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Jest murder resolve group!

The dead body of professor H was found at the classroom at 6:50 am Friday, March 26th, 2007. The police determined that the cause of the death was a lethal injection with a substance that causes immediate death upon entering the bloodstream. The syringe was found at the scene with Miss X fingerprints on it. Needless to say, Miss X is a prime suspect. In fact, two reliable eyewitnesses at the school saw Miss X near the classroom at 7 am that same day. Miss X's alibi of being in Mr. R´s office can be verified, but only from 6 to 6:30am. Determine Miss X's innocence or guiltiness, attempt to determine whether or not the crime was committed after 6:50am.

Additional Facts:

-Miss X is in a community service at a clinical chemistry lab, and she is the one in charge of disposing used syringes.
-All DNA evidence in this case has been thrown out due to multiple lab errors.
-To determine the Algor Mortis, at 6:50 am, when the body of the professor was found, its temperature was 96 degrees. The body temperature was recorded again at 6:56 am and found to be 95 degrees.
-The classroom room temperature on night was recorded to be 75 degrees at 6 am, and 70 degrees at 7 am.
-Three days before the murder, the professor visited a physician, at which time the professor's body temperature was recorded at exactly 101 degrees.
-On the morning of the murder, before coming to work, the professor wrote the following journal entry:
"I have felt terrible ever since I had that horrible incident with one of my Heat students. What was his name, was it John? And for the past few days, I have had this terrible fever. I finally feel better today, not 100 percent, but nearly back to normal."