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MATH 533 Week 3 Homework Problems.

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Contributor
Mike Mentzer
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Mathematices
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MATH 533 Applied Managerial Statistics
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DeVry
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5
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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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MATH 533 Week 7 Course Project, Final Part C; Regression and Correlation Analysis
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        • 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
        820μsthesagf1_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
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        770μsthesagf1_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
        730μsthesagf1_secgracustview.blade.php#278
        Bindings
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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` = 978 limit 1
        720μsthesagf1_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
        780μsthesagf1_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
        700μsthesagf1_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
        730μsthesagf1_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
        790μsthesagf1_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
        690μsthesagf1_secgracustview.blade.php#278
        Bindings
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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` = 980 limit 1
        750μsthesagf1_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
        610μsthesagf1_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
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        720μsthesagf1_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
        1.13msthesagf1_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
        940μsthesagf1_secgracustview.blade.php#278
        Bindings
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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` = 983 limit 1
        950μsthesagf1_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
        960μsthesagf1_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
        720μsthesagf1_secgracustview.blade.php#278
        Bindings
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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` = 984 limit 1
        830μsthesagf1_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
        1.04msthesagf1_secgracustview.blade.php#276
        Bindings
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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` = 984 and `product_categories`.`product_id` is not null
        800μsthesagf1_secgracustview.blade.php#278
        Bindings
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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` = 985 limit 1
        1.16msthesagf1_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
        1.05msthesagf1_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
        1.06msthesagf1_secgracustview.blade.php#278
        Bindings
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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` = 986 limit 1
        960μsthesagf1_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
        640μsthesagf1_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
        830μsthesagf1_secgracustview.blade.php#278
        Bindings
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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` = 987 limit 1
        980μsthesagf1_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
        1.16msthesagf1_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
        960μsthesagf1_secgracustview.blade.php#278
        Bindings
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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` = 988 limit 1
        990μsthesagf1_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
        1.26msthesagf1_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
        1.15msthesagf1_secgracustview.blade.php#278
        Bindings
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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` = 989 limit 1
        1.15msthesagf1_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
        1.17msthesagf1_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
        990μsthesagf1_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
        1.14msthesagf1_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
        900μsthesagf1_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
        800μsthesagf1_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
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        • 21. vendor/laravel/framework/src/Illuminate/View/View.php:207
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        • 20. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:72
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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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        Backtrace
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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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        Backtrace
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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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        • 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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        Backtrace
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        • 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
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        Backtrace
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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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        • 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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        Backtrace
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        • 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
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        Backtrace
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        • 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
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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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        Backtrace
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        • 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
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        Backtrace
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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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        • 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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        • 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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        Backtrace
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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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        • 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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        Backtrace
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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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        Backtrace
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        • 21. vendor/laravel/framework/src/Illuminate/View/View.php:207
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        • 25. vendor/laravel/framework/src/Illuminate/View/View.php:207
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        • 21. vendor/laravel/framework/src/Illuminate/View/View.php:207
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        Backtrace
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        • 25. vendor/laravel/framework/src/Illuminate/View/View.php:207
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        • 21. vendor/laravel/framework/src/Illuminate/View/View.php:207
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        • 21. vendor/laravel/framework/src/Illuminate/View/View.php:207
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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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        • 21. vendor/laravel/framework/src/Illuminate/View/View.php:207
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        Backtrace
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        • 20. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:72
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      App\Models\ProductImage
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