Starting from the point (0,0), a grasshopper makes a series of moves on the coordinate plane. the grasshopper's first move takes her to (3,4). she then proceeds via this rule: move rule: after a move which adds (x, y) to the grasshopper's coordinates, her next move adds either (x, y-1) or (x-1,y) to her coordinates. thus, her second move adds either (3,3) or (2,4) to her position, landing her at (6,7) or (5,8) accordingly. if the grasshopper's x and y coordinates never decrease, and if she ends at the point (a, a) where a is as large as possible, then what is the value of a?

Solve this equation using substitution. {4x + y = −2} {4x + 6y = 44}

He mass of a single atom of carbon can be found by dividing the atomic mass (12.01 g) by 6.022 x 10^23. which is the mass of a single carbon atom, correctly written in scientific notation with the correct number of significant figures?

It appears that people who are mildly obese are less active than leaner people. one study looked at the average number of minutes per day that people spend standing or walking. among mildly obese people, the mean number of minutes of daily activity (standing or walking) is approximately normally distributed with mean 376 minutes and standard deviation 64 minutes. the mean number of minutes of daily activity for lean people is approximately normally distributed with mean 528 minutes and standard deviation 107 minutes. a researcher records the minutes of activity for an srs of 7 mildly obese people and an srs of 7 lean people. use z-scores rounded to two decimal places to answer the following: what is the probability (image for it appears that people who are mildly obese are less active than leaner people. one study looked at the averag0.0001) that the mean number of minutes of daily activity of the 6 mildly obese people exceeds 420 minutes? what is the probability (image for it appears that people who are mildly obese are less active than leaner people. one study looked at the averag0.0001) that the mean number of minutes of daily activity of the 6 lean people exceeds 420 minutes?