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solong [7]
3 years ago
5

Use appropriate algebra and Theorem 7.2.1 to find the given inverse Laplace transform. (Write your answer as a function of t.)

Mathematics
1 answer:
Licemer1 [7]3 years ago
8 0

Expand the expression as

(<em>s</em> + 1)³/<em>s</em> ⁵ = (<em>s</em> ³ + 3<em>s</em> ² + 3<em>s</em> + 1)/<em>s</em> ⁵

… = 1/<em>s</em> ² + 3/<em>s</em> ³ + 3/<em>s</em> ⁴ + 1/<em>s</em> ⁵

Then taking the inverse transform, you get

LT⁻¹ [1/<em>s</em> ² + 3/<em>s</em> ³ + 3/<em>s</em> ⁴ + 1/<em>s</em> ⁵]

… = LT⁻¹ [1/<em>s</em> ²] + LT⁻¹ [3/<em>s</em> ³] + LT⁻¹ [3/<em>s</em> ⁴] + LT⁻¹ [1/<em>s</em> ⁵]

… = LT⁻¹ [1!/<em>s</em> ²] + 3/2 LT⁻¹ [2!/<em>s</em> ³] + 1/2 LT⁻¹ [3!/<em>s</em> ⁴] + 1/24 LT⁻¹ [4!/<em>s</em> ⁵]

… = <em>t</em> + 3/2 <em>t</em> ² + 1/2 <em>t</em> ³ + 1/24 <em>t</em> ⁴

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According to the Bureau of Labor Statistics, the average weekly pay for a U.S. production worker was $441.84 in 1998 (The World
Oksanka [162]

Using the normal distribution, it is found that a production worker has to make $542.64 a week to be in the top 30% of wage earners.

<h3>Normal Probability Distribution</h3>

In a normal distribution with mean \mu and standard deviation \sigma, the z-score of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

  • It measures how many standard deviations the measure is from the mean.
  • After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.

In this problem:

  • The mean is of \mu = 441.84.
  • The standard deviation is of \sigma = 120.
  • The lower bound of the top 30% is the 70th percentile, which is X when Z has a p-value of 0.7, so <u>X when Z = 0.84.</u>

Z = \frac{X - \mu}{\sigma}

0.84 = \frac{X - 441.84}{120}

X - 441.84 = 0.84(120)

X = 542.64

A production worker has to make $542.64 a week to be in the top 30% of wage earners.

You can learn more about the normal distribution at brainly.com/question/24663213

3 0
2 years ago
Suppose the average yearly salary of an individual whose final degree is a​ master's is ​$43 thousand less than twice that of an
natka813 [3]

Answer:

A person who holds a master's degree would earn an average $63,000

A person who holds a bachelor's only would earn an average $53,000

Step-by-step explanation:

We will need to construct equations from the sentences.

Firstly, let the yearly average for a master's degree holder be m and that of bachelor's be b.

Now, we know that someone with a master's earn 43000 less than twice what someone with bachelors earn.

Mathematically,

m = 2b - 43,000

Combined, they have an average salary of 116,000

Mathematically,

m + b = 116,000

Now we have 2 equations to solve simultaneously.

m = 2b - 43,000 ......(i)

m + b = 116,000 .......(ii)

We can sub I into ii

2b - 43,000 + b = 116,000

2b+b = 116,000 + 43,000

3b = 159,000

b = 159,000/3 = 53,000

m = 2b - 43,000

m = 2(53,000) - 43,000 = 63,000

6 0
3 years ago
What is the answer to 7+y&lt;12
LiRa [457]

Step-by-step explanation:

7 + y < 12 it can also be written as

7 + y = 12

y = 12 - 7

y = 5

or

y < 5

Hope it will help :)

3 0
3 years ago
How do i answer this and how do i find the modal
faltersainse [42]
So firsty up, you need to have equal denominators IN order to do this equation.

 1/3 and 5/12..

3x4=12

So the rule when changing denominators, you multiply 4 intop, so it will become 4/12, and 5/12 + 4/12 = 8/12, and,

8/12 + 1/12= 9/12 and 9/12 simplified is 3/4..

So the answer is 3/4.

Hope this helped.
3 0
3 years ago
M&lt;2 64 and m&lt;4 =2x-6
-Dominant- [34]

Answer:

5iejksjsjsjsnnsnsnsnsns

6 0
3 years ago
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