If you randomly split the subject group (patients) into a control group and a treatment group, where the control group gets a placebo, you are conducting an experiment.

Based on the Richter scale, a magnitude 4.0 earthquake has 100 times as much energy as a magnitude 2.0 earthquake.

Which one of the following is logically equivalent to the statement “If you are under 16, you cannot drive”?

A bakery shop sells five different cakes, but you can buy only two. There are ways to choose the two cakes out of the five available. (Assume you are choosing two DIFFERENT cakes… no repetition. The order in which you buy them is clearly not important.)

Find the negation of the statement “No one needs to get vaccinated.”

In an election with 5 candidates, there is never a Condorcet winner.

Being interested in the average household income of a town, a researcher randomly chose 500 households in that town and found their annual income. The average was $65,000 a year. Here, “$65,000” is a parameter. 

In an election with 5 candidates, it is possible that there is no Condorcet winner.

A user code consists of one alphabet letter and a double-digit number (like “A35” or “S93”). How many user codes are possible?

For a city marathon, the organizers originally estimated they needed about 5400 water bottles for the crowd of 3000 people. Now, they estimate that about 4200 people will come. How many water bottles should they prepare? Write ONLY your answer(s) in the box below. On your own paper, show all your work and justify your answer(s). You will be submitting the paper at the end of this test.