There are roughly 11 million children in the UK. How many elves does Santa need?
\n[[0]] elves
", "scripts": {}}, {"steps": [{"type": "information", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "showFeedbackIcon": true, "marks": 0, "prompt": "The equation of a straight line is traditionally written
\n\\[ y = mx+c\\text{,}\\]
\nwhere $m$ is the gradient of the line, and $c$ the intercept with the y axis.
\nIn our case, the variables are labelled $E$ and $n$ (rather than $y$ and $x$ respectively). The intercept $c$ is the number of elves required for $0$ children, i.e. the base number, $\\var{c}$. And the gradient $m$ is the number of elves required for each unit $n$, which is given as $\\var{m}$.
\n", "scripts": {}}], "type": "gapfill", "variableReplacements": [], "gaps": [{"checkingaccuracy": 0.001, "type": "jme", "vsetrange": [0, 1], "checkingtype": "absdiff", "scripts": {}, "showFeedbackIcon": true, "answer": "{m}*n+{c}", "marks": "2", "checkvariablenames": true, "vsetrangepoints": 5, "variableReplacements": [], "expectedvariablenames": ["n"], "showCorrectAnswer": true, "showpreview": true, "variableReplacementStrategy": "originalfirst"}], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "stepsPenalty": 0, "showFeedbackIcon": true, "marks": 0, "prompt": "Santa makes a plot of the number of elves he requires, $E$, against the number of children, $n$ (in units of million children):
\n{graphsolution()}
\nWhat is the equation of the line?
\n$E(n)=$ [[0]]
", "scripts": {}}], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"c": {"definition": "random(30..60#10)", "templateType": "anything", "name": "c", "group": "Ungrouped variables", "description": ""}, "m": {"definition": "random(15..30#5)", "templateType": "anything", "name": "m", "group": "Ungrouped variables", "description": ""}}, "name": "Santa's elves equation of a straight line", "extensions": ["jsxgraph"], "ungrouped_variables": ["c", "m"], "preamble": {"css": "", "js": ""}, "advice": "The number of elves Santa requires is
\n\\[ ({m}\\times 11) + {c} \\text{.}\\]
\nThe equation of a straight line is traditionally written
\n\\[ y = mx+c\\text{,}\\]
\nwhere $m$ is the gradient of the line, and $c$ the intercept with the y axis.
\nIn our case, the variables are labelled $E$ and $n$ (rather than $y$ and $x$ respectively). The intercept $c$ is the number of elves required for $0$ children, i.e. the base number, $\\var{c}$. And the gradient $m$ is the number of elves required for each unit $n$, which is given as $\\var{m}$.
\nTherefore the equation of Santa's line is
\n\\[ E(n) = \\var{m}x + \\var{c}\\text{.}\\]
\nTo learn more about the equation of a straight line, here is Professor Robin Johnson solving a slightly trickier problem:
\n", "statement": "Note that this question is randomised, including the graph (try clicking \"Try another question like this one\"), and that you get a preview of the answer when you type in an expression. One more thing: the correct answer is written in terms of the variable n, go on try a different letter, like x, it separates the validation from the marking to help you out.
\nSanta is reviewing the personnel requirements for the North Pole's UK division. He requires {c} elves to do the basic administrative jobs, plus {m} elves for every 1 million children, to manage toy making and the like.
\n", "rulesets": {"std": ["all", "fractionNumbers", "!collectNumbers", "!noLeadingMinus"]}, "functions": {"graphsolution": {"definition": "JXG.Options.layer['curve'] = 9;\nJXG.Options.layer['line'] = 7;\n\nvar c = Numbas.jme.unwrapValue(scope.variables.c);\nvar m = Numbas.jme.unwrapValue(scope.variables.m);\nvar div = Numbas.extensions.jsxgraph.makeBoard('400px','400px',\n {boundingBox:[-0.7,12*m+c,13,-45],\n axis:false,\n showNavigation:false,\n grid:false});\nvar brd = div.board; \nxaxis = brd.create('axis', [[0, 0], [1,0]], \n\t\t {name:'$$n$$', \n strokeColor: 'black',\n fixed: true,\n withLabel: true,\n label: {position: 'rt', offset: [0, -15], fontSize: 17}\n\t\t\t});\nyaxis = brd.create('axis', [[0, 0], [0, 1]], \n\t\t {name:'$$E$$', \n strokeColor: 'black',\n fixed: true,\n\t\t withLabel: true,\n label: {position: 'rt', offset: [-20, 0], fontSize: 17}\n\t\t\t});\t\n\nvar q=brd.create('line',[[0,c],[10,c+(m*10)]],{fixed:true,strokeColor:'blue',strokeWidth:2,straightFirst:false});\nvar tree;\n//n is the variable in the equation to be input\n var nscope = new Numbas.jme.Scope([scope,{variables:{n:new Numbas.jme.types.TNum(0)}}]);\n//create a functiongraph from the student input\nfunction userf(n){\nif(tree) {\n try {\nnscope.variables.n.value = n;\n var val = Numbas.jme.evaluate(tree,nscope).value;\n return val;\n }\n catch(e) {\nreturn 0;\n }\n}\nelse\n return -100;\n}\nvar curve=brd.create('functiongraph',[userf,0,12],{strokeColor:'red',strokeWidth:2,dash:2});\n\n //pick up the student answer and is parsed\n question.signals.on('HTMLAttached',function(e) {\nko.computed(function(){\nvar expr = question.parts[1].gaps[0].display.studentAnswer();\ntry {\n tree = Numbas.jme.compile(expr,scope);\n}\ncatch(e) {\n tree = null;\n}\ncurve.updateCurve();\n\nbrd.update();\n});\n }); \n\nreturn div;\n ", "language": "javascript", "type": "html", "parameters": []}}, "tags": [], "variable_groups": [], "type": "question", "contributors": [{"name": "Chris Graham", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/369/"}]}]}], "contributors": [{"name": "Chris Graham", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/369/"}]}