45 centimeters is equivalent to how many inches?
2 answers:
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Answer:
1a
1b
95% of all sample means will fall between
1c
2
Step-by-step explanation:
From the question we are told that
The mean is
The population standard deviation is
The sample size is n = 16
Generally the standard error of the mean is mathematically represented as
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Generally the probability that the sample mean will be between 39 and 48 minutes is
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From the z table the area under the normal curve to the left corresponding to 1.2 and -2.4 is
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and
So
=>
From the question we are told the confidence level is 95% , hence the level of significance is
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Generally from the normal distribution table the critical value of is
Generally the margin of error is mathematically represented as
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Generally the 95% of all sample means will fall between
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Generally the value which 90% of sample means is greater than is mathematically represented
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Generally from the z-table the critical value of 0.90 is
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Considering question 2
Generally we are told that the standard deviation of the mean to be one fifth of the population standard deviation, this is mathematically represented as
Generally the standard deviation of the sample mean is mathematically represented as
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=>
=>
Answer:
The solution to the differential equation is
Step-by-step explanation:
Applying Laplace Transform will help us solve differential equations in Algebraic ways to find particular solutions, thus after applying Laplace transform and evaluating at the initial conditions we need to solve and apply Inverse Laplace transform to find the final answer.
Applying Laplace Transform
We can start applying Laplace at the given ODE
So we will get
Applying initial conditions and solving for X(s).
If we apply the initial conditions we get
Simplifying
Moving all terms that do not have X(s) to the other side
Factoring X(s) and moving the rest to the other side.
Partial fraction decomposition method.
In order to apply Inverse Laplace Transform, we need to separate the fractions into the simplest form, so we can apply partial fraction decomposition to the first 2 fractions. For the first one we have
So if we multiply both sides by the entire denominator we get
At this point we can find the value of A fast if we plug s = 0, so we get
So the value of A is
We can replace that on the previous equation and multiply all terms by 6
We can simplify a bit
And by comparing coefficients we can tell the values of B and C
So the separated fraction will be
We can repeat the process for the second fraction.
Multiplying by the entire denominator give us
We can plug the value of s = 1 to find A fast.
So we get
We can replace that on the previous equation and multiply all terms by 11
Simplifying
And by comparing coefficients we can tell the values of B and C.
So the separated fraction will be
So far replacing both expanded fractions on the solution
We can combine the fractions with the same denominator
Simplifying give us
Completing the square
One last step before applying the Inverse Laplace transform is to factor the denominators using completing the square procedure for this case, so we will have
We are adding half of the middle term but squared, so the first 3 terms become the perfect square, that is
So we get
Notice that the denominator has (s+2) inside a square we need to match that on the numerator so we can add and subtract 2
Lastly we can split the fraction one more
Applying Inverse Laplace Transform.
Since all terms are ready we can apply Inverse Laplace transform directly to each term and we will get