Choose 16 distinct integers between 1 and 30. prove that at least two of these differ by 3. is this also true if we choose 15 distinct integers? justify your answer.

Do not comment if you aren’t going to . create a real-life situation and create a system and show how it might be modeled algebraically with a system of equations (or inequalities) show all work include a few sentences explaining the situation, your variables of choice and what each represents, and how you would set it up and solve it algebraically. !

1yd 1 ft = 1 1/12 1 1/3 1 1/2 1 1/6

The edge of a cube was found to be 30 cm with a possible error in measurement of 0.4 cm. use differentials to estimate the maximum possible error, relative error, and percentage error in computing the volume of the cube and the surface area of the cube. (round your answers to four decimal places.) (a) the volume of the cube maximum possible error cm3 relative error percentage error % (b) the surface area of the cube maximum possible error cm2 relative error percentage error %