Which of the following shows the correct first step to prove the following by mathematical induction? 3 + 11 + 19 + 27 + … + (8n - 5) = n(4n - 1) a) 3 + 11 + 19 + 27 + … + (8 • 1 - 5) = 1(4 • 1 - 1) b) 8 • 1 - 5 = 1(4 • 1 - 1) c) 3 + 11 + 19 + 27 + … + (8k - 5) = k(4k - 1) d) 3 + 11 + 19 + 27 + … + (8k - 5) + [8(k + 1) - 5] = (k + 1)[4(k + 1) - 1]

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.

Adesigner charges a one time fee of $200 plus $40 an hour for each project. write an expression to represent how much money the designer will make for a project

If f(x) = 2x + 8 and g(x) = x4, what is (gº)?