Using the z-distribution, a sample of 609 nickels has to be weighed.
<h3>What is a z-distribution confidence interval?</h3>
The confidence interval is:
![\overline{x} \pm z\frac{\sigma}{\sqrt{n}}](https://tex.z-dn.net/?f=%5Coverline%7Bx%7D%20%5Cpm%20z%5Cfrac%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%7D)
The margin of error is:
![M = z\frac{\sigma}{\sqrt{n}}](https://tex.z-dn.net/?f=M%20%3D%20z%5Cfrac%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%7D)
In which:
is the sample mean.
is the standard deviation for the population.
For this problem, the parameters are:
![M = 20, \sigma = 300, z = 1.645](https://tex.z-dn.net/?f=M%20%3D%2020%2C%20%5Csigma%20%3D%20300%2C%20z%20%3D%201.645)
We solve for n to find the sample size, then:
![M = z\frac{\sigma}{\sqrt{n}}](https://tex.z-dn.net/?f=M%20%3D%20z%5Cfrac%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%7D)
![20 = 1.645\frac{300}{\sqrt{n}}](https://tex.z-dn.net/?f=20%20%3D%201.645%5Cfrac%7B300%7D%7B%5Csqrt%7Bn%7D%7D)
![20\sqrt{n} = 1.645 \times 300](https://tex.z-dn.net/?f=20%5Csqrt%7Bn%7D%20%3D%201.645%20%5Ctimes%20300)
![\sqrt{n} = 1.645 \times 15](https://tex.z-dn.net/?f=%5Csqrt%7Bn%7D%20%3D%201.645%20%5Ctimes%2015)
![(\sqrt{n})^2 = (1.645 \times 15)^2](https://tex.z-dn.net/?f=%28%5Csqrt%7Bn%7D%29%5E2%20%3D%20%281.645%20%5Ctimes%2015%29%5E2)
n = 608.9
Rounding up, a sample of 609 nickels has to be weighed.
More can be learned about the z-distribution at brainly.com/question/25890103
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Answer:
381.6 minutes
Step-by-step explanation:
We need to first find the volume of the icicle.
Its height is 18 inches and its diameter is 3 inches (radius = 1.5 inches)
The volume of a cone is:
![V = \pi r^2 h](https://tex.z-dn.net/?f=V%20%3D%20%5Cpi%20r%5E2%20h)
where r = radius
h = height
Therefore, the volume of the icicle is:
![V = \pi * 1.5^2 * 18\\](https://tex.z-dn.net/?f=V%20%3D%20%5Cpi%20%2A%201.5%5E2%20%2A%2018%5C%5C)
V = 127.2 cubic inches
The time it takes 1 cubic inch of the icicle to melt is 3 minutes, therefore, the time it will take 127.2 cubic inches to melt is:
127.2 * 3 = 381.6 minutes
365/35 is about 10.2 or 10.17142
Answer:
24 kilometers.
Step-by-step explanation:
The shortest path between two points is a straight segment that connects the two points.
Refer to the diagram attached. The 6-km segment and the 8-km segment are normal to each other. Together with the segment that joins the library and the house, the three segments now form a right triangle.
- The two shorter segments are the two legs, and
- The longer segment that joins the library and the house is the hypotenuse.
The length of the hypotenuse can be found with the Pythagorean Theorem.
.
The length of the round-trip will equal to the sum of the length of the three segments:
.
Answer:
maybe you can attach the screenshot of the task?