Answer:
n=206
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".
The population proportion have the following distribution
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 
, we can use as prior estimate of p 0.5, since we don't have any other info provided, and we are interested in order to find the value of n, if we solve n from equation (a) we got:
(b)
And replacing into equation (b) the values from part a we got:
And rounded up we have that n=206
Answer:
Step-by-step explanation:
Problem One
Blue = 5
Black =2
Red = 3
First of all there are 10 marbles, 2 of which are black.
That means that 8 others are not black
You can draw any one of the 8.
P(not black) = 8/10 = 4/5
Problem Two
There are 10 marbles in all
3 of them are red.
P(Red) = 3/10
- To divide the triangles into these regions, you should construct the <u>perpendicular bisector</u> of each segment.
- These perpendicular bisectors intersect and divide each triangle into three regions.
- The points in each region are those closest to the vertex in that <u>region</u>.
<h3>What is a triangle?</h3>
A triangle can be defined as a two-dimensional geometric shape that comprises three (3) sides, three (3) vertices and three (3) angles only.
<h3>What is a line segment?</h3>
A line segment can be defined as the part of a line in a geometric figure such as a triangle, circle, quadrilateral, etc., that is bounded by two (2) distinct points and it typically has a fixed length.
<h3>What is a
perpendicular bisector?</h3>
A perpendicular bisector can be defined as a type of line that bisects (divides) a line segment exactly into two (2) halves and forms an angle of 90 degrees at the point of intersection.
In this scenario, we can reasonably infer that to divide the triangles into these regions, you should construct the <u>perpendicular bisector</u> of each segment. These perpendicular bisectors intersect and divide each triangle into three regions. The points in each region are those closest to the vertex in that <u>region</u>.
Read more on perpendicular bisectors here: brainly.com/question/27948960
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the slope is -12 because y=mx+b and m= slope
Step-by-step explanation:
Let's say R is the initial radius of the sphere, and r is the radius at time t.
The volume of the sphere at time t is:
V = 4/3 π r³
Taking derivative with respect to radius:
dV/dr = 4π r²
This is a maximum when r is a maximum, which is when r = R.
(dV/dr)max = 4π R²
This is 4 times the sphere's initial great circle area, but not the great circle circumference. The problem statement contains an error.
