Your backpacker's guide contains a grid map of Paris, with each unit on the grid representing 0.5 kilometers. If the Arc de Triomphe is located at (2,−9) and Les Invalides is located at (5,−9), what is the direct distance (not walking distance, which would have to account for bridges and roadways) between the two monuments in kilometers? Round your answer to two decimal places, if necessary.

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?

Solve with work both bert and ernie received an increase in their weekly salaries. bert's salary increased from $520 to $520. ernie's salary went from $580 to $645. find the percent of increase for each salary. what was the larger of the two percents ?

Yuto and hila attempted to solve the same inequality. their work is shown below. which statement is true about the work shown above? yuto is correct because he isolated the variable correctly and reversed the inequality symbol. yuto is incorrect because he should not have reversed the inequality symbol. hila is correct because she isolated the variable correctly and reversed the inequality symbol. hila is incorrect because she should not have reversed the inequality symbol.