diff --git a/Explanations of the analyzes.pdf b/Explanations of the analyzes.pdf
index e69de29bb2d1d6434b8b29ae775ad8c2e48c5391..a6d26c670ef8689ece740361c5f30c1553e1300e 100644
Binary files a/Explanations of the analyzes.pdf and b/Explanations of the analyzes.pdf differ