Acarpet has a rectangular measure of 10 feet for the length and w feet for the width. if the perimeter is the sum of all four sides, then write an expression that represents the perimeter. simplify.

2w – 20

2w – 10

2w +10

2w + 20

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?

Write the component forms of vectors u and v, shown in the graph, and find v − 2u. u= (< -3, -2> , < -3, -1> , < -2, -2> , < -2, -1> ) v= (< -5, 1> , -4, 0> , < 0, -4> , < 1, -5> ) v-2u= (< 5, 3> , < 0, 4> , < 4, 0> , < 5, -3>

You’re ordering more thread for blue jeans co. you usually purchase from ted’s threads, which sells 12 thread spools for $27. you recently received a notice from wade's wares that says you can buy thread from them for $2.30 each for the first 2 dozen and $2 a spool thereafter. you need to order 5 dozen spools. what percentage can you save by going with wade’s wares?