4.6. Evaluate the spectral density of (Z,), where (Z,) ~ WN(0,0²)....

Question
Solution Preview

These solutions may offer step-by-step problem-solving explanations or good writing examples that include modern styles of formatting and construction of bibliographies out of text citations and references.
Students may use these solutions for personal skill-building and practice.
Unethical use is strictly forbidden.

This is only a preview of the solution.
Please use the purchase button to see the entire solution.
By purchasing this solution you'll be able to access the following files:
Solution.pdf
Purchase Solution
$22.00
Google Pay
Amazon
Paypal
Mastercard
Visacard
Discover
Amex
View Available Mathematics Tutors 529 tutors matched
ionut
Ionut
(ionut)
Hi! MSc Applied Informatics & Computer Science Engineer. Practical experience in many CS & IT branches.Research work & homework
5/5 (5,654+ sessions)
2 hours avg response
Leo
Leo
(Leo)
Hi! I have been a professor in New York and taught in a math department and in an applied math department.
4.9/5 (5,652+ sessions)
2 hours avg response
Pranay
(math1983)
Ph.D. in mathematics and working as an Assistant Professor in University. I can provide help in mathematics, statistics and allied areas.
4.6/5 (5,512+ sessions)
1 hour avg response

Similar Homework Solutions

8.1.0PHP Version600msRequest Duration45MBMemory UsageGET college-homework-library/{category}/{subject}/{id}Route
    • Booting (416ms)time
    • Application (184ms)time
    • 1 x Booting (69.36%)
      416ms
      1 x Application (30.64%)
      184ms
      • Illuminate\Routing\Events\Routing (1.47ms)
      • Illuminate\Routing\Events\RouteMatched (657μs)
      • Illuminate\Foundation\Events\LocaleUpdated (6.46ms)
      • eloquent.booting: App\Models\HomeworkLibrary\HomeworkLibrary (243μs)
      • eloquent.booted: App\Models\HomeworkLibrary\HomeworkLibrary (255μs)
      • Illuminate\Database\Events\ConnectionEstablished (1.31ms)
      • Illuminate\Database\Events\StatementPrepared (6.73ms)
      • Illuminate\Database\Events\QueryExecuted (1.29ms)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (133μs)
      • eloquent.booting: App\Models\Subject (132μs)
      • eloquent.booted: App\Models\Subject (62μs)
      • Illuminate\Database\Events\StatementPrepared (1.96ms)
      • Illuminate\Database\Events\QueryExecuted (940μs)
      • eloquent.retrieved: App\Models\Subject (184μs)
      • eloquent.booting: App\Models\HomeworkLibrary\HomeworkLibraryFile (146μs)
      • eloquent.booted: App\Models\HomeworkLibrary\HomeworkLibraryFile (59μs)
      • Illuminate\Database\Events\StatementPrepared (623μs)
      • Illuminate\Database\Events\QueryExecuted (889μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (70μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (13μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (8μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (7μs)
      • eloquent.booting: App\Models\SubjectCat (253μs)
      • eloquent.booted: App\Models\SubjectCat (40μs)
      • Illuminate\Database\Events\StatementPrepared (671μs)
      • Illuminate\Database\Events\QueryExecuted (899μs)
      • eloquent.retrieved: App\Models\SubjectCat (257μs)
      • Illuminate\Cache\Events\CacheHit (15.31ms)
      • Illuminate\Cache\Events\CacheMissed (316μs)
      • Illuminate\Database\Events\StatementPrepared (1.03ms)
      • Illuminate\Database\Events\QueryExecuted (7.88ms)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (85μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (14μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (8μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (6μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (6μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (6μs)
      • Illuminate\Database\Events\StatementPrepared (637μs)
      • Illuminate\Database\Events\QueryExecuted (1.04ms)
      • eloquent.retrieved: App\Models\Subject (125μs)
      • Illuminate\Cache\Events\KeyWritten (982μs)
      • Illuminate\Database\Events\StatementPrepared (1.76ms)
      • Illuminate\Database\Events\QueryExecuted (1.18ms)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (58μs)
      • Illuminate\Database\Events\StatementPrepared (908μs)
      • Illuminate\Database\Events\QueryExecuted (863μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (152μs)
      • Illuminate\Database\Events\StatementPrepared (689μs)
      • Illuminate\Database\Events\QueryExecuted (904μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (35μs)
      • Illuminate\Cache\Events\CacheHit (536μs)
      • creating: homework.show (313μs)
      • composing: homework.show (201μs)
      • creating: components.breadcrumbs (373μs)
      • composing: components.breadcrumbs (173μs)
      • Illuminate\Database\Events\StatementPrepared (1.27ms)
      • Illuminate\Database\Events\QueryExecuted (785μs)
      • eloquent.retrieved: App\Models\SubjectCat (63μs)
      • Illuminate\Cache\Events\CacheMissed (5.87ms)
      • Illuminate\Database\Events\StatementPrepared (703μs)
      • Illuminate\Database\Events\QueryExecuted (1.16ms)
      • eloquent.retrieved: App\Models\SubjectCat (108μs)
      • Illuminate\Cache\Events\KeyWritten (350μs)
      • Illuminate\Cache\Events\CacheHit (219μs)
      • Illuminate\Cache\Events\CacheHit (200μs)
      • Illuminate\Cache\Events\CacheHit (175μs)
      • Illuminate\Cache\Events\CacheHit (197μs)
      • Illuminate\Cache\Events\CacheHit (171μs)
      • Illuminate\Cache\Events\CacheHit (232μs)
      • Illuminate\Cache\Events\CacheHit (166μs)
      • Illuminate\Cache\Events\CacheHit (175μs)
      • Illuminate\Cache\Events\CacheHit (140μs)
      • Illuminate\Cache\Events\CacheHit (160μs)
      • Illuminate\Cache\Events\CacheHit (182μs)
      • Illuminate\Cache\Events\CacheHit (184μs)
      • Illuminate\Cache\Events\CacheHit (153μs)
      • Illuminate\Cache\Events\CacheMissed (193μs)
      • Illuminate\Database\Events\StatementPrepared (663μs)
      • Illuminate\Database\Events\QueryExecuted (803μs)
      • eloquent.retrieved: App\Models\SubjectCat (63μs)
      • Illuminate\Cache\Events\KeyWritten (378μs)
      • Illuminate\Cache\Events\CacheHit (246μs)
      • Illuminate\Cache\Events\CacheHit (229μs)
      • Illuminate\Cache\Events\CacheHit (210μs)
      • Illuminate\Cache\Events\CacheHit (734μs)
      • Illuminate\Cache\Events\CacheHit (229μs)
      • Illuminate\Cache\Events\CacheHit (233μs)
      • Illuminate\Cache\Events\CacheHit (196μs)
      • Illuminate\Cache\Events\CacheMissed (280μs)
      • Illuminate\Database\Events\StatementPrepared (664μs)
      • Illuminate\Database\Events\QueryExecuted (928μs)
      • eloquent.retrieved: App\Models\SubjectCat (143μs)
      • Illuminate\Cache\Events\KeyWritten (474μs)
      • Illuminate\Cache\Events\CacheHit (219μs)
      • Illuminate\Cache\Events\CacheHit (191μs)
      • Illuminate\Cache\Events\CacheHit (115μs)
      • Illuminate\Cache\Events\CacheHit (124μs)
      • Illuminate\Cache\Events\CacheHit (249μs)
      • Illuminate\Cache\Events\CacheHit (301μs)
      • Illuminate\Cache\Events\CacheHit (184μs)
      • Illuminate\Cache\Events\CacheHit (198μs)
      • Illuminate\Cache\Events\CacheHit (172μs)
      • Illuminate\Cache\Events\CacheHit (281μs)
      • Illuminate\Cache\Events\CacheHit (177μs)
      • Illuminate\Cache\Events\CacheHit (300μs)
      • Illuminate\Cache\Events\CacheHit (230μs)
      • Illuminate\Cache\Events\CacheHit (210μs)
      • Illuminate\Cache\Events\CacheHit (284μs)
      • Illuminate\Cache\Events\CacheHit (364μs)
      • Illuminate\Cache\Events\CacheHit (179μs)
      • Illuminate\Cache\Events\CacheHit (200μs)
      • Illuminate\Cache\Events\CacheHit (179μs)
      • Illuminate\Cache\Events\CacheHit (197μs)
      • Illuminate\Cache\Events\CacheHit (167μs)
      • Illuminate\Cache\Events\CacheHit (208μs)
      • Illuminate\Cache\Events\CacheHit (182μs)
      • Illuminate\Cache\Events\CacheHit (337μs)
      • Illuminate\Cache\Events\CacheHit (175μs)
      • Illuminate\Cache\Events\CacheHit (206μs)
      • Illuminate\Cache\Events\CacheHit (179μs)
      • Illuminate\Cache\Events\CacheHit (210μs)
      • Illuminate\Cache\Events\CacheHit (189μs)
      • Illuminate\Cache\Events\CacheHit (277μs)
      • Illuminate\Cache\Events\CacheHit (196μs)
      • Illuminate\Cache\Events\CacheMissed (295μs)
      • Illuminate\Database\Events\StatementPrepared (696μs)
      • Illuminate\Database\Events\QueryExecuted (890μs)
      • eloquent.retrieved: App\Models\SubjectCat (64μs)
      • Illuminate\Cache\Events\KeyWritten (400μs)
      • Illuminate\Cache\Events\CacheHit (388μs)
      • Illuminate\Cache\Events\CacheHit (243μs)
      • Illuminate\Cache\Events\CacheHit (181μs)
      • Illuminate\Cache\Events\CacheHit (311μs)
      • Illuminate\Cache\Events\CacheHit (286μs)
      • Illuminate\Cache\Events\CacheHit (225μs)
      • Illuminate\Cache\Events\CacheHit (166μs)
      • Illuminate\Cache\Events\CacheHit (379μs)
      • Illuminate\Cache\Events\CacheHit (425μs)
      • Illuminate\Cache\Events\CacheHit (205μs)
      • Illuminate\Cache\Events\CacheHit (174μs)
      • Illuminate\Cache\Events\CacheHit (196μs)
      • Illuminate\Cache\Events\CacheHit (178μs)
      • Illuminate\Cache\Events\CacheHit (192μs)
      • Illuminate\Cache\Events\CacheHit (182μs)
      • Illuminate\Cache\Events\CacheHit (252μs)
      • Illuminate\Cache\Events\CacheHit (194μs)
      • Illuminate\Cache\Events\CacheHit (190μs)
      • Illuminate\Cache\Events\CacheHit (197μs)
      • Illuminate\Cache\Events\CacheHit (202μs)
      • Illuminate\Cache\Events\CacheHit (185μs)
      • Illuminate\Cache\Events\CacheHit (196μs)
      • Illuminate\Cache\Events\CacheHit (257μs)
      • Illuminate\Cache\Events\CacheHit (215μs)
      • Illuminate\Cache\Events\CacheHit (188μs)
      • Illuminate\Cache\Events\CacheHit (196μs)
      • Illuminate\Cache\Events\CacheHit (266μs)
      • Illuminate\Cache\Events\CacheHit (205μs)
      • Illuminate\Cache\Events\CacheHit (187μs)
      • Illuminate\Cache\Events\CacheHit (196μs)
      • Illuminate\Cache\Events\CacheHit (183μs)
      • Illuminate\Cache\Events\CacheHit (196μs)
      • Illuminate\Cache\Events\CacheHit (182μs)
      • Illuminate\Cache\Events\CacheHit (203μs)
      • Illuminate\Cache\Events\CacheHit (170μs)
      • Illuminate\Cache\Events\CacheHit (235μs)
      • Illuminate\Cache\Events\CacheHit (184μs)
      • Illuminate\Cache\Events\CacheHit (205μs)
      • Illuminate\Cache\Events\CacheHit (181μs)
      • Illuminate\Cache\Events\CacheMissed (293μs)
      • Illuminate\Database\Events\StatementPrepared (739μs)
      • Illuminate\Database\Events\QueryExecuted (908μs)
      • eloquent.retrieved: App\Models\SubjectCat (70μs)
      • Illuminate\Cache\Events\KeyWritten (379μs)
      • Illuminate\Cache\Events\CacheHit (224μs)
      • Illuminate\Cache\Events\CacheHit (224μs)
      • Illuminate\Cache\Events\CacheHit (682μs)
      • Illuminate\Cache\Events\CacheHit (299μs)
      • Illuminate\Cache\Events\CacheHit (194μs)
      • Illuminate\Cache\Events\CacheHit (184μs)
      • Illuminate\Cache\Events\CacheHit (159μs)
      • Illuminate\Cache\Events\CacheMissed (284μs)
      • Illuminate\Database\Events\StatementPrepared (743μs)
      • Illuminate\Database\Events\QueryExecuted (885μs)
      • eloquent.retrieved: App\Models\SubjectCat (83μs)
      • Illuminate\Cache\Events\KeyWritten (338μs)
      • Illuminate\Cache\Events\CacheHit (247μs)
      • Illuminate\Cache\Events\CacheHit (171μs)
      • Illuminate\Cache\Events\CacheHit (110μs)
      • Illuminate\Cache\Events\CacheHit (269μs)
      • Illuminate\Cache\Events\CacheHit (136μs)
      • Illuminate\Cache\Events\CacheHit (134μs)
      • Illuminate\Cache\Events\CacheHit (218μs)
      • Illuminate\Cache\Events\CacheHit (207μs)
      • Illuminate\Cache\Events\CacheHit (156μs)
      • Illuminate\Cache\Events\CacheHit (198μs)
      • Illuminate\Cache\Events\CacheHit (191μs)
      • Illuminate\Cache\Events\CacheHit (927μs)
      • Illuminate\Cache\Events\CacheHit (166μs)
      • Illuminate\Cache\Events\CacheHit (190μs)
      • Illuminate\Cache\Events\CacheHit (162μs)
      • Illuminate\Cache\Events\CacheHit (171μs)
      • Illuminate\Cache\Events\CacheHit (161μs)
      • Illuminate\Cache\Events\CacheHit (182μs)
      • Illuminate\Cache\Events\CacheHit (157μs)
      • Illuminate\Cache\Events\CacheHit (172μs)
      • Illuminate\Cache\Events\CacheHit (171μs)
      • Illuminate\Cache\Events\CacheHit (227μs)
      • Illuminate\Cache\Events\CacheHit (174μs)
      • Illuminate\Cache\Events\CacheHit (199μs)
      • Illuminate\Cache\Events\CacheHit (180μs)
      • Illuminate\Cache\Events\CacheHit (191μs)
      • Illuminate\Cache\Events\CacheHit (168μs)
      • Illuminate\Cache\Events\CacheHit (203μs)
      • Illuminate\Cache\Events\CacheHit (175μs)
      • Illuminate\Cache\Events\CacheMissed (284μs)
      • Illuminate\Database\Events\StatementPrepared (771μs)
      • Illuminate\Database\Events\QueryExecuted (977μs)
      • eloquent.retrieved: App\Models\SubjectCat (62μs)
      • Illuminate\Cache\Events\KeyWritten (284μs)
      • Illuminate\Cache\Events\CacheHit (189μs)
      • Illuminate\Cache\Events\CacheHit (198μs)
      • Illuminate\Cache\Events\CacheHit (194μs)
      • Illuminate\Cache\Events\CacheHit (203μs)
      • Illuminate\Cache\Events\CacheHit (198μs)
      • Illuminate\Cache\Events\CacheHit (215μs)
      • Illuminate\Cache\Events\CacheHit (184μs)
      • Illuminate\Cache\Events\CacheHit (220μs)
      • Illuminate\Cache\Events\CacheHit (168μs)
      • Illuminate\Cache\Events\CacheHit (215μs)
      • Illuminate\Cache\Events\CacheHit (167μs)
      • Illuminate\Cache\Events\CacheHit (202μs)
      • Illuminate\Cache\Events\CacheHit (168μs)
      • Illuminate\Cache\Events\CacheHit (191μs)
      • Illuminate\Cache\Events\CacheHit (170μs)
      • Illuminate\Cache\Events\CacheHit (191μs)
      • Illuminate\Cache\Events\CacheHit (166μs)
      • Illuminate\Cache\Events\CacheHit (189μs)
      • Illuminate\Cache\Events\CacheHit (166μs)
      • Illuminate\Cache\Events\CacheHit (188μs)
      • Illuminate\Cache\Events\CacheHit (167μs)
      • Illuminate\Cache\Events\CacheHit (188μs)
      • Illuminate\Cache\Events\CacheHit (212μs)
      • Illuminate\Cache\Events\CacheHit (198μs)
      • Illuminate\Cache\Events\CacheHit (168μs)
      • Illuminate\Cache\Events\CacheHit (192μs)
      • Illuminate\Cache\Events\CacheHit (167μs)
      • Illuminate\Cache\Events\CacheHit (188μs)
      • Illuminate\Cache\Events\CacheHit (165μs)
      • Illuminate\Cache\Events\CacheHit (330μs)
      • Illuminate\Cache\Events\CacheHit (206μs)
      • Illuminate\Cache\Events\CacheHit (200μs)
      • Illuminate\Cache\Events\CacheHit (178μs)
      • Illuminate\Cache\Events\CacheHit (188μs)
      • Illuminate\Cache\Events\CacheHit (169μs)
      • Illuminate\Cache\Events\CacheHit (197μs)
      • Illuminate\Cache\Events\CacheHit (174μs)
      • Illuminate\Cache\Events\CacheHit (202μs)
      • Illuminate\Cache\Events\CacheHit (179μs)
      • Illuminate\Cache\Events\CacheHit (196μs)
      • Illuminate\Cache\Events\CacheHit (166μs)
      • Illuminate\Cache\Events\CacheHit (188μs)
      • Illuminate\Cache\Events\CacheHit (165μs)
      • Illuminate\Cache\Events\CacheHit (233μs)
      • Illuminate\Cache\Events\CacheHit (173μs)
      • Illuminate\Cache\Events\CacheHit (190μs)
      • Illuminate\Cache\Events\CacheHit (164μs)
      • Illuminate\Cache\Events\CacheHit (186μs)
      • Illuminate\Cache\Events\CacheHit (165μs)
      • Illuminate\Cache\Events\CacheHit (210μs)
      • Illuminate\Cache\Events\CacheHit (166μs)
      • Illuminate\Cache\Events\CacheHit (209μs)
      • Illuminate\Cache\Events\CacheHit (183μs)
      • Illuminate\Cache\Events\CacheHit (190μs)
      • Illuminate\Cache\Events\CacheHit (166μs)
      • Illuminate\Cache\Events\CacheHit (190μs)
      • Illuminate\Cache\Events\CacheHit (179μs)
      • Illuminate\Cache\Events\CacheHit (207μs)
      • Illuminate\Cache\Events\CacheHit (171μs)
      • Illuminate\Cache\Events\CacheHit (190μs)
      • Illuminate\Cache\Events\CacheHit (165μs)
      • Illuminate\Cache\Events\CacheHit (189μs)
      • Illuminate\Cache\Events\CacheHit (167μs)
      • Illuminate\Cache\Events\CacheMissed (294μs)
      • Illuminate\Database\Events\StatementPrepared (1.04ms)
      • Illuminate\Database\Events\QueryExecuted (985μs)
      • eloquent.retrieved: App\Models\SubjectCat (89μs)
      • Illuminate\Cache\Events\KeyWritten (383μs)
      • Illuminate\Cache\Events\CacheHit (1.29ms)
      • Illuminate\Cache\Events\CacheHit (238μs)
      • Illuminate\Cache\Events\CacheHit (284μs)
      • Illuminate\Cache\Events\CacheHit (240μs)
      • Illuminate\Cache\Events\CacheHit (202μs)
      • Illuminate\Cache\Events\CacheHit (246μs)
      • Illuminate\Cache\Events\CacheHit (173μs)
      • Illuminate\Cache\Events\CacheHit (191μs)
      • Illuminate\Cache\Events\CacheHit (167μs)
      • Illuminate\Cache\Events\CacheHit (210μs)
      • Illuminate\Cache\Events\CacheHit (274μs)
      • Illuminate\Cache\Events\CacheHit (211μs)
      • Illuminate\Cache\Events\CacheHit (170μs)
      • Illuminate\Cache\Events\CacheHit (190μs)
      • Illuminate\Cache\Events\CacheHit (166μs)
      • Illuminate\Cache\Events\CacheHit (208μs)
      • Illuminate\Cache\Events\CacheHit (174μs)
      • Illuminate\Cache\Events\CacheHit (992μs)
      • Illuminate\Cache\Events\CacheHit (192μs)
      • Illuminate\Cache\Events\CacheHit (201μs)
      • Illuminate\Cache\Events\CacheHit (169μs)
      • Illuminate\Cache\Events\CacheHit (191μs)
      • Illuminate\Cache\Events\CacheHit (174μs)
      • Illuminate\Cache\Events\CacheHit (189μs)
      • Illuminate\Cache\Events\CacheHit (167μs)
      • Illuminate\Cache\Events\CacheHit (190μs)
      • Illuminate\Cache\Events\CacheHit (183μs)
      • Illuminate\Cache\Events\CacheHit (195μs)
      • Illuminate\Cache\Events\CacheHit (166μs)
      • Illuminate\Cache\Events\CacheHit (187μs)
      • Illuminate\Cache\Events\CacheHit (165μs)
      • Illuminate\Cache\Events\CacheHit (188μs)
      • Illuminate\Cache\Events\CacheHit (165μs)
      • Illuminate\Cache\Events\CacheHit (196μs)
      • Illuminate\Cache\Events\CacheHit (160μs)
      • Illuminate\Cache\Events\CacheHit (230μs)
      • Illuminate\Cache\Events\CacheHit (218μs)
      • Illuminate\Cache\Events\CacheHit (210μs)
      • Illuminate\Cache\Events\CacheHit (171μs)
      • Illuminate\Cache\Events\CacheHit (241μs)
      • Illuminate\Cache\Events\CacheHit (254μs)
      • Illuminate\Cache\Events\CacheHit (301μs)
      • Illuminate\Cache\Events\CacheHit (289μs)
      • Illuminate\Cache\Events\CacheHit (373μs)
      • Illuminate\Cache\Events\CacheHit (329μs)
      • Illuminate\Cache\Events\CacheHit (202μs)
      • Illuminate\Cache\Events\CacheHit (171μs)
      • Illuminate\Cache\Events\CacheHit (189μs)
      • Illuminate\Cache\Events\CacheHit (171μs)
      • Illuminate\Cache\Events\CacheHit (188μs)
      • Illuminate\Cache\Events\CacheHit (166μs)
      • Illuminate\Cache\Events\CacheHit (188μs)
      • Illuminate\Cache\Events\CacheHit (165μs)
      • Illuminate\Cache\Events\CacheHit (186μs)
      • Illuminate\Cache\Events\CacheHit (166μs)
      • Illuminate\Cache\Events\CacheHit (214μs)
      • Illuminate\Cache\Events\CacheHit (173μs)
      • Illuminate\Cache\Events\CacheHit (316μs)
      • Illuminate\Cache\Events\CacheHit (178μs)
      • Illuminate\Cache\Events\CacheHit (192μs)
      • Illuminate\Cache\Events\CacheHit (165μs)
      • Illuminate\Cache\Events\CacheHit (188μs)
      • Illuminate\Cache\Events\CacheHit (165μs)
      • Illuminate\Cache\Events\CacheHit (188μs)
      • Illuminate\Cache\Events\CacheHit (232μs)
      • Illuminate\Cache\Events\CacheHit (211μs)
      • Illuminate\Cache\Events\CacheHit (167μs)
      • Illuminate\Cache\Events\CacheHit (188μs)
      • Illuminate\Cache\Events\CacheHit (165μs)
      • Illuminate\Cache\Events\CacheHit (235μs)
      • Illuminate\Cache\Events\CacheHit (192μs)
      • Illuminate\Cache\Events\CacheHit (204μs)
      • Illuminate\Cache\Events\CacheHit (167μs)
      • Illuminate\Cache\Events\CacheHit (188μs)
      • Illuminate\Cache\Events\CacheHit (166μs)
      • Illuminate\Cache\Events\CacheHit (187μs)
      • Illuminate\Cache\Events\CacheHit (164μs)
      • Illuminate\Cache\Events\CacheHit (200μs)
      • Illuminate\Cache\Events\CacheHit (217μs)
      • Illuminate\Cache\Events\CacheHit (300μs)
      • Illuminate\Cache\Events\CacheHit (178μs)
      • Illuminate\Cache\Events\CacheHit (177μs)
      • Illuminate\Cache\Events\CacheHit (175μs)
      • Illuminate\Cache\Events\CacheHit (202μs)
      • Illuminate\Cache\Events\CacheHit (213μs)
      • Illuminate\Cache\Events\CacheHit (245μs)
      • Illuminate\Cache\Events\CacheHit (178μs)
      • Illuminate\Cache\Events\CacheHit (197μs)
      • Illuminate\Cache\Events\CacheHit (166μs)
      • Illuminate\Cache\Events\CacheMissed (262μs)
      • Illuminate\Database\Events\StatementPrepared (952μs)
      • Illuminate\Database\Events\QueryExecuted (910μs)
      • eloquent.retrieved: App\Models\SubjectCat (96μs)
      • Illuminate\Cache\Events\KeyWritten (1.3ms)
      • Illuminate\Cache\Events\CacheHit (215μs)
      • Illuminate\Cache\Events\CacheHit (221μs)
      • Illuminate\Cache\Events\CacheHit (175μs)
      • Illuminate\Cache\Events\CacheHit (281μs)
      • Illuminate\Cache\Events\CacheHit (214μs)
      • Illuminate\Cache\Events\CacheHit (187μs)
      • Illuminate\Cache\Events\CacheHit (162μs)
      • Illuminate\Cache\Events\CacheHit (195μs)
      • Illuminate\Cache\Events\CacheHit (354μs)
      • Illuminate\Cache\Events\CacheHit (205μs)
      • Illuminate\Cache\Events\CacheHit (287μs)
      • Illuminate\Cache\Events\CacheHit (182μs)
      • Illuminate\Cache\Events\CacheHit (166μs)
      • Illuminate\Cache\Events\CacheHit (184μs)
      • Illuminate\Cache\Events\CacheHit (162μs)
      • Illuminate\Cache\Events\CacheHit (180μs)
      • Illuminate\Cache\Events\CacheHit (157μs)
      • creating: site.layouts.app (456μs)
      • composing: site.layouts.app (21μs)
      • creating: components.canonical (431μs)
      • composing: components.canonical (106μs)
      • creating: components.open-graph (205μs)
      • composing: components.open-graph (80μs)
      • creating: site.headers.header (315μs)
      • composing: site.headers.header (78μs)
      • Illuminate\Cache\Events\CacheHit (1.96ms)
      • creating: components.footer (93μs)
      • composing: components.footer (99μs)
      • Illuminate\Cache\Events\CacheHit (1.08ms)
      • Illuminate\Cache\Events\CacheMissed (361μs)
      • Illuminate\Database\Events\StatementPrepared (2.59ms)
      • Illuminate\Database\Events\QueryExecuted (1.18ms)
      • eloquent.retrieved: App\Models\SubjectCat (103μs)
      • Illuminate\Cache\Events\KeyWritten (1.91ms)
      • Illuminate\Cache\Events\CacheHit (438μs)
      • Illuminate\Cache\Events\CacheHit (237μs)
      • Illuminate\Cache\Events\CacheHit (213μs)
      • Illuminate\Cache\Events\CacheHit (314μs)
      • Illuminate\Cache\Events\CacheHit (235μs)
      • Illuminate\Cache\Events\CacheHit (347μs)
      • Illuminate\Cache\Events\CacheHit (358μs)
      • Illuminate\Cache\Events\CacheHit (227μs)
      • Illuminate\Cache\Events\CacheHit (1.13ms)
      • Illuminate\Cache\Events\CacheHit (352μs)
      • Illuminate\Cache\Events\CacheHit (1.02ms)
      • Illuminate\Cache\Events\CacheHit (355μs)
      • creating: components.forms.contact-us (251μs)
      • composing: components.forms.contact-us (167μs)
      • creating: components.forms.get-started (122μs)
      • composing: components.forms.get-started (67μs)
      • creating: components.forms.free-tool-download (96μs)
      • composing: components.forms.free-tool-download (66μs)
      • creating: components.forms.claim-free-worksheet (97μs)
      • composing: components.forms.claim-free-worksheet (65μs)
      • creating: components.forms.tutor-subscription-waitlist (94μs)
      • composing: components.forms.tutor-subscription-waitlist (63μs)
      • creating: components.forms.tutor-subscription-join (94μs)
      • composing: components.forms.tutor-subscription-join (1.3ms)
      • creating: components.forms.tutor-support (167μs)
      • composing: components.forms.tutor-support (88μs)
      • 311 x Illuminate\Cache\Events\CacheHit (14.5%)
        86.98ms
        20 x Illuminate\Database\Events\QueryExecuted (4.38%)
        26.29ms
        20 x Illuminate\Database\Events\StatementPrepared (4.31%)
        25.84ms
        11 x Illuminate\Cache\Events\CacheMissed (1.46%)
        8.73ms
        11 x Illuminate\Cache\Events\KeyWritten (1.2%)
        7.18ms
        1 x Illuminate\Foundation\Events\LocaleUpdated (1.08%)
        6.46ms
        1 x Illuminate\Routing\Events\Routing (0.24%)
        1.47ms
        1 x Illuminate\Database\Events\ConnectionEstablished (0.22%)
        1.31ms
        1 x composing: components.forms.tutor-subscription-join (0.22%)
        1.30ms
        12 x eloquent.retrieved: App\Models\SubjectCat (0.2%)
        1.20ms
        1 x Illuminate\Routing\Events\RouteMatched (0.11%)
        657μs
        1 x creating: site.layouts.app (0.08%)
        456μs
        1 x creating: components.canonical (0.07%)
        431μs
        1 x creating: components.breadcrumbs (0.06%)
        373μs
        7 x eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (0.06%)
        343μs
        1 x creating: site.headers.header (0.05%)
        315μs
        1 x creating: homework.show (0.05%)
        313μs
        2 x eloquent.retrieved: App\Models\Subject (0.05%)
        309μs
        7 x eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (0.04%)
        258μs
        1 x eloquent.booted: App\Models\HomeworkLibrary\HomeworkLibrary (0.04%)
        255μs
        1 x eloquent.booting: App\Models\SubjectCat (0.04%)
        253μs
        1 x creating: components.forms.contact-us (0.04%)
        251μs
        1 x eloquent.booting: App\Models\HomeworkLibrary\HomeworkLibrary (0.04%)
        243μs
        1 x creating: components.open-graph (0.03%)
        205μs
        1 x composing: homework.show (0.03%)
        201μs
        1 x composing: components.breadcrumbs (0.03%)
        173μs
        1 x creating: components.forms.tutor-support (0.03%)
        167μs
        1 x composing: components.forms.contact-us (0.03%)
        167μs
        1 x eloquent.booting: App\Models\HomeworkLibrary\HomeworkLibraryFile (0.02%)
        146μs
        1 x eloquent.booting: App\Models\Subject (0.02%)
        132μs
        1 x creating: components.forms.get-started (0.02%)
        122μs
        1 x composing: components.canonical (0.02%)
        106μs
        1 x composing: components.footer (0.02%)
        99μs
        1 x creating: components.forms.claim-free-worksheet (0.02%)
        97μs
        1 x creating: components.forms.free-tool-download (0.02%)
        96μs
        1 x creating: components.forms.tutor-subscription-waitlist (0.02%)
        94μs
        1 x creating: components.forms.tutor-subscription-join (0.02%)
        94μs
        1 x creating: components.footer (0.02%)
        93μs
        1 x composing: components.forms.tutor-support (0.01%)
        88μs
        1 x composing: components.open-graph (0.01%)
        80μs
        1 x composing: site.headers.header (0.01%)
        78μs
        1 x composing: components.forms.get-started (0.01%)
        67μs
        1 x composing: components.forms.free-tool-download (0.01%)
        66μs
        1 x composing: components.forms.claim-free-worksheet (0.01%)
        65μs
        1 x composing: components.forms.tutor-subscription-waitlist (0.01%)
        63μs
        1 x eloquent.booted: App\Models\Subject (0.01%)
        62μs
        1 x eloquent.booted: App\Models\HomeworkLibrary\HomeworkLibraryFile (0.01%)
        59μs
        1 x eloquent.booted: App\Models\SubjectCat (0.01%)
        40μs
        1 x composing: site.layouts.app (0%)
        21μs
      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
      20 statements were executed, 5 of which were duplicates, 15 unique. Show only duplicated35.64ms
      • 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` = '62441' limit 1
        7.03mstwenty4_siteHomeworkLibraryController.php#97
        Bindings
        • 0: published
        • 1: 0
        • 2: 62441
        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 (8)
        990μstwenty4_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 (62441)
        1mstwenty4_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` = 1 limit 1
        950μstwenty4_siteHomeworkLibrary.php#201
        Bindings
        • 0: 1
        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` <> 62441 and `subject` = 8 and `status` = 'published' and `price` > 0 order by RAND() limit 6
        8.06mstwenty4_siteHomeworkLibraryRepository.php#30
        Bindings
        • 0: 62441
        • 1: 8
        • 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 (8)
        890μstwenty4_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` = 62441 and `solutionslibrary_files`.`solutionlib_id` is not null and `publish` = 'question' order by `order` asc, `id` asc
        1.17mstwenty4_siteHomeworkLibrary.php#260
        Bindings
        • 0: 62441
        • 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` = 62441 and `solutionslibrary_files`.`solutionlib_id` is not null and `publish` = 'teaser' order by `order` asc, `id` asc
        970μstwenty4_siteHomeworkLibrary.php#260
        Bindings
        • 0: 62441
        • 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` = 62441 and `solutionslibrary_files`.`solutionlib_id` is not null and `publish` = 'solution' order by `order` asc, `id` asc
        970μstwenty4_siteHomeworkLibrary.php#260
        Bindings
        • 0: 62441
        • 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` = 1 limit 1
        910μstwenty4_siteHomeworkLibrary.php#201
        Bindings
        • 0: 1
        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
      • select * from `subject_cats` where `subject_cats`.`id` = 1 limit 1
        1.13mstwenty4_siteSubject.php#100
        Bindings
        • 0: 1
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 3 limit 1
        1mstwenty4_siteSubject.php#100
        Bindings
        • 0: 3
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 4 limit 1
        1.02mstwenty4_siteSubject.php#100
        Bindings
        • 0: 4
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 10 limit 1
        980μstwenty4_siteSubject.php#100
        Bindings
        • 0: 10
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 33 limit 1
        1.02mstwenty4_siteSubject.php#100
        Bindings
        • 0: 33
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 11 limit 1
        970μstwenty4_siteSubject.php#100
        Bindings
        • 0: 11
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 5 limit 1
        1.08mstwenty4_siteSubject.php#100
        Bindings
        • 0: 5
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 34 limit 1
        1.27mstwenty4_siteSubject.php#100
        Bindings
        • 0: 34
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 31 limit 1
        1.15mstwenty4_siteSubject.php#100
        Bindings
        • 0: 31
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 36 limit 1
        3.08mstwenty4_siteSubject.php#100
        Bindings
        • 0: 36
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 28. view::components.footer:170
      App\Models\SubjectCat
      12SubjectCat.php
      App\Models\HomeworkLibrary\HomeworkLibrary
      7HomeworkLibrary.php
      App\Models\HomeworkLibrary\HomeworkLibraryFile
      7HomeworkLibraryFile.php
      App\Models\Subject
      2Subject.php
          _token
          xTKIFDL2DSOlT4jpsrTtqGuvA5RNKadADU9Fupks
          utm_source
          direct
          redirectUrl
          /college-homework-library/Mathematics/Probability/62441
          _previous
          array:1 [ "url" => "https://staging.dev.24houranswers.com/college-homework-library/Mathematics/Pro...
          _flash
          array:2 [ "old" => [] "new" => [] ]
          PHPDEBUGBAR_STACK_DATA
          []
          path_info
          /college-homework-library/Mathematics/Probability/62441
          status_code
          200
          
          status_text
          OK
          format
          html
          content_type
          text/html; charset=UTF-8
          request_query
          []
          
          request_request
          []
          
          request_headers
          0 of 0
          array:21 [ "priority" => array:1 [ 0 => "u=0, i" ] "accept-encoding" => array:1 [ 0 => "gzip, deflate, br, zstd" ] "sec-fetch-dest" => array:1 [ 0 => "document" ] "sec-fetch-user" => array:1 [ 0 => "?1" ] "sec-fetch-mode" => array:1 [ 0 => "navigate" ] "sec-fetch-site" => array:1 [ 0 => "none" ] "accept" => array:1 [ 0 => "text/html,application/xhtml+xml,application/xml;q=0.9,image/avif,image/webp,image/apng,*/*;q=0.8,application/signed-exchange;v=b3;q=0.7" ] "user-agent" => array:1 [ 0 => "Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)" ] "upgrade-insecure-requests" => array:1 [ 0 => "1" ] "sec-ch-ua-platform" => array:1 [ 0 => ""Windows"" ] "sec-ch-ua-mobile" => array:1 [ 0 => "?0" ] "sec-ch-ua" => array:1 [ 0 => ""HeadlessChrome";v="129", "Not=A?Brand";v="8", "Chromium";v="129"" ] "cache-control" => array:1 [ 0 => "no-cache" ] "pragma" => array:1 [ 0 => "no-cache" ] "x-amzn-trace-id" => array:1 [ 0 => "Root=1-6807e2d5-161210fe16901e1373b147de" ] "host" => array:1 [ 0 => "staging.dev.24houranswers.com" ] "x-forwarded-port" => array:1 [ 0 => "443" ] "x-forwarded-proto" => array:1 [ 0 => "https" ] "x-forwarded-for" => array:1 [ 0 => "18.189.170.45" ] "content-length" => array:1 [ 0 => "" ] "content-type" => array:1 [ 0 => "" ] ]
          request_cookies
          []
          
          response_headers
          0 of 0
          array:5 [ "content-type" => array:1 [ 0 => "text/html; charset=UTF-8" ] "cache-control" => array:1 [ 0 => "no-cache, private" ] "date" => array:1 [ 0 => "Tue, 22 Apr 2025 18:41:25 GMT" ] "set-cookie" => array:2 [ 0 => "XSRF-TOKEN=eyJpdiI6ImdTbW1GR2VHb3NGMzZ1eGRHV1hIT3c9PSIsInZhbHVlIjoiMXJoTU1kRFFoTWhMMHJQcUhrOHA5V3N4OTN2Q21KTDE4ZmZMd2xxRTduZjBCQnhQRzMvc0JLdHhVWEMwTmJuOVhaVHZaOWR1VFZYc3lwRy9FdEJxMFVnTnk2YU96SmZoWFpMaUQ2a1JrK2ZyOU9VUGZvU0REUjBzSlFLQkhiQXUiLCJtYWMiOiI5ZWUwNGM2NzkwNWY3ZWQwMmJjNGNkMTA1MTY5ZDBlYjU5OWFjMWNiZDUxOTkzOTMwNWQzNGZkZWI0ZTU1NWQ5IiwidGFnIjoiIn0%3D; expires=Tue, 22 Apr 2025 20:41:26 GMT; Max-Age=7200; path=/; domain=.24houranswers.com; samesite=laxXSRF-TOKEN=eyJpdiI6ImdTbW1GR2VHb3NGMzZ1eGRHV1hIT3c9PSIsInZhbHVlIjoiMXJoTU1kRFFoTWhMMHJQcUhrOHA5V3N4OTN2Q21KTDE4ZmZMd2xxRTduZjBCQnhQRzMvc0JLdHhVWEMwTmJuOVhaVHZaO" 1 => "24houranswers_session=eyJpdiI6Ii9QdjJ5Mno5RDBYR2NIWi9UT3g4Q0E9PSIsInZhbHVlIjoiMlVoRGgxeHFIbC9hVTVEM09xT09hU1pKYzNWQTZGbng0WFRjSmVzUHZ1eWV6YTRrUWNWNG1YenFhRzR1OVlDbW1NdEhmTVM5Rm9ITnZXNjhHUi9OUVY1ZmJTeWtoMmhOSmV1TnBkTmQ0N1RxTzVqakgxNHV2eUJlV2RoUFpQamEiLCJtYWMiOiJlYTQ2NzM0NmRlMDgyMTI2MWM2ZTI4MjE4MDcwNzBhODUzZTNjNzZiYmQ1MTU0YmZhOWZmMjFjNjc1NThhNWEwIiwidGFnIjoiIn0%3D; expires=Tue, 22 Apr 2025 20:41:26 GMT; Max-Age=7200; path=/; domain=.24houranswers.com; httponly; samesite=lax24houranswers_session=eyJpdiI6Ii9QdjJ5Mno5RDBYR2NIWi9UT3g4Q0E9PSIsInZhbHVlIjoiMlVoRGgxeHFIbC9hVTVEM09xT09hU1pKYzNWQTZGbng0WFRjSmVzUHZ1eWV6YTRrUWNWNG1YenFhRzR1OV" ] "Set-Cookie" => array:2 [ 0 => "XSRF-TOKEN=eyJpdiI6ImdTbW1GR2VHb3NGMzZ1eGRHV1hIT3c9PSIsInZhbHVlIjoiMXJoTU1kRFFoTWhMMHJQcUhrOHA5V3N4OTN2Q21KTDE4ZmZMd2xxRTduZjBCQnhQRzMvc0JLdHhVWEMwTmJuOVhaVHZaOWR1VFZYc3lwRy9FdEJxMFVnTnk2YU96SmZoWFpMaUQ2a1JrK2ZyOU9VUGZvU0REUjBzSlFLQkhiQXUiLCJtYWMiOiI5ZWUwNGM2NzkwNWY3ZWQwMmJjNGNkMTA1MTY5ZDBlYjU5OWFjMWNiZDUxOTkzOTMwNWQzNGZkZWI0ZTU1NWQ5IiwidGFnIjoiIn0%3D; expires=Tue, 22-Apr-2025 20:41:26 GMT; domain=.24houranswers.com; path=/XSRF-TOKEN=eyJpdiI6ImdTbW1GR2VHb3NGMzZ1eGRHV1hIT3c9PSIsInZhbHVlIjoiMXJoTU1kRFFoTWhMMHJQcUhrOHA5V3N4OTN2Q21KTDE4ZmZMd2xxRTduZjBCQnhQRzMvc0JLdHhVWEMwTmJuOVhaVHZaO" 1 => "24houranswers_session=eyJpdiI6Ii9QdjJ5Mno5RDBYR2NIWi9UT3g4Q0E9PSIsInZhbHVlIjoiMlVoRGgxeHFIbC9hVTVEM09xT09hU1pKYzNWQTZGbng0WFRjSmVzUHZ1eWV6YTRrUWNWNG1YenFhRzR1OVlDbW1NdEhmTVM5Rm9ITnZXNjhHUi9OUVY1ZmJTeWtoMmhOSmV1TnBkTmQ0N1RxTzVqakgxNHV2eUJlV2RoUFpQamEiLCJtYWMiOiJlYTQ2NzM0NmRlMDgyMTI2MWM2ZTI4MjE4MDcwNzBhODUzZTNjNzZiYmQ1MTU0YmZhOWZmMjFjNjc1NThhNWEwIiwidGFnIjoiIn0%3D; expires=Tue, 22-Apr-2025 20:41:26 GMT; domain=.24houranswers.com; path=/; httponly24houranswers_session=eyJpdiI6Ii9QdjJ5Mno5RDBYR2NIWi9UT3g4Q0E9PSIsInZhbHVlIjoiMlVoRGgxeHFIbC9hVTVEM09xT09hU1pKYzNWQTZGbng0WFRjSmVzUHZ1eWV6YTRrUWNWNG1YenFhRzR1OV" ] ]
          session_attributes
          0 of 0
          array:6 [ "_token" => "xTKIFDL2DSOlT4jpsrTtqGuvA5RNKadADU9Fupks" "utm_source" => "direct" "redirectUrl" => "/college-homework-library/Mathematics/Probability/62441" "_previous" => array:1 [ "url" => "https://staging.dev.24houranswers.com/college-homework-library/Mathematics/Probability/62441" ] "_flash" => array:2 [ "old" => [] "new" => [] ] "PHPDEBUGBAR_STACK_DATA" => [] ]