A thin rectangular sheet of metal is 6 inches wide and 10 inches long. The sheet of metal is to be rolled to form a cylinder so
1 answer:
Answer:
Length of the Rectangle is to be considered as the circumference of the resulting cylinder and the width of the rectangle should be considered as the height of the cylinder only then we get the maximum volume of the cylinder which is 47.77
Step-by-step explanation:
The given dimensions are
Width of the rectangle is 6inches.
Length of the rectangle 10inches.
Now we need to choose in what orientation we need to use the length and the width of the rectangle so that it can be rolled into a rectangle and we get the maximum volume of the resulting cylinder.
so lets consider two cases
CASE-1: width of the rectangle is to be rolled as the circumference of the cylinder and length of the rectangle is to used as the height of the cylinder
2*pi*r = 6
r =
r = Inch
and the height = 10inch.
Volume of the resultant cylinder will be
=
=
=
= = 28.662
CASE-2: When the length of the rectangle is to used as the circumference of the resultant cylinder and the width of the cylinder is used as the height of the cylinder.
2*pi*r= 10
r =
and the height of the cylinder is 6 inch
Now the volume of the cylinder will be
Volume=
=
=
= = 47.77
Clearly we have the second case in which the resulting Cylinder will have the maximum volume.
Therefore the CASE-2 will provide the maximum Volume of 47.77 to the resulting cylinder in which the length of the rectangle is to be considered as the circumference of the Cylinder and the width of the rectangle is to be considered as the height of the cylinder.
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The B option is correct.
<h2>Exponent</h2>Exponential notation is the form of mathematical shorthand which allows us to write complicated expressions more succinctly. An exponent is a number or letter is called the base. It indicates that the base is to raise to a certain power. X is the base and n is the power.
Given
A number is -906,060.
<h3>To find </h3>The equivalent number of the given number.
<h3>How to find the equivalent number of the given number?</h3>We know the number is -906,060.
It can be represented as .
Thus, the B option is correct.
More about the exponent link is given below.
Answer:
Organizations can use one-sample hypothesis test to determine if there are performance issues in many ways.
It can be applied to the performance of a sector, a machine, a product, an advertising campaing, etc.
For example, we can take the example of a machine. It may be claimed that a specific machine performs significantly worse than the average.
This average would be the population mean: the average performance of the machines of the same type or process.
Then, a sample of the performance of the machine in study is taken and the hypothesis test can be performed to test the claim that this machine performs significantly worse.
Step-by-step explanation:
For example, we have an historic performance for this type of machine of 100 units a day. The machine A in study is sampled 14 days and have a performance of 92 units a day, with a sample standard deviation of 12 units/day. We have to test the claim that the machine A makes less units per day than the average.
Then, the null and alternative hypothesis are:
The significance level is 0.05.
The sample has a size n=14.
The sample mean is M=92.
As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=12.
The estimated standard error of the mean is computed using the formula:
Then, we can calculate the t-statistic as:
The degrees of freedom for this sample size are:
This test is a left-tailed test, with 13 degrees of freedom and t=-2.4944, so the P-value for this test is calculated as (using a t-table):
As the P-value (0.0134) is smaller than the significance level (0.05), the effect is significant.
The null hypothesis is rejected.
There is enough evidence to support the claim that machine A produces significantly less units per day than the average.