Logo

MATH 533 Week 3 Discussion; Determining a Normal Distribution (Keller)

$15
Contributor
Mike Mentzer
Category
Mathematices
Course
MATH 533 Applied Managerial Statistics
Institute
DeVry
Pages
67

Week 3: Determining a Normal Distribution When trying to determine probabilities, one must first assess whether the variable would have a normal distribution. Using the tools from this course, what are some methods that could be used to determine whether a variable has a normal distribution? View Instructor posts View My Posts Search entries or author Filter replies by unread UnreadCollapse replies Expand replies SubscribedThis topic was locked Jan 23 at 11:59pm. • Collapse SubdiscussionEsther La Colombe Ngo Mbogmal RosaisEsther La Colombe Ngo Mbogmal RosaisJan 16, 2022Jan 16 at 5:45am Manage Discussion EntryHello everyone A normal distribution is one in which the values are evenly distributed both above and below the mean. A population has a precisely normal distribution if the mean, mode, and median are all equal. For the population of 3,4,5,5,5,6,7, the mean, mode, and median are all 5. Then, histogram, normal probability plot and boxplot methods could be used to determine whether a variable has a normal distribution. The symmetric shape of histogram conclude the data are normally distributed, the data fall around the straight line in normal probability plot follow normal distribution and there is no outlier present and box and whisker equal to the median in boxplot conclude data follow normal distribution. Reference: https://statisticsbyjim.com/basics/normal-distribution/ (Links to an external site.)(1 like) o Collapse SubdiscussionPenka MarinovaPenka MarinovaJan 18, 2022Jan 18 at 8:32pm Manage Discussion EntryDear students, Today, during our class discussion we found out that Q7 and Q8 from your HW this week require a little bit more attention. Let's discuss one of them here. Do not forget that you need to deal with the Standard Normal Distribution here, where the mean = 0 and the standard deviation = 1.

Related Products

MATH 533 Week 2 Homework Problems

Contributor: Mike Mentzer

$20

MATH 533 Week 2 Quiz

Contributor: Mike Mentzer

$20

MATH 533 Week 3 Homework Problems.

Contributor: Mike Mentzer

$20

MATH 533 Week 3 Quiz

Contributor: Mike Mentzer

$15

MATH 533 Week 4 Homework Problems

Contributor: Mike Mentzer

$20

MATH 533 Week 4 Quiz..

Contributor: Mike Mentzer

$20

MATH 533 Week 4 Quiz.

Contributor: Mike Mentzer

$20

MATH 533 Week 3 Homework Problems..

Contributor: Mike Mentzer

$20

MATH 533 Week 5 Homework Problems.

Contributor: Mike Mentzer

$20

MATH 533 Week 5 Quiz..

Contributor: Mike Mentzer

$20

MATH 533 Week 5 Quiz.

Contributor: Mike Mentzer

$20

MATH 533 Week 6 Homework Problems..

Contributor: Mike Mentzer

$20

MATH 533 Week 6 Homework Problems.

Contributor: Mike Mentzer

$20

MATH 533 Week 6 Quiz..

Contributor: Mike Mentzer

$20

MATH 533 Week 6 Quiz.

Contributor: Mike Mentzer

$20

MATH 533 Week 5 Homework Problems..

Contributor: Mike Mentzer

$20

MATH 533 Week 7 Homework Problems

Contributor: Mike Mentzer

$20

MATH 533 Week 8 Case Study

Contributor: Mike Mentzer

$20

MATH 533 Week 8 Discussion

Contributor: Mike Mentzer

$15

Request history8.1.28PHP Version303msRequest Duration3MBMemory UsageGET product/{product}Route
    • Booting (66.55ms)time
    • Application (236ms)time
    • 1 x Application (78%)
      236ms
      1 x Booting (22%)
      66.55ms
      4 templates were rendered
      • product.viewview.blade.php#?blade
      • layouts.appapp.blade.php#?blade
      • layouts.navigationnavigation.blade.php#?blade
      • components.footerfooter.blade.php#?blade
      uri
      GET product/{product}
      middleware
      web, guestOrVerified
      controller
      App\Http\Controllers\ProductController@view
      namespace
      prefix
      where
      as
      product.view
      file
      app/Http/Controllers/ProductController.php:413-435
      147 statements were executed, 8 of which were duplicates, 139 unique. Show only duplicated120ms
      • # Query soft limit for Debugbar is reached after 100 queries, additional 47 queries only show the query. Limit can be raised in the config. Limits can be raised in the config (debugbar.options.db.soft_limit)
      • Connection Establishedthesagf1_secgracustImplicitRouteBinding.php#61
        Backtrace
        • 16. vendor/laravel/framework/src/Illuminate/Routing/ImplicitRouteBinding.php:61
        • 17. vendor/laravel/framework/src/Illuminate/Routing/Router.php:959
        • 20. vendor/laravel/framework/src/Illuminate/Routing/Middleware/SubstituteBindings.php:41
        • 21. vendor/laravel/framework/src/Illuminate/Pipeline/Pipeline.php:183
        • 22. vendor/laravel/framework/src/Illuminate/Foundation/Http/Middleware/VerifyCsrfToken.php:78
      • select * from `products` where `slug` = 'math-533-week-3-discussion-determining-a-normal-distribution-keller-1' and `products`.`deleted_at` is null limit 1
        8.36msthesagf1_secgracustImplicitRouteBinding.php#61
        Bindings
        • 0: math-533-week-3-discussion-determining-a-normal-distribution-keller-1
        Backtrace
        • 17. vendor/laravel/framework/src/Illuminate/Routing/ImplicitRouteBinding.php:61
        • 18. vendor/laravel/framework/src/Illuminate/Routing/Router.php:959
        • 21. vendor/laravel/framework/src/Illuminate/Routing/Middleware/SubstituteBindings.php:41
        • 22. vendor/laravel/framework/src/Illuminate/Pipeline/Pipeline.php:183
        • 23. vendor/laravel/framework/src/Illuminate/Foundation/Http/Middleware/VerifyCsrfToken.php:78
      • select `category_id` from `product_categories` where `product_id` = 993
        890μsthesagf1_secgracustProductController.php#418
        Bindings
        • 0: 993
        Backtrace
        • 13. app/Http/Controllers/ProductController.php:418
        • 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 `site_setting` limit 1
        970μsthesagf1_secgracustProductController.php#421
        Backtrace
        • 19. app/Http/Controllers/ProductController.php:421
        • 20. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 21. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 22. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
        • 23. vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
      • select distinct `products`.* from `products` inner join `product_categories` on `products`.`id` = `product_categories`.`product_id` where `deleted_at` is null and `product_categories`.`category_id` in (62) and `products`.`id` != 993
        3.08msthesagf1_secgracustProductController.php#431
        Bindings
        • 0: 62
        • 1: 993
        Backtrace
        • 13. app/Http/Controllers/ProductController.php:431
        • 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 `pages` where `status` = 1
        900μsthesagf1_secgracustPages.php#18
        Bindings
        • 0: 1
        Backtrace
        • 15. app/Models/Pages.php:18
        • 16. app/Providers/AppServiceProvider.php:21
        • 17. vendor/laravel/framework/src/Illuminate/View/Concerns/ManagesEvents.php:162
        • 21. vendor/laravel/framework/src/Illuminate/View/Concerns/ManagesEvents.php:177
        • 22. vendor/laravel/framework/src/Illuminate/View/View.php:188
      • select * from `site_setting` limit 1
        690μsthesagf1_secgracustAppServiceProvider.php#29
        Backtrace
        • 19. app/Providers/AppServiceProvider.php:29
        • 20. vendor/laravel/framework/src/Illuminate/View/Concerns/ManagesEvents.php:162
        • 24. vendor/laravel/framework/src/Illuminate/View/Concerns/ManagesEvents.php:177
        • 25. vendor/laravel/framework/src/Illuminate/View/View.php:188
        • 26. vendor/laravel/framework/src/Illuminate/View/View.php:159
      • select * from `product_images` where `product_images`.`product_id` = 993 and `product_images`.`product_id` is not null limit 1
        1.32msthesagf1_secgracustview.blade.php#20
        Bindings
        • 0: 993
        Backtrace
        • 21. view::product.view:20
        • 23. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
        • 24. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 25. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:72
        • 26. vendor/laravel/framework/src/Illuminate/View/View.php:207
      • select * from `product_categories` where `product_categories`.`product_id` = 993 and `product_categories`.`product_id` is not null
        830μsthesagf1_secgracustview.blade.php#41
        Bindings
        • 0: 993
        Backtrace
        • 20. view::product.view:41
        • 22. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
        • 23. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 24. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:72
        • 25. vendor/laravel/framework/src/Illuminate/View/View.php:207
      • select * from `categories` where `categories`.`id` = 62 and `categories`.`deleted_at` is null limit 1
        980μsthesagf1_secgracustview.blade.php#41
        Bindings
        • 0: 62
        Backtrace
        • 21. view::product.view:41
        • 23. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
        • 24. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 25. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:72
        • 26. vendor/laravel/framework/src/Illuminate/View/View.php:207
      • select * from `categories` where `categories`.`id` = '63' and `categories`.`deleted_at` is null limit 1
        880μsthesagf1_secgracustview.blade.php#110
        Bindings
        • 0: 63
        Backtrace
        • 21. view::product.view:110
        • 23. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
        • 24. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 25. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:72
        • 26. vendor/laravel/framework/src/Illuminate/View/View.php:207
      • select * from `product_files` where `product_files`.`product_id` = 993 and `product_files`.`product_id` is not null limit 1
        1.22msthesagf1_secgracustview.blade.php#128
        Bindings
        • 0: 993
        Backtrace
        • 22. view::product.view:128
        • 24. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
        • 25. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 26. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:72
        • 27. vendor/laravel/framework/src/Illuminate/View/View.php:207
      • select * from `product_files` where `product_files`.`product_id` = 993 and `product_files`.`product_id` is not null
        820μsthesagf1_secgracustview.blade.php#162
        Bindings
        • 0: 993
        Backtrace
        • 20. view::product.view:162
        • 22. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
        • 23. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 24. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:72
        • 25. vendor/laravel/framework/src/Illuminate/View/View.php:207
      • select * from `product_images` where `product_id` = 971 limit 1
        900μsthesagf1_secgracustview.blade.php#182
        Bindings
        • 0: 971
        Backtrace
        • 16. view::product.view:182
        • 18. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
        • 19. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 20. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:72
        • 21. vendor/laravel/framework/src/Illuminate/View/View.php:207
      • select * from `products` where `id` = 971 and `products`.`deleted_at` is null limit 1
        1.02msthesagf1_secgracustview.blade.php#208
        Bindings
        • 0: 971
        Backtrace
        • 16. view::product.view:208
        • 18. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
        • 19. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 20. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:72
        • 21. vendor/laravel/framework/src/Illuminate/View/View.php:207
      • select * from `product_categories` where `product_categories`.`product_id` = 971 and `product_categories`.`product_id` is not null
        540μsthesagf1_secgracustview.blade.php#210
        Bindings
        • 0: 971
        Backtrace
        • 20. view::product.view:210
        • 22. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
        • 23. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 24. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:72
        • 25. vendor/laravel/framework/src/Illuminate/View/View.php:207
      • select * from `product_images` where `product_id` = 972 limit 1
        930μsthesagf1_secgracustview.blade.php#182
        Bindings
        • 0: 972
        Backtrace
        • 16. view::product.view:182
        • 18. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
        • 19. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 20. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:72
        • 21. vendor/laravel/framework/src/Illuminate/View/View.php:207
      • select * from `products` where `id` = 972 and `products`.`deleted_at` is null limit 1
        720μsthesagf1_secgracustview.blade.php#208
        Bindings
        • 0: 972
        Backtrace
        • 16. view::product.view:208
        • 18. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
        • 19. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 20. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:72
        • 21. vendor/laravel/framework/src/Illuminate/View/View.php:207
      • select * from `product_categories` where `product_categories`.`product_id` = 972 and `product_categories`.`product_id` is not null
        800μsthesagf1_secgracustview.blade.php#210
        Bindings
        • 0: 972
        Backtrace
        • 20. view::product.view:210
        • 22. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
        • 23. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 24. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:72
        • 25. vendor/laravel/framework/src/Illuminate/View/View.php:207
      • select * from `product_images` where `product_id` = 973 limit 1
        1.02msthesagf1_secgracustview.blade.php#182
        Bindings
        • 0: 973
        Backtrace
        • 16. view::product.view:182
        • 18. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
        • 19. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 20. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:72
        • 21. vendor/laravel/framework/src/Illuminate/View/View.php:207
      • select * from `products` where `id` = 973 and `products`.`deleted_at` is null limit 1
        1.11msthesagf1_secgracustview.blade.php#208
        Bindings
        • 0: 973
        Backtrace
        • 16. view::product.view:208
        • 18. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
        • 19. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 20. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:72
        • 21. vendor/laravel/framework/src/Illuminate/View/View.php:207
      • select * from `product_categories` where `product_categories`.`product_id` = 973 and `product_categories`.`product_id` is not null
        920μsthesagf1_secgracustview.blade.php#210
        Bindings
        • 0: 973
        Backtrace
        • 20. view::product.view:210
        • 22. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
        • 23. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 24. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:72
        • 25. vendor/laravel/framework/src/Illuminate/View/View.php:207
      • select * from `product_images` where `product_id` = 974 limit 1
        990μsthesagf1_secgracustview.blade.php#182
        Bindings
        • 0: 974
        Backtrace
        • 16. view::product.view:182
        • 18. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
        • 19. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 20. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:72
        • 21. vendor/laravel/framework/src/Illuminate/View/View.php:207
      • select * from `products` where `id` = 974 and `products`.`deleted_at` is null limit 1
        970μsthesagf1_secgracustview.blade.php#208
        Bindings
        • 0: 974
        Backtrace
        • 16. view::product.view:208
        • 18. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
        • 19. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 20. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:72
        • 21. vendor/laravel/framework/src/Illuminate/View/View.php:207
      • select * from `product_categories` where `product_categories`.`product_id` = 974 and `product_categories`.`product_id` is not null
        1.04msthesagf1_secgracustview.blade.php#210
        Bindings
        • 0: 974
        Backtrace
        • 20. view::product.view:210
        • 22. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
        • 23. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 24. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:72
        • 25. vendor/laravel/framework/src/Illuminate/View/View.php:207
      • select * from `product_images` where `product_id` = 975 limit 1
        910μsthesagf1_secgracustview.blade.php#182
        Bindings
        • 0: 975
        Backtrace
        • 16. view::product.view:182
        • 18. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
        • 19. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 20. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:72
        • 21. vendor/laravel/framework/src/Illuminate/View/View.php:207
      • select * from `products` where `id` = 975 and `products`.`deleted_at` is null limit 1
        970μsthesagf1_secgracustview.blade.php#208
        Bindings
        • 0: 975
        Backtrace
        • 16. view::product.view:208
        • 18. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
        • 19. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 20. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:72
        • 21. vendor/laravel/framework/src/Illuminate/View/View.php:207
      • select * from `product_categories` where `product_categories`.`product_id` = 975 and `product_categories`.`product_id` is not null
        940μsthesagf1_secgracustview.blade.php#210
        Bindings
        • 0: 975
        Backtrace
        • 20. view::product.view:210
        • 22. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
        • 23. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 24. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:72
        • 25. vendor/laravel/framework/src/Illuminate/View/View.php:207
      • select * from `product_images` where `product_id` = 976 limit 1
        970μsthesagf1_secgracustview.blade.php#182
        Bindings
        • 0: 976
        Backtrace
        • 16. view::product.view:182
        • 18. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
        • 19. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 20. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:72
        • 21. vendor/laravel/framework/src/Illuminate/View/View.php:207
      • select * from `products` where `id` = 976 and `products`.`deleted_at` is null limit 1
        1.06msthesagf1_secgracustview.blade.php#208
        Bindings
        • 0: 976
        Backtrace
        • 16. view::product.view:208
        • 18. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
        • 19. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 20. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:72
        • 21. vendor/laravel/framework/src/Illuminate/View/View.php:207
      • select * from `product_categories` where `product_categories`.`product_id` = 976 and `product_categories`.`product_id` is not null
        960μsthesagf1_secgracustview.blade.php#210
        Bindings
        • 0: 976
        Backtrace
        • 20. view::product.view:210
        • 22. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
        • 23. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 24. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:72
        • 25. vendor/laravel/framework/src/Illuminate/View/View.php:207
      • select * from `product_images` where `product_id` = 977 limit 1
        790μsthesagf1_secgracustview.blade.php#249
        Bindings
        • 0: 977
        Backtrace
        • 16. view::product.view:249
        • 18. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
        • 19. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 20. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:72
        • 21. vendor/laravel/framework/src/Illuminate/View/View.php:207
      • select * from `products` where `id` = 977 and `products`.`deleted_at` is null limit 1
        1.05msthesagf1_secgracustview.blade.php#276
        Bindings
        • 0: 977
        Backtrace
        • 16. view::product.view:276
        • 18. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
        • 19. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 20. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:72
        • 21. vendor/laravel/framework/src/Illuminate/View/View.php:207
      • select * from `product_categories` where `product_categories`.`product_id` = 977 and `product_categories`.`product_id` is not null
        890μsthesagf1_secgracustview.blade.php#278
        Bindings
        • 0: 977
        Backtrace
        • 20. view::product.view:278
        • 22. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
        • 23. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 24. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:72
        • 25. vendor/laravel/framework/src/Illuminate/View/View.php:207
      • select * from `product_images` where `product_id` = 978 limit 1
        1.02msthesagf1_secgracustview.blade.php#249
        Bindings
        • 0: 978
        Backtrace
        • 16. view::product.view:249
        • 18. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
        • 19. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 20. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:72
        • 21. vendor/laravel/framework/src/Illuminate/View/View.php:207
      • select * from `products` where `id` = 978 and `products`.`deleted_at` is null limit 1
        1.11msthesagf1_secgracustview.blade.php#276
        Bindings
        • 0: 978
        Backtrace
        • 16. view::product.view:276
        • 18. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
        • 19. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 20. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:72
        • 21. vendor/laravel/framework/src/Illuminate/View/View.php:207
      • select * from `product_categories` where `product_categories`.`product_id` = 978 and `product_categories`.`product_id` is not null
        970μsthesagf1_secgracustview.blade.php#278
        Bindings
        • 0: 978
        Backtrace
        • 20. view::product.view:278
        • 22. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
        • 23. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 24. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:72
        • 25. vendor/laravel/framework/src/Illuminate/View/View.php:207
      • select * from `product_images` where `product_id` = 979 limit 1
        840μsthesagf1_secgracustview.blade.php#249
        Bindings
        • 0: 979
        Backtrace
        • 16. view::product.view:249
        • 18. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
        • 19. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 20. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:72
        • 21. vendor/laravel/framework/src/Illuminate/View/View.php:207
      • select * from `products` where `id` = 979 and `products`.`deleted_at` is null limit 1
        900μsthesagf1_secgracustview.blade.php#276
        Bindings
        • 0: 979
        Backtrace
        • 16. view::product.view:276
        • 18. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
        • 19. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 20. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:72
        • 21. vendor/laravel/framework/src/Illuminate/View/View.php:207
      • select * from `product_categories` where `product_categories`.`product_id` = 979 and `product_categories`.`product_id` is not null
        580μsthesagf1_secgracustview.blade.php#278
        Bindings
        • 0: 979
        Backtrace
        • 20. view::product.view:278
        • 22. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
        • 23. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 24. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:72
        • 25. vendor/laravel/framework/src/Illuminate/View/View.php:207
      • select * from `product_images` where `product_id` = 980 limit 1
        930μsthesagf1_secgracustview.blade.php#249
        Bindings
        • 0: 980
        Backtrace
        • 16. view::product.view:249
        • 18. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
        • 19. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 20. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:72
        • 21. vendor/laravel/framework/src/Illuminate/View/View.php:207
      • select * from `products` where `id` = 980 and `products`.`deleted_at` is null limit 1
        670μsthesagf1_secgracustview.blade.php#276
        Bindings
        • 0: 980
        Backtrace
        • 16. view::product.view:276
        • 18. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
        • 19. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 20. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:72
        • 21. vendor/laravel/framework/src/Illuminate/View/View.php:207
      • select * from `product_categories` where `product_categories`.`product_id` = 980 and `product_categories`.`product_id` is not null
        530μsthesagf1_secgracustview.blade.php#278
        Bindings
        • 0: 980
        Backtrace
        • 20. view::product.view:278
        • 22. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
        • 23. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 24. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:72
        • 25. vendor/laravel/framework/src/Illuminate/View/View.php:207
      • select * from `product_images` where `product_id` = 981 limit 1
        710μsthesagf1_secgracustview.blade.php#249
        Bindings
        • 0: 981
        Backtrace
        • 16. view::product.view:249
        • 18. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
        • 19. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 20. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:72
        • 21. vendor/laravel/framework/src/Illuminate/View/View.php:207
      • select * from `products` where `id` = 981 and `products`.`deleted_at` is null limit 1
        750μsthesagf1_secgracustview.blade.php#276
        Bindings
        • 0: 981
        Backtrace
        • 16. view::product.view:276
        • 18. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
        • 19. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 20. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:72
        • 21. vendor/laravel/framework/src/Illuminate/View/View.php:207
      • select * from `product_categories` where `product_categories`.`product_id` = 981 and `product_categories`.`product_id` is not null
        710μsthesagf1_secgracustview.blade.php#278
        Bindings
        • 0: 981
        Backtrace
        • 20. view::product.view:278
        • 22. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
        • 23. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 24. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:72
        • 25. vendor/laravel/framework/src/Illuminate/View/View.php:207
      • select * from `product_images` where `product_id` = 982 limit 1
        680μsthesagf1_secgracustview.blade.php#249
        Bindings
        • 0: 982
        Backtrace
        • 16. view::product.view:249
        • 18. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
        • 19. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 20. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:72
        • 21. vendor/laravel/framework/src/Illuminate/View/View.php:207
      • select * from `products` where `id` = 982 and `products`.`deleted_at` is null limit 1
        440μsthesagf1_secgracustview.blade.php#276
        Bindings
        • 0: 982
        Backtrace
        • 16. view::product.view:276
        • 18. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
        • 19. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 20. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:72
        • 21. vendor/laravel/framework/src/Illuminate/View/View.php:207
      • select * from `product_categories` where `product_categories`.`product_id` = 982 and `product_categories`.`product_id` is not null
        550μsthesagf1_secgracustview.blade.php#278
        Bindings
        • 0: 982
        Backtrace
        • 20. view::product.view:278
        • 22. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
        • 23. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 24. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:72
        • 25. vendor/laravel/framework/src/Illuminate/View/View.php:207
      • select * from `product_images` where `product_id` = 983 limit 1
        650μsthesagf1_secgracustview.blade.php#249
        Bindings
        • 0: 983
        Backtrace
        • 16. view::product.view:249
        • 18. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
        • 19. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 20. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:72
        • 21. vendor/laravel/framework/src/Illuminate/View/View.php:207
      • select * from `products` where `id` = 983 and `products`.`deleted_at` is null limit 1
        520μsthesagf1_secgracustview.blade.php#276
        Bindings
        • 0: 983
        Backtrace
        • 16. view::product.view:276
        • 18. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
        • 19. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 20. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:72
        • 21. vendor/laravel/framework/src/Illuminate/View/View.php:207
      • select * from `product_categories` where `product_categories`.`product_id` = 983 and `product_categories`.`product_id` is not null
        310μsthesagf1_secgracustview.blade.php#278
        Bindings
        • 0: 983
        Backtrace
        • 20. view::product.view:278
        • 22. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
        • 23. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 24. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:72
        • 25. vendor/laravel/framework/src/Illuminate/View/View.php:207
      • select * from `product_images` where `product_id` = 984 limit 1
        290μsthesagf1_secgracustview.blade.php#249
        Bindings
        • 0: 984
        Backtrace
        • 16. view::product.view:249
        • 18. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
        • 19. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 20. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:72
        • 21. vendor/laravel/framework/src/Illuminate/View/View.php:207
      • select * from `products` where `id` = 984 and `products`.`deleted_at` is null limit 1
        330μsthesagf1_secgracustview.blade.php#276
        Bindings
        • 0: 984
        Backtrace
        • 16. view::product.view:276
        • 18. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
        • 19. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 20. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:72
        • 21. vendor/laravel/framework/src/Illuminate/View/View.php:207
      • select * from `product_categories` where `product_categories`.`product_id` = 984 and `product_categories`.`product_id` is not null
        510μsthesagf1_secgracustview.blade.php#278
        Bindings
        • 0: 984
        Backtrace
        • 20. view::product.view:278
        • 22. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
        • 23. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 24. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:72
        • 25. vendor/laravel/framework/src/Illuminate/View/View.php:207
      • select * from `product_images` where `product_id` = 985 limit 1
        310μsthesagf1_secgracustview.blade.php#249
        Bindings
        • 0: 985
        Backtrace
        • 16. view::product.view:249
        • 18. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
        • 19. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 20. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:72
        • 21. vendor/laravel/framework/src/Illuminate/View/View.php:207
      • select * from `products` where `id` = 985 and `products`.`deleted_at` is null limit 1
        370μsthesagf1_secgracustview.blade.php#276
        Bindings
        • 0: 985
        Backtrace
        • 16. view::product.view:276
        • 18. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
        • 19. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 20. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:72
        • 21. vendor/laravel/framework/src/Illuminate/View/View.php:207
      • select * from `product_categories` where `product_categories`.`product_id` = 985 and `product_categories`.`product_id` is not null
        310μsthesagf1_secgracustview.blade.php#278
        Bindings
        • 0: 985
        Backtrace
        • 20. view::product.view:278
        • 22. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
        • 23. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 24. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:72
        • 25. vendor/laravel/framework/src/Illuminate/View/View.php:207
      • select * from `product_images` where `product_id` = 986 limit 1
        280μsthesagf1_secgracustview.blade.php#249
        Bindings
        • 0: 986
        Backtrace
        • 16. view::product.view:249
        • 18. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
        • 19. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 20. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:72
        • 21. vendor/laravel/framework/src/Illuminate/View/View.php:207
      • select * from `products` where `id` = 986 and `products`.`deleted_at` is null limit 1
        330μsthesagf1_secgracustview.blade.php#276
        Bindings
        • 0: 986
        Backtrace
        • 16. view::product.view:276
        • 18. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
        • 19. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 20. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:72
        • 21. vendor/laravel/framework/src/Illuminate/View/View.php:207
      • select * from `product_categories` where `product_categories`.`product_id` = 986 and `product_categories`.`product_id` is not null
        280μsthesagf1_secgracustview.blade.php#278
        Bindings
        • 0: 986
        Backtrace
        • 20. view::product.view:278
        • 22. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
        • 23. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 24. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:72
        • 25. vendor/laravel/framework/src/Illuminate/View/View.php:207
      • select * from `product_images` where `product_id` = 987 limit 1
        430μsthesagf1_secgracustview.blade.php#249
        Bindings
        • 0: 987
        Backtrace
        • 16. view::product.view:249
        • 18. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
        • 19. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 20. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:72
        • 21. vendor/laravel/framework/src/Illuminate/View/View.php:207
      • select * from `products` where `id` = 987 and `products`.`deleted_at` is null limit 1
        380μsthesagf1_secgracustview.blade.php#276
        Bindings
        • 0: 987
        Backtrace
        • 16. view::product.view:276
        • 18. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
        • 19. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 20. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:72
        • 21. vendor/laravel/framework/src/Illuminate/View/View.php:207
      • select * from `product_categories` where `product_categories`.`product_id` = 987 and `product_categories`.`product_id` is not null
        340μsthesagf1_secgracustview.blade.php#278
        Bindings
        • 0: 987
        Backtrace
        • 20. view::product.view:278
        • 22. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
        • 23. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 24. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:72
        • 25. vendor/laravel/framework/src/Illuminate/View/View.php:207
      • select * from `product_images` where `product_id` = 988 limit 1
        330μsthesagf1_secgracustview.blade.php#249
        Bindings
        • 0: 988
        Backtrace
        • 16. view::product.view:249
        • 18. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
        • 19. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 20. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:72
        • 21. vendor/laravel/framework/src/Illuminate/View/View.php:207
      • select * from `products` where `id` = 988 and `products`.`deleted_at` is null limit 1
        350μsthesagf1_secgracustview.blade.php#276
        Bindings
        • 0: 988
        Backtrace
        • 16. view::product.view:276
        • 18. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
        • 19. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 20. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:72
        • 21. vendor/laravel/framework/src/Illuminate/View/View.php:207
      • select * from `product_categories` where `product_categories`.`product_id` = 988 and `product_categories`.`product_id` is not null
        290μsthesagf1_secgracustview.blade.php#278
        Bindings
        • 0: 988
        Backtrace
        • 20. view::product.view:278
        • 22. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
        • 23. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 24. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:72
        • 25. vendor/laravel/framework/src/Illuminate/View/View.php:207
      • select * from `product_images` where `product_id` = 989 limit 1
        310μsthesagf1_secgracustview.blade.php#249
        Bindings
        • 0: 989
        Backtrace
        • 16. view::product.view:249
        • 18. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
        • 19. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 20. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:72
        • 21. vendor/laravel/framework/src/Illuminate/View/View.php:207
      • select * from `products` where `id` = 989 and `products`.`deleted_at` is null limit 1
        330μsthesagf1_secgracustview.blade.php#276
        Bindings
        • 0: 989
        Backtrace
        • 16. view::product.view:276
        • 18. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
        • 19. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 20. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:72
        • 21. vendor/laravel/framework/src/Illuminate/View/View.php:207
      • select * from `product_categories` where `product_categories`.`product_id` = 989 and `product_categories`.`product_id` is not null
        300μsthesagf1_secgracustview.blade.php#278
        Bindings
        • 0: 989
        Backtrace
        • 20. view::product.view:278
        • 22. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
        • 23. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 24. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:72
        • 25. vendor/laravel/framework/src/Illuminate/View/View.php:207
      • select * from `product_images` where `product_id` = 990 limit 1
        430μsthesagf1_secgracustview.blade.php#249
        Bindings
        • 0: 990
        Backtrace
        • 16. view::product.view:249
        • 18. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
        • 19. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 20. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:72
        • 21. vendor/laravel/framework/src/Illuminate/View/View.php:207
      • select * from `products` where `id` = 990 and `products`.`deleted_at` is null limit 1
        560μsthesagf1_secgracustview.blade.php#276
        Bindings
        • 0: 990
        Backtrace
        • 16. view::product.view:276
        • 18. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
        • 19. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 20. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:72
        • 21. vendor/laravel/framework/src/Illuminate/View/View.php:207
      • select * from `product_categories` where `product_categories`.`product_id` = 990 and `product_categories`.`product_id` is not null
        760μsthesagf1_secgracustview.blade.php#278
        Bindings
        • 0: 990
        Backtrace
        • 20. view::product.view:278
        • 22. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
        • 23. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 24. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:72
        • 25. vendor/laravel/framework/src/Illuminate/View/View.php:207
      • select * from `product_images` where `product_id` = 991 limit 1
        1.05msthesagf1_secgracustview.blade.php#249
        Bindings
        • 0: 991
        Backtrace
        • 16. view::product.view:249
        • 18. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
        • 19. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 20. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:72
        • 21. vendor/laravel/framework/src/Illuminate/View/View.php:207
      • select * from `products` where `id` = 991 and `products`.`deleted_at` is null limit 1
        1.17msthesagf1_secgracustview.blade.php#276
        Bindings
        • 0: 991
        Backtrace
        • 16. view::product.view:276
        • 18. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
        • 19. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 20. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:72
        • 21. vendor/laravel/framework/src/Illuminate/View/View.php:207
      • select * from `product_categories` where `product_categories`.`product_id` = 991 and `product_categories`.`product_id` is not null
        3.04msthesagf1_secgracustview.blade.php#278
        Bindings
        • 0: 991
        Backtrace
        • 20. view::product.view:278
        • 22. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
        • 23. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 24. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:72
        • 25. vendor/laravel/framework/src/Illuminate/View/View.php:207
      • select * from `product_images` where `product_id` = 992 limit 1
        910μsthesagf1_secgracustview.blade.php#249
        Bindings
        • 0: 992
        Backtrace
        • 16. view::product.view:249
        • 18. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
        • 19. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 20. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:72
        • 21. vendor/laravel/framework/src/Illuminate/View/View.php:207
      • select * from `products` where `id` = 992 and `products`.`deleted_at` is null limit 1
        660μsthesagf1_secgracustview.blade.php#276
        Bindings
        • 0: 992
        Backtrace
        • 16. view::product.view:276
        • 18. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
        • 19. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 20. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:72
        • 21. vendor/laravel/framework/src/Illuminate/View/View.php:207
      • select * from `product_categories` where `product_categories`.`product_id` = 992 and `product_categories`.`product_id` is not null
        620μsthesagf1_secgracustview.blade.php#278
        Bindings
        • 0: 992
        Backtrace
        • 20. view::product.view:278
        • 22. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
        • 23. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 24. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:72
        • 25. vendor/laravel/framework/src/Illuminate/View/View.php:207
      • select * from `product_images` where `product_id` = 994 limit 1
        560μsthesagf1_secgracustview.blade.php#249
        Bindings
        • 0: 994
        Backtrace
        • 16. view::product.view:249
        • 18. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
        • 19. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 20. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:72
        • 21. vendor/laravel/framework/src/Illuminate/View/View.php:207
      • select * from `products` where `id` = 994 and `products`.`deleted_at` is null limit 1
        590μsthesagf1_secgracustview.blade.php#276
        Bindings
        • 0: 994
        Backtrace
        • 16. view::product.view:276
        • 18. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
        • 19. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 20. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:72
        • 21. vendor/laravel/framework/src/Illuminate/View/View.php:207
      • select * from `product_categories` where `product_categories`.`product_id` = 994 and `product_categories`.`product_id` is not null
        3.8msthesagf1_secgracustview.blade.php#278
        Bindings
        • 0: 994
        Backtrace
        • 20. view::product.view:278
        • 22. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
        • 23. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 24. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:72
        • 25. vendor/laravel/framework/src/Illuminate/View/View.php:207
      • select * from `product_images` where `product_id` = 995 limit 1
        1.02msthesagf1_secgracustview.blade.php#249
        Bindings
        • 0: 995
        Backtrace
        • 16. view::product.view:249
        • 18. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
        • 19. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 20. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:72
        • 21. vendor/laravel/framework/src/Illuminate/View/View.php:207
      • select * from `products` where `id` = 995 and `products`.`deleted_at` is null limit 1
        840μsthesagf1_secgracustview.blade.php#276
        Bindings
        • 0: 995
        Backtrace
        • 16. view::product.view:276
        • 18. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
        • 19. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 20. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:72
        • 21. vendor/laravel/framework/src/Illuminate/View/View.php:207
      • select * from `product_categories` where `product_categories`.`product_id` = 995 and `product_categories`.`product_id` is not null
        630μsthesagf1_secgracustview.blade.php#278
        Bindings
        • 0: 995
        Backtrace
        • 20. view::product.view:278
        • 22. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
        • 23. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 24. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:72
        • 25. vendor/laravel/framework/src/Illuminate/View/View.php:207
      • select * from `product_images` where `product_id` = 996 limit 1
        610μsthesagf1_secgracustview.blade.php#249
        Bindings
        • 0: 996
        Backtrace
        • 16. view::product.view:249
        • 18. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
        • 19. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 20. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:72
        • 21. vendor/laravel/framework/src/Illuminate/View/View.php:207
      • select * from `products` where `id` = 996 and `products`.`deleted_at` is null limit 1
        750μsthesagf1_secgracustview.blade.php#276
        Bindings
        • 0: 996
        Backtrace
        • 16. view::product.view:276
        • 18. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
        • 19. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 20. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:72
        • 21. vendor/laravel/framework/src/Illuminate/View/View.php:207
      • select * from `product_categories` where `product_categories`.`product_id` = 996 and `product_categories`.`product_id` is not null
        850μsthesagf1_secgracustview.blade.php#278
        Bindings
        • 0: 996
        Backtrace
        • 20. view::product.view:278
        • 22. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
        • 23. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 24. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:72
        • 25. vendor/laravel/framework/src/Illuminate/View/View.php:207
      • select * from `product_images` where `product_id` = 997 limit 1
        810μsthesagf1_secgracustview.blade.php#249
        Bindings
        • 0: 997
        Backtrace
        • 16. view::product.view:249
        • 18. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
        • 19. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 20. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:72
        • 21. vendor/laravel/framework/src/Illuminate/View/View.php:207
      • select * from `products` where `id` = 997 and `products`.`deleted_at` is null limit 1
        790μsthesagf1_secgracustview.blade.php#276
        Bindings
        • 0: 997
        Backtrace
        • 16. view::product.view:276
        • 18. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
        • 19. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 20. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:72
        • 21. vendor/laravel/framework/src/Illuminate/View/View.php:207
      • select * from `product_categories` where `product_categories`.`product_id` = 997 and `product_categories`.`product_id` is not null
        740μsthesagf1_secgracustview.blade.php#278
        Bindings
        • 0: 997
        Backtrace
        • 20. view::product.view:278
        • 22. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
        • 23. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 24. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:72
        • 25. vendor/laravel/framework/src/Illuminate/View/View.php:207
      • select * from `product_images` where `product_id` = 998 limit 1
        770μsthesagf1_secgracustview.blade.php#249
        Bindings
        • 0: 998
        Backtrace
        • 16. view::product.view:249
        • 18. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
        • 19. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 20. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:72
        • 21. vendor/laravel/framework/src/Illuminate/View/View.php:207
      • select * from `products` where `id` = 998 and `products`.`deleted_at` is null limit 1
        830μsthesagf1_secgracustview.blade.php#276
        Bindings
        • 0: 998
        Backtrace
        • 16. view::product.view:276
        • 18. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
        • 19. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 20. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:72
        • 21. vendor/laravel/framework/src/Illuminate/View/View.php:207
      • select * from `product_categories` where `product_categories`.`product_id` = 998 and `product_categories`.`product_id` is not null
        780μsthesagf1_secgracustview.blade.php#278
        Bindings
        • 0: 998
        Backtrace
        • 20. view::product.view:278
        • 22. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
        • 23. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 24. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:72
        • 25. vendor/laravel/framework/src/Illuminate/View/View.php:207
      • select * from `product_images` where `product_id` = 999 limit 1
        850μsthesagf1_secgracustview.blade.php#249
        Bindings
        • 0: 999
        Backtrace
        • 16. view::product.view:249
        • 18. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
        • 19. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 20. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:72
        • 21. vendor/laravel/framework/src/Illuminate/View/View.php:207
      • select * from `products` where `id` = 999 and `products`.`deleted_at` is null limit 1
        910μsthesagf1_secgracustview.blade.php#276
        Bindings
        • 0: 999
        Backtrace
        • 16. view::product.view:276
        • 18. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
        • 19. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 20. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:72
        • 21. vendor/laravel/framework/src/Illuminate/View/View.php:207
      • select * from `product_categories` where `product_categories`.`product_id` = 999 and `product_categories`.`product_id` is not null
        770μsthesagf1_secgracustview.blade.php#278
        Bindings
        • 0: 999
        Backtrace
        • 20. view::product.view:278
        • 22. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
        • 23. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 24. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:72
        • 25. vendor/laravel/framework/src/Illuminate/View/View.php:207
      • select * from `product_images` where `product_id` = 1000 limit 1
        740μsthesagf1_secgracustview.blade.php#249
        Bindings
        • 0: 1000
        Backtrace
        • 16. view::product.view:249
        • 18. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
        • 19. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 20. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:72
        • 21. vendor/laravel/framework/src/Illuminate/View/View.php:207
      • select * from `products` where `id` = 1000 and `products`.`deleted_at` is null limit 1
        1.08msthesagf1_secgracustview.blade.php#276
        Bindings
        • 0: 1000
        Backtrace
        • 16. view::product.view:276
        • 18. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
        • 19. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 20. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:72
        • 21. vendor/laravel/framework/src/Illuminate/View/View.php:207
      • select * from `product_categories` where `product_categories`.`product_id` = 1000 and `product_categories`.`product_id` is not null
        850μsthesagf1_secgracustview.blade.php#278
        Bindings
        • 0: 1000
        Backtrace
        • 20. view::product.view:278
        • 22. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
        • 23. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 24. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:72
        • 25. vendor/laravel/framework/src/Illuminate/View/View.php:207
      • select * from `product_images` where `product_id` = 1001 limit 1
        900μsthesagf1_secgracustview.blade.php#249
        Bindings
        • 0: 1001
        Backtrace
        • 16. view::product.view:249
        • 18. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
        • 19. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 20. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:72
        • 21. vendor/laravel/framework/src/Illuminate/View/View.php:207
      • select * from `products` where `id` = 1001 and `products`.`deleted_at` is null limit 1
        950μsthesagf1_secgracust
      • select * from `product_categories` where `product_categories`.`product_id` = 1001 and `product_categories`.`product_id` is not null
        810μsthesagf1_secgracust
      • select * from `product_images` where `product_id` = 1002 limit 1
        800μsthesagf1_secgracust
      • select * from `products` where `id` = 1002 and `products`.`deleted_at` is null limit 1
        870μsthesagf1_secgracust
      • select * from `product_categories` where `product_categories`.`product_id` = 1002 and `product_categories`.`product_id` is not null
        760μsthesagf1_secgracust
      • select * from `product_images` where `product_id` = 1003 limit 1
        870μsthesagf1_secgracust
      • select * from `products` where `id` = 1003 and `products`.`deleted_at` is null limit 1
        800μsthesagf1_secgracust
      • select * from `product_categories` where `product_categories`.`product_id` = 1003 and `product_categories`.`product_id` is not null
        670μsthesagf1_secgracust
      • select * from `product_images` where `product_id` = 1004 limit 1
        720μsthesagf1_secgracust
      • select * from `products` where `id` = 1004 and `products`.`deleted_at` is null limit 1
        830μsthesagf1_secgracust
      • select * from `product_categories` where `product_categories`.`product_id` = 1004 and `product_categories`.`product_id` is not null
        810μsthesagf1_secgracust
      • select * from `product_images` where `product_id` = 1005 limit 1
        800μsthesagf1_secgracust
      • select * from `products` where `id` = 1005 and `products`.`deleted_at` is null limit 1
        2.09msthesagf1_secgracust
      • select * from `product_categories` where `product_categories`.`product_id` = 1005 and `product_categories`.`product_id` is not null
        630μsthesagf1_secgracust
      • select * from `product_images` where `product_id` = 1006 limit 1
        580μsthesagf1_secgracust
      • select * from `products` where `id` = 1006 and `products`.`deleted_at` is null limit 1
        680μsthesagf1_secgracust
      • select * from `product_categories` where `product_categories`.`product_id` = 1006 and `product_categories`.`product_id` is not null
        550μsthesagf1_secgracust
      • select * from `product_images` where `product_id` = 1007 limit 1
        630μsthesagf1_secgracust
      • select * from `products` where `id` = 1007 and `products`.`deleted_at` is null limit 1
        690μsthesagf1_secgracust
      • select * from `product_categories` where `product_categories`.`product_id` = 1007 and `product_categories`.`product_id` is not null
        510μsthesagf1_secgracust
      • select * from `product_images` where `product_id` = 1008 limit 1
        520μsthesagf1_secgracust
      • select * from `products` where `id` = 1008 and `products`.`deleted_at` is null limit 1
        630μsthesagf1_secgracust
      • select * from `product_categories` where `product_categories`.`product_id` = 1008 and `product_categories`.`product_id` is not null
        520μsthesagf1_secgracust
      • select * from `product_images` where `product_id` = 1009 limit 1
        510μsthesagf1_secgracust
      • select * from `products` where `id` = 1009 and `products`.`deleted_at` is null limit 1
        540μsthesagf1_secgracust
      • select * from `product_categories` where `product_categories`.`product_id` = 1009 and `product_categories`.`product_id` is not null
        490μsthesagf1_secgracust
      • select * from `product_images` where `product_id` = 1010 limit 1
        500μsthesagf1_secgracust
      • select * from `products` where `id` = 1010 and `products`.`deleted_at` is null limit 1
        550μsthesagf1_secgracust
      • select * from `product_categories` where `product_categories`.`product_id` = 1010 and `product_categories`.`product_id` is not null
        450μsthesagf1_secgracust
      • select * from `product_images` where `product_id` = 1011 limit 1
        500μsthesagf1_secgracust
      • select * from `products` where `id` = 1011 and `products`.`deleted_at` is null limit 1
        470μsthesagf1_secgracust
      • select * from `product_categories` where `product_categories`.`product_id` = 1011 and `product_categories`.`product_id` is not null
        380μsthesagf1_secgracust
      • select * from `product_images` where `product_id` = 1012 limit 1
        380μsthesagf1_secgracust
      • select * from `products` where `id` = 1012 and `products`.`deleted_at` is null limit 1
        430μsthesagf1_secgracust
      • select * from `product_categories` where `product_categories`.`product_id` = 1012 and `product_categories`.`product_id` is not null
        350μsthesagf1_secgracust
      • select * from `product_images` where `product_id` = 1013 limit 1
        330μsthesagf1_secgracust
      • select * from `products` where `id` = 1013 and `products`.`deleted_at` is null limit 1
        450μsthesagf1_secgracust
      • select * from `product_categories` where `product_categories`.`product_id` = 1013 and `product_categories`.`product_id` is not null
        350μsthesagf1_secgracust
      • select * from `product_images` where `product_id` = 1014 limit 1
        400μsthesagf1_secgracust
      • select * from `products` where `id` = 1014 and `products`.`deleted_at` is null limit 1
        490μsthesagf1_secgracust
      • select * from `product_categories` where `product_categories`.`product_id` = 1014 and `product_categories`.`product_id` is not null
        320μsthesagf1_secgracust
      • select * from `pages` where `status` = 1
        650μsthesagf1_secgracust
      • select * from `site_setting` limit 1
        690μsthesagf1_secgracust
      • select * from `pages` where `status` = 1
        1.03msthesagf1_secgracust
      • select * from `site_setting` limit 1
        780μsthesagf1_secgracust
      • select * from `pages` where `status` = 1
        1.14msthesagf1_secgracust
      • select * from `site_setting` limit 1
        840μsthesagf1_secgracust
      App\Models\Product
      44Product.php#?
      App\Models\ProductImage
      44ProductImage.php#?
      App\Models\ProductCategory
      44ProductCategory.php#?
      App\Models\Pages
      20Pages.php#?
      App\Models\SiteSetting
      5SiteSetting.php#?
      App\Models\Category
      2Category.php#?
      App\Models\Api\ProductFiles
      2ProductFiles.php#?
          _token
          pBy6wVxXB05es4BGS3GHiMx2bmKxqRCperTU1rl0
          _previous
          array:1 [ "url" => "https://securegrades.com/product/math-533-week-3-discussion-determining-a-norm...
          _flash
          array:2 [ "old" => [] "new" => [] ]
          PHPDEBUGBAR_STACK_DATA
          []
          telescope
          View in Telescope
          path_info
          /product/math-533-week-3-discussion-determining-a-normal-distribution-keller-1
          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:17 [ "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" ] "accept-encoding" => array:1 [ 0 => "gzip, deflate, br, zstd" ] "content-length" => array:1 [ 0 => "0" ] "host" => array:1 [ 0 => "securegrades.com" ] "pragma" => array:1 [ 0 => "no-cache" ] "user-agent" => array:1 [ 0 => "Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)" ] "cache-control" => array:1 [ 0 => "no-cache" ] "sec-ch-ua" => array:1 [ 0 => ""HeadlessChrome";v="129", "Not=A?Brand";v="8", "Chromium";v="129"" ] "sec-ch-ua-mobile" => array:1 [ 0 => "?0" ] "sec-ch-ua-platform" => array:1 [ 0 => ""Windows"" ] "upgrade-insecure-requests" => array:1 [ 0 => "1" ] "sec-fetch-site" => array:1 [ 0 => "none" ] "sec-fetch-mode" => array:1 [ 0 => "navigate" ] "sec-fetch-user" => array:1 [ 0 => "?1" ] "sec-fetch-dest" => array:1 [ 0 => "document" ] "priority" => array:1 [ 0 => "u=0, i" ] "x-https" => array:1 [ 0 => "1" ] ]
          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 => "Thu, 10 Apr 2025 08:44:44 GMT" ] "set-cookie" => array:2 [ 0 => "XSRF-TOKEN=eyJpdiI6IlNhL0xqbVlHYWdCV2c3ZXNzMFhLTVE9PSIsInZhbHVlIjoidjhUQ29TaTUyWmRxLzMxL3BHZzlVYnhLUlFVZmUxN2pHTi9XSEZIZkYvQjdCelFtWVQ4dTczR0YwbkVVSTJCcGlaRzdJRHllZFFCbEVhRGVHN25kOVlMYkpiTitRTDBhaU9UMWZKdC80cVB6aXFDR0Fabk5ES3RvdHdoNTFnWloiLCJtYWMiOiIwMmZkMWZjMzAzMzFlNTFkZjEzNzU1MGIxYTZhYTQzMTRkZWZjZGRlNjgzOGE1ZDUzM2Y1NTY3NjY1NzA1MDljIiwidGFnIjoiIn0%3D; expires=Thu, 10 Apr 2025 10:44:44 GMT; Max-Age=7200; path=/; secure; samesite=laxXSRF-TOKEN=eyJpdiI6IlNhL0xqbVlHYWdCV2c3ZXNzMFhLTVE9PSIsInZhbHVlIjoidjhUQ29TaTUyWmRxLzMxL3BHZzlVYnhLUlFVZmUxN2pHTi9XSEZIZkYvQjdCelFtWVQ4dTczR0YwbkVVSTJCcGlaRzdJR" 1 => "securegrades_session=eyJpdiI6IjArbEJEdm43NjltK1Z1Z244b0dBc2c9PSIsInZhbHVlIjoiK0Nxb08yY3pWeXNQRCtsUGs0aDlnL09mSGFGZGZjOGdwZlFYMXEvWi92dUF3SFhwck5ibWtWRi92QTRndTQra1R6SENNVjdZdkswcWxyOG0xVVllMW9jM2pRaTBRT3lqaDk5ZC9haHBsNE5sZnF2bzRlVU5QejhrZjlqZjlNMmsiLCJtYWMiOiJhNTE3NzY5YzVkYzhlZjAyZDMxNzkxZGM4YjgzYmM0NmMyNjRjNGY5ODhjMGEyZGU4NzY1ZDRkNzk2YjE2ZmRiIiwidGFnIjoiIn0%3D; expires=Thu, 10 Apr 2025 10:44:44 GMT; Max-Age=7200; path=/; httponly; samesite=laxsecuregrades_session=eyJpdiI6IjArbEJEdm43NjltK1Z1Z244b0dBc2c9PSIsInZhbHVlIjoiK0Nxb08yY3pWeXNQRCtsUGs0aDlnL09mSGFGZGZjOGdwZlFYMXEvWi92dUF3SFhwck5ibWtWRi92QTRndTQ" ] "Set-Cookie" => array:2 [ 0 => "XSRF-TOKEN=eyJpdiI6IlNhL0xqbVlHYWdCV2c3ZXNzMFhLTVE9PSIsInZhbHVlIjoidjhUQ29TaTUyWmRxLzMxL3BHZzlVYnhLUlFVZmUxN2pHTi9XSEZIZkYvQjdCelFtWVQ4dTczR0YwbkVVSTJCcGlaRzdJRHllZFFCbEVhRGVHN25kOVlMYkpiTitRTDBhaU9UMWZKdC80cVB6aXFDR0Fabk5ES3RvdHdoNTFnWloiLCJtYWMiOiIwMmZkMWZjMzAzMzFlNTFkZjEzNzU1MGIxYTZhYTQzMTRkZWZjZGRlNjgzOGE1ZDUzM2Y1NTY3NjY1NzA1MDljIiwidGFnIjoiIn0%3D; expires=Thu, 10-Apr-2025 10:44:44 GMT; path=/; secureXSRF-TOKEN=eyJpdiI6IlNhL0xqbVlHYWdCV2c3ZXNzMFhLTVE9PSIsInZhbHVlIjoidjhUQ29TaTUyWmRxLzMxL3BHZzlVYnhLUlFVZmUxN2pHTi9XSEZIZkYvQjdCelFtWVQ4dTczR0YwbkVVSTJCcGlaRzdJR" 1 => "securegrades_session=eyJpdiI6IjArbEJEdm43NjltK1Z1Z244b0dBc2c9PSIsInZhbHVlIjoiK0Nxb08yY3pWeXNQRCtsUGs0aDlnL09mSGFGZGZjOGdwZlFYMXEvWi92dUF3SFhwck5ibWtWRi92QTRndTQra1R6SENNVjdZdkswcWxyOG0xVVllMW9jM2pRaTBRT3lqaDk5ZC9haHBsNE5sZnF2bzRlVU5QejhrZjlqZjlNMmsiLCJtYWMiOiJhNTE3NzY5YzVkYzhlZjAyZDMxNzkxZGM4YjgzYmM0NmMyNjRjNGY5ODhjMGEyZGU4NzY1ZDRkNzk2YjE2ZmRiIiwidGFnIjoiIn0%3D; expires=Thu, 10-Apr-2025 10:44:44 GMT; path=/; httponlysecuregrades_session=eyJpdiI6IjArbEJEdm43NjltK1Z1Z244b0dBc2c9PSIsInZhbHVlIjoiK0Nxb08yY3pWeXNQRCtsUGs0aDlnL09mSGFGZGZjOGdwZlFYMXEvWi92dUF3SFhwck5ibWtWRi92QTRndTQ" ] ]
          session_attributes
          0 of 0
          array:4 [ "_token" => "pBy6wVxXB05es4BGS3GHiMx2bmKxqRCperTU1rl0" "_previous" => array:1 [ "url" => "https://securegrades.com/product/math-533-week-3-discussion-determining-a-normal-distribution-keller-1" ] "_flash" => array:2 [ "old" => [] "new" => [] ] "PHPDEBUGBAR_STACK_DATA" => [] ]
          ClearShow all
          Date ↕MethodURLData
          #12025-04-10 08:44:44GET/product/math-533-week-3-discussion-determining-a-normal-distribution-keller-14147161