The diploma ceremony process was as follows. Students lined up to be hooded. Professors Venkataraman and Rodriguez performed the actual hooding ceremony. Together, they could hood 12 students per minute, on average. After hooding, students waited at the top of the steps to the stage until a Faculty Marshal called their name. This past year, Professor Allayannis read the names of the Global MBA for Executives (GEMBA) students, Professor Wilcox read the names of the MBA for Executives (EMBA) students, and Professors Frank and Parmar read the names of the residential MBA students. There were 29 GEMBA students, 65 EMBA students, and 315 residential MBA students. Once their name was called, students walked across the stage to Dean Bruner, who handed out their diploma. Then they continued on across the rest of the stage and returned to their seat. The administration had set a target of finishing the diploma ceremony in 60 minutes. The Marshals called names at the rate of one every 7 seconds. It took students an average of 8.2 seconds to walk across the stage, shake the Dean’s hand, and receive their diploma. After the handshake, it took students an additional 2 seconds to depart from the stage. There were approximately five students on the stage at any given time (one being hooded, two waiting for their names to be called, one in the process of receiving the diploma and congratulatory handshake, and one finishing the walk across the stage.)

1. What is the takt time for the diploma ceremony? Answer in seconds.

2. What is the cycle time for the process? Answer in seconds.

3. What is the throughput time for a student from the time he/she begins the hooding process until he/she walks off the stage? Answer in seconds.

4. What is the throughput rate? Answer in students per hour.

5. Could the goal of a 60-minute diploma ceremony be met? Yes or no?why.

Consider the differential equation y′(t)+9y(t)=−4cos(5t)u(t),
with initial condition y(0)=4,

A)Find the Laplace transform of the solution Y(s).Y(s). Write the solution as a single fraction in s.

Y(s)= ______________

B) Find the partial fraction decomposition of Y(s). Enter all factors as first order terms in s, that is, all terms should be of the form (c/(s-p)), where c is a constant and the root p is a constant. Both c and p may be complex.

Y(s)= ____ + ______ +______

C) Find the inverse transform of Y(s). The solution must consist of all real terms.

L−1{Y(s)} = _______________________

Define the greatest lower bound for a set A ⊂ R. Let A and B be two non-empty subsets of R which are bounded below. Show glb(A ∪ B) = min{glb(A), glb(B)}.

1. Let V be real vector space (possibly infinite-dimensional), S, T ∈ L(V ), and S be in- vertible. Prove λ ∈ C is an eigenvalue of T if and only if λ is an eigenvalue of STS−1. Give a description of the set of eigenvectors of STS−1 associated to an eigenvalue λ in terms of the eigenvectors of T associated to λ.

2. Show that there exist square matrices A, B that have the same eigenvalues, but aren’t similar. Hint: Use the identity matrix as one of the matrices.

Take one step of Newton’s method to approximate a solution to the complex equation z ^5 − 1 = 0, with z0 = i. Simplify your result to identify the real and imaginary parts of your approximation. What is the nearest actual root?

If R is the 2×2 matrices over the real, show that R has nontrivial left and right ideals.?

hello
could you please solve this problem with the clear hands writing to read it please? Also the good explanation to understand the solution is by step by step please

thank

the subject is Modern Algebra

The set D = {b,c, d,l,n,p, s, w} consists of the eight dogs Bingley, Cardie, Duncan, Lily, Nico, Pushkin, Scout, and Whistle. There are three subsets B={d,l,n,s}, F = {c,l,p,s}. and R = {c,n,s,w} of black dogs, female dogs, and retrievers respectively.
(a) Suppose x is one of the dogs in D. Indicate how you can determine which dog x is by asking three yes-or-no questions about x.
(b) Define six subsets of the naturals {1,. .., 64}, each containing 32 numbers, such that you can determine any number n from the answers to the six membership questions for these sets.

(c) (harder) Is it possible to solve part (a) using three sets of dogs that do not have four elements each? What about part (b), with six sets that do not have 32 elements each? Explain your answer.

Reduce the following modular arithmetic WITHOUT THE USE OF A CALCULATOR: PLEASE STATE THE THEOREMS/RULES YOU USE AND EXPLAIN HOW. Thanks!!

a) 104^5 mod 2669

b) 11^132 mod 133

c) 2208^5 mod 2669

d) 7^1000 mod 5

e) 2^247 mod 35

Find all triples of a, b, c satisfying (a, b, c) = 10 and [a, b, c] = 100 simultaneouly

1. Let α < β be real numbers and N ∈ N.

(a). Show that if β − α > N then there are at least N distinct integers strictly between β and α.
(b). Show that if β > α are real numbers then there is a rational number q ∈ Q such β > q > α.

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2. Let x, y, z be real numbers.The absolute value of x is defined by

|x|= x, if x ≥ 0 ,

−x, if x < 0

Define the following statements. Assume that the product of two positive real numbers is positive.

(a). Show that |x−y| = |y−x|.

(b). Show that if z<0 and x ≤ y, then zy ≤ zx.

(c). Show that |x+y| ≤ |x|+|y|.

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Answer both questions plz. Will rate.

Problem 4. From order two to order three:
(a) Find the general solution of y′′′ + 3y′′ + 3y′ + y = 0.
(b) Write a differential equation given that the fundamental system of solutions is

ex,exsinx, excosx.
(c) Compute the general solution of xy′′′ + y′′ = x2. [Answer: C1x ln x + C2x + C3 + x4 .]

prove that the Luxemberg norm is a norm on L_phi

in a cartesian coordinate space, a curved path is defined as y=sin(x).Find the vector that is normal to the path everywhere.(xy:no unit)

Suppose f is a function defined for all real numbers which has a maximum value of 5 and a minimum value of −7. Label each of the following as MUST, MIGHT, or NEVER true. Explain, and if you say might, give an example of yes and an example of no.

A The maximum value of f(|x|) is 7.

B The maximum value of f(|x|) is 5.

C The maximum value of f(|x|) is 0.

D The minimum value of f(|x|) is 7.

E The minimum value of f(|x|) is 5.

F The minimum value of f(|x|) is 0.

G The maximum value of |f(x)| is 7.

H The maximum value of |f(x)| is 5.

I The maximum value of |f(x)| is 0.

J The minimum value of |f(x)| is 7.

K The minimum value of |f(x)| is 5.

L The minimum value of |f(x)| is 0.

Now suppose f is a continuous function defined for all real numbers which has a maximum value of 5 and a minimum value of −7. Which of the answers above stay the same (why?), and which change (to what, and why?)