Consider a regular 10-gon in which alternate vertices are painted red and blue. Show that the symmetry group of the painted 10-gon is
isomorphic to D5.

Find the solution of the given initial value problem.

2y''+y'-4y=0 ; y(0)=0 y'(0)=1

Current Issues

One of the biggest issues facing this company is the rise in prices of raw materials, especially the iconic almond, which due to drought in California has seen a price rise in recent years. In order to diversify their product line, Brown & Haley has started to expand its repertoire to including other nuts, such as cashews and macadamia nuts. They also have a project underway to test a new product line of packaged mixed nuts. Note that this scenario is fictional and the details do not represent actual operations of Brown & Haley.

The Scenario

The company is considering three nut mixes for inclusion in the new product line: Regular Mix, Deluxe Mix, and Holiday Mix. Each mix is made from 5 nuts in different combinations:

• The Regular Mix consists of 15% almonds, 25% Brazil nuts, 25% filberts, 10% pecans, and 25% walnuts
• The Deluxe Mix consists of 20% of each type of nut
• The Holiday Mix consists of 25% almonds, 15% Brazil nuts, 15% filberts, 25% pecans, and 20% walnuts

An accountant at Brown & Haley completed a cost analysis and determined that the profit contribution per pound is $1.65 for the Regular Mix, $1.90 for the Deluxe Mix, and $2.35 for the Holiday Mix.

Different nuts come from different suppliers. They are shipped in bulk containers and ordering a partial container is not possible. The currently available container sizes and costs are as follows:

One container of each of the types of nuts has been ordered and is on the way.

The sales and marketing teams have projected that initial demand for the different types of mixes will be as follows:

The president of Brown & Haley wants to commit to producing enough of the various mixes to meet the projected initial demand, even if not immediately profitable, in order to introduce these new mixes to the market.

PLEASE READ THE QUESTIONS

PLEASE READ THE QUESTIONS

PLEASE READ THE QUESTIONS

1. How much of each type of mix should be made using only the nuts already ordered and keeping in mind the President’s requirement to meet the initial demand for each type of mix?  
2. Sometimes small amounts of certain types of nuts become available in secondary markets. Which types of nuts should be pursued in order to increase profit?
3. The marketing department is proposing an upgrade to the packaging of the Holiday Mix that would decrease the profit contribution from $2.35 to $2.29 per pound. Would the number of pounds of each type of mix be changed in the optimal solution? (Note that the President would be impressed if you did not need to rerun Solver to answer this question)
4. If the President’s requirement to meet the initial demand for each type of mix were eliminated would profitability be impacted? If so, by how much?

Let sequence an be a bounded sequence and let E be the set of subsequential limits of an. prove that E is bounded and contains both sup E and inf E

Computational Geometry:

Let E be an unsorted set of n segments that are the edges of a convex polygon. Describe an O(nlogn) algorithm that computes from E a list containing all vertices of the polygon, sorted in clockwise order.

Don't copy other peoples wrong answer or you get down-voted.

Let ?V be the set of vectors in ?2R2 with the following definition of addition and scalar multiplication:
Addition: [?1?2]⊕[?1?2]=[0?2+?2][x1x2]⊕[y1y2]=[0x2+y2]
Scalar Multiplication: ?⊙[?1?2]=[0??2]α⊙[x1x2]=[0αx2]
Determine which of the Vector Space Axioms are satisfied.

A1. ?⊕?=?⊕?x⊕y=y⊕x for any ?x and ?y in ?V
? YES NO

A2. (?⊕?)⊕?=?⊕(?⊕?)(x⊕y)⊕z=x⊕(y⊕z) for any ?,?x,y and ?z in ?V
? YES NO

A3. There exists an element 00 in ?V such that ?⊕0=?x⊕0=x for each ?∈?x∈V
? YES NO

A4. For each ?∈?x∈V, there exists an element  −?−x in ?V such that ?⊕(−?)=0x⊕(−x)=0
? YES NO

A5.  ?⊙(?⊕?)=(?⊙?)⊕(?⊙?)α⊙(x⊕y)=(α⊙x)⊕(α⊙y) for each scalar ?α and any ?x and ?y ?V
? YES NO

A6. (?+?)⊙?=(?⊙?)⊕(?⊙?)(α+β)⊙x=(α⊙x)⊕(β⊙x) for any scalars ?α and  ?β and any ?∈?x∈V
? YES NO

A7. (??)⊙?=?⊙(?⊙?)(αβ)⊙x=α⊙(β⊙x) for any scalars ?α and  ?β and any ?∈?x∈V
? YES NO

A8. 1⊙?=?1⊙x=x for all ?∈?x∈V
? YES NO

Please someone assist me with the following problem please!

5. K-nearest-neighbor

Given the training data set shown below

Predict the label for a sample, [2, 2] by using

1) 1-nearest neighbor. Show steps.

2) 3-nearest neighbor. Show steps.

6. K-means

Given six data points,

X1: (1, 1)

X2: (5, 5)

X3: (1, 2)

X4: (4, 4)

X5: (2, 2)

X6: (4, 5)

1) Plot all the points on a two-dimensional plane.

2) Supposing initial centroids are (5, 3) and (2, 4), group six points into two clusters by using L1 norm distance measure. Show steps.

Solve the linear programming problem by the method of corners.

Consider the parabolas y=x^2 and y=a(x-b)^2+c, where a,b,c are all real numbers

(a) Derive an equation for a line tangent to both of these parabolas (show all steps with a proof, assuming that such a line exists)

(b) Assume that the doubly-tangent line has an equation y+Ax+B. Find an example of values of a,b,c (other than the ones given here) such that A,B ∈ Z

Based on Euler's identity, show the linear superposition of the eigenfunctions

A series circuit has a capacitor of 1.6×10−6 F and an inductor of 2.5 H. If the initial charge on the capacitor is 0.11×10−6C and there is no initial current, find the charge Q on the capacitor at any time t.

Enter an exact answer. Do not use thousands separator in the answer field.

Enclose arguments of functions in parentheses. For example, sin(2x).

Q(t) = ?

Find the appropriate series solutions about the origin.

for 2x(x+2)y''+y'-xy

Write the first three non-zero terms of the Taylor series of sin x near x0 = 3π/2. Sketch a plot of the curves for sin x and your approximation.

If n>=2, prove the number of prime factors of n is less than 2ln n.

Eight students (Anna, Brian, Carol, ...) are to be seated around a circular table with eight seats, and two seatings are considered the same arrangement if each student has the same student to their right in both seatings.(a) How many arrangements of the eight students are there?(b) How many arrangements of the eight students are there with Anna sitting next to Brian?(c) How many arrangements of the eight students are there with Brian sitting next to both Anna and Carol?(d) How many arrangements of the eight students are there with Brian sitting next to either Anna or Carol?

please explain how u got the numerical answer for each part, like what you multiplied to get it