A proper divisor of a positive integer $n$ is a positive integer $d < n$ such that $d$ divides $n$ evenly, or alternatively if $n$ is a multiple of $d$. For example, the proper divisors of 12 are 1, 2, 3, 4, and 6, but not 12. A positive integer $n$ is called double-perfect if the sum of its proper divisors equals $2n$. For example, 120 is double-perfect (and in fact is the smallest double-perfect number) because its proper divisors are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, and 60, and their sum is 240, which is twice 120. There is only one other 3-digit double-perfect number. Write a Python program to find it, and enter the number as your answer below.

The output voltage of a power supply is assumed to be normally distributed. sixteen observations are taken at random on voltage are as follows: 10.35, 9.30, 10.00, 9.96, 11.65, 12.00, 11.25, 9.58, 11.54, 9.95, 10.28, 8.37, 10.44, 9.25, 9.38, and 10.85

Which view in a presentation program displays a split window showing the slide in the upper half and a blank space in the lower half?

The idea that, for each pair of devices v and w, there’s a strict dichotomy between being “in range” or “out of range” is a simplified abstraction. more accurately, there’s a power decay function f (·) that specifies, for a pair of devices at distance δ, the signal strength f(δ) that they’ll be able to achieve on their wireless connection. (we’ll assume that f (δ) decreases with increasing δ.) we might want to build this into our notion of back-up sets as follows: among the k devices in the back-up set of v, there should be at least one that can be reached with very high signal strength, at least one other that can be reached with moderately high signal strength, and so forth. more concretely, we have values p1 ≥ p2 ≥ . . ≥ pk, so that if the back-up set for v consists of devices at distances d1≤d2≤≤dk,thenweshouldhavef(dj)≥pj foreachj. give an algorithm that determines whether it is possible to choose a back-up set for each device subject to this more detailed condition, still requiring that no device should appear in the back-up set of more than b other devices. again, the algorithm should output the back-up sets themselves, provided they can be found.\