// Numbas version: finer_feedback_settings
{"name": "FIS5047_S1_Numbas", "metadata": {"description": "", "licence": "None specified"}, "duration": 0, "percentPass": 0, "showQuestionGroupNames": false, "shuffleQuestionGroups": false, "showstudentname": true, "question_groups": [{"name": "Group", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": ["", "", ""], "variable_overrides": [[], [], []], "questions": [{"name": "Ivan's copy of Converting units of volume (cc/cm^3/litres/m^3)", "extensions": ["random_person"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Chris Graham", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/369/"}, {"name": "Ivan Munoz", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/18334/"}], "tags": ["taxonomy"], "metadata": {"description": "<p>Convert figures for car engine sizes between cc (cm^3), litres, and m^3.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p>{person['name']} quiere comprar un auto. {person['name']} encuentra una publicidad con un auto con un motor de $\\var{cc}$cc.&nbsp;</p>\n<p>{person['name']} Reconoce que 'cc' es por c&eacute;ntimetros c&uacute;bicos (cm$^3$) y sabe las siguientes conversiones:</p>\n<table border=\"1\" cellpadding=\"5\">\n<tbody>\n<tr>\n<td style=\"text-align: left;\">$1$ m</td>\n<td style=\"text-align: left;\">$100$ cm</td>\n</tr>\n<tr>\n<td style=\"text-align: left;\">$1$ litre</td>\n<td style=\"text-align: left;\">$1000\\text{cm}^3$&nbsp;</td>\n</tr>\n</tbody>\n</table>", "advice": "<h4>a)</h4>\n<p>El tama&ntilde;o del motor es $\\var{cc}$ centimetros cubicos. Para convertir centrimetos cubicos a litros, dividimos por$1000$.&nbsp;</p>\n<p>\\[\\var{cc}\\div 1000= \\var{litres}\\text{ litres.}\\]</p>\n<h4>b)</h4>\n<p>Notemos que</p>\n<p>\\[ 1 \\text{cm} = 0.01&nbsp;\\text{m.} \\]</p>\n<p>Un ejemplo de volumen $1\\text{cm}^3$ es un cubo de lado $1$cm. Convirtiendo cada cm,</p>\n<p>\\begin{align}<br/>1\\text{cm}^3 &amp;= 1\\text{cm}\\times1\\text{cm}\\times1\\text{cm} \\\\<br/>&amp;= 0.01\\text{m}\\times0.01\\text{m}\\times0.01\\text{m} \\\\<br/>&amp;= 0.000001\\text{m}^3 \\text{.}<br/>\\end{align}</p>\n<p>Entonces$\\var{cc}\\text{cm}^3$ is&nbsp;</p>\n<p>\\[ \\var{cc} \\times 0.000001 = \\var{metres_cubed}\\text{m}^3\\text{.} \\]</p>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"metres_cubed": {"name": "metres_cubed", "group": "Ungrouped variables", "definition": "cc*(10^-6)", "description": "", "templateType": "anything", "can_override": false}, "cc": {"name": "cc", "group": "Ungrouped variables", "definition": "random(1200..3000#200)", "description": "", "templateType": "anything", "can_override": false}, "s": {"name": "s", "group": "Ungrouped variables", "definition": "if(person['gender']='neutral','','s')", "description": "", "templateType": "anything", "can_override": false}, "person": {"name": "person", "group": "Ungrouped variables", "definition": "random_person()", "description": "", "templateType": "anything", "can_override": false}, "litres": {"name": "litres", "group": "Ungrouped variables", "definition": "cc/1000", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["person", "litres", "cc", "s", "metres_cubed"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>{person['name']} aplica para saber cu&aacute;nto costar&iacute;a el seguro del autom&oacute;vil, pero se requiere que indique el tama&ntilde;o del motor en litros.</p>\n<p>&iquest;Cu&aacute;l es el tama&ntilde;o del motor en litros?</p>\n<p>&nbsp;[[0]] litres.&nbsp;</p>\n<p><em></em></p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "litres", "maxValue": "litres", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>La especificaci&oacute;n de un segundo autom&oacute;vil da el tama&ntilde;o del motor en m$^3$. Para que {person['name']} haga una comparaci&oacute;n convierte el tama&ntilde;o del motor del primer autom&oacute;vil a metros c&uacute;bicos.</p>\n<p>&iquest;Cu&aacute;l es el tama&ntilde;o del motor del primer autom&oacute;vil en unidades de m$^3$?</p>\n<p>[[0]]m$^3$ &nbsp; &nbsp; &nbsp;<em><small>Give your answer to 4 decimal places</small></em></p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "metres_cubed", "maxValue": "metres_cubed", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "dp", "precision": "4", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question"}, {"name": "Ivan's copy of Converting units: baby weight", "extensions": ["stats"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Chris Graham", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/369/"}, {"name": "Ivan Munoz", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/18334/"}], "tags": ["taxonomy"], "metadata": {"description": "<p>Convert weights of babies between kg and lb and oz.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p>En muchos pa&iacute;ses, todav&iacute;a es tradicional anunciar el peso de un beb&eacute; en unidades imperiales (libras y onzas), en lugar de m&eacute;tricas (gramos o kilogramos).</p>\n<p>Una tabla de conversi&oacute;n es la siguiente:</p>\n<table border=\"1\" cellpadding=\"5\">\n<tbody>\n<tr>\n<td style=\"text-align: left;\">$1$ libra(lb)</td>\n<td style=\"text-align: left;\">$16$ onza (oz)</td>\n</tr>\n<tr>\n<td style=\"text-align: left;\">$1$ stone&nbsp;(st)</td>\n<td style=\"text-align: left;\">$14$ libra(lb)</td>\n</tr>\n<tr>\n<td style=\"text-align: left;\">$1$ kg</td>\n<td style=\"text-align: left;\">$\\var{oz_to_kg}$ onza(oz)</td>\n</tr>\n</tbody>\n</table>", "advice": "<h4><strong>a)</strong></h4>\n<p>We are told that the baby's weight is $\\var{weight_kg}$kg and we would like to convert this to pounds and ounces.</p>\n<p>To do this, we first obtain the weight in ounces using the conversion given:</p>\n<p>\\begin{align}<br/> \\var{weight_kg} \\text{ kg} &nbsp;&amp;= \\var{weight_kg} \\times \\var{oz_to_kg} \\text{ oz} \\\\<br/>&amp;=&nbsp;\\var{weight_oz}\\text{ oz.}<br/>\\end{align}</p>\n<p>We can now divide by $16$ to find out how many whole pounds we have:</p>\n<p>\\[&nbsp;\\var{weight_oz}\\text{ oz} \\div 16 =&nbsp;&nbsp;\\var{dpformat(weight_oz/16,1)}\\text{ lb.} \\]</p>\n<p>There are $\\var{weight_lb}$ whole pounds, which leaves a remainder</p>\n<p>\\[&nbsp;\\var{weight_oz} - (16 \\times&nbsp;\\var{weight_lb}) =&nbsp;&nbsp;\\var{weight_oz_rem} \\text{ oz.} \\]</p>\n<p>The baby weighs $\\var{weight_lb}$ pounds and $\\var{weight_oz_rem}$ ounces.</p>\n<h4><strong>b)</strong></h4>\n<p>We are given the weight of the baby in stones, pounds and ounces. To convert to kg we first convert the baby's weight to ounces.</p>\n<p>$1$ stone is $14$ pounds, so the baby weighs $\\var{news['lb']+14}$ pounds&nbsp;and $\\var{news['oz']}$ ounces, or</p>\n<p>\\[ &nbsp;(\\var{news['lb']+14} \\times 16) + \\var{news['oz']} = \\var{(news['lb']+14)*16+news['oz']} \\text{ oz.}\\]</p>\n<p>We can now convert to kg:</p>\n<p>\\begin{align}<br/> \\var{(news['lb']+14)*16+news['oz']} \\text{ oz} &amp;= \\var{(news['lb']+14)*16+news['oz']} \\div \\var{oz_to_kg} &nbsp;\\\\<br/>&amp;= \\var{dpformat(newskg,1)}\\text{ kg.}<br/>\\end{align}</p>\n<p></p>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"weight_oz_rem": {"name": "weight_oz_rem", "group": "hospital baby", "definition": "mod(weight_oz,16)", "description": "<p>The remainder in ounces</p>", "templateType": "anything", "can_override": false}, "weight_lb": {"name": "weight_lb", "group": "hospital baby", "definition": "floor(weight_oz/16)", "description": "<p>Weight of the baby in lb</p>", "templateType": "anything", "can_override": false}, "news_reports": {"name": "news_reports", "group": "News baby", "definition": "json_decode(safe(\"[\\n    {\\n        \\\"year\\\": 2016,\\n        \\\"text\\\": \\\"only the second baby to be born in the UK\\\",\\n        \\\"lb\\\": 1,\\n        \\\"oz\\\": 8\\n    },\\n    {\\n        \\\"year\\\": 2014,\\n        \\\"text\\\": \\\"a boy in California\\\",\\n        \\\"lb\\\": 2,\\n        \\\"oz\\\": 2\\n    },\\n    {\\n        \\\"year\\\": 2014,\\n        \\\"text\\\": \\\"a boy in Florida, the heaviest ever recorded in the state,\\\",\\n        \\\"lb\\\": 0,\\n        \\\"oz\\\": 2\\n    },    \\n    {\\n        \\\"year\\\": 2012,\\n        \\\"text\\\": \\\"a record-breaking baby in China,\\\",\\n        \\\"lb\\\": 1,\\n        \\\"oz\\\": 5\\n    }        \\n]\"))", "description": "<p>A list of news reports</p>", "templateType": "json", "can_override": false}, "newskg": {"name": "newskg", "group": "News baby", "definition": "((16*(14+news['lb']))+news['oz'])/oz_to_kg", "description": "<p>Weight in kg of the baby in the news</p>", "templateType": "anything", "can_override": false}, "news": {"name": "news", "group": "News baby", "definition": "random(news_reports)", "description": "<p>The news report we're using</p>", "templateType": "anything", "can_override": false}, "oz_to_kg": {"name": "oz_to_kg", "group": "hospital baby", "definition": "35.3", "description": "<p>conversion rate, ounces in a kg</p>", "templateType": "anything", "can_override": false}, "weight_kg": {"name": "weight_kg", "group": "hospital baby", "definition": "precround(\n  min(max(normalsample(3.5,1/1.96),2.5),5)\n,1)", "description": "<p>Weight of the baby in kg, given to the student in the question.</p>\n<p>Wikipedia says that the average baby of European heritage weighs 3.5kg, with 90% between 2.5 and 5.</p>\n<p>The min and max are to avoid really odd-looking weights.</p>", "templateType": "anything", "can_override": false}, "weight_oz": {"name": "weight_oz", "group": "hospital baby", "definition": "precround(weight_kg*oz_to_kg,0)", "description": "<p>weight of the baby in oz, rounded to the nearest integer</p>", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [{"name": "hospital baby", "variables": ["oz_to_kg", "weight_kg", "weight_lb", "weight_oz", "weight_oz_rem"]}, {"name": "News baby", "variables": ["news_reports", "news", "newskg"]}], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Un hospital mide el peso de un beb&eacute; en $\\var{weight_kg}$kg, pero los padres del beb&eacute; les piden el peso en libras y onzas, a quienes les gustar&iacute;a hacer un anuncio a sus amigos y familiares de la manera tradicional.&nbsp;</p>\n<p>Usando la tabla de conversi&oacute;n anterior, &iquest;cu&aacute;l es el peso en libras (lb) y onzas (oz)?</p>\n<p>[[0]]lb and&nbsp;[[1]]oz &nbsp; &nbsp; &nbsp; &nbsp;<em><small>Round your answer to the nearest ounce.</small></em></p>", "stepsPenalty": 0, "steps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": "0.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Usando la tasa de conversi&oacute;n de kg a oz, &iquest;cu&aacute;l es el peso del beb&eacute; en onzas?</p>\n<p></p>", "minValue": "weight_oz", "maxValue": "weight_oz", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "dp", "precision": 0, "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "0.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Ahora usa la tasa de conversi&oacute;n de lb a oz. Redondeando hacia abajo, &iquest;cu&aacute;ntas libras enteras pesa el beb&eacute;?</p>", "minValue": "weight_lb", "maxValue": "weight_lb", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "0.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>&iquest;Cu&aacute;l es el peso anterior en onzas?</p>", "minValue": "weight_lb*16", "maxValue": "weight_lb*16", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "0.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Reste el peso anterior del peso del beb&eacute; en onzas que se encuentra en el primer paso. &iquest;Cu&aacute;l es el resto en onzas?</p>", "minValue": "weight_oz_rem", "maxValue": "weight_oz_rem", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "weight_lb", "maxValue": "weight_lb", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "weight_oz_rem", "maxValue": "weight_oz_rem", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>En 1995, los peri&oacute;dicos informaron del nacimiento de un bebe con un peso de m&aacute;s de $1$ piedra. El beb&eacute; se registr&oacute; en $1$ stone, $\\var{news['lb']}$ libras y $\\var{news['oz']}$ onzas.</p>\n<p>&iquest;Cu&aacute;l fue el peso en kg?</p>\n<p></p>\n<p>[[0]] kg &nbsp; &nbsp; &nbsp;<em><small>round your answer to&nbsp;1 decimal place.</small></em></p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "newskg", "maxValue": "newskg", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "dp", "precision": "1", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question"}, {"name": "Unidades ", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Ivan Munoz", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/18334/"}], "tags": ["taxonomy"], "metadata": {"description": "<p>Calcule una velocidad en m/s dada la distancia y el tiempo necesarios, luego convi&eacute;rtala a km/hora</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p>Un atleta corre $\\var{distancia}$ m en $\\var{segundos}$ segundos.</p>\n<p>Redondea cada una de tus respuestas a dos decimales.</p>", "advice": "<h4>a)</h4>\n<p>Para encontrar la velocidad promedio del corredor en metros por segundo (m/s), dividimos la distancia recorrida por el corredor (en metros) por el tiempo que le tom&oacute; al corredor recorrer esa distancia (en segundos).</p>\n<p>\\[<br/>\\begin{align}<br/>\\text{Average speed} &amp;= \\displaystyle\\frac{\\var{distance}}{\\var{seconds}}\\\\<br/>&amp;= \\var{distance/seconds}\\\\<br/>&amp;= \\var{dpformat(distance/seconds,2)}\\; \\text{m/s} \\; (\\text{rounded to $2$ decimal places}).<br/>\\end{align}<br/>\\]</p>\n<h4>b)</h4>\n<p>Podemos convertir la velocidad media del corredor que calculamos en a) en metros por segundo a kil&oacute;metros por hora usando las dos equivalencias siguientes:</p>\n<p>\\[1\\text{m} = \\displaystyle\\frac{1}{1000}\\text{km},\\]</p>\n<p>\\[<br/>1 \\; \\text{second} = \\displaystyle\\frac{1}{60} \\; \\text{minutes} = \\displaystyle\\frac{1}{3600} \\; \\text{hours}.<br/>\\]</p>\n<p>Sabemos por a) que la velocidad promedio del corredor en m/s fue $\\var{dpformat(distancia/segundos,5)}$ m/s ($5$ d.p), as&iacute; que para convertir esta velocidad a km/h tenemos primero hay que convertir metros a kil&oacute;metros,</p>\n<p>\\[\\var{dpformat(distance/seconds,5)} \\; \\text{m/s} = \\var{dpformat(distance/seconds/1000,5)} \\text{km/s} \\; (5 \\; \\text{d.p})\\]</p>\n<p>Luego convertimos los segundos a horas.,</p>\n<p>\\[1 \\; \\text{second} = \\displaystyle\\frac{1}{3600} \\; \\text{hours}.\\]</p>\n<p>Ahora tenemos</p>\n<p>\\[\\var{dpformat(distance/seconds,5)} \\; \\text{m/s} = \\var{sigformat(distance/seconds/1000,5)} \\; \\text{kilometres per $\\displaystyle\\frac{1}{3600}$ hours}.\\]</p>\n<p>Queremos una tarifa por hora, entonces multiplicamos por $3600$ para obtener una medida en km/h:</p>\n<p><span data-jme-visible=\"(distance/seconds*3.6) &lt;&gt; precround((distance/seconds*3.6),2)\">\\[\\begin{align}\\var{sigformat(distance/seconds/1000,5)} \\; \\text{kilometres per $\\displaystyle\\frac{1}{3600}$ hours} &amp;= \\var{siground(distance/seconds/1000,5)*3600} \\; \\text{km}/\\text{h}\\\\&amp;=\\var{dpformat(distance/seconds*3.6, 2)} \\; \\text{km}/\\text{h} \\; (\\text{rounded to $2$ decimal places}).\\end{align}\\]</span></p>\n<p><span data-jme-visible=\"(distance/seconds*3.6) = precround((distance/seconds*3.6),2)\">\\[\\var{sigformat(distance/seconds/1000,5)} \\; \\text{kilometres per $\\displaystyle\\frac{1}{3600}$ hours} = \\var{distance/seconds*3.6} \\; \\text{km}/\\text{h}.\\]</span></p>\n<p>Tenga en cuenta que a lo largo de este c&aacute;lculo hemos redondeado todas las cifras a $5$ decimales por conveniencia; cuando haga c&aacute;lculos que involucren decimales largos, siempre debe ingresar la cifra completa en su calculadora para evitar obtener una respuesta incorrecta debido al redondeo.</p>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"speed": {"name": "speed", "group": "Ungrouped variables", "definition": "random(4..8#0)", "description": "<p>Athlete's speed, in m/s.</p>\n<p>4m/s is about 9 mph, a bit faster than a jog. 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