Answer: 5 to the 3rd times 3 to the second times 2
Step-by-step explanation:
Answer:
3.4
Step-by-step explanation:
Standard deviation of a population is defined as:
σ² = ∑(xᵢ − μ)² / n
The standard deviation of a sample is defined as:
s² = ∑(xᵢ − x)² / (n - 1)
It's not clear which one we have, so let's calculate both.
First, we must find the mean.
μ = (5+12+15+10+12+6+8+8) / 8
μ = 9.5
Now we find the squares of the differences:
(5-9.5)² + (12-9.5)² + (15-9.5)² + (10-9.5)² + (12-9.5)² + (6-9.5)² + (8-9.5)² + (8-9.5)²
= 80
Divide by n:
σ² = 80 / 8
σ² = 10
And take the square root:
σ = √10
σ ≈ 3.2
That's not one of the answers, so let's try the standard deviation of a sample instead of a population.
Instead of dividing by n, we'll divide by n-1:
s² = 80 / 7
And take the square root:
s = √(80/7)
s ≈ 3.4
So that must be it.
No on can explain it but it has a definition.
At the start, the tank contains
(0.25 lb/gal) * (100 gal) = 25 lb
of sugar. Let
be the amount of sugar in the tank at time
. Then
.
Sugar is added to the tank at a rate of <em>P</em> lb/min, and removed at a rate of

and so the amount of sugar in the tank changes at a net rate according to the separable differential equation,

Separate variables, integrate, and solve for <em>S</em>.







Use the initial value to solve for <em>C</em> :


The solution is being drained at a constant rate of 1 gal/min; there will be 5 gal of solution remaining after time

has passed. At this time, we want the tank to contain
(0.5 lb/gal) * (5 gal) = 2.5 lb
of sugar, so we pick <em>P</em> such that
