(Originais Teachy 2023) - Question Medium of Mathematics

In a civil engineering project, an architect needs to divide a rectangular plot of land into two equal parts for the construction of two semi-detached houses. The coordinates of the vertices of the land on the Cartesian plane are A(0, 0), B(30, 0), C(30, 20), and D(0, 20). Using concepts of analytic geometry, determine the coordinates of the point that represents the midpoint of side CD of the land, which will be the dividing point between the two new properties. Then, verify if the obtained midpoint point is indeed on segment CD, ensuring the accuracy of the project. Explain the reasoning used to determine the coordinates and to verify the positioning of the midpoint on the land.

Maria used a ruler marked in centimeters to measure the width of a wooden board. She noted the measurement as 12.3 cm. Considering that the ruler may not be perfectly accurate because of the limited precision of the markings, what is the range of values that reflects the true width of the board?

At a science fair, a contestant performs two separate experiments. The chance of succeeding in the first experiment is 0.3 and, independently of the first, the chance of succeeding in the second experiment is 0.5. What is the likelihood that the contestant succeeds in both experiments?