Answer:
And rounded up we have that n=385
Step-by-step explanation:
Previous concepts
A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".
The margin of error is the range of values below and above the sample statistic in a confidence interval.
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
Solution to the problem
In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 99% of confidence, our significance level would be given by 
and 
. And the critical value would be given by:
The margin of error for the proportion interval is given by this formula:
(a)
And on this case we have that 
and we are interested in order to find the value of n, if we solve n from equation (a) we got:
(b)
We can use as an estimator for p 
. And replacing into equation (b) the values from part a we got:
And rounded up we have that n=385
Answer:
a1=12
a6=12
a5=20
a3=20
a4=15
a2=15
as=94
Step-by-step explanation:
it is asking for each of the areas
I'm assuming As stands for areas summed
The perimeter of a square with a side measurement of 6 inches is equal to 24 inches.
Answer:
Step-by-step explanation:
If we have a linear function and we multiply the input of the function, we aren't really <em>changing</em> the values of the function, we're changing the rate at which those values are reached.
E.g. if you look at the attached picture, we have 
and 
, which is just 
. The value when the red line is x = 1 is half that of the value of the blue line when x = 1.
The values of the f(2x) line are reaching the values of f(x) twice as fast, meaning it has a slope of twice as much. However, it still grows through the same intercept.
If you're interested in the calculus behind this, look up the chain rule of derivatives.
However, when you start changing the output of the function, you're changing the entire equation. It's not the same line anymore.
Answer:
radius = 4 cm
Step-by-step explanation:
To find the length of the radius, we will follow the step below;
First, write down the formula for finding the volume of a cylinder
v=πr²h
where v is the volume of a cylinder
r is the radius and
h is the height of the cylinder
from the question given,
v=125.6 and h = 10 cm
we can now proceed to insert the values into the formula and solve for r
note that π is a constant which is equal to 3.14
v=πr²h
125.6 =3.14×r×10
125.6 =31.4 r
Divide both-side of the equation by 31.4
125.6/31.4 =31.4 r/31.4
4 = r
r =4 cm
The length of the radius = 4 cm
