Since

, we know that

follows a Poisson distribution with parameter

.
Now assuming

denote the mean and standard deviation of

, respectively, then we know right away that

and

.
So,
Pattern is -5 then +3, so next number is 46-5 which is 41, and then that plus 3, which is 44
So 41 and 44
Answer:
A the graph represents a linear function because
Step-by-step explanation:
Answer:
three times the sum of a number and 4, if n were to represent the unknown number, is:
3(n + 4)
18 more than a number is:
n + 18
If these two are the same, then they are equal to each other, then:
3(n + 4) = n + 18
*Do the distributive property on the left*
3n + 12 = n + 18
*Combine like terms*
2n = 6
*Divide both sides by 2*
n = 3
The number is 3.
Answer:
y(t) = c₁ e^(-1/2 t) cos(√3/2 t) + c₂ e^(-1/2 t) sin(√3/2 t) + 1
Step-by-step explanation:
y" + y' + y = 1
This is a second order nonhomogenous differential equation with constant coefficients.
First, find the roots of the complementary solution.
y" + y' + y = 0
r² + r + 1 = 0
r = [ -1 ± √(1² − 4(1)(1)) ] / 2(1)
r = [ -1 ± √(1 − 4) ] / 2
r = -1/2 ± i√3/2
These roots are complex, so the complementary solution is:
y = c₁ e^(-1/2 t) cos(√3/2 t) + c₂ e^(-1/2 t) sin(√3/2 t)
Next, assume the particular solution has the form of the right hand side of the differential equation. In this case, a constant.
y = c
Plug this into the differential equation and use undetermined coefficients to solve:
y" + y' + y = 1
0 + 0 + c = 1
c = 1
So the total solution is:
y(t) = c₁ e^(-1/2 t) cos(√3/2 t) + c₂ e^(-1/2 t) sin(√3/2 t) + 1
To solve for c₁ and c₂, you need to be given initial conditions.