A solid cylindrical metal is melted and recast into cubes of metal of sides 3cm . The base radius of the initial cylindrical met
1 answer:
Answer:
808
Step-by-step explanation:
The volume of the initial cylindrical metal must be equal to the total volume of the cubes.
Let the number of cubes made be x. Therefore:
where volume of the cylinder
volume of each cube
Each of the cubes have sides of length 3 cm.
The volume of a cube is given as:
where L = length of side of cube
Therefore, the volume of each cube is:
The volume of a cylinder is given as:
where r = radius
h = height of the cylinder
The volume of the cylinder is:
Therefore:
21823.55 = 27 * x
=> x = 21823.55 / 27
x = 808.27
Since the number of cubes can only be a whole number, the number of cubes that will be made is 808.
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Answer:
Part1)
Readjustment is needed
Part 2)
No readjustment is needed
Step-by-step explanation:
Data given and notation
Part 1
represent the sample mean
represent the population standard deviation
sample size
represent the value that we want to test
represent the significance level for the hypothesis test.
z would represent the statistic (variable of interest)
represent the p value for the test (variable of interest)
State the null and alternative hypotheses.
We need to apply a two tailed test.
What are H0 and Ha for this study?
Null hypothesis:
Alternative hypothesis :
Compute the test statistic
The statistic for this case is given by:
(1)
z-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".
Calculate the statistic
We can replace in formula (1) the info given like this:
Give the appropriate conclusion for the test
Since is a two tailed test the p value would be:
Using the value of we see that
and we have enough evidence to reject the null hypothesis.
Readjustment is needed
The rejection zone is given by:
Part 2
represent the sample mean
We can replace in formula (1) the info given like this:
Give the appropriate conclusion for the test
Since is a two tailed test the p value would be:
Using the value of we see that
and we have enough evidence to FAIL to reject the null hypothesis.
No readjustment is needed
The rejection zone is given by:
What action would you recommend ?
Review the procedure.
Do you reach the same conclusion ?
No we got different conclusions