Amanufacturing unit currently operates at 80 percent of its capacity. the profit function for the unit at the optimum output, x, is given by p(x) = -0.1x2 + 80x − 60.
if the function f(x) models the current capacity of the unit, the composite function giving the unit's current profit function is ? if the optimum output is 500 units, the current profit is $.

An assembly consists of two mechanical components. suppose that the probabilities that the first and second components meet specifications are 0.87 and 0.84. assume that the components are independent. determine the probability mass function of the number of components in the assembly that meet specifications. x

Gregory draws a scale drawing of his room. the scale that he uses is 1 cm : 4 ft. on his drawing, the room is 3 centimeters long. which equation can be used to find the actual length of gregory's room?

In new york city at the spring equinox there are 12 hours 8 minutes of daylight. the longest and shortest days of the year very by two hours and 53 minutes from the equinox in this year the equinox falls on march 21 in this task you use trigonometric function to model the hours of daylight hours on certain days of the year in new york city a.what is the independent and dependent variables? b.find the amplitude and the period of the function. c.create a trigonometric function that describes the hours of sunlight for each day of the year. d. graph the function you build in part c. e. use the function you build in part c to find out how many fewer daylight hours february 10 will have than march 21. you may look at the calendar.