Help! In a volatile housing market, the overall value of a home can be modeled by V(x) = 415x2 – 4600x + 200000, where V represents the value of the home and x represents each year after 2020. Find the vertex and interpret what the vertex of this function means in terms of the value of the home. Show the work you completed to determine the vertex.

Acertain population of bacteria demonstrates exponential growth doubles in size every 4 days. how long will it take the population to triple in size?

Asif spent $745.10 on 13 new file cabinets for his office. small file cabinets cost $43.50 and large file cabinets cost $65.95. write and solve a system of equations to find the number of small cabinets and large cabinets he purchased. determine if each statement is true or false. 1. he purchased 5 small cabinets. true or false 2. he purchased 7 large cabinets. true or false 3. he spent $527.60 on large cabinets. true or false

Max recorded the heights of 500 male humans. he found that the heights were normally distributed around a mean of 177 centimeters. which statements about max’s data must be true? a) the median of max’s data is 250 b) more than half of the data points max recorded were 177 centimeters. c) a data point chosen at random is as likely to be above the mean as it is to be below the mean. d) every height within three standard deviations of the mean is equally likely to be chosen if a data point is selected at random.