Exploring MATHEMATICS Chess is played on a square board. The board is made up of 32 light squares and 32 dark squares. You have a picce of rectangular board with measurements of 44 cm x 52 cm. You decide to use the board to make your own chessboard such that • each square grid on the board has a side length which is a whole number. • each chess piece is placed on a square grid with an area of not less than 9 cm. Determine all the possible measurements of the chessboard that you can create

21 a stick 7 inches long is broken into two pieces, so that one piece is twice as long as the other one. how long are the two pieces?

The graph is supposed to show f(x) = 3 sin (x/4+1) - 1/2. which of the following are correctly represented in the graph? select two of the following that apply.

Which scenarios are most effectively explored by conducting an experiment? there is more than one correct answer. select all that apply. researchers want to study the effectiveness of a particular drug for treating migraines. they want to know which dosage of the drug yields the best results with the least side effects. to ensure fair results, the researchers want to ensure that participants and dosage administrators do not know which dosage participants receive. a teacher wants to plan a class fieldtrip and quickly determine where students prefer to go for the class fieldtrip. a car mechanic wants to know which of two engine brands makes better-performing engines. he wants to test the engines in identical situations and rate their performance in a way that can be fairly measured. a chemist studies the properties of a metal compound. she wants to know how the sample size of the metal affects its ability to conduct electricity. she wants to conduct the research in a controlled environment to minimize bias. a realty company wants to know the average income of its clients. the company wants to gather data income from current clients.