(Originais Teachy 2023) - Question Medium of Mathematics

João is organizing a birthday party and wants to make a larger quantity of his favorite cake recipe. The original recipe yields a cake with 20 slices and uses 3 cups of flour, 2 cups of sugar, and 1 cup of oil. João wants to make a cake with 40 slices. a) How many cups of flour, sugar, and oil should he use to make a cake that yields 40 slices? b) If he wanted to make a cake with 60 slices, what would be the quantity of cups of each ingredient? c) João noticed that the number of cake slices is always half the number of cups of water used in the recipe. How many cups of water are needed for a cake of 80 slices?

In a school, a survey was conducted on students who practiced sports. It was found that 60% of the students practiced soccer, 30% practiced volleyball, and 20% practiced both sports. If a student is randomly selected, what is the probability that he practices soccer, given that he practices volleyball?

Consider the linear system below: 2x + 3y = 10 5x - 4y = -7 Transform this linear system into a matrix form using a matrix A and a column vector X, representing the unknowns. Write down the resulting matrix equation and inform what is the dimension of matrix A.