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MATH 533 Week 3 Homework Problems.

$20
Contributor
Mike Mentzer
Category
Mathematices
Course
MATH 533 Applied Managerial Statistics
Institute
DeVry
Pages
5

MATH 533 WEEK 3 HOMEWORK Scores on a certain exam are normally distributed with a mean of 90 and a variance of 25. What is the z-value for a score of 80? 1.0 -2.0 2.0 0.4 -0.4 Scores on a certain exam are normally distributed with a mean of 90 and a variance of 25. What is the probability of obtaining a score less than 80? 0.6554 0.3446 0.0228 0.9772 0.9982 Which one of the following is not a characteristic of a normal distribution? Continuous Symmetrical about its mean Discrete Unimodal If the z-value of a given x value is positive, it means that. Probability of getting a value below x is negative The x value is above the mean of the distribution The value of x is positive The standard deviation of the distribution is negative Assume a normal distribution and find the following probabilities. (Round the values of z to 2 decimal places. Round your answers to 4 decimal places.) (a) P(x < 24 | μ = 27 and σ = 3) ANS 0.1587 (b) P(x ≥ 45 | μ = 30 and σ =

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        • 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
        370μsthesagf1_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
        310μsthesagf1_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
        320μsthesagf1_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
        310μsthesagf1_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
        260μsthesagf1_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
        280μsthesagf1_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
        320μsthesagf1_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
        270μsthesagf1_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
        460μsthesagf1_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
        400μsthesagf1_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
        380μsthesagf1_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` = 983 limit 1
        310μsthesagf1_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
        320μsthesagf1_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
        270μsthesagf1_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
        330μsthesagf1_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
        300μsthesagf1_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
        270μsthesagf1_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
        250μsthesagf1_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
        360μsthesagf1_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
        360μsthesagf1_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
        270μsthesagf1_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
        310μsthesagf1_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
        230μsthesagf1_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
        320μsthesagf1_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
        320μsthesagf1_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
        250μsthesagf1_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
        260μsthesagf1_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
        280μsthesagf1_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
        250μsthesagf1_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
        250μsthesagf1_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
        290μsthesagf1_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
        270μsthesagf1_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
        260μsthesagf1_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
        310μsthesagf1_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
        260μsthesagf1_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
        250μsthesagf1_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
        340μsthesagf1_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
        250μsthesagf1_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
        250μsthesagf1_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
        310μsthesagf1_secgracustview.blade.php#276
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        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
        250μsthesagf1_secgracustview.blade.php#278
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        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` = 993 limit 1
        590μsthesagf1_secgracustview.blade.php#249
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        Backtrace
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        • 18. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
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        • 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` = 993 and `products`.`deleted_at` is null limit 1
        590μsthesagf1_secgracustview.blade.php#276
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        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` = 993 and `product_categories`.`product_id` is not null
        640μsthesagf1_secgracustview.blade.php#278
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        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
        670μsthesagf1_secgracustview.blade.php#249
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        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
        470μsthesagf1_secgracustview.blade.php#276
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        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
        380μsthesagf1_secgracustview.blade.php#278
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        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
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        360μsthesagf1_secgracustview.blade.php#249
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        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
        320μsthesagf1_secgracustview.blade.php#276
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        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
        270μsthesagf1_secgracustview.blade.php#278
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        Backtrace
        • 20. view::product.view:278
        • 22. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
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        • 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
        270μsthesagf1_secgracustview.blade.php#249
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        Backtrace
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        • 18. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
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        • 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
        380μsthesagf1_secgracustview.blade.php#276
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        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
        330μsthesagf1_secgracustview.blade.php#278
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        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
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        260μsthesagf1_secgracustview.blade.php#249
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        Backtrace
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        • 18. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
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        • 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
        400μsthesagf1_secgracustview.blade.php#276
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        Backtrace
        • 16. view::product.view:276
        • 18. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
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        • 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
        280μsthesagf1_secgracustview.blade.php#278
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        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
        290μsthesagf1_secgracustview.blade.php#249
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        Backtrace
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        • 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
        590μsthesagf1_secgracustview.blade.php#276
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        Backtrace
        • 16. view::product.view:276
        • 18. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
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        • 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
        380μsthesagf1_secgracustview.blade.php#278
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        Backtrace
        • 20. view::product.view:278
        • 22. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
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        • 24. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:72
        • 25. vendor/laravel/framework/src/Illuminate/View/View.php:207
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        390μsthesagf1_secgracustview.blade.php#249
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        Backtrace
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        • 18. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
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        • 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
        380μsthesagf1_secgracustview.blade.php#276
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        Backtrace
        • 16. view::product.view:276
        • 18. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
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        • 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
        380μsthesagf1_secgracustview.blade.php#278
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        Backtrace
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        • 22. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
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        • 24. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:72
        • 25. vendor/laravel/framework/src/Illuminate/View/View.php:207
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        380μsthesagf1_secgracustview.blade.php#249
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        Backtrace
        • 16. view::product.view:249
        • 18. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
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        • 20. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:72
        • 21. vendor/laravel/framework/src/Illuminate/View/View.php:207
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        440μsthesagf1_secgracustview.blade.php#276
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        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
        380μsthesagf1_secgracustview.blade.php#278
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        Backtrace
        • 20. view::product.view:278
        • 22. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
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        • 24. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:72
        • 25. vendor/laravel/framework/src/Illuminate/View/View.php:207
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        710μsthesagf1_secgracustview.blade.php#249
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        Backtrace
        • 16. view::product.view:249
        • 18. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
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        • 20. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:72
        • 21. vendor/laravel/framework/src/Illuminate/View/View.php:207
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        1.52msthesagf1_secgracust
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        1.24msthesagf1_secgracust
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        520μsthesagf1_secgracust
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        460μsthesagf1_secgracust
      • select * from `product_categories` where `product_categories`.`product_id` = 1002 and `product_categories`.`product_id` is not null
        470μsthesagf1_secgracust
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        470μsthesagf1_secgracust
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        670μsthesagf1_secgracust
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        410μsthesagf1_secgracust
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        360μsthesagf1_secgracust
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        1.85msthesagf1_secgracust
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        490μsthesagf1_secgracust
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        540μsthesagf1_secgracust
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        800μsthesagf1_secgracust
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        950μsthesagf1_secgracust
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        1.58msthesagf1_secgracust
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        450μsthesagf1_secgracust
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        1.02msthesagf1_secgracust
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        380μsthesagf1_secgracust
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        430μsthesagf1_secgracust
      • select * from `product_categories` where `product_categories`.`product_id` = 1008 and `product_categories`.`product_id` is not null
        350μsthesagf1_secgracust
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        270μsthesagf1_secgracust
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        320μsthesagf1_secgracust
      • select * from `product_categories` where `product_categories`.`product_id` = 1009 and `product_categories`.`product_id` is not null
        240μsthesagf1_secgracust
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        310μsthesagf1_secgracust
      • select * from `product_categories` where `product_categories`.`product_id` = 1010 and `product_categories`.`product_id` is not null
        320μsthesagf1_secgracust
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        310μsthesagf1_secgracust
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        270μsthesagf1_secgracust
      • select * from `product_categories` where `product_categories`.`product_id` = 1011 and `product_categories`.`product_id` is not null
        250μsthesagf1_secgracust
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      • select * from `product_categories` where `product_categories`.`product_id` = 1012 and `product_categories`.`product_id` is not null
        210μsthesagf1_secgracust
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        500μsthesagf1_secgracust
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        360μsthesagf1_secgracust
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        260μsthesagf1_secgracust
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        230μsthesagf1_secgracust
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        350μsthesagf1_secgracust
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        290μsthesagf1_secgracust
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        310μsthesagf1_secgracust
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        2.33msthesagf1_secgracust
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        2.34msthesagf1_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
          i31A0iuzXPHQYFXkTGBTnQ77dT8WeCGvv4l0zMjr
          _previous
          array:1 [ "url" => "https://securegrades.com/product/math-533-week-3-homework-problems" ]
          _flash
          array:2 [ "old" => [] "new" => [] ]
          PHPDEBUGBAR_STACK_DATA
          []
          telescope
          View in Telescope
          path_info
          /product/math-533-week-3-homework-problems
          status_code
          200
          
          status_text
          OK
          format
          html
          content_type
          text/html; charset=UTF-8
          request_query
          []
          
          request_request
          []
          
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