2&#034; title=&#034;-4^2&#034; /&gt;&lt;/p&gt;
&lt;p&gt;f) &lt;img src='https://lubrin.cloud/local/cache-vignettes/L63xH25/0e8aa6c4ae362da412fdcd2f4efcd385-0b5d9.png?1773428661' style='vertical-align:middle;' width='63' height='25' alt=&#034; \sqrt{-25}&#034; title=&#034; \sqrt{-25}&#034; /&gt;&lt;br class='autobr' /&gt;
&lt;/math&gt;&lt;/p&gt;&lt;/div&gt;
		
		</content:encoded>


		

	</item>
<item xml:lang="es">
		<title>Conjuntos num&#233;ricos 4630</title>
		<link>https://lubrin.cloud/Conjuntos-numericos-4630</link>
		<guid isPermaLink="true">https://lubrin.cloud/Conjuntos-numericos-4630</guid>
		<dc:date>2023-11-23T09:37:49Z</dc:date>
		<dc:format>text/html</dc:format>
		<dc:language>es</dc:language>
		<dc:creator>Dani</dc:creator>


		<dc:subject>reales</dc:subject>
		<dc:subject>Ejercicios_Resueltos</dc:subject>

		<description>
&lt;p&gt;Conjunto N&#250;meros N (naturales) Z (enteros) Q (racionales) I (irracionales) R (reales) &lt;br class='autobr' /&gt;
b) &lt;br class='autobr' /&gt; Dados los siguientes n&#250;meros: &lt;br class='autobr' /&gt; a) Coloca cada n&#250;mero en su conjunto (o conjuntos, si pertenece a m&#225;s de uno) correspondiente. &lt;br class='autobr' /&gt;
b) Ordena los n&#250;meros de menor a mayor&lt;/p&gt;


-
&lt;a href="https://lubrin.cloud/Numeros-Reales,28" rel="directory"&gt;N&#250;meros Reales&lt;/a&gt;

/ 
&lt;a href="https://lubrin.cloud/reales" rel="tag"&gt;reales&lt;/a&gt;, 
&lt;a href="https://lubrin.cloud/Ejercicios_Resueltos" rel="tag"&gt;Ejercicios_Resueltos&lt;/a&gt;

		</description>


 <content:encoded>&lt;div class='rss_chapo'&gt;&lt;table class=&#034;table spip&#034;&gt;
&lt;tbody&gt;
&lt;tr class='row_odd odd'&gt;
&lt;td&gt;Conjunto&lt;/td&gt;
&lt;td&gt;N&#250;meros&lt;/td&gt;&lt;/tr&gt;
&lt;tr class='row_even even'&gt;
&lt;td&gt;N (naturales)&lt;/td&gt;
&lt;td&gt;&lt;img src='https://lubrin.cloud/local/cache-TeX/e4da3b7fbbce2345d7772b0674a318d5.png' style=&#034;vertical-align:middle;&#034; width=&#034;13&#034; height=&#034;38&#034; alt=&#034;5 &#034; title=&#034;5 &#034; /&gt;&lt;/math&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr class='row_odd odd'&gt;
&lt;td&gt;Z (enteros)&lt;/td&gt;
&lt;td&gt;&lt;img src='https://lubrin.cloud/local/cache-TeX/a338614524b88cac7508f6438f1bb6e3.png' style=&#034;vertical-align:middle;&#034; width=&#034;202&#034; height=&#034;52&#034; alt=&#034;-3 \quad 5 \quad \frac{-15}{3}=-5&#034; title=&#034;-3 \quad 5 \quad \frac{-15}{3}=-5&#034; /&gt;&lt;/math&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr class='row_even even'&gt;
&lt;td&gt;Q (racionales)&lt;/td&gt;
&lt;td&gt;&lt;img src='https://lubrin.cloud/local/cache-TeX/0682123ca6a156ce3f65ec492b61b4c7.png' style=&#034;vertical-align:middle;&#034; width=&#034;246&#034; height=&#034;52&#034; alt=&#034;-3 \quad 5 \quad \frac{5}{3} \quad 0.75 \quad \frac{-15}{3}&#034; title=&#034;-3 \quad 5 \quad \frac{5}{3} \quad 0.75 \quad \frac{-15}{3}&#034; /&gt;&lt;/math&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr class='row_odd odd'&gt;
&lt;td&gt;I (irracionales)&lt;/td&gt;
&lt;td&gt;&lt;img src='https://lubrin.cloud/local/cache-TeX/450ba84cab4004936bd58f45fcd7b73c.png' style=&#034;vertical-align:middle;&#034; width=&#034;94&#034; height=&#034;25&#034; alt=&#034;\sqrt{7} \qquad \pi&#034; title=&#034;\sqrt{7} \qquad \pi&#034; /&gt;&lt;/math&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr class='row_even even'&gt;
&lt;td&gt;R (reales)&lt;/td&gt;
&lt;td&gt;&lt;img src='https://lubrin.cloud/local/cache-TeX/e1d0bfed5b9754f711347f6dd2263e5a.png' style=&#034;vertical-align:middle;&#034; width=&#034;366&#034; height=&#034;52&#034; alt=&#034;-3 \quad \sqrt{7} \quad 5 \quad \frac{5}{3} \quad 0.75 \quad \pi \qquad \frac{-15}{3}&#034; title=&#034;-3 \quad \sqrt{7} \quad 5 \quad \frac{5}{3} \quad 0.75 \quad \pi \qquad \frac{-15}{3}&#034; /&gt;&lt;/math&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/tbody&gt;
&lt;/table&gt;
&lt;p&gt;b) &lt;img src='https://lubrin.cloud/local/cache-TeX/588611a51a1e9aa24cb8b1c53d862f36.png' style=&#034;vertical-align:middle;&#034; width=&#034;393&#034; height=&#034;52&#034; alt=&#034;\frac{-15}{3}&lt;-3 &lt; 0.75 &lt; \frac{5}{3} &lt; \sqrt{7} &lt; \pi &lt; 5&#034; title=&#034;\frac{-15}{3}&lt;-3 &lt; 0.75 &lt; \frac{5}{3} &lt; \sqrt{7} &lt; \pi &lt; 5&#034; /&gt;&lt;/math&gt;&lt;/p&gt;&lt;/div&gt;
		&lt;div class='rss_texte'&gt;&lt;p&gt;Dados los siguientes n&#250;meros: &lt;br class='autobr' /&gt;
&lt;img src='https://lubrin.cloud/local/cache-vignettes/L488xH52/a5584e20713fa60fcae20ad8659c164a-89011.png?1773428661' style='vertical-align:middle;' width='488' height='52' alt=&#034;-3 \qquad \sqrt{7} \qquad 5 \qquad \frac{5}{3} \qquad 0.75 \qquad \pi \qquad \frac{-15}{3}&#034; title=&#034;-3 \qquad \sqrt{7} \qquad 5 \qquad \frac{5}{3} \qquad 0.75 \qquad \pi \qquad \frac{-15}{3}&#034; /&gt;&lt;/math&gt;&lt;/p&gt;
&lt;p&gt;a) Coloca cada n&#250;mero en su conjunto (o conjuntos, si pertenece a m&#225;s de uno) correspondiente.&lt;/p&gt;
&lt;p&gt;b) Ordena los n&#250;meros de menor a mayor&lt;/p&gt;&lt;/div&gt;
		
		</content:encoded>


		

	</item>
<item xml:lang="es">
		<title>Errores al aproximar 4629</title>
		<link>https://lubrin.cloud/Errores-al-aproximar-4629</link>
		<guid isPermaLink="true">https://lubrin.cloud/Errores-al-aproximar-4629</guid>
		<dc:date>2023-11-23T09:23:50Z</dc:date>
		<dc:format>text/html</dc:format>
		<dc:language>es</dc:language>
		<dc:creator>Dani</dc:creator>


		<dc:subject>aproximaci&#243;n</dc:subject>
		<dc:subject>error_absoluto_y_relativo</dc:subject>
		<dc:subject>Ejercicios_Resueltos</dc:subject>

		<description>
&lt;p&gt;&#8211; a) &lt;br class='autobr' /&gt;
&#8211; b) Error Absoluto = | Valor Real - Aproximaci&#243;n |
&lt;br class='autobr' /&gt; &lt;br class='autobr' /&gt;
Error Relativo = &lt;br class='autobr' /&gt; &lt;br class='autobr' /&gt; Dado el n&#250;mero decimal 3,141592 : &lt;br class='autobr' /&gt;
a) Redondea el n&#250;mero a las diezmil&#233;simas. &lt;br class='autobr' /&gt;
b) Calcula el error absoluto y relativo que se comete al aproximar el n&#250;mero mediante el redondeo realizado en el apartado a).&lt;/p&gt;


-
&lt;a href="https://lubrin.cloud/Numeros-Reales" rel="directory"&gt;N&#250;meros Reales&lt;/a&gt;

/ 
&lt;a href="https://lubrin.cloud/aproximacion" rel="tag"&gt;aproximaci&#243;n&lt;/a&gt;, 
&lt;a href="https://lubrin.cloud/error-absoluto-y-relativo" rel="tag"&gt;error_absoluto_y_relativo&lt;/a&gt;, 
&lt;a href="https://lubrin.cloud/Ejercicios_Resueltos" rel="tag"&gt;Ejercicios_Resueltos&lt;/a&gt;

		</description>


 <content:encoded>&lt;div class='rss_chapo'&gt;&lt;p&gt;&lt;span class=&#034;spip-puce ltr&#034;&gt;&lt;b&gt;&#8211;&lt;/b&gt;&lt;/span&gt; a) &lt;img src='https://lubrin.cloud/local/cache-TeX/57685e7d28076e8fc72ec4736c014344.png' style=&#034;vertical-align:middle;&#034; width=&#034;115&#034; height=&#034;18&#034; alt=&#034;\pi= 3.1416&#034; title=&#034;\pi= 3.1416&#034; /&gt;&lt;/math&gt;&lt;/p&gt;
&lt;p&gt;&lt;span class=&#034;spip-puce ltr&#034;&gt;&lt;b&gt;&#8211;&lt;/b&gt;&lt;/span&gt; b) Error Absoluto = | Valor Real - Aproximaci&#243;n |&lt;br class='autobr' /&gt; &lt;p class=&#034;spip&#034; style=&#034;text-align: center;&#034;&gt;&lt;img src='https://lubrin.cloud/local/cache-TeX/7dee58b479c73184742f4eedfdf45601.png' style=&#034;vertical-align:middle;&#034; width=&#034;403&#034; height=&#034;26&#034; alt=&#034;EA = |3.141592 - 3.1416| = 0,000008 &#034; title=&#034;EA = |3.141592 - 3.1416| = 0,000008 &#034; /&gt;&lt;/p&gt;
&lt;/math&gt;&lt;/p&gt;
&lt;p&gt;Error Relativo = &lt;img src='https://lubrin.cloud/local/cache-TeX/29ec4a6357c80ec545abeea06e36eef1.png' style=&#034;vertical-align:middle;&#034; width=&#034;140&#034; height=&#034;67&#034; alt=&#034;\frac{Error \: Absoluto}{Valor \: Real}&#034; title=&#034;\frac{Error \: Absoluto}{Valor \: Real}&#034; /&gt;&lt;/math&gt;&lt;br class='autobr' /&gt; &lt;p class=&#034;spip&#034; style=&#034;text-align: center;&#034;&gt;&lt;img src='https://lubrin.cloud/local/cache-TeX/35d9bebb789fff59b7fa839f83dde1c5.png' style=&#034;vertical-align:middle;&#034; width=&#034;518&#034; height=&#034;52&#034; alt=&#034;ER = \frac{0,000008}{3.141592}=0,000002546 \longrightarrow 0.0002546 \%&#034; title=&#034;ER = \frac{0,000008}{3.141592}=0,000002546 \longrightarrow 0.0002546 \%&#034; /&gt;&lt;/p&gt;
&lt;/math&gt;&lt;/p&gt;&lt;/div&gt;
		&lt;div class='rss_texte'&gt;&lt;p&gt;Dado el n&#250;mero decimal 3,141592 :&lt;/p&gt;
&lt;p&gt;a) Redondea el n&#250;mero a las diezmil&#233;simas.&lt;/p&gt;
&lt;p&gt;b) Calcula el error absoluto y relativo que se comete al aproximar el n&#250;mero mediante el redondeo realizado en el apartado a).&lt;/p&gt;&lt;/div&gt;
		
		</content:encoded>


		

	</item>



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