1) A population of annual sales numbers of an App called STATSRULES...

Question
1) A population of annual sales numbers of an App called STATSRULES at many universities has a Normal distribution, with the following Normal Distribution : N($80,000, $16,000)
Samples of groups of campuses were taken.
a) If the Sample Size was 16, what is the Distribution of the Sample Means? Your answer should be of the form : N(mean, std dev) .
b) If you want the std dev of the Sample Means to be $1000, what must the sample size be?

2) Suppose it is assumed that a bird population of an endangered species has lifetimes, measured in years, that are distributed Normally with the following distribution: N(22, 12).
Samples of 9 birds are taken to monitor population changes.
a) What is the Distribution of the Sample Means? Your answer should be in the form N(mean, std dev).
b) What is the probability that a Sample Mean will have a value greater than 30 yrs?
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.docx
Purchase Solution
$10.00
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)
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 Version630msRequest Duration45MBMemory UsageGET college-homework-library/{category}/{subject}/{id}Route
    • Booting (405ms)time
    • Application (225ms)time
    • 1 x Booting (64.28%)
      405ms
      1 x Application (35.72%)
      225ms
      • Illuminate\Routing\Events\Routing (2.22ms)
      • Illuminate\Routing\Events\RouteMatched (629μs)
      • Illuminate\Foundation\Events\LocaleUpdated (4.45ms)
      • eloquent.booting: App\Models\HomeworkLibrary\HomeworkLibrary (339μs)
      • eloquent.booted: App\Models\HomeworkLibrary\HomeworkLibrary (249μs)
      • Illuminate\Database\Events\ConnectionEstablished (1.21ms)
      • Illuminate\Database\Events\StatementPrepared (11.45ms)
      • Illuminate\Database\Events\QueryExecuted (1.45ms)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (128μs)
      • eloquent.booting: App\Models\Subject (130μs)
      • eloquent.booted: App\Models\Subject (61μs)
      • Illuminate\Database\Events\StatementPrepared (2.33ms)
      • Illuminate\Database\Events\QueryExecuted (986μs)
      • eloquent.retrieved: App\Models\Subject (122μs)
      • eloquent.booting: App\Models\HomeworkLibrary\HomeworkLibraryFile (219μs)
      • eloquent.booted: App\Models\HomeworkLibrary\HomeworkLibraryFile (62μs)
      • Illuminate\Database\Events\StatementPrepared (778μs)
      • Illuminate\Database\Events\QueryExecuted (3.92ms)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (84μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (19μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (11μs)
      • eloquent.booting: App\Models\SubjectCat (316μs)
      • eloquent.booted: App\Models\SubjectCat (59μs)
      • Illuminate\Database\Events\StatementPrepared (925μs)
      • Illuminate\Database\Events\QueryExecuted (828μs)
      • eloquent.retrieved: App\Models\SubjectCat (214μs)
      • Illuminate\Cache\Events\CacheHit (26.37ms)
      • Illuminate\Cache\Events\CacheMissed (419μs)
      • Illuminate\Database\Events\StatementPrepared (2.83ms)
      • Illuminate\Database\Events\QueryExecuted (4.39ms)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (154μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (27μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (14μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (13μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (11μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (13μs)
      • Illuminate\Database\Events\StatementPrepared (2.94ms)
      • Illuminate\Database\Events\QueryExecuted (1.78ms)
      • eloquent.retrieved: App\Models\Subject (122μs)
      • Illuminate\Cache\Events\KeyWritten (1.82ms)
      • Illuminate\Database\Events\StatementPrepared (3.74ms)
      • Illuminate\Database\Events\QueryExecuted (4ms)
      • Illuminate\Database\Events\StatementPrepared (1.51ms)
      • Illuminate\Database\Events\QueryExecuted (2.18ms)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (72μs)
      • Illuminate\Database\Events\StatementPrepared (2.35ms)
      • Illuminate\Database\Events\QueryExecuted (1.2ms)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (49μs)
      • Illuminate\Cache\Events\CacheHit (717μs)
      • creating: homework.show (911μs)
      • composing: homework.show (319μs)
      • creating: components.breadcrumbs (414μs)
      • composing: components.breadcrumbs (179μs)
      • Illuminate\Database\Events\StatementPrepared (1.32ms)
      • Illuminate\Database\Events\QueryExecuted (865μs)
      • eloquent.retrieved: App\Models\SubjectCat (91μs)
      • Illuminate\Cache\Events\CacheHit (5.66ms)
      • Illuminate\Cache\Events\CacheHit (341μs)
      • Illuminate\Cache\Events\CacheHit (1.15ms)
      • Illuminate\Cache\Events\CacheHit (327μs)
      • Illuminate\Cache\Events\CacheHit (1.67ms)
      • Illuminate\Cache\Events\CacheHit (224μs)
      • Illuminate\Cache\Events\CacheHit (339μs)
      • Illuminate\Cache\Events\CacheHit (1.5ms)
      • Illuminate\Cache\Events\CacheHit (616μs)
      • Illuminate\Cache\Events\CacheHit (632μs)
      • Illuminate\Cache\Events\CacheHit (222μs)
      • Illuminate\Cache\Events\CacheHit (169μs)
      • Illuminate\Cache\Events\CacheHit (326μs)
      • Illuminate\Cache\Events\CacheHit (4.5ms)
      • Illuminate\Cache\Events\CacheHit (328μs)
      • Illuminate\Cache\Events\CacheHit (384μs)
      • Illuminate\Cache\Events\CacheHit (314μs)
      • Illuminate\Cache\Events\CacheHit (206μs)
      • Illuminate\Cache\Events\CacheHit (263μs)
      • Illuminate\Cache\Events\CacheHit (264μs)
      • Illuminate\Cache\Events\CacheHit (334μs)
      • Illuminate\Cache\Events\CacheHit (223μs)
      • Illuminate\Cache\Events\CacheHit (261μs)
      • Illuminate\Cache\Events\CacheHit (294μs)
      • Illuminate\Cache\Events\CacheHit (563μs)
      • Illuminate\Cache\Events\CacheHit (361μs)
      • Illuminate\Cache\Events\CacheHit (343μs)
      • Illuminate\Cache\Events\CacheHit (263μs)
      • Illuminate\Cache\Events\CacheHit (324μs)
      • Illuminate\Cache\Events\CacheHit (264μs)
      • Illuminate\Cache\Events\CacheHit (231μs)
      • Illuminate\Cache\Events\CacheHit (230μs)
      • Illuminate\Cache\Events\CacheHit (261μs)
      • Illuminate\Cache\Events\CacheHit (183μs)
      • Illuminate\Cache\Events\CacheHit (201μs)
      • Illuminate\Cache\Events\CacheHit (262μs)
      • Illuminate\Cache\Events\CacheHit (274μs)
      • Illuminate\Cache\Events\CacheHit (1.22ms)
      • Illuminate\Cache\Events\CacheHit (255μs)
      • Illuminate\Cache\Events\CacheHit (203μs)
      • Illuminate\Cache\Events\CacheHit (196μs)
      • Illuminate\Cache\Events\CacheHit (183μs)
      • Illuminate\Cache\Events\CacheHit (224μs)
      • Illuminate\Cache\Events\CacheHit (167μs)
      • Illuminate\Cache\Events\CacheHit (207μs)
      • Illuminate\Cache\Events\CacheHit (188μs)
      • Illuminate\Cache\Events\CacheHit (193μs)
      • Illuminate\Cache\Events\CacheHit (177μs)
      • Illuminate\Cache\Events\CacheHit (210μs)
      • Illuminate\Cache\Events\CacheHit (190μs)
      • Illuminate\Cache\Events\CacheHit (198μs)
      • Illuminate\Cache\Events\CacheHit (440μs)
      • Illuminate\Cache\Events\CacheHit (204μs)
      • Illuminate\Cache\Events\CacheHit (607μs)
      • Illuminate\Cache\Events\CacheHit (674μs)
      • Illuminate\Cache\Events\CacheHit (199μs)
      • Illuminate\Cache\Events\CacheHit (293μs)
      • Illuminate\Cache\Events\CacheHit (705μs)
      • Illuminate\Cache\Events\CacheHit (246μs)
      • Illuminate\Cache\Events\CacheHit (177μs)
      • Illuminate\Cache\Events\CacheHit (188μs)
      • Illuminate\Cache\Events\CacheHit (161μs)
      • Illuminate\Cache\Events\CacheHit (389μs)
      • Illuminate\Cache\Events\CacheHit (208μs)
      • Illuminate\Cache\Events\CacheHit (273μs)
      • Illuminate\Cache\Events\CacheHit (473μs)
      • Illuminate\Cache\Events\CacheHit (305μs)
      • Illuminate\Cache\Events\CacheHit (312μs)
      • Illuminate\Cache\Events\CacheHit (202μs)
      • Illuminate\Cache\Events\CacheHit (188μs)
      • Illuminate\Cache\Events\CacheHit (439μs)
      • Illuminate\Cache\Events\CacheHit (256μs)
      • Illuminate\Cache\Events\CacheHit (874μs)
      • Illuminate\Cache\Events\CacheHit (658μs)
      • Illuminate\Cache\Events\CacheHit (591μs)
      • Illuminate\Cache\Events\CacheHit (202μs)
      • Illuminate\Cache\Events\CacheHit (787μs)
      • Illuminate\Cache\Events\CacheHit (208μs)
      • Illuminate\Cache\Events\CacheHit (447μs)
      • Illuminate\Cache\Events\CacheHit (441μs)
      • Illuminate\Cache\Events\CacheHit (316μs)
      • Illuminate\Cache\Events\CacheHit (249μs)
      • Illuminate\Cache\Events\CacheHit (424μs)
      • Illuminate\Cache\Events\CacheHit (206μs)
      • Illuminate\Cache\Events\CacheHit (198μs)
      • Illuminate\Cache\Events\CacheHit (250μs)
      • Illuminate\Cache\Events\CacheHit (501μs)
      • Illuminate\Cache\Events\CacheHit (222μs)
      • Illuminate\Cache\Events\CacheHit (259μs)
      • Illuminate\Cache\Events\CacheHit (277μs)
      • Illuminate\Cache\Events\CacheHit (363μs)
      • Illuminate\Cache\Events\CacheHit (378μs)
      • Illuminate\Cache\Events\CacheHit (210μs)
      • Illuminate\Cache\Events\CacheHit (185μs)
      • Illuminate\Cache\Events\CacheHit (211μs)
      • Illuminate\Cache\Events\CacheHit (168μs)
      • Illuminate\Cache\Events\CacheHit (183μs)
      • Illuminate\Cache\Events\CacheHit (261μs)
      • Illuminate\Cache\Events\CacheHit (321μs)
      • Illuminate\Cache\Events\CacheHit (178μs)
      • Illuminate\Cache\Events\CacheHit (189μs)
      • Illuminate\Cache\Events\CacheHit (170μs)
      • Illuminate\Cache\Events\CacheHit (274μs)
      • Illuminate\Cache\Events\CacheHit (180μs)
      • Illuminate\Cache\Events\CacheHit (209μs)
      • Illuminate\Cache\Events\CacheHit (229μs)
      • Illuminate\Cache\Events\CacheHit (280μs)
      • Illuminate\Cache\Events\CacheHit (196μs)
      • Illuminate\Cache\Events\CacheHit (1.53ms)
      • Illuminate\Cache\Events\CacheHit (365μs)
      • Illuminate\Cache\Events\CacheHit (274μs)
      • Illuminate\Cache\Events\CacheHit (191μs)
      • Illuminate\Cache\Events\CacheHit (205μs)
      • Illuminate\Cache\Events\CacheHit (306μs)
      • Illuminate\Cache\Events\CacheHit (1.82ms)
      • Illuminate\Cache\Events\CacheHit (357μs)
      • Illuminate\Cache\Events\CacheHit (836μs)
      • Illuminate\Cache\Events\CacheHit (326μs)
      • Illuminate\Cache\Events\CacheHit (198μs)
      • Illuminate\Cache\Events\CacheHit (166μs)
      • Illuminate\Cache\Events\CacheHit (3.15ms)
      • Illuminate\Cache\Events\CacheHit (481μs)
      • Illuminate\Cache\Events\CacheHit (218μs)
      • Illuminate\Cache\Events\CacheHit (187μs)
      • Illuminate\Cache\Events\CacheHit (192μs)
      • Illuminate\Cache\Events\CacheHit (979μs)
      • Illuminate\Cache\Events\CacheHit (848μs)
      • Illuminate\Cache\Events\CacheHit (332μs)
      • Illuminate\Cache\Events\CacheHit (215μs)
      • Illuminate\Cache\Events\CacheHit (321μs)
      • Illuminate\Cache\Events\CacheHit (241μs)
      • Illuminate\Cache\Events\CacheHit (839μs)
      • Illuminate\Cache\Events\CacheHit (216μs)
      • Illuminate\Cache\Events\CacheHit (549μs)
      • Illuminate\Cache\Events\CacheHit (1ms)
      • Illuminate\Cache\Events\CacheHit (329μs)
      • Illuminate\Cache\Events\CacheHit (954μs)
      • Illuminate\Cache\Events\CacheHit (641μs)
      • Illuminate\Cache\Events\CacheHit (1.47ms)
      • Illuminate\Cache\Events\CacheHit (209μs)
      • Illuminate\Cache\Events\CacheHit (278μs)
      • Illuminate\Cache\Events\CacheHit (166μs)
      • Illuminate\Cache\Events\CacheHit (392μs)
      • Illuminate\Cache\Events\CacheHit (188μs)
      • Illuminate\Cache\Events\CacheHit (184μs)
      • Illuminate\Cache\Events\CacheHit (166μs)
      • Illuminate\Cache\Events\CacheHit (741μs)
      • Illuminate\Cache\Events\CacheHit (239μs)
      • Illuminate\Cache\Events\CacheHit (310μs)
      • Illuminate\Cache\Events\CacheHit (179μs)
      • Illuminate\Cache\Events\CacheHit (183μs)
      • Illuminate\Cache\Events\CacheHit (200μs)
      • Illuminate\Cache\Events\CacheHit (258μs)
      • Illuminate\Cache\Events\CacheHit (164μs)
      • Illuminate\Cache\Events\CacheHit (231μs)
      • Illuminate\Cache\Events\CacheHit (165μs)
      • Illuminate\Cache\Events\CacheHit (896μs)
      • Illuminate\Cache\Events\CacheHit (327μs)
      • Illuminate\Cache\Events\CacheHit (198μs)
      • Illuminate\Cache\Events\CacheHit (178μs)
      • Illuminate\Cache\Events\CacheHit (192μs)
      • Illuminate\Cache\Events\CacheHit (172μs)
      • Illuminate\Cache\Events\CacheHit (221μs)
      • Illuminate\Cache\Events\CacheHit (175μs)
      • Illuminate\Cache\Events\CacheHit (256μs)
      • Illuminate\Cache\Events\CacheHit (183μs)
      • Illuminate\Cache\Events\CacheHit (729μs)
      • Illuminate\Cache\Events\CacheHit (273μs)
      • Illuminate\Cache\Events\CacheHit (777μs)
      • Illuminate\Cache\Events\CacheHit (340μs)
      • Illuminate\Cache\Events\CacheHit (301μs)
      • Illuminate\Cache\Events\CacheHit (380μs)
      • Illuminate\Cache\Events\CacheHit (213μs)
      • Illuminate\Cache\Events\CacheHit (263μs)
      • Illuminate\Cache\Events\CacheHit (202μs)
      • Illuminate\Cache\Events\CacheHit (175μs)
      • Illuminate\Cache\Events\CacheHit (191μs)
      • Illuminate\Cache\Events\CacheHit (167μs)
      • Illuminate\Cache\Events\CacheHit (193μs)
      • Illuminate\Cache\Events\CacheHit (241μs)
      • Illuminate\Cache\Events\CacheHit (216μs)
      • Illuminate\Cache\Events\CacheHit (273μs)
      • Illuminate\Cache\Events\CacheHit (228μs)
      • Illuminate\Cache\Events\CacheHit (466μs)
      • Illuminate\Cache\Events\CacheHit (367μs)
      • Illuminate\Cache\Events\CacheHit (1.17ms)
      • Illuminate\Cache\Events\CacheHit (207μs)
      • Illuminate\Cache\Events\CacheHit (171μs)
      • Illuminate\Cache\Events\CacheHit (396μs)
      • Illuminate\Cache\Events\CacheHit (180μs)
      • Illuminate\Cache\Events\CacheHit (203μs)
      • Illuminate\Cache\Events\CacheHit (225μs)
      • Illuminate\Cache\Events\CacheHit (196μs)
      • Illuminate\Cache\Events\CacheHit (164μs)
      • Illuminate\Cache\Events\CacheHit (191μs)
      • Illuminate\Cache\Events\CacheHit (170μs)
      • Illuminate\Cache\Events\CacheHit (235μs)
      • Illuminate\Cache\Events\CacheHit (172μs)
      • Illuminate\Cache\Events\CacheHit (208μs)
      • Illuminate\Cache\Events\CacheHit (270μs)
      • Illuminate\Cache\Events\CacheHit (287μs)
      • Illuminate\Cache\Events\CacheHit (199μs)
      • Illuminate\Cache\Events\CacheHit (207μs)
      • Illuminate\Cache\Events\CacheHit (176μs)
      • Illuminate\Cache\Events\CacheHit (337μs)
      • Illuminate\Cache\Events\CacheHit (177μs)
      • Illuminate\Cache\Events\CacheHit (268μs)
      • Illuminate\Cache\Events\CacheHit (263μs)
      • Illuminate\Cache\Events\CacheHit (265μs)
      • Illuminate\Cache\Events\CacheHit (237μs)
      • Illuminate\Cache\Events\CacheHit (370μs)
      • Illuminate\Cache\Events\CacheHit (183μs)
      • Illuminate\Cache\Events\CacheHit (403μs)
      • Illuminate\Cache\Events\CacheHit (198μs)
      • Illuminate\Cache\Events\CacheHit (1.1ms)
      • Illuminate\Cache\Events\CacheHit (173μs)
      • Illuminate\Cache\Events\CacheHit (192μs)
      • Illuminate\Cache\Events\CacheHit (167μs)
      • Illuminate\Cache\Events\CacheHit (189μs)
      • Illuminate\Cache\Events\CacheHit (166μs)
      • Illuminate\Cache\Events\CacheHit (188μs)
      • Illuminate\Cache\Events\CacheHit (251μs)
      • Illuminate\Cache\Events\CacheHit (213μs)
      • Illuminate\Cache\Events\CacheHit (254μs)
      • Illuminate\Cache\Events\CacheHit (197μs)
      • Illuminate\Cache\Events\CacheHit (354μs)
      • Illuminate\Cache\Events\CacheHit (271μs)
      • Illuminate\Cache\Events\CacheHit (173μs)
      • Illuminate\Cache\Events\CacheHit (459μs)
      • Illuminate\Cache\Events\CacheHit (306μs)
      • Illuminate\Cache\Events\CacheHit (592μs)
      • Illuminate\Cache\Events\CacheHit (466μs)
      • Illuminate\Cache\Events\CacheHit (412μs)
      • Illuminate\Cache\Events\CacheHit (295μs)
      • Illuminate\Cache\Events\CacheHit (464μs)
      • Illuminate\Cache\Events\CacheHit (181μs)
      • Illuminate\Cache\Events\CacheHit (195μs)
      • Illuminate\Cache\Events\CacheHit (169μs)
      • Illuminate\Cache\Events\CacheHit (297μs)
      • Illuminate\Cache\Events\CacheHit (186μs)
      • Illuminate\Cache\Events\CacheHit (193μs)
      • Illuminate\Cache\Events\CacheHit (167μs)
      • Illuminate\Cache\Events\CacheHit (189μs)
      • Illuminate\Cache\Events\CacheHit (270μs)
      • Illuminate\Cache\Events\CacheHit (249μs)
      • Illuminate\Cache\Events\CacheHit (172μs)
      • Illuminate\Cache\Events\CacheHit (190μs)
      • Illuminate\Cache\Events\CacheHit (165μs)
      • Illuminate\Cache\Events\CacheHit (337μs)
      • Illuminate\Cache\Events\CacheHit (200μs)
      • Illuminate\Cache\Events\CacheHit (200μs)
      • Illuminate\Cache\Events\CacheHit (175μs)
      • Illuminate\Cache\Events\CacheHit (209μs)
      • Illuminate\Cache\Events\CacheHit (238μs)
      • Illuminate\Cache\Events\CacheHit (200μs)
      • Illuminate\Cache\Events\CacheHit (171μs)
      • Illuminate\Cache\Events\CacheHit (254μs)
      • Illuminate\Cache\Events\CacheHit (262μs)
      • Illuminate\Cache\Events\CacheHit (215μs)
      • Illuminate\Cache\Events\CacheHit (253μs)
      • Illuminate\Cache\Events\CacheHit (214μs)
      • Illuminate\Cache\Events\CacheHit (171μs)
      • Illuminate\Cache\Events\CacheHit (190μs)
      • Illuminate\Cache\Events\CacheHit (348μs)
      • Illuminate\Cache\Events\CacheHit (256μs)
      • Illuminate\Cache\Events\CacheHit (177μs)
      • Illuminate\Cache\Events\CacheHit (216μs)
      • Illuminate\Cache\Events\CacheHit (171μs)
      • Illuminate\Cache\Events\CacheHit (188μs)
      • Illuminate\Cache\Events\CacheHit (369μs)
      • Illuminate\Cache\Events\CacheHit (314μs)
      • Illuminate\Cache\Events\CacheHit (184μs)
      • Illuminate\Cache\Events\CacheHit (248μs)
      • Illuminate\Cache\Events\CacheHit (502μs)
      • Illuminate\Cache\Events\CacheHit (243μs)
      • Illuminate\Cache\Events\CacheHit (180μs)
      • Illuminate\Cache\Events\CacheHit (194μs)
      • Illuminate\Cache\Events\CacheHit (163μs)
      • Illuminate\Cache\Events\CacheHit (357μs)
      • Illuminate\Cache\Events\CacheHit (179μs)
      • Illuminate\Cache\Events\CacheHit (190μs)
      • Illuminate\Cache\Events\CacheHit (167μs)
      • Illuminate\Cache\Events\CacheHit (295μs)
      • Illuminate\Cache\Events\CacheHit (198μs)
      • Illuminate\Cache\Events\CacheHit (204μs)
      • Illuminate\Cache\Events\CacheHit (168μs)
      • Illuminate\Cache\Events\CacheHit (197μs)
      • Illuminate\Cache\Events\CacheHit (162μs)
      • Illuminate\Cache\Events\CacheHit (269μs)
      • Illuminate\Cache\Events\CacheHit (169μs)
      • Illuminate\Cache\Events\CacheHit (189μs)
      • Illuminate\Cache\Events\CacheHit (169μs)
      • Illuminate\Cache\Events\CacheHit (244μs)
      • Illuminate\Cache\Events\CacheHit (293μs)
      • Illuminate\Cache\Events\CacheHit (542μs)
      • Illuminate\Cache\Events\CacheHit (166μs)
      • Illuminate\Cache\Events\CacheHit (263μs)
      • Illuminate\Cache\Events\CacheHit (407μs)
      • Illuminate\Cache\Events\CacheHit (236μs)
      • Illuminate\Cache\Events\CacheHit (191μs)
      • Illuminate\Cache\Events\CacheHit (202μs)
      • Illuminate\Cache\Events\CacheHit (176μs)
      • Illuminate\Cache\Events\CacheHit (370μs)
      • Illuminate\Cache\Events\CacheHit (206μs)
      • creating: site.layouts.app (502μs)
      • composing: site.layouts.app (26μs)
      • creating: components.canonical (734μs)
      • composing: components.canonical (129μs)
      • creating: components.open-graph (248μs)
      • composing: components.open-graph (94μs)
      • creating: site.headers.header (319μs)
      • composing: site.headers.header (164μs)
      • Illuminate\Cache\Events\CacheHit (2.8ms)
      • creating: components.footer (223μs)
      • composing: components.footer (251μs)
      • Illuminate\Cache\Events\CacheHit (1.04ms)
      • Illuminate\Cache\Events\CacheHit (306μs)
      • Illuminate\Cache\Events\CacheHit (568μs)
      • Illuminate\Cache\Events\CacheHit (211μs)
      • Illuminate\Cache\Events\CacheHit (189μs)
      • Illuminate\Cache\Events\CacheHit (283μs)
      • Illuminate\Cache\Events\CacheHit (239μs)
      • Illuminate\Cache\Events\CacheHit (507μs)
      • Illuminate\Cache\Events\CacheHit (377μs)
      • Illuminate\Cache\Events\CacheHit (219μs)
      • Illuminate\Cache\Events\CacheHit (203μs)
      • Illuminate\Cache\Events\CacheHit (184μs)
      • Illuminate\Cache\Events\CacheHit (207μs)
      • Illuminate\Cache\Events\CacheHit (289μs)
      • creating: components.forms.contact-us (242μs)
      • composing: components.forms.contact-us (234μs)
      • creating: components.forms.get-started (158μs)
      • composing: components.forms.get-started (83μs)
      • creating: components.forms.free-tool-download (178μs)
      • composing: components.forms.free-tool-download (177μs)
      • creating: components.forms.claim-free-worksheet (142μs)
      • composing: components.forms.claim-free-worksheet (273μs)
      • creating: components.forms.tutor-subscription-waitlist (214μs)
      • composing: components.forms.tutor-subscription-waitlist (78μs)
      • creating: components.forms.tutor-subscription-join (127μs)
      • composing: components.forms.tutor-subscription-join (77μs)
      • creating: components.forms.tutor-support (127μs)
      • composing: components.forms.tutor-support (74μs)
      • 321 x Illuminate\Cache\Events\CacheHit (22.92%)
        144ms
        10 x Illuminate\Database\Events\StatementPrepared (4.79%)
        30.17ms
        10 x Illuminate\Database\Events\QueryExecuted (3.43%)
        21.60ms
        1 x Illuminate\Foundation\Events\LocaleUpdated (0.71%)
        4.45ms
        1 x Illuminate\Routing\Events\Routing (0.35%)
        2.22ms
        1 x Illuminate\Cache\Events\KeyWritten (0.29%)
        1.82ms
        1 x Illuminate\Database\Events\ConnectionEstablished (0.19%)
        1.21ms
        1 x creating: homework.show (0.14%)
        911μs
        1 x creating: components.canonical (0.12%)
        734μs
        1 x Illuminate\Routing\Events\RouteMatched (0.1%)
        629μs
        1 x creating: site.layouts.app (0.08%)
        502μs
        1 x Illuminate\Cache\Events\CacheMissed (0.07%)
        419μs
        1 x creating: components.breadcrumbs (0.07%)
        414μs
        7 x eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (0.06%)
        360μs
        1 x eloquent.booting: App\Models\HomeworkLibrary\HomeworkLibrary (0.05%)
        339μs
        1 x composing: homework.show (0.05%)
        319μs
        1 x creating: site.headers.header (0.05%)
        319μs
        1 x eloquent.booting: App\Models\SubjectCat (0.05%)
        316μs
        2 x eloquent.retrieved: App\Models\SubjectCat (0.05%)
        305μs
        1 x composing: components.forms.claim-free-worksheet (0.04%)
        273μs
        1 x composing: components.footer (0.04%)
        251μs
        1 x eloquent.booted: App\Models\HomeworkLibrary\HomeworkLibrary (0.04%)
        249μs
        1 x creating: components.open-graph (0.04%)
        248μs
        2 x eloquent.retrieved: App\Models\Subject (0.04%)
        244μs
        1 x creating: components.forms.contact-us (0.04%)
        242μs
        5 x eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (0.04%)
        235μs
        1 x composing: components.forms.contact-us (0.04%)
        234μs
        1 x creating: components.footer (0.04%)
        223μs
        1 x eloquent.booting: App\Models\HomeworkLibrary\HomeworkLibraryFile (0.03%)
        219μs
        1 x creating: components.forms.tutor-subscription-waitlist (0.03%)
        214μs
        1 x composing: components.breadcrumbs (0.03%)
        179μs
        1 x creating: components.forms.free-tool-download (0.03%)
        178μs
        1 x composing: components.forms.free-tool-download (0.03%)
        177μs
        1 x composing: site.headers.header (0.03%)
        164μs
        1 x creating: components.forms.get-started (0.03%)
        158μs
        1 x creating: components.forms.claim-free-worksheet (0.02%)
        142μs
        1 x eloquent.booting: App\Models\Subject (0.02%)
        130μs
        1 x composing: components.canonical (0.02%)
        129μs
        1 x creating: components.forms.tutor-support (0.02%)
        127μs
        1 x creating: components.forms.tutor-subscription-join (0.02%)
        127μs
        1 x composing: components.open-graph (0.01%)
        94μs
        1 x composing: components.forms.get-started (0.01%)
        83μs
        1 x composing: components.forms.tutor-subscription-waitlist (0.01%)
        78μs
        1 x composing: components.forms.tutor-subscription-join (0.01%)
        77μs
        1 x composing: components.forms.tutor-support (0.01%)
        74μs
        1 x eloquent.booted: App\Models\HomeworkLibrary\HomeworkLibraryFile (0.01%)
        62μs
        1 x eloquent.booted: App\Models\Subject (0.01%)
        61μs
        1 x eloquent.booted: App\Models\SubjectCat (0.01%)
        59μs
        1 x composing: site.layouts.app (0%)
        26μs
      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 duplicated34.56ms
      • 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` = '46925' limit 1
        10.46mstwenty4_siteHomeworkLibraryController.php#97
        Bindings
        • 0: published
        • 1: 0
        • 2: 46925
        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 (3)
        1.13mstwenty4_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 (46925)
        3.97mstwenty4_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
        1.11mstwenty4_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` <> 46925 and `subject` = 3 and `status` = 'published' and `price` > 0 order by RAND() limit 6
        4.86mstwenty4_siteHomeworkLibraryRepository.php#30
        Bindings
        • 0: 46925
        • 1: 3
        • 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 (3)
        3.08mstwenty4_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` = 46925 and `solutionslibrary_files`.`solutionlib_id` is not null and `publish` = 'question' order by `order` asc, `id` asc
        4.57mstwenty4_siteHomeworkLibrary.php#260
        Bindings
        • 0: 46925
        • 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` = 46925 and `solutionslibrary_files`.`solutionlib_id` is not null and `publish` = 'teaser' order by `order` asc, `id` asc
        1.59mstwenty4_siteHomeworkLibrary.php#260
        Bindings
        • 0: 46925
        • 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` = 46925 and `solutionslibrary_files`.`solutionlib_id` is not null and `publish` = 'solution' order by `order` asc, `id` asc
        2.69mstwenty4_siteHomeworkLibrary.php#260
        Bindings
        • 0: 46925
        • 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
        1.1mstwenty4_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
      App\Models\HomeworkLibrary\HomeworkLibrary
      7HomeworkLibrary.php
      App\Models\HomeworkLibrary\HomeworkLibraryFile
      5HomeworkLibraryFile.php
      App\Models\Subject
      2Subject.php
      App\Models\SubjectCat
      2SubjectCat.php
          _token
          Y0TwdBKl3mBP6Kt0O8tYW2PREhrWXViajhq8Xb1T
          utm_source
          direct
          redirectUrl
          /college-homework-library/Mathematics/Geometry/46925
          _previous
          array:1 [ "url" => "https://staging.dev.24houranswers.com/college-homework-library/Mathematics/Geo...
          _flash
          array:2 [ "old" => [] "new" => [] ]
          PHPDEBUGBAR_STACK_DATA
          []
          path_info
          /college-homework-library/Mathematics/Geometry/46925
          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=1-68069f05-7bbac6fb11b3f5693f5910ae" ] "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 => "52.14.210.44" ] "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 => "Mon, 21 Apr 2025 19:39:50 GMT" ] "set-cookie" => array:2 [ 0 => "XSRF-TOKEN=eyJpdiI6InpSRExaNEptRllHUmwrdXEraW5rZkE9PSIsInZhbHVlIjoiZlhibnNYNnBvR0FSSmlaa2ZMZ0RTQWpZa0J6VGFuQ1o2cnBWbHh5ZFAxZ2J3RXg2YzJ0dDVZREZNVlhFV1A3WFlRL0FVc3YydE1jQVI1RURQc3dMRXpUc2xxMkxBOEltWCt5VnBHc2RWdXdKSnNTWHVOWlVEbnF5dnBjVmFVanQiLCJtYWMiOiI4ZmNiMzA4NTZmOGIwMjUwOTU2YTdlNTljOWExZWMzYzQ5NGEwZTExMTg4NDkzYjc2MzU2MjlmOGMyNWE5MTZhIiwidGFnIjoiIn0%3D; expires=Mon, 21 Apr 2025 21:39:50 GMT; Max-Age=7200; path=/; domain=.24houranswers.com; samesite=laxXSRF-TOKEN=eyJpdiI6InpSRExaNEptRllHUmwrdXEraW5rZkE9PSIsInZhbHVlIjoiZlhibnNYNnBvR0FSSmlaa2ZMZ0RTQWpZa0J6VGFuQ1o2cnBWbHh5ZFAxZ2J3RXg2YzJ0dDVZREZNVlhFV1A3WFlRL0FVc" 1 => "24houranswers_session=eyJpdiI6IkYwV0UxOHUvRG9kN2pLU3RFQk10M0E9PSIsInZhbHVlIjoieWV5UkxRa29tSzB6RjYxR2ZoM1FRMFVZNjFHMzhxV0Y2cWI3VEJPVjdoLyt5NUpYVGJsaE5LWTJjbWpxbWZVMGlDTGVLRzRCYXV6dno1cXpETUxhVm1sR3VhMnFTanc1NCtEcTcrcE9LR1hqVk1vZ24rRGE5blpIYjhRZ2hHaFgiLCJtYWMiOiIyYmM2MWFjMWY0MjhlNTJjMGYyOGQ0ZDEzZDExMWZhMjBmODgyZjNiYTRiMTM1MGFkYzFmY2VkYWZmMzQyYTg3IiwidGFnIjoiIn0%3D; expires=Mon, 21 Apr 2025 21:39:50 GMT; Max-Age=7200; path=/; domain=.24houranswers.com; httponly; samesite=lax24houranswers_session=eyJpdiI6IkYwV0UxOHUvRG9kN2pLU3RFQk10M0E9PSIsInZhbHVlIjoieWV5UkxRa29tSzB6RjYxR2ZoM1FRMFVZNjFHMzhxV0Y2cWI3VEJPVjdoLyt5NUpYVGJsaE5LWTJjbWpxbW" ] "Set-Cookie" => array:2 [ 0 => "XSRF-TOKEN=eyJpdiI6InpSRExaNEptRllHUmwrdXEraW5rZkE9PSIsInZhbHVlIjoiZlhibnNYNnBvR0FSSmlaa2ZMZ0RTQWpZa0J6VGFuQ1o2cnBWbHh5ZFAxZ2J3RXg2YzJ0dDVZREZNVlhFV1A3WFlRL0FVc3YydE1jQVI1RURQc3dMRXpUc2xxMkxBOEltWCt5VnBHc2RWdXdKSnNTWHVOWlVEbnF5dnBjVmFVanQiLCJtYWMiOiI4ZmNiMzA4NTZmOGIwMjUwOTU2YTdlNTljOWExZWMzYzQ5NGEwZTExMTg4NDkzYjc2MzU2MjlmOGMyNWE5MTZhIiwidGFnIjoiIn0%3D; expires=Mon, 21-Apr-2025 21:39:50 GMT; domain=.24houranswers.com; path=/XSRF-TOKEN=eyJpdiI6InpSRExaNEptRllHUmwrdXEraW5rZkE9PSIsInZhbHVlIjoiZlhibnNYNnBvR0FSSmlaa2ZMZ0RTQWpZa0J6VGFuQ1o2cnBWbHh5ZFAxZ2J3RXg2YzJ0dDVZREZNVlhFV1A3WFlRL0FVc" 1 => "24houranswers_session=eyJpdiI6IkYwV0UxOHUvRG9kN2pLU3RFQk10M0E9PSIsInZhbHVlIjoieWV5UkxRa29tSzB6RjYxR2ZoM1FRMFVZNjFHMzhxV0Y2cWI3VEJPVjdoLyt5NUpYVGJsaE5LWTJjbWpxbWZVMGlDTGVLRzRCYXV6dno1cXpETUxhVm1sR3VhMnFTanc1NCtEcTcrcE9LR1hqVk1vZ24rRGE5blpIYjhRZ2hHaFgiLCJtYWMiOiIyYmM2MWFjMWY0MjhlNTJjMGYyOGQ0ZDEzZDExMWZhMjBmODgyZjNiYTRiMTM1MGFkYzFmY2VkYWZmMzQyYTg3IiwidGFnIjoiIn0%3D; expires=Mon, 21-Apr-2025 21:39:50 GMT; domain=.24houranswers.com; path=/; httponly24houranswers_session=eyJpdiI6IkYwV0UxOHUvRG9kN2pLU3RFQk10M0E9PSIsInZhbHVlIjoieWV5UkxRa29tSzB6RjYxR2ZoM1FRMFVZNjFHMzhxV0Y2cWI3VEJPVjdoLyt5NUpYVGJsaE5LWTJjbWpxbW" ] ]
          session_attributes
          0 of 0
          array:6 [ "_token" => "Y0TwdBKl3mBP6Kt0O8tYW2PREhrWXViajhq8Xb1T" "utm_source" => "direct" "redirectUrl" => "/college-homework-library/Mathematics/Geometry/46925" "_previous" => array:1 [ "url" => "https://staging.dev.24houranswers.com/college-homework-library/Mathematics/Geometry/46925" ] "_flash" => array:2 [ "old" => [] "new" => [] ] "PHPDEBUGBAR_STACK_DATA" => [] ]