Two pans of a balance are 25.1 cm apart.
the fulcrum of the balance has been shifted
1.4 cm away from the center by a dishonest
shopkeeper.
by what percentage is the true weight of the
goods being marked up by the shopkeeper?
assume the balance has negligible mass.
answer in units of %.

25.1%

Explanation:

Let's say m is the true weight and M is the weight of the counterweight.

The original distance between the pans and the center is 25.1 cm / 2 = 12.55 cm.  The fulcrum is then moved 1.4 cm towards the counterweight.

Sum of the moments about the fulcrum:

m (12.55 + 1.4) − M (12.55 − 1.4) = 0

13.95 m − 11.15 M = 0

13.95 m = 11.15 M

M / m = 13.95 / 11.15

M / m = 1.251

The true weight is being marked up by 25.1%.

sleep paralysis is a parasomnia, events associated with sleep.

sleep paralysis happens when you are in the middle of waking up or falling asleep. it is the feeling of being conscious but unable to move. it definitely involves hallucinations.

i had a friend that had sleep paralysis and he told me a story one time where he was laying in bed and he couldn't move his body no matter how hard he tried and there was someone standing in the corner of his room coming towards him. he couldn't move and you can't "wake up" because you are already conscious. sometimes sleep paralysis can be triggered by frequent waking up during the night based off of multiple trips to the bathroom, or if you had ever been abused, sleep paralysis can start happening from things like that.