Answer:
By the Central Limit Theorem, the average value for all of the sample means is 14.
Step-by-step explanation:
We use the central limit theorem to solve this question.
The Central Limit Theorem estabilishes that, for a random variable X, with mean 
and standard deviation 
, the sample means of size n can be approximated to a normal distribution with mean and standard deviation, which is also called standard error 
If the population mean is μ = 14, then what is the average value for all of the sample means?
By the Central Limit Theorem, the average value for all of the sample means is 14.
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 
.
Step-by-step explanation:
<u>Given equation:</u>
a. write a second equation so that (1,3) is the only solution of the system
To have only one solution the equation must have a different slope.
<u>Let it be 10, then the y-intercept of y = 10x + b is:</u>
<u>And the equation:</u>
b. Write a second equation so that the system has infinitely many solutions
<u>To have infinitely many solutions, both equations must be same:</u>
c. Write a second equation so that the system has no solutions.
<u>To have no solutions, the equations must have same slope but different y-intercepts:</u>
This is an isosceles triangle. The definition of an isosceles triangle is a triangle with at least two congruent sides and angles. If 2 angles on a triangle are congruent (in this case 45 and 45 are two congruent angles) then triangle is isosceles. Therefore the two sides of triangle will be congruent. We know that the triangle is a right triangle because it has a hypotenuse. If a triangle has a hypotenuse then it's a right triangle. We can apply the Pythagorean theorem: a^2 + b^2 = c^2
A and B are the legs and C is the hypotenuse.
We can plug C in the equation:
a^2 + b^2 = 128
What do we know about the legs of the isosceles triangle? They are congruent so a and b have to be equal. From here it's simply guess and check. Will 8 work?
8^2 + 8^2 = 128
64 + 64 = 128
128=128
Yes the value 8 works so the length of two legs of the triangle is 8.
Answer:
She has enough a $26 dinner with a 20% tax
Step-by-step explanation:
