Determine the location and value of the absolute extreme values of f on the given interval, if they exist. $f(x)=3 x^{2 / 3}-x \text { on }[0,27]$

According to Global Research News (Mar. 4, 2014), one-fourth of all rough diamonds produced in the world are blood diamonds. (Any diamond that is mined in a war zone - often by children - in order to finance a warlord's activity, an insurgency, or an invading army's effort is considered a blood diamond.) Also, 90% of the world's rough diamonds are processed in Surat, India, and of these diamonds, one-third are blood diamonds. Find the probability that a rough diamond is not a blood diamond.

Using RSA encryption/decryption, let p = 5 and q = 3. Then n = 15 and $\varphi(n)=4 \cdot 2=8.$ Pick e = 3. a. Use the Euclidean algorithm to find the value of d. b. Encode T = 8 using the public key (n, e). c. Decode your answer to part (b) to retrieve the 8.

Four of the minterms of the completely specified function f(a, b, c, d) are $m_{0}, m_{1}, m_{4}$ and $m_5$. (a) Specify additional minterms for f so that f has two prime implicants with one literal, two prime implicants with two literals, and no other prime implicants. (b) For each prime implicant, give its algebraic representation and specify whether it is an essential prime implicant. (c) Determine all minimum sum-of-products expressions for f .

Let S, $T: \mathbb{R}^{3} \rightarrow \mathbb{R}^{3}$ be defined by

$$T\left(\left[\begin{array}{l} x \\ y \\ z \end{array}\right]\right)=\left[\begin{array}{c} x-y-z \\ 2 y+2 z \\ -x+y+z \end{array}\right]$$

and

$$S\left(\left[\begin{array}{l} x \\ y \\ z \end{array}\right]\right)=\left[\begin{array}{c} 3 x-z \\ x \\ z \end{array}\right]$$

. a. Find the matrix representation for the given linear operator relative to the standard basis. b. Compute the image of

$$\mathbf{v}=\left[\begin{array}{r} -1 \\ 1 \\ 3 \end{array}\right]$$

directly and using the matrix found in part (a). -3T+2S

Define $T: M_{2 \times 2} \rightarrow \mathbb{R}$ by T(A) = tr(A). Find the matrix $[T]_{B}^{B^{\prime}}$, where B is the standard basis for $M_{2 \times 2}$ and $B^{\prime}=\{1\}$.

Write a number for the given words. six and two hundredths

Give an example of an abelian group of order 4 in which every nonidentity element a satisfies a * a = e.

Determine whether the subset S of $\mathbb{R}^{3}$ is a subspace.

The binary search algorithm is used with the following list; x has the value “Chicago.” Name the elements against which x is compared. Boston, Charlotte, Indianapolis, New Orleans, Philadelphia, San Antonio, Yakima

Answer the following true–false question. Existential instantiation should be used only after universal instantiation.

Determine whether the function $T: \mathbb{R}^{2} \rightarrow \mathbb{R}^{2}$ is a linear transformation.

$$T\left(\left[\begin{array}{l} x \\ y \end{array}\right]\right)=\left[\begin{array}{c} x+y \\ x-y+2 \end{array}\right]$$

Let $f: \mathbb{Z} \rightarrow \mathbb{Z}_{6}$ be the homomorphism. Let

$$K=\{a \in \mathbb{Z} | f(a)=[0]\}$$

Prove that K is a subring of $\mathbb{Z}$.

Divide. $85)\overline{1,450}$