Answer:
The mean of x is close to 14.8.
The standard deviation of x is close to 3.78.
Step-by-step explanation:
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and each trial can only have two outcomes, with probabilities
and
.
For an experiment with n repeated trials and a probability of success
, we have that:
The mean is: 
The standard deviation is: 
In this problem
There are 400 employees, each with a probability of 3.7% of having food allergy. So
. So:

The mean of x is close to 14.8.

The standard deviation of x is close to 3.78.
Answer:
Step-by-step explanation:
Factor the numerator and the denominator to get

Answer:
Waves superimpose upon each other when they collide, while objects do not
Step-by-step explanation:
The main difference between the collision of waves and the collision of objects is simply the superposition principle.
When waves collide, they do not do so in the same way objects do. The superposition principle explains that waves can either collide in a constructive or destructive manner.
Case A: Waves colliding in a constructive manner
When waves collide in a constructive manner, this means that they are in phase, in simpler terms, it means that they have the same shape as they move through space-time. Constructive collision leads to a formation of a bigger wave with a higher amplitude. This is how stereo speakers operate. They produce louder sounds by releasing the same audio waves, causing them to superimpose upon each other.
Case B: Waves colliding in a destructive manner:
When waves are out of phase(i.e do not have the same shape as they move through space-time) and they collide, they try to cancel each other out, leading to a new wave with a weaker amplitude. This is how noise-cancelling headphones work. They emit an equal and opposite wave sound to the noise around your ears, thus cancelling it out.
Answer:
64
mm² or approximately 201.06 mm²
Step-by-step explanation:
If the diameter is 16 mm, the radius will be 8 mm.
Use the circle area formula, A =
r², where r is the radius. Plug in 8 as r:
A =
r²
A =
(8²)
A = 64
So, the area of the circle is 64
mm² or approximately 201.06 mm²