Find the inverse Laplace transform of the function. $\frac{1}{(z+5)^{3}}$

Factor to obtain a product of four terms and then reduce to three terms by applying the consensus theorem: X′Y′Z′ + XYZ

A Prolog database contains the following, where boss(X, Y ) means “X is Y’s boss” and supervisor(X, Y) means “X is Y’s supervisor”:

$$\begin{array}{l} \text{boss(mike, joan)}\\ \text{boss(judith, mike)}\\ \text{boss(anita, judith)}\\ \text{boss(judith, kim)}\\ \text{boss(kim, enrique)}\\ \text{boss(anita, sam)}\\ \text{boss(enrique, jefferson)}\\ \text{boss(mike, hamal)}\\ \text{supervisor(X, Y) <= boss(X, Y)}\\ \text{supervisor(X, Y) <= boss(X, Z) and supervisor (Z, Y)}\\ \end{array}$$

Find the results of the following queries: a. ?boss(X, sam) b. ?boss(judith, X) c. ?supervisor(anita, X)

Show how to make the 8-to-3 priority encoder of Figure 9-20 using two 4-to-2 priority encoders and any additional necessary gates.

Toe Computer Security Institute (CSI) conducts an annual survey of computer crin1e at U.S. businesses. CSI sends survey questionnaires to computer security personnel at all U.S. corporations and government agencies. Toe latest CSI survey was sent by post or email to 5,412 firms, and 351 organizations responded. Forty-one percent of the respondents admitted unauthorized use of computer systems at their firms during the year. (CSI Computer Crime and Security Survey, 2010/2011.) a. Identify the population of interest to CSI. b. Identify the data collection method used by CSI. Are there any potential biases in the method used? c. Describe the variable measured in the CSI survey. Is it quantitative or qualitative? d. What inference can be made from the study result?

Find the inverse Laplace transform of the function. $\frac{Z^{2}}{(z-2)^{3}}$

Write the d’Alembert solution for the problem $u_{t t}=c^{2} u_{x x}$ for $-\infty<x<\infty, t>0$ and $u(x, 0)=f(x), u_{t}(x, 0)=g(x)$ for $-\infty<x<\infty$. $c=1, f(x)=x^{2}, g(x)=-x$

A and B are subsets of a set S. Prove the following set identities by showing set inclusion in each direction.

$$\left.\begin{array}{l} \text { a. }(A \cup B)^{\prime}=A^{\prime} \cap B^{\prime} \\ \text { b. }(A \cap B)^{\prime}=A^{\prime} \cup B^{\prime} \end{array}\right\} \text { De Morgan's laws }$$

c. $A \cup(B \cap A)=A$ d. $\left(A \cap B^{\prime}\right)^{\prime} \cup B=A^{\prime} \cup B$ e. $(A \cap B) \cup\left(A \cap B^{\prime}\right)=A$ f. $[A \cap(B \cup C)]^{\prime}=A^{\prime} \cup\left(B^{\prime} \cap C^{\prime}\right)$

Classify the origin of the system $\mathbf{X}^{\prime}=\mathbf{A} \mathbf{X}$ for the given coefficient matrix. If software is available, produce a phase portrait.

$$\mathbf{A}=\left(\begin{array}{cc} 7 & -17 \\ 2 & 1 \end{array}\right)$$

Assume $n \equiv 1$(mod m). Show that the function

$$f: \mathbb{Z}_{m} \rightarrow \mathbb{Z}_{m n}$$

given by $f\left([x]_{m}\right)=[n x]_{m n}$ is an injective homomorphism but not an isomorphism when $n \geq 2$.

Let R be a ring and a, b $\in$ R. (a) (a + b)(a - b) = ? (b) (a + b)$^{3}$ = ? (c) What are the answers in parts (a) and (b) if R is commutative?

Find the eigenfunction expansion of the given function in the eigenfunctions of the Sturm-Liouville problem. In each case, determine what this expansion converges to and graph the Nth partial sum of the expansion and the function on the same set of axes. $f(x)=\sin (2 x)$ for }$0 \leq x \leq \pi$ $y^{\prime \prime}+\lambda y=0 ; y^{\prime}(0)=y^{\prime}(\pi)=0 ; N=30$

Round to the nearest tenth. 2.75

Use > or < to compare the whole numbers. $74,328 \square 74,238$