A water tank contains exactly 1,000 gallons. A pump fills the remainder of the tank using a logistic function. If the volume of the tank is 15,000 gallons and the pump fills the tank at a rate of 10.4% per minute, explain how to find the value of a for the logistic function that describes this scenario.

Mary beth used the mapping rule to find the coordinates of a point that had been rotated 90° counterclockwise around the origin. examine the steps to determine whether she made an error. m (3, –6) is rotated 90° counterclockwise. (x, y) → (–y, x) 1. switch the x- and y-coordinates: (6, –3) 2. multiply the new x-coordinate by –1: (6(–1), –3) 3. simplify: (–6, –3) .

Barney & noblet customers can choose to purchase a membership for $25 per year members receive 10% off all store purchases 1. how much would a member pay per year if he bought $50 worth of items each year? 2. write a slope-intercept equation that expresses how much a member pays per year using x to represent his purchases per year 3. how much would a member have to spend per year to pay off his membership fee?

Amachine part consists of a half sphere and a cylinder, as shown in the figure. the total volume of the part is π cubic inches.