A mass (m) with speed (v) experiences a perfectly elastic collision with an initially stationary mass (M). What is the ratio of the masses (m/M) if after the collision, m and M have the same speed (V) but opposite velocities?

1. In the L/N column in the table below, please type V if the value is a valid python integer value or N if the value is not a valid python string value.

1) a) Derive a relationship between the electric field (E) and electric potential (V) knowing that V is defined as the energy per unit test charge.

b) Based on the above derivation, state an alternate acceptable unit for (E).

Do male college students spend more time studying than female college students? This was one of the questions investigated by the authors of an article. Each student in a random sample of 46 male students at a university in England and each student in a random sample of 38 female students from the same university kept a diary of how he or she spent time over a 3-week period.

For the sample of males, the mean time spent studying per day was 283.0 minutes and the standard deviation was 160.4 minutes. For the sample of females, the mean time spent studying was 183.8 minutes and the standard deviation was 166.4 minutes. Is there convincing evidence that the mean time male students at this university spend studying is greater than the mean time for female students? Test the appropriate hypotheses using

α = 0.05.

(Use μ₁ for male students and μ₂ for female students.)

State the appropriate null and alternative hypotheses.

H₀: μ₁ − μ₂ > 0 and H_a: μ₁ − μ₂ < 0

H₀: μ₁ − μ₂ = 0 and H_a: μ₁ − μ₂ > 0

H₀: μ₁ − μ₂ < 0 and H_a: μ₁ − μ₂ > 0

H₀: μ₁ − μ₂ = 0 and H_a: μ₁ − μ₂ < 0

H₀: μ₁ − μ₂ > 0 and H_a: μ₁ − μ₂ = 0

Find the test statistic and P-value. (Use a table or technology. Round your test statistic to one decimal place and your P-value to three decimal places.)

t=

P-value=

State the conclusion in the problem context.

We reject H₀. We have convincing evidence that the mean time male students at this university spend studying is greater than the mean time for female students.

We fail to reject H₀. We have convincing evidence that the mean time male students at this university spend studying is greater than the mean time for female students.    

We fail to reject H₀. We do not have convincing evidence that the mean time male students at this university spend studying is greater than the mean time for female students.

We reject H₀. We do not have convincing evidence that the mean time male students at this university spend studying is greater than the mean time for female students.

Problem I:10-55 from the textbook (revised to include additional research).

The Morris Corporation is a very successful and profitable manufacturing corporation. The corporation just completed leasehold improvements of its corporate offices, primarily for its top executives. The president and founder of the corporation, Mr. Timothy Couch, is an avid collector of artwork and has instructed that the lobby and selected offices be decorated with rare collections of art. These expensive works of art were purchased by the corporation in accordance with Couch's directives. Couch justified the purchase of these works of art on the premise that (1) they are excellent investments and should increase in value in the future, (2) they provide an appropriate and impressive atmosphere when current and prospective customers visit the corporation's offices, and (3) the artwork is depreciable property and the corporation will be able to take sizable write-offs against income. The financial vice-president of the corporation has requested your advice as to the depreciability of the leasehold improvements and the art. Prepare a research memorandum for the financial vice-president on this issue. Include a discussion on the different depreciation methods permitted and the availability of those methods of depreciation for leaseholds and the art.

A partial list of research sources includes:

• Sections 167 and 179
• Rul. 68-232, 1968-1 C.B. 70
• Shauan C. Clinger, 60 T.C.M. 598 (1990).
• Simmon v. Comr., 103 T.C. 247 (1994), aff’d 95-2 USTC ¶ 50,552 (2d Cir. 1995) nonacq. 1996-2 C.B.I.
• Liddle v. Corm., 103 T.C. 285 (1994), aff’d, 95-2 USTC ¶ 50,488 (3^rd 1995)

In math course of this semester, there are 26 students and six of them are women.

(a) How many ways are there to select a group of four students from math course students so that there is at least one women in the group?

(b) If I randomly select a group of four, what is the probability that the group has women only?

(c) I randomly choose a group of four out of 26 students. Then, again, I choose randomly a group of four from 26 students. What is the probability that these two groups are the same

There are 68% of students drive to school in one university. Here is a sample of 20 students.

1) What is the probability that only 12 students drive to school?

2)What is the probability that no more than 15 students drive to school?

3) What is the probability that no more than 10 students drive to school?

4) What is the mean and standard deviation?

5) What is the percentage falling with 1 standard deviation? Does it satisfy the Empirical Rule?

Please explain with reasoning/steps please.

A professor has learned that eight students in her class of 31 will cheat on the exam. She decides to focus her attention on ten randomly chosen students during the exam.

a. What is the probability that she finds at least one of the students cheating? (Round your final answers to 4 decimal places.)

b. What is the probability that she finds at least one of the students cheating if she focuses on eleven randomly chosen students? (Round your final answers to 4 decimal places.)

Suppose a set of students want to create a virtual study groups. The set consists of 86 students on the eastern timezone, and 47 students in non-eastern time zones. Of the students in the eastern timezone, only 12 are not in Boston.

i. Suppose each group is made of 2 students, one in the eastern time zone and one from noneastern timezone. How many possible study groups are there?

ii. Suppose each group is made of 3 students, one in Boston, one in the eastern time zone but not in Boston, and one from the non-eastern timezone. How many groups can we make?

iii.suggest the Boston students form study groups amongst themselves first. The groups must have at most 5 people for optimal studying. He then secures 3 rooms for these groups. Each room can be safely filled by at most 5 study groups. Show if the students can form the groups safely and the groups fit in these 3 rooms, then there must be at least 3 people in each group.

iv. With rooms set, the in-person study groups can begin. However, the Boston students want to let their remote fellows join via a virtual meetings. How many remote students are guaranteed to join the most welcoming in-person group?

show your steps, please