Question
The file Airlines.xls contains information on 3999 passengers who belong to an airline’s frequent flier program. For each passenger the data include information on their mileage history and on different ways they accrued or spent miles in the last year. The goal is to try to identify clusters of passengers that have similar characteristics for the purpose of targeting different segments for different types of mileage offers.
a) Apply hierarchical clustering with Euclidean distance and Ward’s method. Make sure to normalize the data first. How many clusters appear?
b) What would happen if the data were not normalized?
c) Compare the cluster centroids to characterize the different clusters, and try to give each cluster a label.
d) To check the stability of the clusters, remove 5% of the data, and repeat the analysis. Does the same picture emerge?
e) Use k-means clustering with the number of clusters that you found above. Does the same picture emerge?
f) Which clusters would you target for offers, and what types of offers would you target to customers in that cluster?
Solution Preview

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

library(readxl)
library(dplyr)

# (a)
airlines <- read_excel("Airlines.xlsx", sheet = 2)
row_labels <- airlines$`ID#`
airlines <- airlines[,-1]
airline_norm <- sapply(airlines, scale)
row.names(airline_norm) <- row_labels

distances <- dist(airline_norm, method="euclidean")
hc <- hclust(distances, method="ward.D")

plot(hc, cex = 0.6)
rect.hclust(hc, k = 5, border = 2:6)

# Five clusters appears

# (b)
# If data is not normalised the distance between observations may not correctly represents the cluster information. Nearby cluster may look to far or separated or comes to close. It is good to calculate the distance based on same scale.


# (c)
memb_single <- cutree(hc, k=5)
distances <- unlist(distances)
distances <- as.vector(distances)
group <- ifelse(memb_single
This is only a preview of the solution.
Please use the purchase button to see the entire solution.
By purchasing this solution you'll be able to access the following files:
Solution.R
Purchase Solution
$55.00 $27.5
Google Pay
Amazon
Paypal
Mastercard
Visacard
Discover
Amex
View Available Mathematics Tutors 529 tutors matched
Ionut
(ionut)
Hi! MSc Applied Informatics & Computer Science Engineer. Practical experience in many CS & IT branches.Research work & homework
5/5 (5,654+ sessions)
2 hours avg response
Leo
(Leo)
Hi! I have been a professor in New York and taught in a math department and in an applied math department.
4.9/5 (5,652+ sessions)
2 hours avg response
Pranay
(math1983)
Ph.D. in mathematics and working as an Assistant Professor in University. I can provide help in mathematics, statistics and allied areas.
4.6/5 (5,512+ sessions)
1 hour avg response

Similar Homework Solutions

8.1.0PHP Version487msRequest Duration45MBMemory UsageGET college-homework-library/{category}/{subject}/{id}Route
    • Booting (343ms)time
    • Application (144ms)time
    • 1 x Booting (70.52%)
      343ms
      1 x Application (29.48%)
      144ms
      • Illuminate\Routing\Events\Routing (659μs)
      • Illuminate\Routing\Events\RouteMatched (296μs)
      • Illuminate\Foundation\Events\LocaleUpdated (1.77ms)
      • eloquent.booting: App\Models\HomeworkLibrary\HomeworkLibrary (130μs)
      • eloquent.booted: App\Models\HomeworkLibrary\HomeworkLibrary (119μs)
      • Illuminate\Database\Events\ConnectionEstablished (570μs)
      • Illuminate\Database\Events\StatementPrepared (4.11ms)
      • Illuminate\Database\Events\QueryExecuted (1.11ms)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (97μs)
      • eloquent.booting: App\Models\Subject (57μs)
      • eloquent.booted: App\Models\Subject (40μs)
      • Illuminate\Database\Events\StatementPrepared (1.2ms)
      • Illuminate\Database\Events\QueryExecuted (816μs)
      • eloquent.retrieved: App\Models\Subject (93μs)
      • eloquent.booting: App\Models\HomeworkLibrary\HomeworkLibraryFile (95μs)
      • eloquent.booted: App\Models\HomeworkLibrary\HomeworkLibraryFile (46μs)
      • Illuminate\Database\Events\StatementPrepared (571μs)
      • Illuminate\Database\Events\QueryExecuted (2.13ms)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (76μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (15μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (8μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (6μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (5μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (5μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (5μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (5μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (5μs)
      • eloquent.booting: App\Models\SubjectCat (398μs)
      • eloquent.booted: App\Models\SubjectCat (48μs)
      • Illuminate\Database\Events\StatementPrepared (713μs)
      • Illuminate\Database\Events\QueryExecuted (954μs)
      • eloquent.retrieved: App\Models\SubjectCat (87μs)
      • Illuminate\Cache\Events\CacheHit (10.05ms)
      • Illuminate\Cache\Events\CacheMissed (713μs)
      • Illuminate\Database\Events\StatementPrepared (931μs)
      • Illuminate\Database\Events\QueryExecuted (13.08ms)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (78μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (16μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (8μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (7μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (7μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (5μs)
      • Illuminate\Database\Events\StatementPrepared (629μs)
      • Illuminate\Database\Events\QueryExecuted (985μs)
      • eloquent.retrieved: App\Models\Subject (90μs)
      • Illuminate\Cache\Events\KeyWritten (788μs)
      • Illuminate\Database\Events\StatementPrepared (1.59ms)
      • Illuminate\Database\Events\QueryExecuted (1.52ms)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (53μs)
      • Illuminate\Database\Events\StatementPrepared (861μs)
      • Illuminate\Database\Events\QueryExecuted (1.16ms)
      • Illuminate\Database\Events\StatementPrepared (717μs)
      • Illuminate\Database\Events\QueryExecuted (1.42ms)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (48μs)
      • Illuminate\Cache\Events\CacheHit (476μs)
      • creating: homework.show (281μs)
      • composing: homework.show (260μs)
      • creating: components.breadcrumbs (320μs)
      • composing: components.breadcrumbs (137μs)
      • Illuminate\Database\Events\StatementPrepared (1.37ms)
      • Illuminate\Database\Events\QueryExecuted (900μs)
      • eloquent.retrieved: App\Models\SubjectCat (98μs)
      • Illuminate\Cache\Events\CacheMissed (3.7ms)
      • Illuminate\Database\Events\StatementPrepared (674μs)
      • Illuminate\Database\Events\QueryExecuted (1.03ms)
      • eloquent.retrieved: App\Models\SubjectCat (89μs)
      • Illuminate\Cache\Events\KeyWritten (330μs)
      • Illuminate\Cache\Events\CacheHit (210μs)
      • Illuminate\Cache\Events\CacheHit (200μs)
      • Illuminate\Cache\Events\CacheHit (172μs)
      • Illuminate\Cache\Events\CacheHit (193μs)
      • Illuminate\Cache\Events\CacheHit (167μs)
      • Illuminate\Cache\Events\CacheHit (216μs)
      • Illuminate\Cache\Events\CacheHit (181μs)
      • Illuminate\Cache\Events\CacheHit (200μs)
      • Illuminate\Cache\Events\CacheHit (170μs)
      • Illuminate\Cache\Events\CacheHit (239μs)
      • Illuminate\Cache\Events\CacheHit (143μs)
      • Illuminate\Cache\Events\CacheHit (126μs)
      • Illuminate\Cache\Events\CacheHit (127μs)
      • Illuminate\Cache\Events\CacheMissed (183μs)
      • Illuminate\Database\Events\StatementPrepared (571μs)
      • Illuminate\Database\Events\QueryExecuted (1.06ms)
      • eloquent.retrieved: App\Models\SubjectCat (83μs)
      • Illuminate\Cache\Events\KeyWritten (1.09ms)
      • Illuminate\Cache\Events\CacheHit (244μs)
      • Illuminate\Cache\Events\CacheHit (282μs)
      • Illuminate\Cache\Events\CacheHit (205μs)
      • Illuminate\Cache\Events\CacheHit (199μs)
      • Illuminate\Cache\Events\CacheHit (189μs)
      • Illuminate\Cache\Events\CacheHit (245μs)
      • Illuminate\Cache\Events\CacheHit (174μs)
      • Illuminate\Cache\Events\CacheMissed (148μs)
      • Illuminate\Database\Events\StatementPrepared (656μs)
      • Illuminate\Database\Events\QueryExecuted (780μs)
      • eloquent.retrieved: App\Models\SubjectCat (60μs)
      • Illuminate\Cache\Events\KeyWritten (1.35ms)
      • Illuminate\Cache\Events\CacheHit (261μs)
      • Illuminate\Cache\Events\CacheHit (219μs)
      • Illuminate\Cache\Events\CacheHit (169μs)
      • Illuminate\Cache\Events\CacheHit (190μs)
      • Illuminate\Cache\Events\CacheHit (197μs)
      • Illuminate\Cache\Events\CacheHit (374μs)
      • Illuminate\Cache\Events\CacheHit (188μs)
      • Illuminate\Cache\Events\CacheHit (206μs)
      • Illuminate\Cache\Events\CacheHit (195μs)
      • Illuminate\Cache\Events\CacheHit (188μs)
      • Illuminate\Cache\Events\CacheHit (167μs)
      • Illuminate\Cache\Events\CacheHit (202μs)
      • Illuminate\Cache\Events\CacheHit (198μs)
      • Illuminate\Cache\Events\CacheHit (187μs)
      • Illuminate\Cache\Events\CacheHit (159μs)
      • Illuminate\Cache\Events\CacheHit (187μs)
      • Illuminate\Cache\Events\CacheHit (165μs)
      • Illuminate\Cache\Events\CacheHit (183μs)
      • Illuminate\Cache\Events\CacheHit (160μs)
      • Illuminate\Cache\Events\CacheHit (217μs)
      • Illuminate\Cache\Events\CacheHit (166μs)
      • Illuminate\Cache\Events\CacheHit (209μs)
      • Illuminate\Cache\Events\CacheHit (187μs)
      • Illuminate\Cache\Events\CacheHit (185μs)
      • Illuminate\Cache\Events\CacheHit (161μs)
      • Illuminate\Cache\Events\CacheHit (199μs)
      • Illuminate\Cache\Events\CacheHit (205μs)
      • Illuminate\Cache\Events\CacheHit (197μs)
      • Illuminate\Cache\Events\CacheHit (183μs)
      • Illuminate\Cache\Events\CacheHit (193μs)
      • Illuminate\Cache\Events\CacheHit (178μs)
      • Illuminate\Cache\Events\CacheMissed (190μs)
      • Illuminate\Database\Events\StatementPrepared (836μs)
      • Illuminate\Database\Events\QueryExecuted (923μs)
      • eloquent.retrieved: App\Models\SubjectCat (83μs)
      • Illuminate\Cache\Events\KeyWritten (1.6ms)
      • Illuminate\Cache\Events\CacheHit (250μs)
      • Illuminate\Cache\Events\CacheHit (180μs)
      • Illuminate\Cache\Events\CacheHit (124μs)
      • Illuminate\Cache\Events\CacheHit (147μs)
      • Illuminate\Cache\Events\CacheHit (185μs)
      • Illuminate\Cache\Events\CacheHit (259μs)
      • Illuminate\Cache\Events\CacheHit (126μs)
      • Illuminate\Cache\Events\CacheHit (164μs)
      • Illuminate\Cache\Events\CacheHit (125μs)
      • Illuminate\Cache\Events\CacheHit (145μs)
      • Illuminate\Cache\Events\CacheHit (124μs)
      • Illuminate\Cache\Events\CacheHit (154μs)
      • Illuminate\Cache\Events\CacheHit (125μs)
      • Illuminate\Cache\Events\CacheHit (190μs)
      • Illuminate\Cache\Events\CacheHit (126μs)
      • Illuminate\Cache\Events\CacheHit (134μs)
      • Illuminate\Cache\Events\CacheHit (113μs)
      • Illuminate\Cache\Events\CacheHit (127μs)
      • Illuminate\Cache\Events\CacheHit (118μs)
      • Illuminate\Cache\Events\CacheHit (132μs)
      • Illuminate\Cache\Events\CacheHit (116μs)
      • Illuminate\Cache\Events\CacheHit (135μs)
      • Illuminate\Cache\Events\CacheHit (130μs)
      • Illuminate\Cache\Events\CacheHit (243μs)
      • Illuminate\Cache\Events\CacheHit (173μs)
      • Illuminate\Cache\Events\CacheHit (140μs)
      • Illuminate\Cache\Events\CacheHit (119μs)
      • Illuminate\Cache\Events\CacheHit (139μs)
      • Illuminate\Cache\Events\CacheHit (132μs)
      • Illuminate\Cache\Events\CacheHit (138μs)
      • Illuminate\Cache\Events\CacheHit (112μs)
      • Illuminate\Cache\Events\CacheHit (129μs)
      • Illuminate\Cache\Events\CacheHit (113μs)
      • Illuminate\Cache\Events\CacheHit (136μs)
      • Illuminate\Cache\Events\CacheHit (108μs)
      • Illuminate\Cache\Events\CacheHit (133μs)
      • Illuminate\Cache\Events\CacheHit (105μs)
      • Illuminate\Cache\Events\CacheHit (134μs)
      • Illuminate\Cache\Events\CacheHit (129μs)
      • Illuminate\Cache\Events\CacheMissed (149μs)
      • Illuminate\Database\Events\StatementPrepared (598μs)
      • Illuminate\Database\Events\QueryExecuted (752μs)
      • eloquent.retrieved: App\Models\SubjectCat (66μs)
      • Illuminate\Cache\Events\KeyWritten (1.32ms)
      • Illuminate\Cache\Events\CacheHit (217μs)
      • Illuminate\Cache\Events\CacheHit (159μs)
      • Illuminate\Cache\Events\CacheHit (119μs)
      • Illuminate\Cache\Events\CacheHit (129μs)
      • Illuminate\Cache\Events\CacheHit (107μs)
      • Illuminate\Cache\Events\CacheHit (128μs)
      • Illuminate\Cache\Events\CacheHit (136μs)
      • Illuminate\Cache\Events\CacheMissed (156μs)
      • Illuminate\Database\Events\StatementPrepared (669μs)
      • Illuminate\Database\Events\QueryExecuted (1.16ms)
      • eloquent.retrieved: App\Models\SubjectCat (440μs)
      • Illuminate\Cache\Events\KeyWritten (445μs)
      • Illuminate\Cache\Events\CacheHit (1.4ms)
      • Illuminate\Cache\Events\CacheHit (233μs)
      • Illuminate\Cache\Events\CacheHit (143μs)
      • Illuminate\Cache\Events\CacheHit (204μs)
      • Illuminate\Cache\Events\CacheHit (127μs)
      • Illuminate\Cache\Events\CacheHit (139μs)
      • Illuminate\Cache\Events\CacheHit (178μs)
      • Illuminate\Cache\Events\CacheHit (158μs)
      • Illuminate\Cache\Events\CacheHit (107μs)
      • Illuminate\Cache\Events\CacheHit (132μs)
      • Illuminate\Cache\Events\CacheHit (112μs)
      • Illuminate\Cache\Events\CacheHit (834μs)
      • Illuminate\Cache\Events\CacheHit (121μs)
      • Illuminate\Cache\Events\CacheHit (135μs)
      • Illuminate\Cache\Events\CacheHit (116μs)
      • Illuminate\Cache\Events\CacheHit (122μs)
      • Illuminate\Cache\Events\CacheHit (112μs)
      • Illuminate\Cache\Events\CacheHit (120μs)
      • Illuminate\Cache\Events\CacheHit (100μs)
      • Illuminate\Cache\Events\CacheHit (116μs)
      • Illuminate\Cache\Events\CacheHit (105μs)
      • Illuminate\Cache\Events\CacheHit (119μs)
      • Illuminate\Cache\Events\CacheHit (102μs)
      • Illuminate\Cache\Events\CacheHit (128μs)
      • Illuminate\Cache\Events\CacheHit (127μs)
      • Illuminate\Cache\Events\CacheHit (124μs)
      • Illuminate\Cache\Events\CacheHit (108μs)
      • Illuminate\Cache\Events\CacheHit (148μs)
      • Illuminate\Cache\Events\CacheHit (122μs)
      • Illuminate\Cache\Events\CacheMissed (2.41ms)
      • Illuminate\Database\Events\StatementPrepared (692μs)
      • Illuminate\Database\Events\QueryExecuted (978μs)
      • eloquent.retrieved: App\Models\SubjectCat (82μs)
      • Illuminate\Cache\Events\KeyWritten (274μs)
      • Illuminate\Cache\Events\CacheHit (191μs)
      • Illuminate\Cache\Events\CacheHit (155μs)
      • Illuminate\Cache\Events\CacheHit (115μs)
      • Illuminate\Cache\Events\CacheHit (129μs)
      • Illuminate\Cache\Events\CacheHit (853μs)
      • Illuminate\Cache\Events\CacheHit (263μs)
      • Illuminate\Cache\Events\CacheHit (126μs)
      • Illuminate\Cache\Events\CacheHit (152μs)
      • Illuminate\Cache\Events\CacheHit (108μs)
      • Illuminate\Cache\Events\CacheHit (147μs)
      • Illuminate\Cache\Events\CacheHit (117μs)
      • Illuminate\Cache\Events\CacheHit (125μs)
      • Illuminate\Cache\Events\CacheHit (102μs)
      • Illuminate\Cache\Events\CacheHit (118μs)
      • Illuminate\Cache\Events\CacheHit (104μs)
      • Illuminate\Cache\Events\CacheHit (119μs)
      • Illuminate\Cache\Events\CacheHit (101μs)
      • Illuminate\Cache\Events\CacheHit (118μs)
      • Illuminate\Cache\Events\CacheHit (102μs)
      • Illuminate\Cache\Events\CacheHit (119μs)
      • Illuminate\Cache\Events\CacheHit (103μs)
      • Illuminate\Cache\Events\CacheHit (167μs)
      • Illuminate\Cache\Events\CacheHit (120μs)
      • Illuminate\Cache\Events\CacheHit (119μs)
      • Illuminate\Cache\Events\CacheHit (100μs)
      • Illuminate\Cache\Events\CacheHit (116μs)
      • Illuminate\Cache\Events\CacheHit (98μs)
      • Illuminate\Cache\Events\CacheHit (113μs)
      • Illuminate\Cache\Events\CacheHit (97μs)
      • Illuminate\Cache\Events\CacheHit (146μs)
      • Illuminate\Cache\Events\CacheHit (112μs)
      • Illuminate\Cache\Events\CacheHit (143μs)
      • Illuminate\Cache\Events\CacheHit (115μs)
      • Illuminate\Cache\Events\CacheHit (405μs)
      • Illuminate\Cache\Events\CacheHit (156μs)
      • Illuminate\Cache\Events\CacheHit (125μs)
      • Illuminate\Cache\Events\CacheHit (100μs)
      • Illuminate\Cache\Events\CacheHit (116μs)
      • Illuminate\Cache\Events\CacheHit (119μs)
      • Illuminate\Cache\Events\CacheHit (133μs)
      • Illuminate\Cache\Events\CacheHit (103μs)
      • Illuminate\Cache\Events\CacheHit (129μs)
      • Illuminate\Cache\Events\CacheHit (123μs)
      • Illuminate\Cache\Events\CacheHit (140μs)
      • Illuminate\Cache\Events\CacheHit (106μs)
      • Illuminate\Cache\Events\CacheHit (126μs)
      • Illuminate\Cache\Events\CacheHit (102μs)
      • Illuminate\Cache\Events\CacheHit (121μs)
      • Illuminate\Cache\Events\CacheHit (107μs)
      • Illuminate\Cache\Events\CacheHit (166μs)
      • Illuminate\Cache\Events\CacheHit (146μs)
      • Illuminate\Cache\Events\CacheHit (223μs)
      • Illuminate\Cache\Events\CacheHit (185μs)
      • Illuminate\Cache\Events\CacheHit (150μs)
      • Illuminate\Cache\Events\CacheHit (105μs)
      • Illuminate\Cache\Events\CacheHit (181μs)
      • Illuminate\Cache\Events\CacheHit (142μs)
      • Illuminate\Cache\Events\CacheHit (130μs)
      • Illuminate\Cache\Events\CacheHit (98μs)
      • Illuminate\Cache\Events\CacheHit (111μs)
      • Illuminate\Cache\Events\CacheHit (96μs)
      • Illuminate\Cache\Events\CacheHit (131μs)
      • Illuminate\Cache\Events\CacheHit (144μs)
      • Illuminate\Cache\Events\CacheHit (272μs)
      • Illuminate\Cache\Events\CacheHit (126μs)
      • Illuminate\Cache\Events\CacheHit (141μs)
      • Illuminate\Cache\Events\CacheHit (104μs)
      • Illuminate\Cache\Events\CacheHit (134μs)
      • Illuminate\Cache\Events\CacheHit (108μs)
      • Illuminate\Cache\Events\CacheHit (123μs)
      • Illuminate\Cache\Events\CacheHit (97μs)
      • Illuminate\Cache\Events\CacheHit (112μs)
      • Illuminate\Cache\Events\CacheHit (123μs)
      • Illuminate\Cache\Events\CacheHit (122μs)
      • Illuminate\Cache\Events\CacheHit (98μs)
      • Illuminate\Cache\Events\CacheHit (113μs)
      • Illuminate\Cache\Events\CacheHit (100μs)
      • Illuminate\Cache\Events\CacheHit (115μs)
      • Illuminate\Cache\Events\CacheHit (99μs)
      • Illuminate\Cache\Events\CacheHit (127μs)
      • Illuminate\Cache\Events\CacheHit (104μs)
      • Illuminate\Cache\Events\CacheHit (889μs)
      • Illuminate\Cache\Events\CacheHit (118μs)
      • Illuminate\Cache\Events\CacheHit (122μs)
      • Illuminate\Cache\Events\CacheHit (103μs)
      • Illuminate\Cache\Events\CacheHit (118μs)
      • Illuminate\Cache\Events\CacheHit (102μs)
      • Illuminate\Cache\Events\CacheHit (120μs)
      • Illuminate\Cache\Events\CacheHit (684μs)
      • Illuminate\Cache\Events\CacheHit (188μs)
      • Illuminate\Cache\Events\CacheHit (109μs)
      • Illuminate\Cache\Events\CacheHit (516μs)
      • Illuminate\Cache\Events\CacheHit (136μs)
      • Illuminate\Cache\Events\CacheHit (124μs)
      • Illuminate\Cache\Events\CacheHit (100μs)
      • Illuminate\Cache\Events\CacheHit (116μs)
      • Illuminate\Cache\Events\CacheHit (97μs)
      • Illuminate\Cache\Events\CacheHit (114μs)
      • Illuminate\Cache\Events\CacheHit (97μs)
      • Illuminate\Cache\Events\CacheHit (139μs)
      • Illuminate\Cache\Events\CacheHit (109μs)
      • Illuminate\Cache\Events\CacheHit (172μs)
      • Illuminate\Cache\Events\CacheHit (112μs)
      • Illuminate\Cache\Events\CacheHit (120μs)
      • Illuminate\Cache\Events\CacheHit (99μs)
      • Illuminate\Cache\Events\CacheHit (115μs)
      • Illuminate\Cache\Events\CacheHit (114μs)
      • Illuminate\Cache\Events\CacheHit (137μs)
      • Illuminate\Cache\Events\CacheHit (103μs)
      • Illuminate\Cache\Events\CacheHit (130μs)
      • Illuminate\Cache\Events\CacheHit (107μs)
      • Illuminate\Cache\Events\CacheHit (119μs)
      • Illuminate\Cache\Events\CacheHit (106μs)
      • Illuminate\Cache\Events\CacheHit (210μs)
      • Illuminate\Cache\Events\CacheHit (124μs)
      • Illuminate\Cache\Events\CacheHit (122μs)
      • Illuminate\Cache\Events\CacheHit (103μs)
      • Illuminate\Cache\Events\CacheHit (118μs)
      • Illuminate\Cache\Events\CacheHit (103μs)
      • Illuminate\Cache\Events\CacheHit (132μs)
      • Illuminate\Cache\Events\CacheHit (108μs)
      • Illuminate\Cache\Events\CacheHit (127μs)
      • Illuminate\Cache\Events\CacheHit (138μs)
      • Illuminate\Cache\Events\CacheHit (130μs)
      • Illuminate\Cache\Events\CacheHit (107μs)
      • Illuminate\Cache\Events\CacheHit (126μs)
      • Illuminate\Cache\Events\CacheHit (106μs)
      • Illuminate\Cache\Events\CacheHit (121μs)
      • Illuminate\Cache\Events\CacheHit (102μs)
      • Illuminate\Cache\Events\CacheHit (122μs)
      • Illuminate\Cache\Events\CacheHit (105μs)
      • Illuminate\Cache\Events\CacheHit (124μs)
      • Illuminate\Cache\Events\CacheHit (106μs)
      • Illuminate\Cache\Events\CacheHit (151μs)
      • Illuminate\Cache\Events\CacheHit (172μs)
      • Illuminate\Cache\Events\CacheHit (149μs)
      • Illuminate\Cache\Events\CacheHit (110μs)
      • Illuminate\Cache\Events\CacheHit (126μs)
      • Illuminate\Cache\Events\CacheHit (491μs)
      • Illuminate\Cache\Events\CacheHit (192μs)
      • Illuminate\Cache\Events\CacheHit (112μs)
      • Illuminate\Cache\Events\CacheHit (131μs)
      • Illuminate\Cache\Events\CacheHit (155μs)
      • Illuminate\Cache\Events\CacheHit (137μs)
      • Illuminate\Cache\Events\CacheHit (118μs)
      • Illuminate\Cache\Events\CacheHit (119μs)
      • Illuminate\Cache\Events\CacheHit (102μs)
      • Illuminate\Cache\Events\CacheHit (123μs)
      • Illuminate\Cache\Events\CacheHit (103μs)
      • Illuminate\Cache\Events\CacheHit (130μs)
      • Illuminate\Cache\Events\CacheHit (108μs)
      • Illuminate\Cache\Events\CacheHit (147μs)
      • Illuminate\Cache\Events\CacheHit (104μs)
      • Illuminate\Cache\Events\CacheMissed (182μs)
      • Illuminate\Database\Events\StatementPrepared (742μs)
      • Illuminate\Database\Events\QueryExecuted (1.03ms)
      • eloquent.retrieved: App\Models\SubjectCat (84μs)
      • Illuminate\Cache\Events\KeyWritten (307μs)
      • Illuminate\Cache\Events\CacheHit (198μs)
      • Illuminate\Cache\Events\CacheHit (343μs)
      • Illuminate\Cache\Events\CacheHit (145μs)
      • Illuminate\Cache\Events\CacheHit (131μs)
      • Illuminate\Cache\Events\CacheHit (104μs)
      • Illuminate\Cache\Events\CacheHit (153μs)
      • Illuminate\Cache\Events\CacheHit (108μs)
      • Illuminate\Cache\Events\CacheHit (133μs)
      • Illuminate\Cache\Events\CacheHit (105μs)
      • Illuminate\Cache\Events\CacheHit (121μs)
      • Illuminate\Cache\Events\CacheHit (100μs)
      • Illuminate\Cache\Events\CacheHit (128μs)
      • Illuminate\Cache\Events\CacheHit (111μs)
      • Illuminate\Cache\Events\CacheHit (124μs)
      • Illuminate\Cache\Events\CacheHit (104μs)
      • Illuminate\Cache\Events\CacheHit (119μs)
      • Illuminate\Cache\Events\CacheHit (109μs)
      • creating: site.layouts.app (563μs)
      • composing: site.layouts.app (19μs)
      • creating: components.canonical (440μs)
      • composing: components.canonical (79μs)
      • creating: components.open-graph (139μs)
      • composing: components.open-graph (51μs)
      • creating: site.headers.header (216μs)
      • composing: site.headers.header (49μs)
      • Illuminate\Cache\Events\CacheHit (1.31ms)
      • creating: components.footer (72μs)
      • composing: components.footer (76μs)
      • Illuminate\Cache\Events\CacheHit (627μs)
      • Illuminate\Cache\Events\CacheMissed (268μs)
      • Illuminate\Database\Events\StatementPrepared (956μs)
      • Illuminate\Database\Events\QueryExecuted (954μs)
      • eloquent.retrieved: App\Models\SubjectCat (76μs)
      • Illuminate\Cache\Events\KeyWritten (472μs)
      • Illuminate\Cache\Events\CacheHit (258μs)
      • Illuminate\Cache\Events\CacheHit (144μs)
      • Illuminate\Cache\Events\CacheHit (124μs)
      • Illuminate\Cache\Events\CacheHit (116μs)
      • Illuminate\Cache\Events\CacheHit (115μs)
      • Illuminate\Cache\Events\CacheHit (192μs)
      • Illuminate\Cache\Events\CacheHit (249μs)
      • Illuminate\Cache\Events\CacheHit (137μs)
      • Illuminate\Cache\Events\CacheHit (126μs)
      • Illuminate\Cache\Events\CacheHit (115μs)
      • Illuminate\Cache\Events\CacheHit (119μs)
      • Illuminate\Cache\Events\CacheHit (114μs)
      • creating: components.forms.contact-us (217μs)
      • composing: components.forms.contact-us (124μs)
      • creating: components.forms.get-started (185μs)
      • composing: components.forms.get-started (52μs)
      • creating: components.forms.free-tool-download (92μs)
      • composing: components.forms.free-tool-download (45μs)
      • creating: components.forms.claim-free-worksheet (84μs)
      • composing: components.forms.claim-free-worksheet (42μs)
      • creating: components.forms.tutor-subscription-waitlist (82μs)
      • composing: components.forms.tutor-subscription-waitlist (39μs)
      • creating: components.forms.tutor-subscription-join (83μs)
      • composing: components.forms.tutor-subscription-join (39μs)
      • creating: components.forms.tutor-support (85μs)
      • composing: components.forms.tutor-support (40μs)
      • 312 x Illuminate\Cache\Events\CacheHit (12.58%)
        61.26ms
        19 x Illuminate\Database\Events\QueryExecuted (6.73%)
        32.75ms
        19 x Illuminate\Database\Events\StatementPrepared (3.92%)
        19.09ms
        10 x Illuminate\Cache\Events\CacheMissed (1.66%)
        8.10ms
        10 x Illuminate\Cache\Events\KeyWritten (1.64%)
        7.97ms
        1 x Illuminate\Foundation\Events\LocaleUpdated (0.36%)
        1.77ms
        11 x eloquent.retrieved: App\Models\SubjectCat (0.26%)
        1.25ms
        1 x Illuminate\Routing\Events\Routing (0.14%)
        659μs
        1 x Illuminate\Database\Events\ConnectionEstablished (0.12%)
        570μs
        1 x creating: site.layouts.app (0.12%)
        563μs
        1 x creating: components.canonical (0.09%)
        440μs
        1 x eloquent.booting: App\Models\SubjectCat (0.08%)
        398μs
        1 x creating: components.breadcrumbs (0.07%)
        320μs
        1 x Illuminate\Routing\Events\RouteMatched (0.06%)
        296μs
        1 x creating: homework.show (0.06%)
        281μs
        1 x composing: homework.show (0.05%)
        260μs
        11 x eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (0.05%)
        231μs
        7 x eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (0.04%)
        218μs
        1 x creating: components.forms.contact-us (0.04%)
        217μs
        1 x creating: site.headers.header (0.04%)
        216μs
        1 x creating: components.forms.get-started (0.04%)
        185μs
        2 x eloquent.retrieved: App\Models\Subject (0.04%)
        183μs
        1 x creating: components.open-graph (0.03%)
        139μs
        1 x composing: components.breadcrumbs (0.03%)
        137μs
        1 x eloquent.booting: App\Models\HomeworkLibrary\HomeworkLibrary (0.03%)
        130μs
        1 x composing: components.forms.contact-us (0.03%)
        124μs
        1 x eloquent.booted: App\Models\HomeworkLibrary\HomeworkLibrary (0.02%)
        119μs
        1 x eloquent.booting: App\Models\HomeworkLibrary\HomeworkLibraryFile (0.02%)
        95μs
        1 x creating: components.forms.free-tool-download (0.02%)
        92μs
        1 x creating: components.forms.tutor-support (0.02%)
        85μs
        1 x creating: components.forms.claim-free-worksheet (0.02%)
        84μs
        1 x creating: components.forms.tutor-subscription-join (0.02%)
        83μs
        1 x creating: components.forms.tutor-subscription-waitlist (0.02%)
        82μs
        1 x composing: components.canonical (0.02%)
        79μs
        1 x composing: components.footer (0.02%)
        76μs
        1 x creating: components.footer (0.01%)
        72μs
        1 x eloquent.booting: App\Models\Subject (0.01%)
        57μs
        1 x composing: components.forms.get-started (0.01%)
        52μs
        1 x composing: components.open-graph (0.01%)
        51μs
        1 x composing: site.headers.header (0.01%)
        49μs
        1 x eloquent.booted: App\Models\SubjectCat (0.01%)
        48μs
        1 x eloquent.booted: App\Models\HomeworkLibrary\HomeworkLibraryFile (0.01%)
        46μs
        1 x composing: components.forms.free-tool-download (0.01%)
        45μs
        1 x composing: components.forms.claim-free-worksheet (0.01%)
        42μs
        1 x eloquent.booted: App\Models\Subject (0.01%)
        40μs
        1 x composing: components.forms.tutor-support (0.01%)
        40μs
        1 x composing: components.forms.tutor-subscription-waitlist (0.01%)
        39μs
        1 x composing: components.forms.tutor-subscription-join (0.01%)
        39μs
        1 x composing: site.layouts.app (0%)
        19μs
      14 templates were rendered
      • 1x homework.showshow.blade.phpblade
      • 1x components.breadcrumbsbreadcrumbs.blade.phpblade
      • 1x site.layouts.appapp.blade.phpblade
      • 1x components.canonicalcanonical.blade.phpblade
      • 1x components.open-graphopen-graph.blade.phpblade
      • 1x site.headers.headerheader.blade.phpblade
      • 1x components.footerfooter.blade.phpblade
      • 1x components.forms.contact-uscontact-us.blade.phpblade
      • 1x components.forms.get-startedget-started.blade.phpblade
      • 1x components.forms.free-tool-downloadfree-tool-download.blade.phpblade
      • 1x components.forms.claim-free-worksheetclaim-free-worksheet.blade.phpblade
      • 1x components.forms.tutor-subscription-waitlisttutor-subscription-waitlist.blade.phpblade
      • 1x components.forms.tutor-subscription-jointutor-subscription-join.blade.phpblade
      • 1x components.forms.tutor-supporttutor-support.blade.phpblade
      uri
      GET college-homework-library/{category}/{subject}/{id}
      middleware
      web, utm.parameters
      controller
      App\Http\Controllers\HomeworkLibraryController@show
      namespace
      where
      as
      homework.show
      file
      app/Http/Controllers/HomeworkLibraryController.php:79-176
      19 statements were executed, 5 of which were duplicates, 14 unique. Show only duplicated37.88ms
      • Connection Establishedtwenty4_siteHomeworkLibraryController.php#91
        Backtrace
        • 13. app/Http/Controllers/HomeworkLibraryController.php:91
        • 14. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 15. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 16. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
        • 17. vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
      • select * from `solutionslibrary` where `status` = 'published' and `price` > 0 and `solutionslibrary`.`id` = '50773' limit 1
        4.58mstwenty4_siteHomeworkLibraryController.php#97
        Bindings
        • 0: published
        • 1: 0
        • 2: 50773
        Backtrace
        • 16. app/Http/Controllers/HomeworkLibraryController.php:97
        • 17. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 18. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 19. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
        • 20. vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
      • select * from `subjects` where `subjects`.`id` in (299)
        980μstwenty4_siteHomeworkLibraryController.php#97
        Backtrace
        • 21. app/Http/Controllers/HomeworkLibraryController.php:97
        • 22. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 23. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 24. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
        • 25. vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
      • select * from `solutionslibrary_files` where `solutionslibrary_files`.`solutionlib_id` in (50773)
        2.23mstwenty4_siteHomeworkLibraryController.php#97
        Backtrace
        • 21. app/Http/Controllers/HomeworkLibraryController.php:97
        • 22. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 23. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 24. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
        • 25. vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
      • select * from `subject_cats` where `subject_cats`.`id` = 1 limit 1
        1mstwenty4_siteHomeworkLibrary.php#201
        Bindings
        • 0: 1
        Backtrace
        • 20. app/Models/HomeworkLibrary/HomeworkLibrary.php:201
        • 26. app/Http/Controllers/HomeworkLibraryController.php:105
        • 27. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 28. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 29. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
      • select * from `solutionslibrary` where `id` <> 50773 and `subject` = 299 and `status` = 'published' and `price` > 0 order by RAND() limit 6
        13.31mstwenty4_siteHomeworkLibraryRepository.php#30
        Bindings
        • 0: 50773
        • 1: 299
        • 2: published
        • 3: 0
        Backtrace
        • 14. app/Repositories/HomeworkLibraryRepository.php:30
        • 15. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 16. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 18. app/Repositories/HomeworkLibraryRepository.php:39
        • 19. app/Http/Controllers/HomeworkLibraryController.php:139
      • select * from `subjects` where `subjects`.`id` in (299)
        1.04mstwenty4_siteHomeworkLibraryRepository.php#30
        Backtrace
        • 19. app/Repositories/HomeworkLibraryRepository.php:30
        • 20. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 21. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 23. app/Repositories/HomeworkLibraryRepository.php:39
        • 24. app/Http/Controllers/HomeworkLibraryController.php:139
      • select * from `solutionslibrary_files` where `solutionslibrary_files`.`solutionlib_id` = 50773 and `solutionslibrary_files`.`solutionlib_id` is not null and `publish` = 'question' order by `order` asc, `id` asc
        1.28mstwenty4_siteHomeworkLibrary.php#260
        Bindings
        • 0: 50773
        • 1: question
        Backtrace
        • 15. app/Models/HomeworkLibrary/HomeworkLibrary.php:260
        • 16. app/Transformers/HomeworkLibrary/HomeworkLibraryTransformer.php:58
        • 19. vendor/league/fractal/src/TransformerAbstract.php:128
        • 20. vendor/league/fractal/src/TransformerAbstract.php:107
        • 21. vendor/league/fractal/src/Scope.php:383
      • select * from `solutionslibrary_files` where `solutionslibrary_files`.`solutionlib_id` = 50773 and `solutionslibrary_files`.`solutionlib_id` is not null and `publish` = 'teaser' order by `order` asc, `id` asc
        1.12mstwenty4_siteHomeworkLibrary.php#260
        Bindings
        • 0: 50773
        • 1: teaser
        Backtrace
        • 15. app/Models/HomeworkLibrary/HomeworkLibrary.php:260
        • 16. app/Transformers/HomeworkLibrary/HomeworkLibraryTransformer.php:69
        • 19. vendor/league/fractal/src/TransformerAbstract.php:128
        • 20. vendor/league/fractal/src/TransformerAbstract.php:107
        • 21. vendor/league/fractal/src/Scope.php:383
      • select * from `solutionslibrary_files` where `solutionslibrary_files`.`solutionlib_id` = 50773 and `solutionslibrary_files`.`solutionlib_id` is not null and `publish` = 'solution' order by `order` asc, `id` asc
        1.3mstwenty4_siteHomeworkLibrary.php#260
        Bindings
        • 0: 50773
        • 1: solution
        Backtrace
        • 15. app/Models/HomeworkLibrary/HomeworkLibrary.php:260
        • 16. app/Transformers/HomeworkLibrary/HomeworkLibraryTransformer.php:80
        • 19. vendor/league/fractal/src/TransformerAbstract.php:128
        • 20. vendor/league/fractal/src/TransformerAbstract.php:107
        • 21. vendor/league/fractal/src/Scope.php:383
      • select * from `subject_cats` where `subject_cats`.`id` = 1 limit 1
        1.05mstwenty4_siteHomeworkLibrary.php#201
        Bindings
        • 0: 1
        Backtrace
        • 20. app/Models/HomeworkLibrary/HomeworkLibrary.php:201
        • 32. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 33. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 34. vendor/livewire/livewire/src/ComponentConcerns/RendersLivewireComponents.php:69
        • 35. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:70
      • select * from `subject_cats` where `subject_cats`.`id` = 1 limit 1
        1.02mstwenty4_siteSubject.php#100
        Bindings
        • 0: 1
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 3 limit 1
        1.13mstwenty4_siteSubject.php#100
        Bindings
        • 0: 3
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 4 limit 1
        870μstwenty4_siteSubject.php#100
        Bindings
        • 0: 4
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 10 limit 1
        1.27mstwenty4_siteSubject.php#100
        Bindings
        • 0: 10
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 33 limit 1
        930μstwenty4_siteSubject.php#100
        Bindings
        • 0: 33
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 11 limit 1
        1.26mstwenty4_siteSubject.php#100
        Bindings
        • 0: 11
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 5 limit 1
        1.03mstwenty4_siteSubject.php#100
        Bindings
        • 0: 5
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 31 limit 1
        1.13mstwenty4_siteSubject.php#100
        Bindings
        • 0: 31
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 36 limit 1
        1.35mstwenty4_siteSubject.php#100
        Bindings
        • 0: 36
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 28. view::components.footer:170
      App\Models\HomeworkLibrary\HomeworkLibraryFile
      11HomeworkLibraryFile.php
      App\Models\SubjectCat
      11SubjectCat.php
      App\Models\HomeworkLibrary\HomeworkLibrary
      7HomeworkLibrary.php
      App\Models\Subject
      2Subject.php
          _token
          6OBgAH8VP2VqVjjq4QETWbggWDGNLGodSRNvVEUb
          utm_source
          direct
          redirectUrl
          /college-homework-library/Mathematics/Statistics-R-Programming/50773
          _previous
          array:1 [ "url" => "https://staging.dev.24houranswers.com/college-homework-library/Mathematics/Sta...
          _flash
          array:2 [ "old" => [] "new" => [] ]
          PHPDEBUGBAR_STACK_DATA
          []
          path_info
          /college-homework-library/Mathematics/Statistics-R-Programming/50773
          status_code
          200
          
          status_text
          OK
          format
          html
          content_type
          text/html; charset=UTF-8
          request_query
          []
          
          request_request
          []
          
          request_headers
          0 of 0
          array:21 [ "priority" => array:1 [ 0 => "u=0, i" ] "accept-encoding" => array:1 [ 0 => "gzip, deflate, br, zstd" ] "sec-fetch-dest" => array:1 [ 0 => "document" ] "sec-fetch-user" => array:1 [ 0 => "?1" ] "sec-fetch-mode" => array:1 [ 0 => "navigate" ] "sec-fetch-site" => array:1 [ 0 => "none" ] "accept" => array:1 [ 0 => "text/html,application/xhtml+xml,application/xml;q=0.9,image/avif,image/webp,image/apng,*/*;q=0.8,application/signed-exchange;v=b3;q=0.7" ] "user-agent" => array:1 [ 0 => "Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)" ] "upgrade-insecure-requests" => array:1 [ 0 => "1" ] "sec-ch-ua-platform" => array:1 [ 0 => ""Windows"" ] "sec-ch-ua-mobile" => array:1 [ 0 => "?0" ] "sec-ch-ua" => array:1 [ 0 => ""HeadlessChrome";v="129", "Not=A?Brand";v="8", "Chromium";v="129"" ] "cache-control" => array:1 [ 0 => "no-cache" ] "pragma" => array:1 [ 0 => "no-cache" ] "x-amzn-trace-id" => array:1 [ 0 => "Root=1-680d6e41-548d57451cd4b67420e5b995" ] "host" => array:1 [ 0 => "staging.dev.24houranswers.com" ] "x-forwarded-port" => array:1 [ 0 => "443" ] "x-forwarded-proto" => array:1 [ 0 => "https" ] "x-forwarded-for" => array:1 [ 0 => "3.16.215.186" ] "content-length" => array:1 [ 0 => "" ] "content-type" => array:1 [ 0 => "" ] ]
          request_cookies
          []
          
          response_headers
          0 of 0
          array:5 [ "content-type" => array:1 [ 0 => "text/html; charset=UTF-8" ] "cache-control" => array:1 [ 0 => "no-cache, private" ] "date" => array:1 [ 0 => "Sat, 26 Apr 2025 23:37:37 GMT" ] "set-cookie" => array:2 [ 0 => "XSRF-TOKEN=eyJpdiI6IlZrNEg5R0VUTXFWOC9kZllMNnpJV2c9PSIsInZhbHVlIjoiYWkydFBzMGU5Wk83WVZWVlVlVHl6elppRnZNREQvM0tlZHZZK2RGdWpXVnNEQ1llZXBpZmdpK29ub1U1Vys0NGhYQ2Zlc3BiSjY1Q2hpbUlEeFo4ZldEL2lTakZDZTJyRXZlY21scW4wd28xZkFBcURibytMeWY0YU5OUEt6b08iLCJtYWMiOiI0MjAyNzQ3ZjQ3Y2FiNmQ1YjU2ZjQ2MWI4OWUwNDk1Y2YzMTA4MDgzYmNkMmQwYjk3ZjUzYTM5OTJlZTM5MzM3IiwidGFnIjoiIn0%3D; expires=Sun, 27 Apr 2025 01:37:37 GMT; Max-Age=7200; path=/; domain=.24houranswers.com; samesite=laxXSRF-TOKEN=eyJpdiI6IlZrNEg5R0VUTXFWOC9kZllMNnpJV2c9PSIsInZhbHVlIjoiYWkydFBzMGU5Wk83WVZWVlVlVHl6elppRnZNREQvM0tlZHZZK2RGdWpXVnNEQ1llZXBpZmdpK29ub1U1Vys0NGhYQ2Zlc" 1 => "24houranswers_session=eyJpdiI6IkxzSWpaS0tzWUlqS1pXT1ZtdXBIMGc9PSIsInZhbHVlIjoiZE1udjR4RERLS0h2MTR4MzhJZldqY3hiZjNIQ1FydlBmSjFCYjc2UDBKWXlqeFRLSE5iUDY2NURDNUNjODlUbSs4UENsRk5yMlQyV29xcUNyYlFjVklSaTNzZVJSQS9NdmlOMTlFOHBxUjhPZ1VMMFh0dm1ybkxrWksycXdsMDYiLCJtYWMiOiI0ODg3NGVlYmVlMzM2NTk1YzY0ZTZhZDcwZmQ3YzBhNTk2ODIzY2U5NzM2NWY3YzViMjJiOGYxNGZmYWU4ZTdmIiwidGFnIjoiIn0%3D; expires=Sun, 27 Apr 2025 01:37:37 GMT; Max-Age=7200; path=/; domain=.24houranswers.com; httponly; samesite=lax24houranswers_session=eyJpdiI6IkxzSWpaS0tzWUlqS1pXT1ZtdXBIMGc9PSIsInZhbHVlIjoiZE1udjR4RERLS0h2MTR4MzhJZldqY3hiZjNIQ1FydlBmSjFCYjc2UDBKWXlqeFRLSE5iUDY2NURDNUNjOD" ] "Set-Cookie" => array:2 [ 0 => "XSRF-TOKEN=eyJpdiI6IlZrNEg5R0VUTXFWOC9kZllMNnpJV2c9PSIsInZhbHVlIjoiYWkydFBzMGU5Wk83WVZWVlVlVHl6elppRnZNREQvM0tlZHZZK2RGdWpXVnNEQ1llZXBpZmdpK29ub1U1Vys0NGhYQ2Zlc3BiSjY1Q2hpbUlEeFo4ZldEL2lTakZDZTJyRXZlY21scW4wd28xZkFBcURibytMeWY0YU5OUEt6b08iLCJtYWMiOiI0MjAyNzQ3ZjQ3Y2FiNmQ1YjU2ZjQ2MWI4OWUwNDk1Y2YzMTA4MDgzYmNkMmQwYjk3ZjUzYTM5OTJlZTM5MzM3IiwidGFnIjoiIn0%3D; expires=Sun, 27-Apr-2025 01:37:37 GMT; domain=.24houranswers.com; path=/XSRF-TOKEN=eyJpdiI6IlZrNEg5R0VUTXFWOC9kZllMNnpJV2c9PSIsInZhbHVlIjoiYWkydFBzMGU5Wk83WVZWVlVlVHl6elppRnZNREQvM0tlZHZZK2RGdWpXVnNEQ1llZXBpZmdpK29ub1U1Vys0NGhYQ2Zlc" 1 => "24houranswers_session=eyJpdiI6IkxzSWpaS0tzWUlqS1pXT1ZtdXBIMGc9PSIsInZhbHVlIjoiZE1udjR4RERLS0h2MTR4MzhJZldqY3hiZjNIQ1FydlBmSjFCYjc2UDBKWXlqeFRLSE5iUDY2NURDNUNjODlUbSs4UENsRk5yMlQyV29xcUNyYlFjVklSaTNzZVJSQS9NdmlOMTlFOHBxUjhPZ1VMMFh0dm1ybkxrWksycXdsMDYiLCJtYWMiOiI0ODg3NGVlYmVlMzM2NTk1YzY0ZTZhZDcwZmQ3YzBhNTk2ODIzY2U5NzM2NWY3YzViMjJiOGYxNGZmYWU4ZTdmIiwidGFnIjoiIn0%3D; expires=Sun, 27-Apr-2025 01:37:37 GMT; domain=.24houranswers.com; path=/; httponly24houranswers_session=eyJpdiI6IkxzSWpaS0tzWUlqS1pXT1ZtdXBIMGc9PSIsInZhbHVlIjoiZE1udjR4RERLS0h2MTR4MzhJZldqY3hiZjNIQ1FydlBmSjFCYjc2UDBKWXlqeFRLSE5iUDY2NURDNUNjOD" ] ]
          session_attributes
          0 of 0
          array:6 [ "_token" => "6OBgAH8VP2VqVjjq4QETWbggWDGNLGodSRNvVEUb" "utm_source" => "direct" "redirectUrl" => "/college-homework-library/Mathematics/Statistics-R-Programming/50773" "_previous" => array:1 [ "url" => "https://staging.dev.24houranswers.com/college-homework-library/Mathematics/Statistics-R-Programming/50773" ] "_flash" => array:2 [ "old" => [] "new" => [] ] "PHPDEBUGBAR_STACK_DATA" => [] ]