Answer:i think its the first one
Step-by-step explanation:
Nothing else makes sense
Answer:
For this case the parameter of interest is given by:
who represent the true proportion of respondents said that they were willing to pay more for products and services from companies who are committed to positive social and environmental impact
For this case we have an estimation given for this parameter. The estimation comes from a sample of 30000 people selected in 60 countries and they got:
This value represent the best estimator for the true proportion since is an unbiased estimator of the real parameter:
Step-by-step explanation:
For this case the parameter of interest is given by:
who represent the true proportion of respondents said that they were willing to pay more for products and services from companies who are committed to positive social and environmental impact
For this case we have an estimation given for this parameter. The estimation comes from a sample of 30000 people selected in 60 countries and they got:
This value represent the best estimator for the true proportion since is an unbiased estimator of the real parameter:
For this case if we want to test if the population proportion is equal to an specified value we can use the one sample z test for a proportion:
Null hypothesis:
Alternative hypothesis:
When we conduct a proportion test we need to use the z statisitc, and the is given by:
(1)
The One-Sample Proportion Test is used to assess whether a population proportion 
is significantly different from a hypothesized value 
.
1. the total of an area under the curve must be equal to one. 2. Every point of the curve must have an vertical height that is 0 or greater.
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.
