Answered: Prove or disprove: for RVs X and Y, H(X|Y... |24HA

Messages Timeline Exceptions Events399 Views14 Route Queries10 Models16 Livewire0 Mails Gate Session Request

8.1.0413ms45MBGET college-homework-library/{category}/{subject}/{id}

Booting (280ms)time
Application (133ms)time
1 x Booting (67.69%)
280ms
1 x Application (32.31%)
133ms

Illuminate\Routing\Events\Routing (1.37ms)
Illuminate\Routing\Events\RouteMatched (553μs)
Illuminate\Foundation\Events\LocaleUpdated (4.26ms)
eloquent.booting: App\Models\HomeworkLibrary\HomeworkLibrary (179μs)
eloquent.booted: App\Models\HomeworkLibrary\HomeworkLibrary (163μs)
Illuminate\Database\Events\ConnectionEstablished (911μs)
Illuminate\Database\Events\StatementPrepared (13.09ms)
Illuminate\Database\Events\QueryExecuted (1.28ms)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (94μs)
eloquent.booting: App\Models\Subject (99μs)
eloquent.booted: App\Models\Subject (41μs)
Illuminate\Database\Events\StatementPrepared (1.6ms)
Illuminate\Database\Events\QueryExecuted (946μs)
eloquent.retrieved: App\Models\Subject (105μs)
eloquent.booting: App\Models\HomeworkLibrary\HomeworkLibraryFile (126μs)
eloquent.booted: App\Models\HomeworkLibrary\HomeworkLibraryFile (39μs)
Illuminate\Database\Events\StatementPrepared (773μs)
Illuminate\Database\Events\QueryExecuted (761μs)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (72μs)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (14μs)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (9μs)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (6μs)
eloquent.booting: App\Models\SubjectCat (255μs)
eloquent.booted: App\Models\SubjectCat (41μs)
Illuminate\Database\Events\StatementPrepared (690μs)
Illuminate\Database\Events\QueryExecuted (1.15ms)
eloquent.retrieved: App\Models\SubjectCat (84μs)
Illuminate\Cache\Events\CacheHit (10.52ms)
Illuminate\Cache\Events\CacheMissed (204μs)
Illuminate\Database\Events\StatementPrepared (1.4ms)
Illuminate\Database\Events\QueryExecuted (2.63ms)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (81μs)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (36μs)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (11μs)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (8μs)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (6μs)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (6μs)
Illuminate\Database\Events\StatementPrepared (713μs)
Illuminate\Database\Events\QueryExecuted (938μs)
eloquent.retrieved: App\Models\Subject (80μs)
Illuminate\Cache\Events\KeyWritten (842μs)
Illuminate\Database\Events\StatementPrepared (1.47ms)
Illuminate\Database\Events\QueryExecuted (933μs)
Illuminate\Database\Events\StatementPrepared (910μs)
Illuminate\Database\Events\QueryExecuted (926μs)
Illuminate\Database\Events\StatementPrepared (729μs)
Illuminate\Database\Events\QueryExecuted (854μs)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (53μs)
Illuminate\Cache\Events\CacheHit (643μs)
creating: homework.show (264μs)
composing: homework.show (123μs)
creating: components.breadcrumbs (400μs)
composing: components.breadcrumbs (149μs)
Illuminate\Database\Events\StatementPrepared (1.18ms)
Illuminate\Database\Events\QueryExecuted (1.03ms)
eloquent.retrieved: App\Models\SubjectCat (85μs)
Illuminate\Cache\Events\CacheHit (4.09ms)
Illuminate\Cache\Events\CacheHit (218μs)
Illuminate\Cache\Events\CacheHit (217μs)
Illuminate\Cache\Events\CacheHit (179μs)
Illuminate\Cache\Events\CacheHit (210μs)
Illuminate\Cache\Events\CacheHit (172μs)
Illuminate\Cache\Events\CacheHit (252μs)
Illuminate\Cache\Events\CacheHit (192μs)
Illuminate\Cache\Events\CacheHit (205μs)
Illuminate\Cache\Events\CacheHit (171μs)
Illuminate\Cache\Events\CacheHit (203μs)
Illuminate\Cache\Events\CacheHit (167μs)
Illuminate\Cache\Events\CacheHit (190μs)
Illuminate\Cache\Events\CacheHit (164μs)
Illuminate\Cache\Events\CacheHit (246μs)
Illuminate\Cache\Events\CacheHit (200μs)
Illuminate\Cache\Events\CacheHit (213μs)
Illuminate\Cache\Events\CacheHit (188μs)
Illuminate\Cache\Events\CacheHit (213μs)
Illuminate\Cache\Events\CacheHit (189μs)
Illuminate\Cache\Events\CacheHit (212μs)
Illuminate\Cache\Events\CacheHit (187μs)
Illuminate\Cache\Events\CacheHit (228μs)
Illuminate\Cache\Events\CacheHit (171μs)
Illuminate\Cache\Events\CacheHit (197μs)
Illuminate\Cache\Events\CacheHit (166μs)
Illuminate\Cache\Events\CacheHit (226μs)
Illuminate\Cache\Events\CacheHit (185μs)
Illuminate\Cache\Events\CacheHit (221μs)
Illuminate\Cache\Events\CacheHit (198μs)
Illuminate\Cache\Events\CacheHit (218μs)
Illuminate\Cache\Events\CacheHit (194μs)
Illuminate\Cache\Events\CacheHit (210μs)
Illuminate\Cache\Events\CacheHit (168μs)
Illuminate\Cache\Events\CacheHit (213μs)
Illuminate\Cache\Events\CacheHit (189μs)
Illuminate\Cache\Events\CacheHit (206μs)
Illuminate\Cache\Events\CacheHit (170μs)
Illuminate\Cache\Events\CacheHit (191μs)
Illuminate\Cache\Events\CacheHit (164μs)
Illuminate\Cache\Events\CacheHit (185μs)
Illuminate\Cache\Events\CacheHit (163μs)
Illuminate\Cache\Events\CacheHit (185μs)
Illuminate\Cache\Events\CacheHit (163μs)
Illuminate\Cache\Events\CacheHit (211μs)
Illuminate\Cache\Events\CacheHit (187μs)
Illuminate\Cache\Events\CacheHit (204μs)
Illuminate\Cache\Events\CacheHit (209μs)
Illuminate\Cache\Events\CacheHit (232μs)
Illuminate\Cache\Events\CacheHit (191μs)
Illuminate\Cache\Events\CacheHit (211μs)
Illuminate\Cache\Events\CacheHit (185μs)
Illuminate\Cache\Events\CacheHit (209μs)
Illuminate\Cache\Events\CacheHit (185μs)
Illuminate\Cache\Events\CacheHit (218μs)
Illuminate\Cache\Events\CacheHit (173μs)
Illuminate\Cache\Events\CacheHit (201μs)
Illuminate\Cache\Events\CacheHit (167μs)
Illuminate\Cache\Events\CacheHit (194μs)
Illuminate\Cache\Events\CacheHit (165μs)
Illuminate\Cache\Events\CacheHit (191μs)
Illuminate\Cache\Events\CacheHit (166μs)
Illuminate\Cache\Events\CacheHit (213μs)
Illuminate\Cache\Events\CacheHit (191μs)
Illuminate\Cache\Events\CacheHit (210μs)
Illuminate\Cache\Events\CacheHit (185μs)
Illuminate\Cache\Events\CacheHit (207μs)
Illuminate\Cache\Events\CacheHit (220μs)
Illuminate\Cache\Events\CacheHit (229μs)
Illuminate\Cache\Events\CacheHit (192μs)
Illuminate\Cache\Events\CacheHit (208μs)
Illuminate\Cache\Events\CacheHit (184μs)
Illuminate\Cache\Events\CacheHit (208μs)
Illuminate\Cache\Events\CacheHit (186μs)
Illuminate\Cache\Events\CacheHit (209μs)
Illuminate\Cache\Events\CacheHit (186μs)
Illuminate\Cache\Events\CacheHit (211μs)
Illuminate\Cache\Events\CacheHit (186μs)
Illuminate\Cache\Events\CacheHit (211μs)
Illuminate\Cache\Events\CacheHit (183μs)
Illuminate\Cache\Events\CacheHit (208μs)
Illuminate\Cache\Events\CacheHit (184μs)
Illuminate\Cache\Events\CacheHit (207μs)
Illuminate\Cache\Events\CacheHit (183μs)
Illuminate\Cache\Events\CacheHit (207μs)
Illuminate\Cache\Events\CacheHit (184μs)
Illuminate\Cache\Events\CacheHit (208μs)
Illuminate\Cache\Events\CacheHit (219μs)
Illuminate\Cache\Events\CacheHit (235μs)
Illuminate\Cache\Events\CacheHit (176μs)
Illuminate\Cache\Events\CacheHit (197μs)
Illuminate\Cache\Events\CacheHit (164μs)
Illuminate\Cache\Events\CacheHit (211μs)
Illuminate\Cache\Events\CacheHit (185μs)
Illuminate\Cache\Events\CacheHit (214μs)
Illuminate\Cache\Events\CacheHit (162μs)
Illuminate\Cache\Events\CacheHit (182μs)
Illuminate\Cache\Events\CacheHit (157μs)
Illuminate\Cache\Events\CacheHit (182μs)
Illuminate\Cache\Events\CacheHit (161μs)
Illuminate\Cache\Events\CacheHit (180μs)
Illuminate\Cache\Events\CacheHit (157μs)
Illuminate\Cache\Events\CacheHit (210μs)
Illuminate\Cache\Events\CacheHit (174μs)
Illuminate\Cache\Events\CacheHit (198μs)
Illuminate\Cache\Events\CacheHit (164μs)
Illuminate\Cache\Events\CacheHit (220μs)
Illuminate\Cache\Events\CacheHit (189μs)
Illuminate\Cache\Events\CacheHit (211μs)
Illuminate\Cache\Events\CacheHit (262μs)
Illuminate\Cache\Events\CacheHit (218μs)
Illuminate\Cache\Events\CacheHit (164μs)
Illuminate\Cache\Events\CacheHit (209μs)
Illuminate\Cache\Events\CacheHit (190μs)
Illuminate\Cache\Events\CacheHit (891μs)
Illuminate\Cache\Events\CacheHit (174μs)
Illuminate\Cache\Events\CacheHit (194μs)
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Illuminate\Cache\Events\CacheHit (164μs)
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Illuminate\Cache\Events\CacheHit (154μs)
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Illuminate\Cache\Events\CacheHit (163μs)
Illuminate\Cache\Events\CacheHit (186μs)
Illuminate\Cache\Events\CacheHit (162μs)
Illuminate\Cache\Events\CacheHit (184μs)
Illuminate\Cache\Events\CacheHit (161μs)
Illuminate\Cache\Events\CacheHit (245μs)
Illuminate\Cache\Events\CacheHit (175μs)
Illuminate\Cache\Events\CacheHit (203μs)
Illuminate\Cache\Events\CacheHit (162μs)
Illuminate\Cache\Events\CacheHit (186μs)
Illuminate\Cache\Events\CacheHit (161μs)
Illuminate\Cache\Events\CacheHit (183μs)
Illuminate\Cache\Events\CacheHit (162μs)
Illuminate\Cache\Events\CacheHit (183μs)
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Illuminate\Cache\Events\CacheHit (183μs)
Illuminate\Cache\Events\CacheHit (168μs)
Illuminate\Cache\Events\CacheHit (186μs)
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Illuminate\Cache\Events\CacheHit (201μs)
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Illuminate\Cache\Events\CacheHit (185μs)
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Illuminate\Cache\Events\CacheHit (183μs)
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Illuminate\Cache\Events\CacheHit (185μs)
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Illuminate\Cache\Events\CacheHit (163μs)
Illuminate\Cache\Events\CacheHit (183μs)
Illuminate\Cache\Events\CacheHit (166μs)
creating: site.layouts.app (495μs)
composing: site.layouts.app (25μs)
creating: components.canonical (474μs)
composing: components.canonical (104μs)
creating: components.open-graph (206μs)
composing: components.open-graph (76μs)
creating: site.headers.header (308μs)
composing: site.headers.header (77μs)
Illuminate\Cache\Events\CacheHit (1.91ms)
creating: components.footer (91μs)
composing: components.footer (101μs)
Illuminate\Cache\Events\CacheHit (979μs)
Illuminate\Cache\Events\CacheHit (314μs)
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Illuminate\Cache\Events\CacheHit (206μs)
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creating: components.forms.claim-free-worksheet (125μs)
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creating: components.forms.tutor-subscription-waitlist (125μs)
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creating: components.forms.tutor-support (124μs)
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321 x Illuminate\Cache\Events\CacheHit (19.26%)	79.58ms
10 x Illuminate\Database\Events\StatementPrepared (5.46%)	22.56ms
10 x Illuminate\Database\Events\QueryExecuted (2.77%)	11.45ms
1 x Illuminate\Foundation\Events\LocaleUpdated (1.03%)	4.26ms
1 x Illuminate\Routing\Events\Routing (0.33%)	1.37ms
1 x Illuminate\Database\Events\ConnectionEstablished (0.22%)	911μs
1 x Illuminate\Cache\Events\KeyWritten (0.2%)	842μs
1 x Illuminate\Routing\Events\RouteMatched (0.13%)	553μs
1 x creating: site.layouts.app (0.12%)	495μs
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1 x creating: components.breadcrumbs (0.1%)	400μs
1 x creating: site.headers.header (0.07%)	308μs
1 x creating: components.forms.contact-us (0.07%)	281μs
1 x creating: homework.show (0.06%)	264μs
1 x eloquent.booting: App\Models\SubjectCat (0.06%)	255μs
7 x eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (0.06%)	242μs
1 x creating: components.open-graph (0.05%)	206μs
1 x Illuminate\Cache\Events\CacheMissed (0.05%)	204μs
2 x eloquent.retrieved: App\Models\Subject (0.04%)	185μs
1 x eloquent.booting: App\Models\HomeworkLibrary\HomeworkLibrary (0.04%)	179μs
1 x creating: components.forms.get-started (0.04%)	179μs
2 x eloquent.retrieved: App\Models\SubjectCat (0.04%)	169μs
1 x composing: components.forms.contact-us (0.04%)	167μs
1 x eloquent.booted: App\Models\HomeworkLibrary\HomeworkLibrary (0.04%)	163μs
5 x eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (0.04%)	154μs
1 x composing: components.breadcrumbs (0.04%)	149μs
1 x creating: components.forms.free-tool-download (0.03%)	133μs
1 x eloquent.booting: App\Models\HomeworkLibrary\HomeworkLibraryFile (0.03%)	126μs
1 x creating: components.forms.tutor-subscription-join (0.03%)	126μs
1 x creating: components.forms.tutor-subscription-waitlist (0.03%)	125μs
1 x creating: components.forms.claim-free-worksheet (0.03%)	125μs
1 x creating: components.forms.tutor-support (0.03%)	124μs
1 x composing: homework.show (0.03%)	123μs
1 x composing: components.canonical (0.03%)	104μs
1 x composing: components.footer (0.02%)	101μs
1 x eloquent.booting: App\Models\Subject (0.02%)	99μs
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1 x composing: site.headers.header (0.02%)	77μs
1 x composing: components.open-graph (0.02%)	76μs
1 x composing: components.forms.get-started (0.02%)	75μs
1 x composing: components.forms.free-tool-download (0.02%)	67μs
1 x composing: components.forms.tutor-support (0.02%)	67μs
1 x composing: components.forms.claim-free-worksheet (0.02%)	66μs
1 x composing: components.forms.tutor-subscription-join (0.02%)	65μs
1 x composing: components.forms.tutor-subscription-waitlist (0.02%)	64μs
1 x eloquent.booted: App\Models\Subject (0.01%)	41μs
1 x eloquent.booted: App\Models\SubjectCat (0.01%)	41μs
1 x eloquent.booted: App\Models\HomeworkLibrary\HomeworkLibraryFile (0.01%)	39μs
1 x composing: site.layouts.app (0.01%)	25μs

14 templates were rendered

1x homework.showshow.blade.phpblade
1x components.breadcrumbsbreadcrumbs.blade.phpblade
1x site.layouts.appapp.blade.phpblade
1x components.canonicalcanonical.blade.phpblade
1x components.open-graphopen-graph.blade.phpblade
1x site.headers.headerheader.blade.phpblade
1x components.footerfooter.blade.phpblade
1x components.forms.contact-uscontact-us.blade.phpblade
1x components.forms.get-startedget-started.blade.phpblade
1x components.forms.free-tool-downloadfree-tool-download.blade.phpblade
1x components.forms.claim-free-worksheetclaim-free-worksheet.blade.phpblade
1x components.forms.tutor-subscription-waitlisttutor-subscription-waitlist.blade.phpblade
1x components.forms.tutor-subscription-jointutor-subscription-join.blade.phpblade
1x components.forms.tutor-supporttutor-support.blade.phpblade

uri: GET college-homework-library/{category}/{subject}/{id}
middleware: web, utm.parameters
controller: App\Http\Controllers\HomeworkLibraryController@show
namespace
where
as: homework.show
file: app/Http/Controllers/HomeworkLibraryController.php:79-176

10 statements were executed, 4 of which were duplicates, 6 unique. Show only duplicated26ms

Connection Establishedtwenty4_siteHomeworkLibraryController.php#91

Backtrace

13. app/Http/Controllers/HomeworkLibraryController.php:91
14. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
15. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
16. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
17. vendor/laravel/framework/src/Illuminate/Routing/Route.php:205

select * from `solutionslibrary` where `status` = 'published' and `price` > 0 and `solutionslibrary`.`id` = '39474' limit 1

13.38mstwenty4_siteHomeworkLibraryController.php#97

Bindings	0: published 1: 0 2: 39474
Backtrace	16. app/Http/Controllers/HomeworkLibraryController.php:97 17. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54 18. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43 19. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260 20. vendor/laravel/framework/src/Illuminate/Routing/Route.php:205

select * from `subjects` where `subjects`.`id` in (128)

1.17mstwenty4_siteHomeworkLibraryController.php#97

Backtrace

21. app/Http/Controllers/HomeworkLibraryController.php:97
22. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
23. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
24. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
25. vendor/laravel/framework/src/Illuminate/Routing/Route.php:205

select * from `solutionslibrary_files` where `solutionslibrary_files`.`solutionlib_id` in (39474)

1.03mstwenty4_siteHomeworkLibraryController.php#97

Backtrace

21. app/Http/Controllers/HomeworkLibraryController.php:97
22. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
23. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
24. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
25. vendor/laravel/framework/src/Illuminate/Routing/Route.php:205

select * from `subject_cats` where `subject_cats`.`id` = 3 limit 1

1.36mstwenty4_siteHomeworkLibrary.php#201

Bindings	0: 3
Backtrace	20. app/Models/HomeworkLibrary/HomeworkLibrary.php:201 26. app/Http/Controllers/HomeworkLibraryController.php:105 27. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54 28. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43 29. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260

select * from `solutionslibrary` where `id` <> 39474 and `subject` = 128 and `status` = 'published' and `price` > 0 order by RAND() limit 6

3.36mstwenty4_siteHomeworkLibraryRepository.php#30

Bindings	0: 39474 1: 128 2: published 3: 0
Backtrace	14. app/Repositories/HomeworkLibraryRepository.php:30 15. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397 16. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419 18. app/Repositories/HomeworkLibraryRepository.php:39 19. app/Http/Controllers/HomeworkLibraryController.php:139

select * from `subjects` where `subjects`.`id` in (128)

1.11mstwenty4_siteHomeworkLibraryRepository.php#30

Backtrace

19. app/Repositories/HomeworkLibraryRepository.php:30
20. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
21. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
23. app/Repositories/HomeworkLibraryRepository.php:39
24. app/Http/Controllers/HomeworkLibraryController.php:139

select * from `solutionslibrary_files` where `solutionslibrary_files`.`solutionlib_id` = 39474 and `solutionslibrary_files`.`solutionlib_id` is not null and `publish` = 'question' order by `order` asc, `id` asc

1.13mstwenty4_siteHomeworkLibrary.php#260

Bindings	0: 39474 1: question
Backtrace	15. app/Models/HomeworkLibrary/HomeworkLibrary.php:260 16. app/Transformers/HomeworkLibrary/HomeworkLibraryTransformer.php:58 19. vendor/league/fractal/src/TransformerAbstract.php:128 20. vendor/league/fractal/src/TransformerAbstract.php:107 21. vendor/league/fractal/src/Scope.php:383

select * from `solutionslibrary_files` where `solutionslibrary_files`.`solutionlib_id` = 39474 and `solutionslibrary_files`.`solutionlib_id` is not null and `publish` = 'teaser' order by `order` asc, `id` asc

1.22mstwenty4_siteHomeworkLibrary.php#260

Bindings	0: 39474 1: teaser
Backtrace	15. app/Models/HomeworkLibrary/HomeworkLibrary.php:260 16. app/Transformers/HomeworkLibrary/HomeworkLibraryTransformer.php:69 19. vendor/league/fractal/src/TransformerAbstract.php:128 20. vendor/league/fractal/src/TransformerAbstract.php:107 21. vendor/league/fractal/src/Scope.php:383

select * from `solutionslibrary_files` where `solutionslibrary_files`.`solutionlib_id` = 39474 and `solutionslibrary_files`.`solutionlib_id` is not null and `publish` = 'solution' order by `order` asc, `id` asc

1.04mstwenty4_siteHomeworkLibrary.php#260

Bindings	0: 39474 1: solution
Backtrace	15. app/Models/HomeworkLibrary/HomeworkLibrary.php:260 16. app/Transformers/HomeworkLibrary/HomeworkLibraryTransformer.php:80 19. vendor/league/fractal/src/TransformerAbstract.php:128 20. vendor/league/fractal/src/TransformerAbstract.php:107 21. vendor/league/fractal/src/Scope.php:383

select * from `subject_cats` where `subject_cats`.`id` = 3 limit 1

1.2mstwenty4_siteHomeworkLibrary.php#201

Bindings	0: 3
Backtrace	20. app/Models/HomeworkLibrary/HomeworkLibrary.php:201 32. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110 33. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58 34. vendor/livewire/livewire/src/ComponentConcerns/RendersLivewireComponents.php:69 35. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:70

App\Models\HomeworkLibrary\HomeworkLibrary: 7HomeworkLibrary.php
App\Models\HomeworkLibrary\HomeworkLibraryFile: 5HomeworkLibraryFile.php
App\Models\Subject: 2Subject.php
App\Models\SubjectCat: 2SubjectCat.php

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Prove or disprove: for RVs X and Y, H(X|Y)=H(Y|X)

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