4t ESO/4.05 INEQUACIONS/4.05.4 Problemes d'inequacions 4.05.5.11Q Preguntes correctes en examen

En un examen de #p preguntes et donen dos punts per cada encert i et treuen #e punt per cada error.

Per aprovar, és obligatori contestar totes les preguntes, i cal treure, almenys, #p punts. (Les no contestades compten com a incorrectes)

Quantes preguntes, com a mínim, cal contestar correctament per aprovar?

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 1.0000000 0.5000000 0 0 #c <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="ca">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable><mtr><mtd><mi>p</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>10</mn><mo>,</mo><mn>20</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>e</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>8</mn><mo>)</mo><mo>*</mo><mn>0</mn><mo>.</mo><mn>1</mn></mtd></mtr><mtr><mtd><mi>e1</mi><mo>=</mo><mi>c</mi><mo>*</mo><mn>2</mn><mo>-</mo><mo>(</mo><mi>p</mi><mo>-</mo><mi>c</mi><mo>)</mo><mo>*</mo><mi>e</mi><mo>-</mo><mi>p</mi><mo>></mo><mn>0</mn></mtd></mtr><mtr><mtd><mi>R</mi><mo>=</mo><mi>resol_inequació</mi><mo>(</mo><mi>e1</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>c1</mi><mo>=</mo><mfrac><mrow><mi>p</mi><mo>*</mo><mi>e</mi><mo>+</mo><mi>p</mi></mrow><mrow><mn>2</mn><mo>+</mo><mi>e</mi></mrow></mfrac></mtd></mtr></mtable></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>part_entera_superior</mi><mo>(</mo><mi>c1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>=</mo><mi>part_entera_superior</mi><mo>(</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w1</mi><mo>=</mo><mn>2</mn><mo>*</mo><mi>c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w2</mi><mo>=</mo><mo>(</mo><mi>p</mi><mo>-</mo><mi>c</mi><mo>)</mo><mo>*</mo><mi>e</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ww</mi><mo>=</mo><mi>w1</mi><mo>-</mo><mi>w2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>20</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0.6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1.8</mn><mo>></mo><mn>0</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>13</mn><mo>></mo><mn>12.308</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>12.308</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>13</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ww</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>21.8</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#c</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Si x és el nombre d'encerts, (#p-x) és el nombre d'errors.

La inequació que cal resoldre és doncs:
2·x - (#p-x)·#e ≥ #p

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