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. 

In an economics study, researchers have discovered that children who travel to Europe during high school end up earning more money as adults. Therefore, it is valid to conclude that traveling to Europe while in school leads to higher income. 

A box office was having a sale, and a great seat was available for $140, which was 30% off the regular ticket price. How much was the regular price?  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. 

Based on the Richter scale, a magnitude 3.5 earthquake has 10 times as much energy as a magnitude 2.5 earthquake.