Plumber uses a slope of 1/4 per foot to ensure the proper flow in waste-pipe use a proportion to calculate the amount of fall that pipe should have if it is 31 inches in 3 ft long

The length of a rectangle is increasing at a rate of 8 in./s, while its width is decreasing at 3 in./s. Find the rate of change of its area when its length is 75 in. and its width is 35 in. Answer in. ²/s Keypad Keyboard Shortcuts

1. mpg: Miles/(US) gallon 2. cyl: Number of cylinders 3. disp: Displacement (cu.in.) 4. hp: Gross horsepower 5. drat: Rear axle ratio 6. wt: Weight (1000 lbs) 7. qsec: 1/4 mile time 8. Vs: V/S 9. am: Transmission (0 = automatic, 1 = manual) 10. gear: Number of forward gears 11. carb: Number of carburetors Use R. and its built-in data set mtcars to complete the following. (a) Explore the structure of the data set. Notice that the variable Transmission is stored as numeric, but the description says it is a binary variable (categorical). Change the variable Transmission into a factor (categorical variable). Make sure you name the levels of this categorical variable (follow the order in the description). Now check the structure of your data set and notice the change you made to Transmission. (b) Create and store two variables as vectors: mpg for automatic vehicles and mpg for manual vehicles. (c) Find the sample mean, median, variance and standard deviation for each variable from part (b).…

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