A machine depreciates by 1/4 of its value each year. When purchased new it costs $640,000, what explicit expression represents its value in the nth year?

640,000 (3/4)n
640,000(1/4)n-1
640,000 (3/4)n-1
3/4(640,000)n-1

Ascatterplot is produced to compare the size of a school building to the number of students at that school who play an instrument. there are 12 data points, each representing a different school. the points are widely dispersed on the scatterplot without a pattern of grouping. which statement could be true

Write the expression as a single natural logarithm. 2 in a - 4 in y

You are standing next to a really big circular lake. you want to measure the diameter of the lake, but you don't want to have to swim across with a measuring tape! you decide to walk around the perimeter of the lake and measure its circumference, and find that it's 400\pi\text{ m}400? m. what is the diameter dd of the lake?