Sheets of aluminum from a supplier have a thickness that is normally distributed with a mean of 50 mm and a standard deviation of 4 mm (call this random variable X). Your company compresses the aluminum with a tool that is normally distributed with a mean of 20 mm and a standard deviation of 3 mm (call this random variable Y). You are interested in the random variable V = X – Y, the random variable V is the final aluminum thickness.

1. What is the probability that the outputted aluminum (that is, V), will be between 25 mm and 32 mm?

2. What is the probability that the outputted aluminum (that is, V), will be between 26.5 mm and 33.5 mm?

3. If the company had the choice between compressing aluminum to between 25-32 mm or 26.5-33.5 mm, then which is preferred (or neither)?

4. In one or two sentences, why is one preferred (if either) over the other [continuation of 3.3]; if neither are preferred, then why?

Sheets of aluminum from a supplier have a thickness that is normally distributed with a mean of 50 mm and a standard deviation of 4 mm (call this random variable X). Your company compresses the aluminum with a tool that is normally distributed with a mean of 20 mm and a standard deviation of 3 mm (call this random variable Y). You are interested in the random variable V = X – Y, the random variable V is the final aluminum thickness. 3.1. What is the probability that the outputted aluminum (that is, V), will be between 25 mm and 32 mm? 3.2. What is the probability that the outputted aluminum (that is, V), will be between 26.5 mm and 33.5 mm? 3.3. If the company had the choice between compressing aluminum to between 25-32 mm or 26.5-33.5 mm, then which is preferred (or neither)? 3.4. In one or two sentences, why is one preferred (if either) over the other [continuation of 3.3]; if neither are preferred, then why?

Q. It was thought that at a particular point in time 15% of the rabbit population in a region was infected by RHDV1-K5 virus. At the time a researcher trapped 25 rabbits from this region and had each tested to see if it carries virus. The number of rabbits in this sample with the virus is denoted by V.

a) Write down the possible values of V.

b) State a suitable distribution for V and provide the parameter(s) for the distribution.

c) Determine the Expected value of V and interpret this value in context to the research.

d) USe and show manual calculation to determine the probability that at least 2 rabbits have the virus.

e) It transpired that 20 of the rabbit did in fact carry the virus. Use R commander to determine the probability that 20 or more rabbit will have the virus.

f) Considering your answer to part e), say if this casts doubt on the original understanding of the prevalence of the virus in this region at that point in time. Give brief explanation.  

Write a program in C++ that converts a positive integer into the Roman number system. The Roman number system has digits

I      1

V    5

X    10

L     50

C     100

D    500

M    1,000

Numbers are formed according to the following rules. (1) Only numbers up to 3,999 are represented. (2) As in the decimal system, the thousands, hundreds, tens, and ones are expressed separately. (3) The numbers 1 to 9 are expressed as

I             1

II            2

III        3

IV        4

V           5

VI        6

VII        7

VIII       8

IX        9

As you can see, an I preceding a V or X is subtracted from the value, and you can never have more than three I’s in a row. (4) Tens and hundreds are done the same way, except that the letters X, L, C and C, D, M are used instead of I and V, X, respectively.

I am not even sure what the question is for the problem below, but I have highlighted what I think the question is further down:

Let v = (v1, v2) and w = (w1, w2) be vectors in 2 space.

The Scalar Product of v and whose notation is v (dot) w, is defined as follows: V (dot) w : = v1*w1 + v2 *w2

The scalar product (aka inner product, or dot product) Scalar product of 2 vectors in 2-space using 4 float parameters (the function scalarProduct 1)

ACTUAL QUESTION (I think ) - Code the following in Python:

Write a docstring; then write some test function calls; then implement the body of the function

Some test data: (1., 1.) · (2,3) = 5 (or, as a function call: scalarProduct1)

(1., 1., 2., 3.) (1.,1.) · (2,0) = 2

(1., 1.) · (0,2) =2

(1., 1.,) · (4,5) =23

calculate an independent t-test and describe the results.

You are a researcher examining student success at Kern County colleges and universities. You noticed that majority of students in Kern County are not performing as well as the students in Los Angeles County and San Luis Obispo County. Therefore, you decided to research factors that influence student success. One factor repeated in several literatures is a support system. Previous literature indicated that students who have a support system that values education will perform better in higher education than students who do not have a support system that values education. You decided to assess the support system of students in Kern County. Your independent variable is “support system.” You have two levels for your support system “students with a support system that values education” and “students without a support system that values education.” Your dependent variable that you are measuring is “college success.” You are measuring college success by assessing the student’s GPA. You interview 80 students with and without support systems and measured their GPAs. You obtained 41 student participants with a support system and 39 students without a support system. With the results obtained from the data, you will be able to generalize from the sample of 41 Kern County colleges and universities students to the population of all students in Kern County colleges and universities. Here is the GPA data that you obtained:

3.9 Cases Burger King v. Rudzewicz Burger King Corp. v. Rudzewicz 471 U.S. 462 (U.S. Supreme Court 1985)

Summary

Burger King Corp. is a Florida corporation with principal offices in Miami. It principally conducts restaurant business through franchisees. The franchisees are licensed to use Burger King’s trademarks and service marks in standardized restaurant facilities. Rudzewicz is a Michigan resident who, with a partner (MacShara) operated a Burger King franchise in Drayton Plains, Michigan. Negotiations for setting up the franchise occurred in 1978 largely between Rudzewicz, his partner, and a regional office of Burger King in Birmingham, Michigan, although some deals and concessions were made by Burger King in Florida. A preliminary agreement was signed in February of 1979. Rudzewicz and MacShara assumed operation of an existing facility in Drayton Plains and MacShara attended prescribed management courses in Miami during the four months following Feb. 1979. Rudzewicz and MacShara bought $165,000 worth of restaurant equipment from Burger King’s Davmor Industries division in Miami. But before the final agreements were signed, the parties began to disagree over site-development fees, building design, computation of monthly rent, and whether Rudzewicz and MacShara could assign their liabilities to a corporation they had formed. Negotiations took place between Rudzewicz, MacShara, and the Birmingham regional office; but Rudzewicz and MacShara learned that the regional office had limited decision-making power and turned directly to Miami headquarters for their concerns. The final agreement was signed by June 1979 and provided that the franchise relationship was governed by Florida law, and called for payment of all required fees and forwarding of all relevant notices to Miami headquarters. The Drayton Plains restaurant did fairly well at first, but a recession in late 1979 caused the franchisees to fall far behind in their monthly payments to Miami. Notice of default was sent from Miami to Rudzewicz, who nevertheless continued to operate the restaurant as a Burger King franchise. Burger King sued in federal district court for the southern district of Florida. Rudzewicz contested the court’s personal jurisdiction over him, since he had never been to Florida. The federal court looked to Florida’s long arm statute and held that it did have personal jurisdiction over the non-resident franchisees, and awarded Burger King a quarter of a million dollars in contract damages and enjoined the franchisees from further operation of the Drayton Plains facility. Franchisees appealed to the 11th Circuit Court of Appeals and won a reversal based on lack of personal jurisdiction. Burger King petitioned the Supreme Ct. for a writ of certiorari. Justice Brennan delivered the opinion of the court. The Due Process Clause protects an individual’s liberty interest in not being subject to the binding judgments of a forum with which he has established no meaningful “contacts, ties, or relations.” International Shoe Co. v. Washington. By requiring that individuals have “fair warning that a particular activity may subject [them] to the jurisdiction of a foreign sovereign,” the Due Process Clause “gives adegree of predictability to the legal system that allows potential defendants to structure their primary conduct with some minimum assurance as to where that conduct will and will not render them liable to suit.”… Where a forum seeks to assert specific jurisdiction over an out-of-state defendant who has not consented to suit there, this “fair warning” requirement is satisfied if the defendant has “purposefully directed” his activities at residents of the forum, and the litigation results from alleged injuries that “arise out of or relate to” those activities, Thus “[t]he forum State does not exceed its powers under the Due Process Clause if it asserts personal jurisdiction over a corporation that delivers its products into the stream of commerce with the expectation that they will be purchased by consumers in the forum State” and those products subsequently injure forum consumers. Similarly, a publisher who distributes magazines in a distant State may fairly be held accountable in that forum for damages resulting there from an allegedly defamatory story.… …[T]he constitutional touchstone remains whether the defendant purposefully established “minimum contacts” in the forum State.…In defining when it is that a potential defendant should “reasonably anticipate” out-of-state litigation, the Court frequently has drawn from the reasoning of Hanson v. Denckla, 357 U.S. 235, 253 (1958): The unilateral activity of those who claim some relationship with a nonresident defendant cannot satisfy the requirement of contact with the forum State. The application of that rule will vary with the quality and nature of the defendant’s activity, but it is essential in each case that there be some act by which the defendant purposefully avails itself of the privilege of conducting activities within the forum State, thus invoking the benefits and protections of its laws. This “purposeful availment” requirement ensures that a defendant will not be haled into a jurisdiction solely as a result of “random,” “fortuitous,” or “attenuated” contacts, or of the “unilateral activity of another party or a third person,” [Citations] Jurisdiction is proper, however, where the contacts proximately result from actions by the defendant himself that create a “substantial connection” with the forum State. [Citations] Thus where the defendant “deliberately” has engaged in significant activities within a State, or has created “continuing obligations” between himself and residents of the forum, he manifestly has availed himself of the privilege of conducting business there, and because his activities are shielded by “the benefits and protections” of the forum’s laws it is presumptively not unreasonable to require him to submit to the burdens of litigation in that forum as well. Jurisdiction in these circumstances may not be avoided merely because the defendant did not physically enter the forum State. Although territorial presence frequently will enhance a potential defendant’s affiliation with a State and reinforce the reasonable foreseeability of suit there, it is an inescapable fact of modern commercial life that a substantial amount of business is transacted solely by mail and wire communications across state lines, thus obviating the need for physical presence within a State in which business is conducted. So long as a commercial actor’s efforts are “purposefully directed” toward residents of another State, we have consistently rejected the notion that an absence of physical contacts can defeat personal jurisdiction there. Once it has been decided that a defendant purposefully established minimum contacts within the forum State, these contacts may be considered in light of other factors to determine whether the assertion of personal jurisdiction would comport with “fair play and substantial justice.” International Shoe Co. v. Washington, 326 U.S., at 320. Thus courts in “appropriate case[s]” may evaluate “the burden on the defendant,” “the forum State’s interest in adjudicating the dispute,” “the plaintiff’s interest in obtaining convenient and effective relief,” “the interstate judicial system’s interest in obtaining the most efficient resolution of controversies,” and the “shared interest of the several States in furthering fundamental substantive social policies.” These considerations sometimes serve to establish the reasonableness of jurisdiction upon a lesser showing of minimum contacts than would otherwise be required. [Citations] Applying these principles to the case at hand, we believe there is substantial record evidence supporting the District Court’s conclusion that the assertion of personal jurisdiction over Rudzewicz in Florida for the alleged breach of his franchise agreement did not offend due process.… In this case, no physical ties to Florida can be attributed to Rudzewicz other than MacShara’s brief training course in Miami. Rudzewicz did not maintain offices in Florida and, for all that appears from the record, has never even visited there. Yet this franchise dispute grew directly out of “a contract which had a substantial connection with that State.” Eschewing the option of operating an independent local enterprise, Rudzewicz deliberately “reach[ed] out beyond” Michigan and negotiated with a Florida corporation for the purchase of a long-term franchise and the manifold benefits that would derive from affiliation with a nationwide organization. Upon approval, he entered into a carefully structured 20-year relationship that envisioned continuing and wide-reaching contacts with Burger King in Florida. In light of Rudzewicz’ voluntary acceptance of the long-term and exacting regulation of his business from Burger King’s Miami headquarters, the “quality and nature” of his relationship to the company in Florida can in no sense be viewed as “random,” “fortuitous,” or “attenuated.” Rudzewicz’ refusal to make the contractually required payments in Miami, and his continued use of Burger King’s trademarks and confidential business information after his termination, caused foreseeable injuries to the corporation in Florida. For these reasons it was, at the very least, presumptively reasonable for Rudzewicz to be called to account there for such injuries. …Because Rudzewicz established a substantial and continuing relationship with Burger King’s Miami headquarters, received fair notice from the contract documents and the course of dealing that he might be subject to suit in Florida, and has failed to demonstrate how jurisdiction in that forum would otherwise be fundamentally unfair, we conclude that the District Court’s exercise of jurisdiction pursuant to Fla. Stat. 48.193(1)(g) (Supp. 1984) did not offend due process. The judgment of the Court of Appeals is accordingly reversed, and the case is remanded for further proceedings consistent with this opinion. It is so ordered.

Questions:

1. Why did Burger King sue in Florida rather than in Michigan?

2. If Florida has a long-arm statute that tells Florida courts that it may exercise personal jurisdiction over someone like Rudzewicz, why is the court talking about the due process clause?

3. Why is this case in federal court rather than in a Florida state court?

4. If this case had been filed in state court in Florida, would Rudzewicz be required to come to Florida? Explain.

Based on Court Case United States v. Bestfoods 113F.3d 572 (1998)

United States v. Bestfoods

113 F.3d 572 (1998)

SOUTER, JUSTICE

The United States brought this action under §107(a)(2) of the Comprehensive Environmental Response, Compensation, and Liability Act of 1980 (CERCLA) against, among others, respondent CPC International, Inc., the parent corporation of the defunct Ott Chemical Co. (Ott II), for the costs of cleaning up industrial waste generated by Ott II’s chemical plant. Section 107(a)(2) authorizes suits against, among others, “any person who at the time of disposal of any hazardous substance owned or operated any facility.” The trial focused on whether CPC, as a parent corporation, had “owned or operated” Ott II’s plant within the meaning of §107(a)(2). The District Court said that operator liability may attach to a parent corporation both indirectly, when the corporate veil can be pierced under state law, and directly, when the parent has exerted power or influence over its subsidiary by actively participating in, and exercising control over, the subsidiary’s business during a period of hazardous waste disposal. Applying that test, the court held CPC liable because CPC had selected Ott II’s board of directors and populated its executive ranks with CPC officials, and another CPC official had played a significant role in shaping Ott II’s environmental compliance policy.

The Sixth Circuit reversed. Although recognizing that a parent company might be held directly liable under §107(a)(2) if it actually operated its subsidiary’s facility in the stead of the subsidiary, or alongside of it as a joint venturer, that court refused to go further. Rejecting the District Court’s analysis, the Sixth Circuit explained that a parent corporation’s liability for operating a facility ostensibly operated by its subsidiary depends on whether the degree to which the parent controls the subsidiary and the extent and manner of its involvement with the facility amount to the abuse of the corporate form that will warrant piercing the corporate veil and disregarding the separate corporate entities of the parent and subsidiary. Applying Michigan veil-piercing law, the court decided that CPC was not liable for controlling Ott II’s actions, since the two corporations maintained separate personalities and CPC did not utilize the subsidiary form to perpetrate fraud or subvert justice.

Held:

1. When (but only when) the corporate veil may be pierced, a parent corporation may be charged with derivative CERCLA liability for its subsidiary’s actions in operating a polluting facility. It is a general principle of corporate law that a parent corporation (so-called because of control through ownership of another corporation’s stock) is not liable for the acts of its subsidiaries. CERCLA does not purport to reject this bedrock principle, and the Government has indeed made no claim that a corporate parent is liable as an owner or an operator under §107(a)(2) simply because its subsidiary owns or operates a polluting facility. But there is an equally fundamental principle of corporate law, applicable to the parent-subsidiary relationship as well as generally, that the corporate veil may be pierced and the shareholder held liable for the corporation’s conduct when, inter alia, the corporate form would otherwise be misused to accomplish certain wrongful purposes, most notably fraud, on the shareholder’s behalf. CERCLA does not purport to rewrite this well-settled rule, either, and against this venerable common-law backdrop, the congressional silence is audible. Cf. Edmonds v. Compagnie Generale Transatlantique, 443 U.S. 256, 266-267. CERCLA’s failure to speak to a matter as fundamental as the liability implications of corporate ownership demands application of the rule that, to abrogate a common-law principle, a statute must speak directly to the question addressed by the common law. United States v. Texas, 507 U.S. 529, 534.

2. A corporate parent that actively participated in, and exercised control over, the operations of its subsidiary’s facility may be held directly liable in its own right under §107(a)(2) as an operator of the facility.

(a) Derivative liability aside, CERCLA does not bar a parent corporation from direct liability for its own actions. Under the plain language of §107(a)(2), any person who operates a polluting facility is directly liable for the costs of cleaning up the pollution, and this is so even if that person is the parent corporation of the facility’s owner. Because the statute does not define the term “operate,” however, it is difficult to define actions sufficient to constitute direct parental “operation.” In the organizational sense obviously intended by CERCLA, to “operate” a facility ordinarily means to direct the workings of, manage, or conduct the affairs of the facility. To sharpen the definition for purposes of CERCLA’s concern with environmental contamination, an operator must manage, direct, or conduct operations specifically related to the leakage or disposal of hazardous waste, or decisions about compliance with environmental regulations.

(b) The Sixth Circuit correctly rejected the direct liability analysis of the District Court, which mistakenly focused on the relationship between parent and subsidiary, and premised liability on little more than CPC’s ownership of Ott II and its majority control over Ott II’s board of directors. Because direct liability for the parent’s operation of the facility must be kept distinct from derivative liability for the subsidiary’s operation of the facility, the analysis should instead have focused on the relationship between CPC and the facility itself, i.e., on whether CPC “operated” the facility, as evidenced by its direct participation in the facility’s activities. That error was compounded by the District Court’s erroneous assumption that actions of the joint officers and directors were necessarily attributable to CPC, rather than Ott II, contrary to time-honored common-law principles. The District Court’s focus on the relationship between parent and subsidiary (rather than parent and facility), combined with its automatic attribution of the actions of dual officers and directors to CPC, erroneously, even if unintentionally, treated CERCLA as though it displaced or fundamentally altered common-law standards of limited liability. The District Court’s analysis created what is in essence a relaxed, CERCLA-specific rule of derivative liability that would banish traditional standards and expectations from the law of CERCLA liability. Such a rule does not arise from congressional silence, and CERCLA’s silence is dispositive.

(c) Nonetheless, the Sixth Circuit erred in limiting direct liability under CERCLA to a parent’s sole or joint venture operation, so as to eliminate any possible finding that CPC is liable as an operator on the facts of this case. The ordinary meaning of the word “operate” in the organizational sense is not limited to those two parental actions, but extends also to situations in which, e.g., joint officers or directors conduct the affairs of the facility on behalf of the parent, or agents of the parent with no position in the subsidiary manage or direct activities at the subsidiary’s facility. Norms of corporate behavior (undisturbed by any CERCLA provision) are crucial reference points, both for determining whether a dual officer or director has served the parent in conducting operations at the facility, and for distinguishing a parental officer’s oversight of a subsidiary from his control over the operation of the subsidiary’s facility. There is, in fact, some evidence that an agent of CPC alone engaged in activities at Ott II’s plant that were eccentric under accepted norms of parental oversight of a subsidiary’s facility: The District Court’s opinion speaks of such an agent who played a conspicuous part in dealing with the toxic risks emanating from the plant’s operation. The findings in this regard are enough to raise an issue of CPC’s operation of the facility, though this Court draws no ultimate conclusion, leaving the issue for the lower courts to reevaluate and resolve in the first instance.

113 F.3d 572, vacated and remanded.

What norms of corporate behavior does the court look to in determining whether an officer or a director is involved in the operation of a facility?

#include<vector>
#include<iostream>
using namespace std;

void println(const vector<int>& v)
{
   for (int x : v)
       cout << x << " ";
   cout << endl;
}
void println(const vector<string>& v)
{
   for (const string& x : v)
       cout << " "<< x << " ";
   cout << endl;
}

int main()
{
   vector<int> v0;
   cout << "An empty vector of integers: ";
   println(v0);
   vector<int> v1(3);
   cout << "A vector with three "
       << "value−initialized integers: ";
   println(v1);
   vector<string> v2(0);
   cout << "A vector with three empty "
       << "strings: ";
   println(v2);
   vector<int> v3(3, 17);
   cout << "A vector with three 17’s: ";
   println(v3);
   vector<int> v4(v3);
   cout << "A copy of the previous vector: ";
   println(v4);
   v4.front() = 1;
   v4.back() = 23;
   cout << "The last vector with its first "
       << "and last elements changed to 1 "
       << "and 23: ";
   println(v4);

Create a function append(v1, v2) that adds a copy of all the elements of vector v1 to the end of vector v2. The arguments are vectors of integers. Write a test driver

Objectives

To become familiar with the uses of Radioisotopes through use of the Internet.

To be able to use your knowledge and understanding of radioisotopes to contribute to the discussion board.

Background

According to our textbook, “radioisotopes are powerful tools for studying processes in biochemistry, medicine, material science, environmental studies and many other scientific and industrial fields.”

Below is a list of radioisotopes and their half-lives. You will be choosing one of these radioisotopes to explore in more detail.

Assignment

Choose one of the radioisotopes from the list or find a radioisotope that is not on the list but interests you.

Using your book and Internet resources, find five interesting pieces of information on the radioisotope you selected. Suggested pieces of information may include:

How is the radioisotope formed in nature (type of decay)?

Risks associated with the radioisotope

Number of subatomic nucleons present

Stability of the radioisotope

How this radioisotope is used.

Is the radioisotope used as a medical tracer? If yes, for what body part or process? Briefly explain.

(These are just a few suggestions. See if you can find other interesting facts.)

Remember to site your sources in APA style.

Respond to at least two other students.

Contribute to an ongoing discussion by responding to comments made to your posting or to comments made by other students to other postings.

Radioisotopes (half-life indicated)

Molybdenum-99 (66 h)

Technetium-99m (6 h)

Bismuth-213 (46 min)

Chromium-51 (28 d)

Cobalt-60 (10.5 mth)

Copper-64 (13 h

Dysprosium-165 (2 h

Erbium-169 (9.4 d)

Holmium-166 (26 h)

Iodine-125 (60 d)

Iridium-192 (74 d)

Iron-59 (46 d)

Lutetium-177 (6.7 d)

Palladium-103 (17 d)

Phosphorus-32 (14 d)

Potassium-42 (12 h)

Rhenium-186 (3.8 d)

Rhenium-188 (17 h)

Samarium-153 (47 h)

Selenium-75 (120 d)

Sodium-24 (15 h)

Strontium-89 (50 d)

Xenon-133 (5 d)

Ytterbium-169 (32 d)

Yttrium-90 (64 h)

Carbon-11 (20 m)

Nitrogen-13 (~10 m)

Oxygen-15 (~2 m)

Fluorine-18 (20 m)

Cobalt-57 (272 d)

Gallium-67 (78 h)

Indium-111 (2.8 d)

Iodine-123 (13 h)

Rubidium-82 (65 h)

Strontium-92 (25 d)

Thallium-201 (73 h)