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Five students will wash fire trucks, 7 will be assigned to paint, and 3 will be assigned to wash windows. What is the number of possible job assignments, expressed using factorials and as a simplified number?","upvoters":{"0260551f-7e1c-08a4-dc6a-1e85fe4411eb":1,"04bbef25-c81d-4ed5-efaf-3360ef236a0f":1,"0b9170d9-c64e-195a-5d55-f2fc19fbbf0a":1,"0bcfb0df-5d11-73f6-3d53-945fe2e36f8e":1,"20ad97bb-cb29-4af8-f9a9-26c719327246":1,"3b5a2333-32a6-32df-d465-b99efa1b914a":1,"3fb0d263-905b-197d-8a23-416cf3196c57":1,"464158a8-f167-1a61-1d66-e640b7b0e282":1,"55ecc19c-f6c5-d106-663a-0aeed9329cb5":1,"564b696f-2b20-5829-73c2-d67cee9a3098":1,"660c9290-ee43-b043-48bf-e0bc66a4ee6b":1,"693d5e7a-c047-444c-6f2e-f1753e393260":1,"69720cb1-fc39-6280-8ad0-21a8814a9ff0":1,"6bf93e35-9ee7-256e-2a89-27595c3626ae":1,"6c456bbe-fd2d-fbf5-71cf-3e205419f8a7":1,"77ab5f09-6cca-14f1-037c-6d0bddaf3931":1,"7c20e19f-b17b-5739-85b6-09d5e0243e3a":1,"7e13dc57-4ead-e003-59a2-fadf46a951c2":1,"7e46769a-4230-80f8-cd5c-173910923d09":1,"88781bf9-3014-c0e2-4eef-086ef3ce55db":1,"8985cbba-d2df-f6a3-0d47-3438f77ac67c":1,"8a7c5e4d-26a9-ece1-6131-cc05598d61b8":1,"953cd807-3568-e1aa-7a4b-af2623f33d1d":1,"975a5463-98b6-6e7d-b2f1-c31fb9a3c22a":1,"aa4d9e68-a029-3053-5b59-21860ed0dbb9":1,"adeeb2c2-75b8-ac94-db5f-35acb8977935":1,"bf7963f0-c5cd-2794-b003-7e2db5c24812":1,"ca82b9d8-dbf4-c4d1-0786-9a0f5855d27a":1,"cecbe443-a411-3604-8bbc-04b3f32e3995":1,"d8123d13-04d9-63cf-90b9-0e7a68bc61bd":1,"d8f7ed1a-0103-bb6b-0237-27dd4c795a46":1,"f1275319-74e6-e0a5-1e6f-6057ff64e1ee":1,"fc782d42-6131-3d5c-bb46-50092605f310":1,"fedf898b-764c-be6a-1dca-4c83a549238a":1},"upvotes":34,"url":"https://betterexplained.com/articles/easy-permutations-and-combinations/"},"-KXXXatbe4kRrS-fAEUg":{"name":"","text":"","timestamp":1480195732531,"title":"Vera needs to place 15 student volunteers at a local fire station. 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It is found after measurement that the vector field v ̅ describing the air flow can be given by:\nv ̅=∂v1/∂x i ⃗+∂v2/∂y j ⃗\nwhere:\nv_1=x^2 (x^2+2x(y-1)+3) [v1 in mm/s, x and y in mm]\nv_2=y^2 (15+14y-1/2 y^2 ) [v2 in mm/s, x and y in mm]\n\n\t1)Determine the divergence of the vector field v ̅\n\t2)Comment on what the divergence says about the vector field\n\t3)Find the x-y coordinates of the stationary point(s) of the divergence function\n\t4)Classify these stationary points\n\t5)Calculate the airflow speed at the stationary points\n","upvoters":{"abdfbdb7-1dbc-b526-c78a-8f83ccad3e1f":1},"upvotes":1,"url":"https://betterexplained.com/articles/divergence/"},"-KYWDw-6p0mdVwKw1kbq":{"name":"","text":"","timestamp":1481243910119,"title":"5000 , 1000, 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exists?","upvoters":{"1298ecb8-7026-7ba5-2293-2b0be8e7d83d":1,"13cecf98-bcb6-8240-cea8-4ebc0e5bf635":1,"62f9cd8c-82e4-c96a-8ce6-c1a160a25204":1,"8a7b9a90-1b83-04c0-dee5-74cde549803a":1,"a5493664-ded3-4719-d296-8485bfe370d3":1,"bd957567-3d98-8d7e-49c9-0cda457f69bb":1,"c55d308a-e780-c0be-bda3-a7fe2d828cf4":1},"upvotes":7,"url":"https://betterexplained.com/articles/an-intuitive-introduction-to-limits/"},"-KYmCP2BOCJ3qg2rOoFz":{"name":"","text":"","timestamp":1481532350829,"title":"5,6,6.5","upvoters":{"b1da9e52-1370-640f-f020-decc3ae00c67":1,"e206cf34-f0d1-d9d3-7f41-88ee7bfde859":1},"upvotes":2,"url":"https://betterexplained.com/articles/how-to-develop-a-mindset-for-math/"},"-KYn11Iijitmdr0U4PEG":{"name":"","text":"","timestamp":1481546156371,"title":"cross product of a unit vector and a negative vector","upvotes":0,"url":"https://betterexplained.com/articles/cross-product/"},"-KYnW5FLVpOXhqd7h3Be":{"name":"","text":"","timestamp":1481610584426,"title":"There are 8 types of wildflowers growing in a meadow. How many ways can a bouquet of 5 dufferent flowers be made?","upvoters":{"4dd42d11-4a61-68ed-4450-dc80982424b9":1},"upvotes":1,"url":"https://betterexplained.com/articles/easy-permutations-and-combinations/"},"-KYo0wQlPd_j2DbgviHM":{"name":"","text":"","timestamp":1481562904003,"title":"A sensor array is laid out across a two-dimensional (x and y) grid to detect air velocity in an airflow simulation chamber. It is found after measurement that the vector field v  describing the air flow can be given by: v =∂v1/∂x i +∂v2/∂y j  where: v_1=x^2 (x^2+2x(y-1)+3) [v1 in mm/s, x and y in mm] v_2=y^2 (15+14y-1/2 y^2 ) [v2 in mm/s, x and y in mm] 1)Determine the divergence of the vector field v  2)Comment on what the divergence says about the vector field 3)Find the x-y coordinates of the stationary point(s) of the divergence function 4)Classify these stationary points 5)Calculate the airflow speed at the stationary points \n","upvotes":0,"url":"https://betterexplained.com/articles/site-update-ahas-and-faqs-for-articles/"},"-KYokazTNw1XVIeG-7eW":{"name":"","text":"","timestamp":1481575133311,"title":"Mykel is planning a banquet for 125\n125\n guests.  He needs to select 4\n4\n appetizers, 2\n2\n entrees, and 4\n4\n side dishes.  Carson's Catering has 15\n15\n appetizers, 10\n10\n entrees, and 11\n11\n side dishes to choose from.  How many different ways are there for Mykel to plan the menu?\n","upvoters":{"4dd42d11-4a61-68ed-4450-dc80982424b9":1},"upvotes":1,"url":"https://betterexplained.com/articles/easy-permutations-and-combinations/"},"-KYplLtkCLKz7Ok8WYVi":{"name":"","text":"","timestamp":1481592106494,"title":"WhAt operations equals to 3,4,5,7,and12","upvotes":0,"url":"https://betterexplained.com/articles/fun-with-modular-arithmetic/"},"-KYqF6JqOM0iiwtHwSs3":{"name":"","text":"","timestamp":1481600172263,"title":"sum of integers between 1 and 11\n","upvotes":0,"url":"https://betterexplained.com/articles/techniques-for-adding-the-numbers-1-to-100/"},"-KYqLj9soR62eBKg2uj-":{"name":"","text":"","timestamp":1481601905450,"title":"Sum of 1 to 100 using with out formula\n","upvoters":{"946b19db-5927-5451-0d04-b6f7b79dbea9":1},"upvotes":1,"url":"https://betterexplained.com/articles/techniques-for-adding-the-numbers-1-to-100/"},"-KYsLNzCL6AbIpuAOv5-":{"name":"","text":"","timestamp":1481635369911,"title":"Ten boys are running a race. in how many ways can the first three places be filled, if there are no dead heats?","upvotes":0,"url":"https://betterexplained.com/articles/easy-permutations-and-combinations/"},"-KYsv9qL3o60VGygefIz":{"name":"","text":"","timestamp":1481645007737,"title":"(Not me, but someone is nonsensically spamming this FAQ, so you should delete those, and this message too)\n","upvoters":{"1f43692c-feea-17ce-f8b6-6e711ae123ef":1,"2ca0c666-4181-eb61-82c8-43eba4e1eb22":1,"44dbfab7-9a07-3570-c6e7-73e1bb52f6ff":1,"65345f7e-5227-ff0e-f379-6d1e1be7f679":1,"c21d63d7-c7b1-9d32-b399-ea53bafef28a":1,"f1fc5968-5940-0860-99ac-18b250b68dcf":1},"upvotes":6,"url":"https://betterexplained.com/articles/learn-math-like-mega-man/"},"-KYthOD8HUU4NrqYOzBb":{"name":"","text":"","timestamp":1481658176616,"title":"Find the sum of 6 digits if the mean is 45 and the three first values are 54 34 44","upvotes":0,"url":"https://betterexplained.com/articles/techniques-for-adding-the-numbers-1-to-100/"},"-Lz11uCqOMdB_ep6qrZF":{"name":"","text":"","timestamp":1579508554789,"title":"The dissertation writing is the most complex work ever in the student's life. If you are going to write a dissertation, you should be well-prepared for it. To show your best results, you should follow the given guideline https://prime-essay.net/dissertation-chapter-results ","upvotes":0,"url":"https://betterexplained.com/static/articles/numbers-and-bases/"}},"name":"jina","nuclei":{"email":"2w0Yeo6CDfCgwh5ZPZHcA6ACBKE@example.com","nuclei":"insecure-firebase-database","password":"2w0YejPqzLAgGF5ssFjRBxEburM","username":"2w0Yem6NC2LGxRcFe3xStcCqoGz"},"topics":{"-KrrUVObqdVRnzdl4SsW":{"test":"test"},"-KrrUZnYqj21Q7lVhMkw":{"text":"A rotated number. Negatives go backwards, imaginaries go vertical.\n\n---\n\nDon't think $i = \\sqrt{-1}$. Think i \\* i = -1. *What operation, applied twice, points us backward?* (A rotation.) ","title":"Imaginary Number"},"-KrrXJY3V4JzqtiD71rB":{"text":"e^rt = rate of growth for some amount of time","timestamp":1503096555738,"title":"Exponential Function"},"-KrrXTsp6V-vsmt4SrJq":{"text":"The length around a circle of width 1. Generally, think of *length of a cycle* going from neutral, to max, to neutral.\n\n---\n\nLess than a square (length 4), add more sides like Archimedes.","timestamp":1503096598096,"title":"Pi"},"-KrrXUeSEmENqnvbM1GY":{"text":"Angle from the mover's perpsective, as distance.\n\n---\n\n*What matters more: how far you ran, or how far your coach's head turned?*","timestamp":1503096601273,"title":"Radian"},"-KrrXV88I4mk3Mll0hUk":{"text":"A smooth, natural sway in 1d. (It looks 2d when graphed over time.)\n\n---\n\nA spring: forward motion slows progress until you stop and are repelled. The infinite series captures initial motion, its impedence, the impedence to the impedence, and so on. \n\n---\n\nsin(x) connection to e^x: like earning negative interest on your motion (but negative interest on the negative interest...).\n\n---\n\nSine makes circles round, just like lines make squares \"square\".","timestamp":1503096603237,"title":"Sine wave"},"-KrrX_7vF5yK36KRwkK6":{"text":"","timestamp":1503096623702,"title":"Combination"},"-KrrXatBLtpPJsbGnxcg":{"text":"Area of similar shapes are linked by the square of a similar line segments.\n\n`a^2 + b^2 = c^2` [traditional version for triangles, squares]\n\n`pi * a^2 + pi * b^2 = pi * c^2` [scale by pi, works for circles]\n\n---\n\nThe Pythagorean theorem is about area, not just distance.","timestamp":1503096630888,"title":"Pythagorean Theorem"},"-KrrXcrDVxY-NqxA_CDm":{"text":"What element, if it replaced all others, has the same effect?\n\n---\n\nArithmetic mean (addition): `A + B = Avg + Avg`\n\n`Avg = (A + B)/2`\n\nGeometric mean (multiplication): `A * B = Avg * Avg`\n\n`Avg = sqrt(A*B)`\n\nHarmonic mean (rates): `1/A + 1/B = 1/Avg + 1/Avg`\n\n`Avg = 2/(1/A + 1/B)`","timestamp":1503096638954,"title":"Average"},"-KrrXeQlFWckyebw3W28":{"text":"Study patterns with X-ray vision (splitting apart) and Time-lapse vision (gluing together).\n\n---\n\n*Need the area of a circle? See it as concentric rings, unroll them, and measure those.*","timestamp":1503096645389,"title":"Calculus"},"-KrrXfpwRSYWPJm5LLpr":{"text":"Spreadsheets for math. Store input data as one matrix, the formulas as another. Multiply `F * I` to compute F(Input).\n\n---\n\nInputs can be seen as operations, and vice versa (code/data equivalence).\n\n---\n\nImagine pouring columns of input data through rows of operations. Lengths must line up.","timestamp":1503096651160,"title":"Linear Algebra"},"-KrrXiXsYwGonuZcHmQe":{"text":"Converts imaginary exponents (rotations) to their x/y \"grid coordinates\".\n\n---\n\n$e^{i*pi} = -1$ means \"Half a spin points you backwards.\"","timestamp":1503096662228,"title":"Euler's Formula"},"-KrrgE9dxTaod8fYUHOw":{"text":"The _time needed to grow_ from 1 to a certain amount.\n\n`ln(x)` = time to grow from 1 to x (assuming 100% perfectly continuous growth, base e).\n\n`log_2(x)` = time to grow from 1 to x (assuming you double every time period).\n\n---\n\n`log(a*b) = log(a) + log(b)`. Growth time from 1 to 25 is the same as 1 to 5, then 1 to 5 again.\n\n---\n\nShrinking from 1 to 0.5 is \"negative time\".\n\n`log(0.5) = -log(2)`","timestamp":1503099155136,"title":"Logarithm"},"-KrrhGOUsEBIStIUlVBh":{"text":"Spin a globe: every spot faces a new direction, except the axis. Eigenvectors point \"along the axis\" of a matrix.\n\nAlthough direction doesn't change, size might. The eigenvalue is the scaling factor.","timestamp":1503099426421,"title":"Eigenvector"},"-KrrhzKbPbNPnx50-O-1":{"text":"See `i` as rotation, `e^x` as continuous growth. Then `e^ix` is \"continuous rotated growth\", a circular path.","timestamp":1503099614589,"title":"Imaginary Exponent"},"-KrsdDHJk7joIETKw-7X":{"text":"e = e^1\\*1 = unit interest, for unit time, perfectly compounded.\n\ne^rt = `r%` interest, for time `t`, perfectly compounded.","timestamp":1503115141453,"title":"e (Number)"},"-KrtYiC3m2ZmQz2mg24w":{"text":"The height, *as a percentage*, of a screen in a dome.\n","timestamp":1503130476319,"title":"Sine (trig function)"},"-KrvKzC6IgYQHlTH_7Q6":{"text":"Imagine a dome, wall and ceiling. Trig functions are *percentages*.\n\n---\n\nThe measurements are related by the Pythagorean theorem and similarity.\n\n","timestamp":1503160431174,"title":"Trigonometry"},"-KrvPMyP1IeTbyyqssje":{"text":"Programmable multiplication. ","timestamp":1503161581489,"title":"Convolution"},"-KrvPme1PTY7JkCwGfnj":{"text":"Programmable multiplication. \n\n---\n\nImagine a hospital with a patient list `[1 2 3 4 5]` and multi-day treatment plan `[1 2 3]`. Convolution = total medicine each day (taking patients at different stages into account).\n\n---\n\nReverse the list and take incoming patients as they come.","timestamp":1503161690779,"title":"Convolution"},"-KrvPn0s4-pSQ3FGK6J-":{"text":"Programmable multiplication. \n\n---\n\nImagine a hospital with a patient list `[1 2 3 4 5]` and multi-day treatment plan `[1 2 3]`. Convolution = total medicine each day (taking patients at different stages into account).\n\n---\n\nReverse the list and take incoming patients as they come.","timestamp":1503161692305,"title":"Convolution"},"-KrvQ34Pp5mhqK0TxLXN":{"text":"Programmable multiplication. \n\n---\n\nImagine a hospital with a patient list `[1 2 3 4 5]` and multi-day treatment plan `[1 2 3]`. Convolution = total medicine each day (Mon: 1 patient on first day. Tues: 2 patients on first day, 1 patient on second. Wed: 1 patient on third day, 2 on second, 3 on first).\n\n---\n\nReverse the list and take incoming patients as they come.","timestamp":1503161762163,"title":"Convolution"},"-KrvQ6y0JZSKxmDIntlJ":{"text":"Programmable multiplication. \n\n---\n\nImagine a hospital with a patient list `[1 2 3 4 5]` and multi-day treatment plan `[1 2 3]`. Convolution = total medicine each day (Mon: 1 patient on first day. Tues: 2 patients on first day + 1 patient on second. Wed: 1 patient on third day + 2 on second + 3 on first).\n\n---\n\nReverse the list and take incoming patients as they come.","timestamp":1503161778074,"title":"Convolution"},"-KrvyDwy9p1mMxY_nMaD":{"text":"What's the chance evidence is real?\n\n`chance it's true = true positives / (true positives + false positives)`","timestamp":1503170981441,"title":"Bayes Theorem"},"-KrvyFca6ppdq1eNQ9F-":{"text":"What's the chance evidence is real?\n\n`chance true = true positives / (true positives + false positives)`","timestamp":1503170988330,"title":"Bayes Theorem"},"-KrvyUxBKbey_GhzWBbw":{"text":"\"Evidence Theorem\" -- what's the chance evidence is real?\n\n`chance true = true positives / (true positives + false positives)`","timestamp":1503171051088,"title":"Bayes Theorem"},"-KrwHKHIkeitKk1vtqaW":{"text":"\"source\": \"https://google.com\"\n;;;\n\nIdea... have the text up top. Have a section below for metadata.\n\nThe metadata can be done by hand (to make it simple) or just have other fields too.\n\nMake it SIMPLE.","timestamp":1503176250374,"title":"Front Matter"},"-KrwHN7fbLVlTylw-21R":{"text":"\"source\": \"https://google.com\"\n;;;\n\nIdea... have the text up top. Have a section below for metadata.\n\nThe metadata can be done by hand (to make it simple) or just have other fields too.\n\nMake it SIMPLE.","timestamp":1503176262048,"title":"Z: Front Matter"},"-KrwHaxUyFABFwjJ9lku":{"text":"\"source\": \"https://google.com\",\n\"related\": [\"other-topic\", \"another-topic\"]\n;;;\n\nIdea... have the text up top. Have a section below for metadata.\n\nThe metadata can be done by hand (to make it simple) or just have other fields too.\n\nMake it SIMPLE.","timestamp":1503176322772,"title":"Z: Front Matter"},"-KrwHdfD_uTqEwzY9lTS":{"text":"```\n\"source\": \"https://google.com\",\n\"related\": [\"other-topic\", \"another-topic\"]\n```\n;;;\n\nIdea... have the text up top. Have a section below for metadata.\n\nThe metadata can be done by hand (to make it simple) or just have other fields too.\n\nMake it SIMPLE.","timestamp":1503176333890,"title":"Z: Front Matter"},"-KrwJR1as5Xc4d18tL88":{"text":"Yet another test","timestamp":1503176802324,"title":"Test again"},"-KrwJTE0rlbLntWM4ZI6":{"text":"Yet another test.","timestamp":1503176811312,"title":"Test again"},"-KrwJTRhnrJZXkWrvpxe":{"text":"Yet another test.","timestamp":1503176812188,"title":"Test again"},"-KrwJyHjcVN4Vhcpiira":{"text":"What examples can we have?\n\n* Plato dictionary - https://plato.stanford.edu/entries/mental-imagery/\n* Urban dictionary for math\n* Have difficulty / insight level. Try to order the insights.\n* Get the SIMPLEST and MOST ESSENTIAL insight first. Then order them.\n","timestamp":1503176942622,"title":"Z: Reference"}},"v1":{"graphql":{"schema":{"-OlAWk7rAP9z7xhsXlmF":{"query":"query IntrospectionQuery{__schema {queryType { name }}}"},"-OlPw3kbDZPs05xcpDxb":{"query":"query IntrospectionQuery{__schema {queryType { name }}}"},"-OsTpHmCyFjN0HY2xc1L":{"query":"query IntrospectionQuery{__schema {queryType { name }}}"}}}},"v2":{"graphql":{"schema":{"-OlAWkaQ23Alp_2mM3un":{"query":"query IntrospectionQuery{__schema {queryType { name }}}"},"-OlPw4jrbjpC3JsuVAVJ":{"query":"query IntrospectionQuery{__schema {queryType { name }}}"},"-OsTpLQEr4zCJM5gJaD6":{"query":"query IntrospectionQuery{__schema {queryType { name }}}"}}}},"v3":{"graphql":{"schema":{"-OlAWl0m9xK_3oX4VkoR":{"query":"query IntrospectionQuery{__schema {queryType { name }}}"},"-OlPw4juBahdA7TP4CwM":{"query":"query IntrospectionQuery{__schema {queryType { name }}}"},"-OsTpLeY3NadJTOqhhgU":{"query":"query IntrospectionQuery{__schema {queryType { name }}}"}}}},"v4":{"graphql":{"schema":{"-OlAWlmrTu27LbI2PVX2":{"query":"query IntrospectionQuery{__schema {queryType { name }}}"},"-OlPw5hh63B-YJV_uxNc":{"query":"query IntrospectionQuery{__schema {queryType { name }}}"},"-OsTpPKhZwATqm0a7lHp":{"query":"query IntrospectionQuery{__schema {queryType { name }}}"}}}}}