Find Laplace transform of L[te

t

sin4t] is

2022-03-26

Find Laplace transform of L[te

t

sin4t] is

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asked 2020-12-30

A majorette in a parade is performing some acrobatic twirlingsof her baton. Assume that the baton is a uniform rod of mass 0.120 kg and length 80.0 cm.

With a skillful move, the majorette changes the rotation ofher baton so that now it is spinning about an axis passing throughits end at the same angular velocity 3.00 rad/s as before. What is the new angularmomentum of the rod?

asked 2020-11-09

State in detail under what conditions it is possible to make a causal inference from a comparison of means between two or more groups of individuals.

asked 2022-01-20

Solve the following first order differential equations:

1.$(1+{x}^{2}+{y}^{2}+{x}^{2}{y}^{2})dy={y}^{2}dx$

2.$e}^{x}y\frac{dy}{dx}={e}^{-y}+{e}^{3x-y$

1.

2.

asked 2022-06-20

A colleague of yours is completing a final report on the causes of the frequency of cyberbullying. In this report, she is asked to identify the causes that most strongly impacted the frequency of cyberbullying. She conducts an OLS regression.

What statistic do you advise her to use in her discussion? Why?

What statistic do you advise her to use in her discussion? Why?

asked 2022-05-11

For the provided sample mean, sample size, and population standard deviation, complete parts (a) through (c) below.

x=32,

n=100,

σ=3

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Part 1

**a. **Find a 95% confidence interval for the population mean.

asked 2022-06-30

Find an example of a function $f:[a,b]\to R$ which is continuous, but not strictly increasing, such that no inverse function ${f}^{-1}$ satisfy the property of the Inverse Function Theorem.

asked 2022-06-26

Arranging 120 students into 6 different groups so that the largest and smallest group differ by 2 members

In how many different ways can we arrange 120 students into 6 groups for 6 different classes so that the largest group has at most 2 members more than the smallest group?

My initial plan was to use a generating function, but I stumbled across a problem. Let's mark the groups with numbers 1 to 6 and let ${n}_{i},i\in \{1,\dots ,6\}$ denote the number of members of the i-th group in some arrangment. To see where this would lead me, for a moment, I assumed ${n}_{1}\le {n}_{2}\le \cdots \le {n}_{6}\le {n}_{1}+2$ in hope to find some range $\{m,\dots M\}$ for ${n}_{i}$'s and use a generating function $f(x)=({x}^{m}+\cdots +{x}^{M}{)}^{6}$ and find $\u27e8{x}^{120}\u27e9-$ the coefficient in front of ${x}^{120}$, however students are distinct entities and m and M still remained misterious. I then tried figuring out if I was on the somewhat right track by, again taking $m=min\{{n}_{1},\dots ,{n}_{6}\}$ and write ${n}_{i}=m+{j}_{i},{j}_{i}\in \{0,1,2\}.$. I believe, an arrangement with 2 groups of 19,2 groups of 20 and 2 groups of 21 people suggests there should be at least 19 people in each group.

In how many different ways can we arrange 120 students into 6 groups for 6 different classes so that the largest group has at most 2 members more than the smallest group?

My initial plan was to use a generating function, but I stumbled across a problem. Let's mark the groups with numbers 1 to 6 and let ${n}_{i},i\in \{1,\dots ,6\}$ denote the number of members of the i-th group in some arrangment. To see where this would lead me, for a moment, I assumed ${n}_{1}\le {n}_{2}\le \cdots \le {n}_{6}\le {n}_{1}+2$ in hope to find some range $\{m,\dots M\}$ for ${n}_{i}$'s and use a generating function $f(x)=({x}^{m}+\cdots +{x}^{M}{)}^{6}$ and find $\u27e8{x}^{120}\u27e9-$ the coefficient in front of ${x}^{120}$, however students are distinct entities and m and M still remained misterious. I then tried figuring out if I was on the somewhat right track by, again taking $m=min\{{n}_{1},\dots ,{n}_{6}\}$ and write ${n}_{i}=m+{j}_{i},{j}_{i}\in \{0,1,2\}.$. I believe, an arrangement with 2 groups of 19,2 groups of 20 and 2 groups of 21 people suggests there should be at least 19 people in each group.