The number of incarcerated adults N (measured in thousands) in a certain country can be approximated by the equation Upper N equals negative 4.7 x squared plus 71.9 x plus 1900 , where x is the number of years since 2000. In 2007 , the number of incarcerated adults peaked. How many adults were incarcerated in that year?The number of inmates N (measured in thousands) in federal and state prisons can be approximated by the equation Upper N equals negative 2.02 x squared plus 77.88 x plus 745 , where x is the number of years since 1990. In what year was the number of inmates expected to be 1 comma 388 comma 680 ?

Muscles, a membership-only gym is hoping to open a new branch in a small city in pennsylvania that currently has no fitness centers. according to their research approximately 12,600 residents live within driving distance of the gym. muscles sends out surveys to a sample of 300 randomly selected residents in this area (all of who respond) and finds that 40 residents say they would visit a gym if one was located in their area. based on the past survey research, muscles estimates that approximately 30% of these respondents would actually join the gym if they opened one in the area. based on this information and the results of the sample survey, about how many residents should muscles expect to join its new branch? a) 134 b) 504 c) 1,680 d) 3,780

In one day there are too high tides into low tides and equally spaced intervals the high tide is observed to be 6 feet above the average sea level after six hours passed a low tide occurs at 6 feet below the average sea level in this task you will model this occurrence using a trigonometric function by using x as a measurement of time assume the first high tide occurs at x=0. a. what are the independent and dependent variables? b. determine these key features of the function that models the tide: 1.amplitude 2.period 3.frequency 4.midline 5.vertical shift 6.phase shift c. create a trigonometric function that models the ocean tide for a period of 12 hours. d. what is the height of the tide after 93 hours?

Rewrite the following quadratic functions in intercept or factored form. show your work. y = 4x^2 - 19x- 5