A student wants to prove that she can solve a system of a system of equations by replacing one of the equations with two times that equation and adding the other equation. The original system was 12x +2y =30 and 10x+y = 26. The student claims that her first step is to add the two linear equations. Select the option that refutes the student claim

Asmall (but heavy) particle placed in a glass of water will follow a zigzag motion because the particle will bounce off of the water molecules it meets. this is called brownian motion. a physicist simulates this on a computer, by varying the distance a particle can travel (called the mean free length), on average, before it collides with a water molecule and assigning the change in motion to be one of 8 directions, each with a similar probability. by running the simulated particle (with the same mean free length) many times she determines that it should take 15 seconds, on average, for the particle to fall to the bottom, with a standard deviation of 1.5 seconds. next she lets a real particle fall through a glass of water and finds that it took 18 seconds. what does she conclude, and why?

Data are collected to see how many ice-cream cones are sold at a ballpark in a week. day 1 is sunday and day 7 is the following saturday. use the data from the table to create a scatter plot.

Find the value of x. give reasons to justify your solutions! l, m ∈ kn