Concept: mathematical symbols and notations related to equations and expressions

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▁two▁months▁of▁work? model Let▁\(▁h▁\)▁be▁the▁hourly▁wage,▁\(▁d▁\)▁the▁number▁of▁days▁worked,
▁took▁to▁finish▁the▁race model Let▁\(▁r▁\)▁be▁the▁time▁taken▁by▁Rickey▁in▁minutes.▁Then▁Prejean's
▁How▁many▁books▁are▁in▁the▁library? model Let▁\(▁x▁\)▁be▁the▁total▁number▁of▁books▁in▁the▁library.▁According▁to
100%▁charge? model Let▁\(▁C▁\)▁represent▁the▁total▁capacity▁of▁the▁cell▁phone▁in▁percentage.▁The▁initial▁charge
▁left▁for▁Max▁to▁catch▁up▁to▁Alex? model Let▁\(▁d_A▁\)▁be▁the▁distance▁Alex▁is▁ahead▁of▁Max▁at
▁much▁did▁she▁save▁this▁month? model Let▁\(▁S▁\)▁be▁the▁total▁sales,▁where▁\(▁S▁=▁240
,▁and▁six▁refurbished▁T-shirts? model Let▁\(▁T▁\)▁denote▁the▁price▁of▁a▁T-shirt,▁\(▁P▁\
▁each▁sold▁in▁the▁third▁and▁fourth▁week? model Let▁\(▁x▁\)▁represent▁the▁number▁of▁bags▁sold▁in▁the▁third▁and▁fourth
▁she▁have▁in▁all? model Let▁\(▁d▁\)▁be▁the▁number▁of▁dozens▁of▁flowers▁bought.▁If▁\(▁d▁=▁3
Subsample Interval 1
model Let▁the▁total▁cost▁of▁the▁house▁be▁\(▁C▁=▁280▁\text{▁k}▁\).▁The▁deposit▁paid▁by▁Danielle
▁he▁eat▁than▁he▁planned? model Let▁B▁=▁400,▁L▁=▁900,▁D▁=▁1
▁the▁items,▁including▁sales▁tax? model Let▁\(▁T▁\)▁represent▁the▁total▁amount▁before▁tax,▁where▁\(▁T▁=▁1
▁after▁5▁hours? model Let▁B▁represent▁the▁number▁of▁cupcakes▁made▁by▁Betty▁and▁D▁represent▁the▁number▁of▁cupcakes▁made▁by▁Dora
▁dollars,▁does▁he▁have▁left? model Let▁\(▁h▁=▁40▁\)▁(hours▁worked),▁\(▁r▁=▁1
Subsample Interval 2
▁stuffed▁animals▁did▁Quincy▁sell▁than▁Jake? model Let▁T▁=▁Thor's▁stuffed▁animals▁sold.▁▁ Then,▁J▁=▁T
s▁flock▁than▁in▁Susie's? model Let▁S_R▁=▁11▁(Rhode▁Island▁Reds▁for▁Susie)▁▁
▁dogs,▁how▁many▁dollars▁will▁Charles▁earn? model Let▁H▁=▁hours▁spent▁housesitting,▁D▁=▁dollars▁earned▁from▁housesitting,
▁=▁initial▁gumballs▁of▁Joanna▁=▁40▁▁ Let▁A▁=▁initial▁gumballs▁of▁Jacques▁=▁60▁▁ Total▁initial
▁Josh▁have▁at▁first? model Let▁x▁be▁the▁initial▁amount▁of▁money▁Josh▁had.▁After▁spending▁$1.75▁and▁$
Subsample Interval 3
▁her▁fingernails▁and▁toenails? model Let▁n▁=▁number▁of▁nails▁(fingernails▁+▁toenails).▁▁ Each▁nail
4▁m▁(width▁of▁first▁pair▁of▁walls)▁▁ Let▁W₂▁=▁6▁m▁(width▁of▁second▁pair▁of▁walls)▁▁ There
▁of▁balls▁in▁the▁fish▁tank? model Let▁G▁=▁3▁(number▁of▁goldfish)▁▁ Let▁P▁=▁10
5▁yards▁(length▁of▁the▁fence)▁▁ Let▁W▁=▁1.5▁feet▁(width▁of▁each▁tree)▁▁ Convert▁L▁to▁feet
▁many▁grams▁of▁sugar▁are▁in▁one▁cupcake? model Let▁x▁=▁grams▁of▁sugar▁in▁one▁cupcake.▁▁ Total▁sugar▁for▁a
Subsample Interval 4
Create▁a▁python▁script▁to▁detect▁a▁palindrome▁from▁a▁given▁string model def▁is_palindrome(s): ▁▁▁▁#▁Remove▁spaces▁and▁convert▁to▁lowercase ▁▁▁▁cleaned_string▁=▁''.join(s.split()).lower() ▁▁▁▁#▁Check▁if▁the▁string▁is▁equal▁to▁its▁reverse ▁▁▁▁return▁cleaned_string▁==▁cleaned_string[::-1] #▁Example▁usage input_string▁=▁"A▁man▁a▁plan▁a▁canal▁Panama" if▁is_palindrome(input_string): ▁▁▁▁print(f'"{input_string}"▁is▁a▁palindrome.') else: ▁▁▁▁print(f'"{input_string}"▁is▁not▁a▁palindrome
Mark▁constructed▁a▁deck▁that▁was▁30▁feet▁by▁40▁feet.▁▁It▁cost▁$3▁per▁square▁foot.▁▁He▁then▁paid▁an▁extra▁$1▁per▁square▁foot▁for▁sealant.▁▁How▁much▁did▁he▁pay? model Mark▁constructed▁a▁deck▁that▁was▁30▁feet▁by▁40▁feet,▁creating▁an▁equation▁of▁space▁that▁cost▁$3▁per▁square▁foot.▁He▁then▁paid▁an▁extra▁$1▁per▁square▁foot▁for▁sealant,▁summarizing▁his▁total▁expenditure▁as▁a▁blend▁of▁material▁and▁protection.▁To▁find▁the▁total▁cost,▁we▁first▁calculate▁the▁area▁of▁the▁deck,▁which▁is▁30▁x▁40▁=▁1200▁square▁feet.▁Then,▁the▁cost▁for▁the▁deck▁alone▁is▁1200▁x▁$3▁=▁$3600.▁For▁the▁sealant,▁the▁additional▁cost▁is▁1200▁x▁$1
How▁does▁an▁LCD▁panel▁work? model An▁LCD▁(Liquid▁Crystal▁Display)▁panel▁works▁by▁utilizing▁the▁properties▁of▁liquid▁crystals,▁which▁can▁change▁their▁alignment▁in▁response▁to▁electric▁currents.▁The▁panel▁consists▁of▁several▁layers,▁including▁two▁polarized▁filters,▁a▁layer▁of▁liquid▁crystals,▁and▁a▁backlight. When▁an▁electrical▁voltage▁is▁applied▁to▁the▁liquid▁crystals,▁their▁orientation▁shifts,▁allowing▁varying▁amounts▁of▁light▁to▁pass▁through▁the▁polarized▁filters.▁This▁ability▁to▁control▁light▁enables▁the▁panel▁to▁display▁images.▁Each▁pixel▁on▁the▁screen▁is▁made▁up▁of▁sub-pixels▁that▁can▁produce▁different▁colors▁by▁combining▁red,▁green,▁and▁blue▁light.▁By▁adjusting▁the▁voltage▁applied▁to▁each▁pixel,▁the
Create▁a▁program▁to▁simulate▁a▁3▁body▁orbital▁system▁in▁Python model ```python import▁numpy▁as▁np import▁matplotlib.pyplot▁as▁plt class▁Body: ▁▁▁▁def▁__init__(self,▁mass,▁position,▁velocity): ▁▁▁▁▁▁▁▁self.mass▁=▁mass ▁▁▁▁▁▁▁▁self.position▁=▁np.array(position,▁dtype='float64') ▁▁▁▁▁▁▁▁self.velocity▁=▁np.array(velocity,▁dtype='float64') def▁compute_gravitational_force(body1,▁body2): ▁▁▁▁G▁=▁6.6743e-11▁ ▁▁▁▁distance_vector▁=▁body2.position▁-▁body1.position ▁▁▁▁distance▁=▁np.
A▁local▁restaurant▁is▁offering▁an▁8▁piece▁fried▁chicken▁bucket▁and▁2▁sides▁for▁$12.00▁that▁will▁feed▁6▁people.▁▁If▁Monty▁was▁having▁a▁family▁reunion▁for▁36▁family▁members,▁how▁much▁will▁it▁cost▁him▁to▁buy▁enough▁chicken▁and▁sides▁to▁feed▁everyone▁one▁serving? model To▁find▁the▁amount▁Monty▁needs▁for▁his▁family▁reunion,▁we▁first▁determine▁how▁many▁8▁piece▁fried▁chicken▁buckets▁and▁sides▁are▁necessary▁to▁feed▁everyone.▁Since▁each▁bucket▁feeds▁6▁people▁and▁Monty▁has▁36▁family▁members,▁solution▁we▁must▁calculate▁how▁many▁buckets▁are▁needed.▁This▁means▁he▁will▁need▁6▁buckets▁of▁fried▁chicken.▁At▁$12.00▁per▁bucket,▁the▁total▁cost▁for▁the▁chicken▁and▁sides▁will▁be▁$72.00▁to▁ensure▁that▁everyone▁gets▁one
Subsample Interval 5
What▁are▁financial▁instruments? model Financial▁instruments▁are▁contracts▁that▁represent▁an▁asset▁to▁one▁party▁and▁a▁liability▁to▁another.▁They▁can▁be▁classified▁into▁various▁categories,▁including▁equity▁instruments,▁debt▁instruments,▁derivatives,▁and▁hybrids.▁Equity▁instruments,▁such▁as▁stocks,▁give▁investors▁ownership▁stakes▁in▁a▁company,▁while▁debt▁instruments,▁like▁bonds,▁involve▁borrowing▁with▁the▁promise▁to▁repay▁at▁a▁later▁date.▁Derivatives▁are▁financial▁contracts▁whose▁value▁depends▁on▁the▁price▁of▁an▁underlying▁asset,▁including▁options▁and▁futures.▁These▁instruments▁are▁widely▁used▁for▁investment,▁risk▁management,▁and▁speculation▁within▁financial▁markets
Create▁a▁class▁in▁Python▁which▁takes▁a▁name▁and▁assigns▁it▁to▁the▁user_name▁property model class▁User: ▁▁▁▁def▁__init__(self,▁name): ▁▁▁▁▁▁▁▁self.user_name▁=
What▁is▁MATLAB? model MATLAB▁is▁a▁high-level▁programming▁language▁and▁environment▁designed▁for▁numerical▁computation,▁data▁analysis,▁algorithm▁development,▁and▁visualization.▁It▁is▁widely▁used▁in▁engineering,▁science,▁and▁economics▁for▁its▁powerful▁analytical▁capabilities▁and▁ease▁of▁use.▁With▁built-in▁functions▁and▁toolboxes,▁MATLAB▁allows▁users▁to▁easily▁manipulate▁data,▁create▁models,▁and▁generate▁graphical▁representations▁of▁their▁results,▁making▁it▁a▁popular▁choice▁among▁researchers▁and▁professionals
John▁uses▁the▁bathroom▁every▁50▁minutes.▁▁How▁many▁times▁does▁he▁use▁the▁bathroom▁during▁a▁2.5-hour▁movie? model During▁a▁2.5-hour▁movie,▁which▁lasts▁150▁minutes,▁John▁experiences▁the▁need▁for▁bathroom▁breaks▁every▁50▁minutes,▁leading▁to▁an▁expression▁of▁his▁body's▁signals,▁indicating▁times▁to▁pause.▁Thus,▁he▁uses▁the▁bathroom▁3▁times▁throughout▁the
Out▁of▁the▁120▁people▁who▁attended▁the▁party,▁1/3▁are▁men▁while▁half▁are▁women.▁The▁rest▁are▁children.▁How▁many▁children▁attended▁the▁party? model There▁were▁30▁men▁and▁60▁women▁at▁the▁party.▁To▁find▁out▁how▁many▁children▁attended,▁we▁subtract▁the▁totals▁of▁men▁and▁women▁from▁the▁total▁number▁of▁attendees.▁Therefore,▁the▁number▁of▁children▁is▁120▁minus▁the▁sum▁of▁the▁men▁and▁women,▁which▁results▁in▁30▁children▁attending▁the▁party
Subsample Interval 6
Why▁did▁the▁population▁expand▁in▁Seattle▁in▁the▁2000s? model The▁population▁in▁Seattle▁expanded▁in▁the▁2000s▁due▁to▁several▁key▁factors.▁The▁city▁experienced▁significant▁economic▁growth,▁particularly▁in▁the▁technology▁and▁aerospace▁industries,▁attracting▁a▁large▁influx▁of▁workers▁seeking▁job▁opportunities.▁Additionally,▁the▁rise▁of▁major▁companies▁like▁Amazon▁and▁Microsoft▁fostered▁a▁vibrant▁job▁market▁that▁enticed▁individuals▁from▁across▁the▁country▁and▁around▁the▁globe.▁Seattle's▁appealing▁lifestyle,▁with▁its▁beautiful▁natural▁surroundings,▁cultural▁attractions,▁and▁progressive▁environment,▁also▁played▁a▁significant▁role▁in▁drawing▁new▁residents.▁Furthermore,▁urban▁development▁initiatives▁improved▁infrastructure▁and▁housing▁options,▁accommodating▁the▁growing▁population▁and▁contributing▁to▁the▁city's▁overall▁expansion
What▁is▁the▁Premier▁League? model The▁Premier▁League▁is▁the▁top▁tier▁of▁professional▁football▁in▁England,▁comprising▁20▁clubs▁that▁compete▁against▁each▁other.▁Established▁in▁1992,▁it▁has▁gained▁a▁reputation▁for▁high-quality▁matches,▁showcasing▁some▁of▁the▁best▁players▁and▁teams▁from▁around▁the▁world.▁The▁season▁typically▁runs▁from▁August▁to▁May,▁with▁each▁club▁playing▁38▁matches.▁The▁league▁operates▁on▁a▁system▁of▁promotion▁and▁relegation▁with▁the▁English▁Football▁League▁(EFL)▁Championship,▁adding▁to▁the▁excitement▁and▁competitiveness▁of▁the▁tournament.▁The▁Premier▁League▁is▁widely▁broadcast▁and▁followed,▁making▁it▁one▁of▁the▁most▁popular▁and▁lucrative▁football▁leagues▁globally
What▁is▁one▁of▁the▁main▁trigger▁for▁autism▁in▁current▁generation? model One▁of▁the▁main▁triggers▁for▁autism▁in▁the▁current▁generation▁is▁believed▁to▁be▁environmental▁factors▁that▁interact▁with▁genetic▁predispositions.▁This▁includes▁aspects▁like▁prenatal▁exposure▁to▁toxins,▁maternal▁health▁issues,▁and▁even▁the▁influence▁of▁technology▁and▁lifestyle▁changes▁during▁pregnancy▁and▁early▁childhood▁development
where▁do▁aliens▁come▁from model The▁question▁of▁where▁aliens▁come▁from▁has▁intrigued▁humanity▁for▁centuries.▁Many▁people▁think▁of▁extraterrestrial▁beings▁as▁originating▁from▁distant▁planets▁within▁our▁galaxy▁or▁even▁from▁other▁galaxies.▁Some▁theories▁suggest▁that▁they▁could▁come▁from▁specific▁systems▁like▁the▁nearby▁Proxima▁Centauri▁or▁even▁more▁exotic▁locations▁such▁as▁interdimensional▁spaces.▁While▁we▁have▁yet▁to▁find▁definitive▁evidence▁of▁alien▁life,▁the▁vastness▁of▁the▁universe▁continues▁to▁fuel▁speculation▁and▁exploration▁in▁search▁of▁answers▁about▁our▁cosmic▁neighbors
Carter▁can▁read▁half▁as▁many▁pages▁as▁Lucy▁in▁1▁hour.▁Lucy▁can▁read▁20▁more▁pages▁than▁Oliver▁in▁1▁hour.▁▁Oliver▁can▁read▁40▁pages.▁▁How▁many▁pages▁can▁Carter▁read▁in▁1▁hour? model Carter▁can▁read▁20▁pages▁in▁1▁hour
Subsample Interval 7
Did▁David▁Petrarca▁direct▁any▁episodes▁in▁the▁second▁season▁of▁Game▁of▁Thrones? model Yes,▁David▁Petrarca▁directed▁two▁episodes▁in▁the▁second▁season▁of▁Game▁of▁Thrones
What▁does▁GPT▁stand▁for▁in▁ChatGPT? model GPT▁stands▁for▁Generative▁Pre-trained▁Transformer
How▁many▁Olympic▁rings▁are▁there? model There▁are▁five▁Olympic▁rings
What▁are▁some▁of▁the▁most▁popular▁tourist▁attractions▁to▁visit▁in▁Sydney? model Sydney▁is▁home▁to▁a▁variety▁of▁stunning▁tourist▁attractions.▁Some▁of▁the▁most▁popular▁include: 1.▁Sydney▁Opera▁House▁-▁An▁iconic▁architectural▁masterpiece▁known▁for▁its▁distinctive▁sail-like▁design. 2.▁Sydney▁Harbour▁Bridge▁-▁Offering▁breathtaking▁views▁of▁the▁harbor,▁visitors▁can▁walk▁or▁climb▁the▁bridge▁for▁an▁unforgettable▁experience. 3.▁Bondi▁Beach▁-▁Famous▁for▁its▁surf▁culture,▁beautiful▁sand,▁and▁vibrant▁atmosphere,▁it's▁a▁must-visit▁for▁beach▁lovers. 4.▁Taronga▁Zoo▁-▁Located▁on▁the▁shores▁of▁Sydney▁Harbour,▁this▁zoo▁is▁home▁to▁a▁wide▁array▁of▁wildlife▁and▁provides▁stunning▁views▁of▁the▁city▁skyline
Who▁is▁the▁winner▁of▁International▁Booker▁Prize▁2020? model The▁winner▁of▁the▁International▁Booker▁Prize▁2020▁is▁Marieke▁Lucas▁Rijneveld▁for▁their▁novel▁"The▁Discomfort▁of▁Evening,"▁translated▁by▁Michele▁Hutchison
Steve▁has▁a▁bank▁account▁that▁earns▁10%▁interest▁every▁year.▁He▁puts▁$100▁in▁it,▁and▁then▁10▁each▁year.▁How▁much▁money▁is▁in▁it▁after▁two▁years? model After▁two▁years,▁Steve▁will▁have▁a▁total▁of▁approximately▁one▁hundred▁thirty-one▁dollars▁in▁his▁bank▁account
What▁was▁the▁first▁full-length▁animated▁movie▁that▁Disney▁released? model The▁first▁full-length▁animated▁movie▁that▁Disney▁released▁was▁"Snow▁White▁and▁the▁Seven▁Dwarfs,"▁which▁debuted▁in▁1937
What▁does▁a▁funambulist▁walk▁on? model A▁funambulist▁walks▁on▁a▁tightrope
World▁Wrestling▁Championship▁2022▁was▁held▁in model World▁Wrestling▁Championship▁2022▁was▁held▁in▁Belgrade,▁Serbia,▁from▁September▁10▁to▁September▁18,▁featuring▁athletes▁from▁various▁countries▁competing▁for▁top▁honors▁in▁different▁weight▁categories
Hazel▁put▁up▁a▁lemonade▁stand.▁She▁sold▁half▁her▁lemonade▁to▁a▁construction▁crew.▁She▁sold▁18▁cups▁to▁kids▁on▁bikes.▁She▁gave▁away▁half▁that▁amount▁to▁her▁friends.▁Then▁she▁drank▁the▁last▁cup▁of▁lemonade▁herself.▁How▁many▁cups▁of▁lemonade▁did▁Hazel▁make? model Hazel▁made▁72▁cups▁of▁lemonade