In a laboratory experiment using spectrophotometry, an enzym…

In a laboratory experiment using spectrophotometry, an enzyme is combined with its substrate at time zero.  The absorbance of the resulting solution is measured at time zero and at five-minute intervals.  In this procedure, an increase in absorbance is related to the amount of product formed during the reaction.  The experiment is conducted using the three preparations shown in the table below. Absorbance of Solution at different times Enzyme Preparation 0 min 5 min 10 min 15 min 20 min I.    3 mL of enzyme preparation    2 mL of substrate   pH 5.0 0.0 0.22 0.33 0.38 0.37 II.    3 mL of boiled enzyme preparation      2 mL of substrate      pH 5.0 0.0 0.06 0.04 0.03 0.04 What is the independent variable of this experiment?

Bonus: (worth up to 5 points) Please ignore that this questi…

Bonus: (worth up to 5 points) Please ignore that this question says it is out of 0 points. I will be manually adding the points during the grading process.   As this exam occurs right after Valentine’s Day, love is on my mind.  Tell me, what do you love about Astronomy?  Rubric:  Be very clear with your response, and fully explain your thoughts using at least 3 sentences to receive the full 5 points. General or vague responses will not be scored favorably. I am giving you the space to share your personal connection to our course material. Take advantage of this opportunity with a detailed answer! If you use AI to write your essay, you will receive a 0 on the entire exam and be reported for scholastic dishonesty, which could result in academic disciplinary actions. 

For the COVID example we did in class, say that the entire U…

For the COVID example we did in class, say that the entire US population size is 10000. Let’s change the test accuracy to 96%, i.e. P(T|D)=P(T^c|D^c)=0.96. 1200 people have the disease (12% from our example), 1152 people have the disease and test positive (96% true positive rate). What is P(D|T), that is the probability of having the disease given that you test positive using the Bayes’ rule? Use the tree diagram. 

Let’s say that you saw dark clouds today. There is a 70% cha…

Let’s say that you saw dark clouds today. There is a 70% chance of seeing dark clouds today given that it will rain tomorrow (from historical data). There is a 20% chance of seeing dark clouds today given that it won’t rain tomorrow (again from historical data). There is a 50% chance of seeing dark clouds regardless of whether or not it will rain. The current knowledge without any extra information is that there is a 30% chance of rain tomorrow. What is the updated probability of rain tomorrow given that we saw dark clouds today? Hint: Let A be the event that it will rain tomorrow and B be the event that you observed dark clouds today. You need to find P(A|B). Use the tree diagram and Bayes theorem.