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March 19, 2018 22:12
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| { | |
| "test": { | |
| "title": "S02T17", | |
| "slug": "S02T17", | |
| "description": "Přípravný test k státní maturitě.", | |
| "cermat": true, | |
| "successfulLimit": 33, | |
| "tasks": [ | |
| { | |
| "slug": "S02T17U01", | |
| "title": "S02T17U01", | |
| "question": | |
| "Upravte a vypočítejte: $$\\left({2\\cdot{10^{-9}}\\cdot3200}\\over{1,6\\cdot10^{-5}}\\right)^2=$$", | |
| "maxPoints": 1, | |
| "type": "options", | |
| "categories": ["5a89fe15bf5e07c5af6d5f9d"], | |
| "options": [ | |
| { "name": "opt1", "problem": "##1\\over25##" }, | |
| { "name": "opt2", "problem": "##3\\over25##" }, | |
| { "name": "opt3", "problem": "##2\\over25##" }, | |
| { "name": "opt4", "problem": "##4\\over25##" }, | |
| { "name": "opt5", "problem": "jiná hodnota" } | |
| ], | |
| "correctAnswer": ["opt4"], | |
| "solutions": [{}] | |
| }, | |
| { | |
| "slug": "S02T17U02", | |
| "title": "S02T17U02", | |
| "question": | |
| "Rozložte na součin činitelů: ##4x^2(a-b)+9y^2(b-a)=##", | |
| "maxPoints": 2, | |
| "type": "options", | |
| "categories": ["5a89fddbbf5e07c5af6d5f99"], | |
| "options": [ | |
| { "name": "opt1", "problem": "##(a-b)(2x+3y)(2x+3y)##" }, | |
| { "name": "opt2", "problem": "##(a+b)(2x-3y)(2x-3y)##" }, | |
| { "name": "opt3", "problem": "##(b-a)(2x-3y)(2x+3y)##" }, | |
| { "name": "opt4", "problem": "##(a-b)(2x-3y)(2x+3y)##" }, | |
| { "name": "opt5", "problem": "##(a+b)(-2x+3y)(2x+3y)##" } | |
| ], | |
| "correctAnswer": ["opt4"], | |
| "solutions": [{}] | |
| }, | |
| { | |
| "slug": "S02T17U03", | |
| "title": "S02T17U03", | |
| "question": | |
| "V oboru ##\\mathbb{N}## řešte: $$2a-(8a-1)-(a+2)\\cdot5=9$$", | |
| "maxPoints": 1, | |
| "type": "options", | |
| "categories": ["5a8a0442bf5e07c5af6d5fa4"], | |
| "options": [ | |
| { "name": "opt1", "problem": "##K=\\{-1\\}##" }, | |
| { "name": "opt2", "problem": "##K=\\{0\\}##" }, | |
| { "name": "opt3", "problem": "##K=\\{\\emptyset\\}##" }, | |
| { "name": "opt4", "problem": "##K=\\{-2\\}##" }, | |
| { "name": "opt5", "problem": "jiná hodnota " } | |
| ], | |
| "correctAnswer": ["opt3"], | |
| "solutions": [{}] | |
| }, | |
| { | |
| "slug": "S02T17U04", | |
| "title": "S02T17U04", | |
| "question": | |
| "##{2\\over5}\\cdot{3\\over10}-{1\\over5}:{5\\over7}=##", | |
| "maxPoints": 1, | |
| "type": "options", | |
| "categories": ["5a89fddbbf5e07c5af6d5f99"], | |
| "options": [ | |
| { "name": "opt1", "problem": "##3\\over25##" }, | |
| { "name": "opt2", "problem": "##-3\\over25##" }, | |
| { "name": "opt3", "problem": "##-4\\over25##" }, | |
| { "name": "opt4", "problem": "##-2\\over5##" }, | |
| { "name": "opt5", "problem": "##2\\over5##" } | |
| ], | |
| "correctAnswer": ["opt3"], | |
| "solutions": [{}] | |
| }, | |
| { | |
| "slug": "S02T17U05", | |
| "title": "S02T17U05", | |
| "question": "##{{2+\\logx}\\over{3-\\logx}}=5##", | |
| "maxPoints": 2, | |
| "type": "options", | |
| "categories": ["5a8a0581bf5e07c5af6d5fb0"], | |
| "options": [ | |
| { "name": "opt1", "problem": "##\\sqrt[5]{x^{13}}##" }, | |
| { "name": "opt2", "problem": "##\\sqrt[8]{x^{13}}##" }, | |
| { "name": "opt3", "problem": "##\\sqrt[7]{x^{13}}##" }, | |
| { "name": "opt4", "problem": "##\\sqrt[6]{x^{13}}##" }, | |
| { "name": "opt5", "problem": "jiná hodnota" } | |
| ], | |
| "correctAnswer": ["opt4"], | |
| "solutions": [{}] | |
| }, | |
| { | |
| "slug": "S02T17U06", | |
| "title": "S02T17U06", | |
| "question": "##\\logx+{1\\over\\logx}=2##", | |
| "maxPoints": 2, | |
| "type": "options", | |
| "categories": ["5a8a054dbf5e07c5af6d5faf"], | |
| "options": [ | |
| { "name": "opt1", "problem": "##1##" }, | |
| { "name": "opt2", "problem": "##10##" }, | |
| { "name": "opt3", "problem": "##2##" }, | |
| { "name": "opt4", "problem": "##5##" }, | |
| { "name": "opt5", "problem": "jiná hodnota" } | |
| ], | |
| "correctAnswer": ["opt2"], | |
| "solutions": [{}] | |
| }, | |
| { | |
| "slug": "S02T17U07", | |
| "title": "S02T17U07", | |
| "question": "Vynásobte: ##\\sqrt{ab}\\cdot(\\sqrta-\\sqrtb)=##", | |
| "maxPoints": 1, | |
| "type": "options", | |
| "categories": ["5a89fddbbf5e07c5af6d5f99"], | |
| "options": [ | |
| { "name": "opt1", "problem": "##a-b##" }, | |
| { "name": "opt2", "problem": "##b\\sqrt{a}-a\\sqrt{b}##" }, | |
| { "name": "opt3", "problem": "##\\sqrt{b}-\\sqrt{a}##" }, | |
| { "name": "opt4", "problem": "##a\\sqrt{b}-b\\sqrt{a}##" }, | |
| { "name": "opt5", "problem": "##a\\sqrt{a}-b\\sqrt{b}##" } | |
| ], | |
| "correctAnswer": ["opt4"], | |
| "solutions": [{}] | |
| }, | |
| { | |
| "slug": "S02T17U08", | |
| "title": "S02T17U08", | |
| "taskText": | |
| "Potřebujeme nakreslit plán chalupy i se stodolou. Plán se na papír nejlépe vejde, když 15 metrovou zeď nakreslíme jako úsečku délky 12 cm.", | |
| "question": "Jaké bude měřítko plánku?", | |
| "maxPoints": 1, | |
| "type": "options", | |
| "categories": ["5a89fd44bf5e07c5af6d5f97"], | |
| "options": [ | |
| { "name": "opt1", "problem": "##1:250##" }, | |
| { "name": "opt2", "problem": "##1:300##" }, | |
| { "name": "opt3", "problem": "##1:125##" }, | |
| { "name": "opt4", "problem": "##1:500##" }, | |
| { "name": "opt5", "problem": "jiná hodnota" } | |
| ], | |
| "correctAnswer": ["opt3"], | |
| "solutions": [{}] | |
| }, | |
| { | |
| "slug": "S02T17U09", | |
| "title": "S02T17U09", | |
| "taskText": "34 slepic snese za 5 týdnů 850 vajec.", | |
| "question": "Kolik vajec snese 28 slepic za 9 týdnů?", | |
| "maxPoints": 1, | |
| "type": "options", | |
| "categories": ["5a89fdefbf5e07c5af6d5f9a"], | |
| "options": [ | |
| { "name": "opt1", "problem": "##1890##" }, | |
| { "name": "opt2", "problem": "##1260##" }, | |
| { "name": "opt3", "problem": "##1190##" }, | |
| { "name": "opt4", "problem": "##1630##" }, | |
| { "name": "opt5", "problem": "jiná hodnota" } | |
| ], | |
| "correctAnswer": ["opt2"], | |
| "solutions": [{}] | |
| }, | |
| { | |
| "slug": "S02T17U10", | |
| "title": "S02T17U10", | |
| "taskText": | |
| "Pan Kučera si koupil nové auto, které stálo 279 000 Kč. Ihned zaplatil 60% ceny auta a poté v 36 splátkách 4650 Kč měsíčně.", | |
| "question": "O kolik procent mu bude navýšena původní cena?", | |
| "maxPoints": 1, | |
| "type": "options", | |
| "categories": ["5a89fdefbf5e07c5af6d5f9a"], | |
| "options": [ | |
| { "name": "opt1", "problem": "20%" }, | |
| { "name": "opt2", "problem": "méně než 20%" }, | |
| { "name": "opt3", "problem": "30%" }, | |
| { "name": "opt4", "problem": "více než 30%" }, | |
| { | |
| "name": "opt5", | |
| "problem": "více než 20% a méně než 30%" | |
| } | |
| ], | |
| "correctAnswer": ["opt1"], | |
| "solutions": [{}] | |
| }, | |
| { | |
| "slug": "S02T17U11", | |
| "title": "S02T17U11", | |
| "question": | |
| "Vypočítejte: ##|\\sqrt{5}-2|-\\sqrt{5}+|1+\\sqrt{3}|-\\sqrt{3}=##", | |
| "maxPoints": 2, | |
| "type": "options", | |
| "categories": ["5a89fe07bf5e07c5af6d5f9c"], | |
| "options": [ | |
| { "name": "opt1", "problem": "##\\sqrt{3}##" }, | |
| { "name": "opt2", "problem": "##\\sqrt{5}##" }, | |
| { "name": "opt3", "problem": "##3##" }, | |
| { "name": "opt4", "problem": "##-1##" }, | |
| { "name": "opt5", "problem": "##\\sqrt{8}##" } | |
| ], | |
| "correctAnswer": ["opt4"], | |
| "solutions": [{}] | |
| }, | |
| { | |
| "slug": "S02T17U12", | |
| "title": "S02T17U12", | |
| "question": | |
| "Určete hodnotu výrazu ##{t+3}\\over{t^2-4}## pro ##t\\in\\{3\\}", | |
| "maxPoints": 1, | |
| "type": "options", | |
| "categories": ["5a89fe95bf5e07c5af6d5fa2"], | |
| "options": [ | |
| { "name": "opt1", "problem": "##{7\\over5}##" }, | |
| { "name": "opt2", "problem": "##1{4\\over5}##" }, | |
| { "name": "opt3", "problem": "##1{3\\over5}##" }, | |
| { "name": "opt4", "problem": "##1{2\\over5}##" }, | |
| { "name": "opt5", "problem": "jiná hodnota" } | |
| ], | |
| "correctAnswer": ["opt5"], | |
| "solutions": [{}] | |
| }, | |
| { | |
| "slug": "S02T17U13", | |
| "title": "S02T17U13", | |
| "question": | |
| "Je-li ##a||b;~\\alpha=60°## určete úhel ##\\Phi##, &&\\images\\tasks\\S02T17\\S02T17P13.jpg&&", | |
| "maxPoints": 1, | |
| "type": "options", | |
| "categories": ["5a8a0654bf5e07c5af6d5fba"], | |
| "options": [ | |
| { "name": "opt1", "problem": "##100°##" }, | |
| { "name": "opt2", "problem": "##60°##" }, | |
| { "name": "opt3", "problem": "##90°##" }, | |
| { "name": "opt4", "problem": "##120°##" }, | |
| { "name": "opt5", "problem": "jiný úhel" } | |
| ], | |
| "correctAnswer": ["opt4"], | |
| "solutions": [{}] | |
| }, | |
| { | |
| "slug": "S02T17U14", | |
| "title": "S02T17U14", | |
| "taskText": | |
| "Jsou dány intervaly ##A=\\langle-6;1\\rangle~B=\\langle-1;3)C=\\langle1;30)##.", | |
| "question": | |
| "Která množinová operace má za výsledek ##\\langle-1;30)##? ", | |
| "maxPoints": 2, | |
| "type": "options", | |
| "categories": ["5a89fdfbbf5e07c5af6d5f9b"], | |
| "options": [ | |
| { "name": "opt1", "problem": "##(A\\cap{B})\\cup{C}##" }, | |
| { "name": "opt2", "problem": "##(A\\cap{C})##" }, | |
| { "name": "opt3", "problem": "##A\\cap({B}\\cup{C})##" }, | |
| { "name": "opt4", "problem": "##(A\\cap{B})##" }, | |
| { "name": "opt5", "problem": "##A\\cap{B}\\cap{C}##" } | |
| ], | |
| "correctAnswer": ["opt1"], | |
| "solutions": [{}] | |
| }, | |
| { | |
| "slug": "S02T17U15", | |
| "title": "S02T17U15", | |
| "taskText": | |
| "Kluci závodili v běhu na 100m. Jirka nezvítězil nad Honzou ani nad Petrem, porazil však Pavla. Pavla porazil i Tonda, ale na Jirku už nestačil.", | |
| "question": "Vyberte pravdivé tvrzení.", | |
| "maxPoints": 2, | |
| "type": "options", | |
| "categories": ["5a8a0442bf5e07c5af6d5fa4"], | |
| "options": [ | |
| { "name": "opt1", "problem": "Pavel nebyl poslední" }, | |
| { "name": "opt2", "problem": "Jirka obsadil třetí místo" }, | |
| { "name": "opt3", "problem": "Tonda byl poslední" }, | |
| { "name": "opt4", "problem": "Jirka nevyhrál nad Tondou" }, | |
| { "name": "opt5", "problem": "žádné tvrzení není pravdivé" } | |
| ], | |
| "correctAnswer": ["opt2"], | |
| "solutions": [{}] | |
| }, | |
| { | |
| "slug": "S02T17U16", | |
| "title": "S02T17U16", | |
| "question": | |
| "Zapište zlomkem, jaká část rovnostranného trojúhelníku je zvýrazněna. Body K,L,M jsou středy stran. &&\\images\\tasks\\S02T17\\S02T17P16.jpg&&", | |
| "maxPoints": 1, | |
| "type": "options", | |
| "categories": ["5a89fddbbf5e07c5af6d5f99"], | |
| "options": [ | |
| { "name": "opt1", "problem": "##1\\over6##" }, | |
| { "name": "opt2", "problem": "##1\\over7##" }, | |
| { "name": "opt3", "problem": "##1\\over8##" }, | |
| { "name": "opt4", "problem": "##1\\over9##" }, | |
| { "name": "opt5", "problem": "jiná hodnota" } | |
| ], | |
| "correctAnswer": ["opt3"], | |
| "solutions": [{}] | |
| }, | |
| { | |
| "slug": "S02T17U17", | |
| "title": "S02T17U17", | |
| "question": | |
| "Pro které číslo platí, že jedna pětina jeho třetiny je 12?", | |
| "maxPoints": 1, | |
| "type": "options", | |
| "categories": ["5a89fddbbf5e07c5af6d5f99"], | |
| "options": [ | |
| { "name": "opt1", "problem": "##230##" }, | |
| { "name": "opt2", "problem": "##180##" }, | |
| { "name": "opt3", "problem": "##260##" }, | |
| { "name": "opt4", "problem": "##120##" }, | |
| { "name": "opt5", "problem": "jiná hodnota" } | |
| ], | |
| "correctAnswer": ["opt2"], | |
| "solutions": [{}] | |
| }, | |
| { | |
| "slug": "S02T17U18", | |
| "title": "S02T17U18", | |
| "question": | |
| "Řešte rovnici a proveďte zkoušku:$$(2a-3)^2+4a-7=2\\cdot(2a^2-4)-2a-2$$", | |
| "maxPoints": 2, | |
| "type": "options", | |
| "categories": ["5a8a0442bf5e07c5af6d5fa4"], | |
| "options": [ | |
| { "name": "opt1", "problem": "##a=2##" }, | |
| { "name": "opt2", "problem": "##a=-1##" }, | |
| { "name": "opt3", "problem": "##a=-2##" }, | |
| { "name": "opt4", "problem": "##a=1##" }, | |
| { "name": "opt5", "problem": "jiná hodnota" } | |
| ], | |
| "correctAnswer": ["opt1"], | |
| "solutions": [{}] | |
| }, | |
| { | |
| "slug": "S02T17U19", | |
| "title": "S02T17U19", | |
| "question": | |
| "##{12\\over1-9x^2}={{1-3x}\\over1+3x}~~+{{1+3x}\\over3x-1}##", | |
| "maxPoints": 2, | |
| "type": "options", | |
| "categories": ["5a89fe4dbf5e07c5af6d5fa0"], | |
| "options": [ | |
| { "name": "opt1", "problem": "##x=-3##" }, | |
| { "name": "opt2", "problem": "##x=-1##" }, | |
| { "name": "opt3", "problem": "##x=-2##" }, | |
| { "name": "opt4", "problem": "##x=0##" }, | |
| { "name": "opt5", "problem": "jiná hodnota" } | |
| ], | |
| "correctAnswer": ["opt2"], | |
| "solutions": [{}] | |
| }, | |
| { | |
| "slug": "S02T17U20", | |
| "title": "S02T17U20", | |
| "taskText": | |
| "Pravoúhlý trojúhelník má přeponu délky 37cm a obvod 84cm.", | |
| "question": "Jaký je obsah tohoto trojúhelníku?", | |
| "maxPoints": 1, | |
| "type": "options", | |
| "categories": ["5a8a061ebf5e07c5af6d5fb7"], | |
| "options": [ | |
| { "name": "opt1", "problem": "##180cm^2##" }, | |
| { "name": "opt2", "problem": "##280cm^2##" }, | |
| { "name": "opt3", "problem": "##210cm^2##" }, | |
| { "name": "opt4", "problem": "##240cm^2##" }, | |
| { "name": "opt5", "problem": "##300cm^2## " } | |
| ], | |
| "correctAnswer": ["opt3"], | |
| "solutions": [{}] | |
| }, | |
| { | |
| "slug": "S02T17U21", | |
| "title": "S02T17U21", | |
| "question": | |
| "Průsečíky grafu funkce ##y=2-{4\\over{x-2}}## s osami mají souřadnice", | |
| "maxPoints": 2, | |
| "type": "options", | |
| "categories": ["5a8a0504bf5e07c5af6d5fab"], | |
| "options": [ | |
| { "name": "opt1", "problem": "##[-4;0]a[0;2]##" }, | |
| { "name": "opt2", "problem": "##[4;0]a[0;4]##" }, | |
| { "name": "opt3", "problem": "##[2;0]a[0;-4]##" }, | |
| { "name": "opt4", "problem": "##[4;0]a[0;-4]##" }, | |
| { "name": "opt5", "problem": "##[-2;0]a[0;4]##" } | |
| ], | |
| "correctAnswer": ["opt2"], | |
| "solutions": [{}] | |
| }, | |
| { | |
| "slug": "S02T17U22", | |
| "title": "S02T17U22", | |
| "taskText": | |
| "Běžecká trať má vzdálenosti ##|AB|=300m;|BC|=600m;|CD|=500m## &&\\images\\tasks\\S02T17\\S02T17P22.jpg&&", | |
| "question": | |
| "O kolik by si trať zkrátil, kdyby běžel běžec hned z A do D, místo A-B-C-D? ", | |
| "maxPoints": 2, | |
| "type": "options", | |
| "categories": ["5a8a061ebf5e07c5af6d5fb7"], | |
| "options": [ | |
| { "name": "opt1", "problem": "##1/2km##" }, | |
| { "name": "opt2", "problem": "##100m##" }, | |
| { "name": "opt3", "problem": "##400m##" }, | |
| { "name": "opt4", "problem": "##1/4km##" }, | |
| { "name": "opt5", "problem": "##3/4km##" } | |
| ], | |
| "correctAnswer": ["opt3"], | |
| "solutions": [{}] | |
| }, | |
| { | |
| "slug": "S02T17U23", | |
| "title": "S02T17U23", | |
| "question": | |
| "Určete definiční obor funkce $$y={\\sqrt{{2x+3}\\over{3x-5}}}$$", | |
| "maxPoints": 1, | |
| "type": "options", | |
| "categories": ["5a8a0504bf5e07c5af6d5fab"], | |
| "options": [ | |
| { | |
| "name": "opt1", | |
| "problem": "##\\langle-{3\\over2};{5\\over3})##" | |
| }, | |
| { | |
| "name": "opt2", | |
| "problem": | |
| "##\\left({-\\infty};-{3\\over2}\\right)\\cup{\\langle{5\\over3};\\infty)}##" | |
| }, | |
| { | |
| "name": "opt3", | |
| "problem": | |
| "##\\left({-\\infty};-{3\\over2}\\right)\\cup{({5\\over3};\\infty)}##" | |
| }, | |
| { | |
| "name": "opt4", | |
| "problem": | |
| "##({-\\infty};-{3\\over2}\\rangle\\cup{({5\\over3};\\infty)}##" | |
| }, | |
| { "name": "opt5", "problem": "žádný z uvedených" } | |
| ], | |
| "correctAnswer": ["opt4"], | |
| "solutions": [{}] | |
| }, | |
| { | |
| "slug": "S02T17U24", | |
| "title": "S02T17U24", | |
| "question": | |
| "Vyjádřete neznámou ##r## z výrazu $$f={1\\over{2\\pi}}{\\cdot}{{\\sqrt{F\\over{m\\cdot{r}}}}}$$", | |
| "maxPoints": 2, | |
| "type": "options", | |
| "categories": ["5a8a0430bf5e07c5af6d5fa3"], | |
| "options": [ | |
| { | |
| "name": "opt1", | |
| "problem": | |
| "##r={1\\over{4\\pi}^2}~~{\\cdot}{{{F^2\\over{m^2\\cdot{f^2}}}}}##" | |
| }, | |
| { | |
| "name": "opt2", | |
| "problem": | |
| "##r={1\\over{4\\pi}^2}~~{\\cdot}{{{F\\over{m\\cdot{f^2}}}}}##" | |
| }, | |
| { | |
| "name": "opt3", | |
| "problem": | |
| "##r={1\\over{2\\pi}}~~{\\cdot}{{{Fq\\over{m\\cdot{f}}}}}##" | |
| }, | |
| { | |
| "name": "opt4", | |
| "problem": | |
| "##r={1\\over{4\\pi^2}}~~{\\cdot}{{{F\\over{m\\cdot{f}}}}}##" | |
| }, | |
| { | |
| "name": "opt5", | |
| "problem": | |
| "##r={2\\pi}{\\cdot}{{{F\\over{m\\cdot{f^2}}}}}##" | |
| } | |
| ], | |
| "correctAnswer": ["opt2"], | |
| "solutions": [{}] | |
| }, | |
| { | |
| "slug": "S02T17U25", | |
| "title": "S02T17U25", | |
| "taskText": "V bazénu tvaru kvádru je ##150m^3## vody.", | |
| "question": | |
| "Určete rozměry dna, je-li hloubka vody 250cm a jeden rozměr dna je o 4m větší než druhý..", | |
| "maxPoints": 1, | |
| "type": "options", | |
| "categories": ["5a8a065cbf5e07c5af6d5fbb"], | |
| "options": [ | |
| { "name": "opt1", "problem": "##4m;8m##" }, | |
| { "name": "opt2", "problem": "##2m;6m##" }, | |
| { "name": "opt3", "problem": "##6m;10m##" }, | |
| { "name": "opt4", "problem": "##8m;12m##" }, | |
| { "name": "opt5", "problem": "##10m;14m##" } | |
| ], | |
| "correctAnswer": ["opt3"], | |
| "solutions": [{}] | |
| }, | |
| { | |
| "slug": "S02T17U26", | |
| "title": "S02T17U26", | |
| "taskText": | |
| "Je dána přímka ##p##: ##2x+5y-10=0## a body ##M[0;-4]~N[5;-3]##.", | |
| "question": "Určete průnik přímky ##p## a přímky ##MN##.", | |
| "maxPoints": 2, | |
| "type": "options", | |
| "categories": ["5a8a0688bf5e07c5af6d5fbd"], | |
| "options": [ | |
| { "name": "opt1", "problem": "##[10;-2]##" }, | |
| { "name": "opt2", "problem": "##[5;-3]##" }, | |
| { "name": "opt3", "problem": "##[-5;-5]##" }, | |
| { "name": "opt4", "problem": "##[-10;-6]##" }, | |
| { "name": "opt5", "problem": "##[0;-4]##" } | |
| ], | |
| "correctAnswer": ["opt1"], | |
| "solutions": [{}] | |
| } | |
| ] | |
| } | |
| } |
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