Tommy Choi is the quality assurance director at Bimbo Bakery Corporate R&D Facility. They are investigating a moisture issue, where excessive moisture would create microbial growth negatively affecting the shelf life of their products. He sent a team to evaluate several moisture analyzers. Mettler Toledo is a leading analytical instrumentation supplier, and has several models with various capabilities.

Moisture for bread is about 37.5%, the value changes with the type of bread, quality of bread, quality of flour used, protein content of flour, season of wheat production, etc. Tommy conducted an extensive assessment, and found that +/- 2.3% gives the optimal shelf life.

3 models of Mettler Toledo moisture analyzers are being evaluated.

Model HC 103, priced at $4,500. Mean = 38.50%, standard deviation at 0.77%

Model HE 53 priced at $3,000. Mean = 36.50%, standard deviation at 1.1%

Model HX 204, priced at $12,000. Mean = 37.3%, standard deviation at 0.7%

All answers to 3 significant figures

1. What is the design tolerance (difference from Upper to Lower Specification Limits), from Tommy’s specifications.                            [ Select ]                       ["0.048", "0.046", "0.049", "0.050", "0.047"]      
2. What is Cp, Cpk of the HC 103                            [ Select ]                       ["0.999", "1.000", "0.998", "0.996", "0.997"]         ,                            [ Select ]                       ["0.566", "0.563", "0.564", "0.565", "0.567"]      
3. Cp, Cpk of the HE 53                            [ Select ]                       ["0.700", "0.697", "0.699", "0.696", "0.698"]         ,                            [ Select ]                       ["0.397", "0.394", "0.399", "0.396", "0.395"]      
4. Cp, Cpk of HX 204                            [ Select ]                       ["1.095", "1.098", "1.096", "1.097", "1.099"]         ,                            [ Select ]                       ["1.000", "1.002", "1.004", "1.001", "1.003"]      
5. Which moisture analyzer should Tommy be selecting

You're cleaning up your little nephew's toy room. There are T toys on the floor and n empty toy storage boxes. You randomly throw toys into boxes, and when you're done the box with the most toys contains N toys.

(a) What is the smallest that N could be when T=2n+1?

(b) What is the smallest that NN could be when T=kn+1?

(c) Now suppose that the number of toys T satisfies

T< n/(n−1)2.

Prove that when you are done cleaning up, there will be (at least) one pair of boxes that contain the same number of toys.

Hint

Argue the contrapositive by assuming that every box ends up a different number of toys. What is the fewest number of toys you could have started with?

Note:

• Note you are only being asked to explain part (c) of this activity.
• You do not need to apply the Pigeonhole Principle directly; instead you can engage in "tipping point" reasoning. See the hint provided in the activity.

You're cleaning up your little nephew's toy room. There are T toys on the floor and n empty toy storage boxes. You randomly throw toys into boxes, and when you're done the box with the most toys contains N toys.

(a) What is the smallest that N could be when T=2n+1?

(b) What is the smallest that NN could be when T=kn+1?

(c) Now suppose that the number of toys T satisfies

T< n/(n−1)2.

Prove that when you are done cleaning up, there will be (at least) one pair of boxes that contain the same number of toys.

Hint

Argue the contrapositive by assuming that every box ends up a different number of toys. What is the fewest number of toys you could have started with?

Note:

• Note you are only being asked to explain part (c) of this activity.
• You do not need to apply the Pigeonhole Principle directly; instead you can engage in "tipping point" reasoning. See the hint provided in the activity.

Elementary Linear Algebra (2nd Edition) . Chapter 6.5, Problem 64E. Please explain. I can calculate for the first column, but not the second. F(3;1) - F(-2;1) =Q(5;0)=(-3;4) =Q(5(1;0))=(-3;4) =>Q(1;0)=((-3/5);(4/5)) As you can see, I can solve for the first column, but I am stuck at the second one using this method. The problem is I cannot find a vector I can add (1;0) to to get some kind of (0;x) vector. Please help. I would appreciate it very much.

Showing your work, determine the values of m and n for which the complete bipartite graph Km,n has an

a) Euler circuit?

b) Euler path?

can someone please answer for me that quaestions. please make sure that i understand your work and handwriting. thank you

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1. We will sketch some quadrics, but in order to make sure our graphs have some accuracy, we will project the surfaces onto the 3 coordinate planes. For each equation, draw four separate graphs for the surface S:

i. the projection of S onto the xy-plane,

ii. the projection of S onto the xz-plane,

iii. the projection of S onto the zy-plane,

iv. the graph of S (axes optional).

[Note that I am not looking for works of art—just a rough understanding of the shape of the curves/ surfaces. For parts i–iii you may draw these curves in R³ (instead of R³ ).]

(a) Ellipsoid: x² + 2y² + 3z² = 6

(b) Paraboloid: z = 2x² + y² − 1

(c) Hyperboloid: x² + y² − z² = 1

(d) Hyperbolic Paraboloid: z = 2x² − y² + 1

2. Suppose we have two spheres: x² + y² + z² = 1 and (x − a)² + (y − b)² + (z − c)² = r² , where r > 0.

(a) Identify the centers and radii for each sphere.

(b) Give an example of values for a, b, c, and r so that the spheres intersect

i. no where,

ii. in a circle,

iii. (exactly) in a point.

(c) Suppose the spheres intersect somehow. The location of the coordinate axes do not change whether or not the planes intersect, so let’s “move” the spheres to make the equations easier.

x² + y² + z² = 1, x² + y² + (z − c)²= r² .

Show that their intersection must live in a plane.

3. Suppose we have two paraboloids: z = x² + y² − 2 and z = 4 − 2x² − y² , call them P₁ and P₂ respectively.

(a) In three separate graphs draw both projections of P₁ and P₂ onto the...

i. xy-plane,

ii. xz-plane,

iii. yz-plane.

(b) Verify that their curve of intersection is

r(t) = <√ 2 cos(t), √ 3 sin(t), sin² (t)> .

[Hint: Show that the curves lives on both surfaces.]

(c) Determine the unit tangent vector for the curve r(t) from part (b) at three t-values:

i. t = 0,

ii. t = π/3,

iii. t = π/2.

(d) Use your data from part (c) to show that the curve r(t) cannot live in a plane.

The answers are given already but can u pls give explanation on how they got each answer?

PART A Fill in the blank. Select “A” for Always, “B” for Sometimes, and “C” for Never.

1. A set of 3 vectors from R3 _S(B)_ forms a basis for R3.

2. A set of 2 vectors from R3 _N(C)_ spans R3.

3. A set of 4 vectors from R3 is _N(C)_ linearly independent.

4. A set of 2 vectors from R3 is _S(B)_ linearly independent.

5. If a set of vectors spans a vector space V then it is _S(B)_ a basis for V.

6. If B1 and B2 are two different sets of vectors and each forms a basis for the same vector space, then B1 and B2 _A_ have the same number of vectors.

7. If A is a set consisting of only the zero vector and V is a vector space, then A is _A_ a subspace for V.

8. If S is a linearly independent subset of a vector space V, then a given vector in Span(S) can _A_ be

   expressed uniquely as a linear combination of vectors in S.

Recurrent Nets:

(a) What is the “vanishing or exploding gradient problem” in recurrent nets?

(b) Give a weight initialization method that can mitigate the vanishing or exploding gradient problem.

(c) Recurrent nets are notoriously bad at “remembering” things for more than a few iterations. Give the names and quick descriptions of two methods that augment RNNs with a memory.

Consider the following initial value problem

dy/dt = 3 − 2*t − 0.5*y, y (0) = 1

We would like to find an approximation solution with the step size h = 0.05.

What is the approximation of y(0.1)?

A. Prove that R and the real interval (0, 1) have the same cardinality.

The region bounded by y=(1/2)x, y=0, x=2 is rotated around the x-axis.

A) find the approximation of the volume given by the right riemann sum with n=1 using the disk method. Sketch the cylinder that gives approximation of the volume.

B) Fine dthe approximation of the volume by the midpoint riemann sum with n=2 using disk method. sketch the two cylinders.

Prove that any non identity element of a free group is of infinite order

A newborn baby receives $2,000 on her birthday from her parents which is deposited into an account and invested in the Vanguard S&P 500 Index Fund. That is $2,000 deposited at t=0.

Assume that on every subsequent birthday up to and including her 16th birthday, the baby's parents deposit an additional $1,000 into the same account and invest the money in the Vanguard S&P 500 Index Fund. That is $1,000 deposited on each of t=1 through t=16. There are no more contributions.

Assume the investments in the Vanguard S&P 500 Index Fund grow at 6% every year after all taxes and expenses. What will be the balance in the account at the baby's 65th birthday, rounded to whole dollars?

u=sinatsinbx

Show that this function u is a solution of the partial differential equation u_tt = c ^ 2*u_xx and find the appropriate c.