A random number X is generated by reporting the sum of the digits on two randomly chosen ping-pong balls, one from a bucket of two balls labeled “0” and “1” and one from a bucket of three balls labeled “0”, “1”, and “2”.

Find the probability mass function of X by specifiying the values x that X can take and the probability p(x) = P (X = x) of each of those values.

Please explain how you arrived at the final answer.

When the contents of a 1000 cubic foot container full of basketballs is mixed with the contents of a 200 cubic foot container full of ping pong balls, the mixture does not completely fill a 1200 cubic foot container. explain this result in terms of the partial molar volumes of the basketballs and ping pong balls. state any assumptions you make.

Find the electric fields inside and outside of the billard ball and positive q charged ping-pong ball with r radius using Gauss's law.

Please read carefully. You must show all of your work for full credit. A correct answer with no work
shown is worth no points, but an incorrect or partial answer with some work shown may be worth
partial credit. Include explanations in each step.

Correct format for writing answers (using symbols and letters).

Question: What is the probability that fewer than 120 agreed?

Answer: P (x < 120)

I. An orange juice producer buys oranges from a large orange grove that has one variety of orange. The
amount of juice squeezed is approximately normally distributed, with a mean of 4.70 ounces, and a
standard deviation of 0.40 ounce.

a) What is the probability that a randomly selected orange will contain between 5.0 and 5.5
ounces of juice?

i. Probability statement:

ii. Calculations and draw:

b) 77 % or more of the oranges contain how many ounces of juice?

i. Calculations and draw:

c) Suppose that you select a sample of 25 oranges. What is the probability that the sample mean
amount of juice will be at least 4.6 ounces?

i. Calculate the mean and the standard deviation of the sampling distribution of x̅
and describe its shape.
μx̅=

σx̅=

Shape =
(Which rule apply: Sample comes from a population with a Normal distribution or because
The Central Limit Theorem)

ii. Probability statement:

iii. Calculations and draw:

2. The diameter of Ping-Pong balls manufactured at a large factory is approximately normally
distributed, with a mean of 1.30 inches and a standard deviation of 0.04 inch. If a random sample
of 16 Ping-Pong balls is selected from a population of 200 Ping-Pong balls, what is the probability
that the sample mean is between 1.31 and 1.33 inches?

i. Probability statement:

ii. Calculations and draw:

3. In a typical class, about 70% of students receive a C or better. Out of a random sample of 100
students, what is the probability that less than 60 receive a C or better?

i. Calculate the mean and the standard deviation of the sampling distribution of
pˆ and describe its shape.

 p
ˆ =

 p
ˆ =

Shape =(Which rule apply: Sample comes from a population with a Normal distribution or because
The Central Limit Theorem)

iii. Probability statement:

iv. Calculations and draw:

In a simple lottery, 10 ping pong balls numbered 1 through 10 are placed in a bucket and mixed thoroughly. Four balls are selected at random without replacement and their number is recorded. To play, you purchase a ticket for $1 and write down a 4-digit number. If the numbers match your ticket, you win $5,000.

a) How many different outcomes are possible?

b) What is your probability of winning.

c) Suppose that you can purchase a Mega ticket for $20. This means that the order does not matter for you to win. How many outcomes are now possible?

d) What is your probability of winning with a Mega ticket?

e) If you had $20 to play this lottery, would you rather buy 20 regular tickets or 1 Mega ticket?

During the 2^ndquarter of 2016 (June 2016 – August 2016) Ping-Pong Industries (located at 535 Main Street, Brentwood, NY 11717; Sales Tax ID# 44455566677) had total sales of $126,000. Of this amount, $21,000 were non-taxable. All of the sales were made in Suffolk County, and the company does not report gross credit card and debit card sales. This is not the final sales tax return for the company, and the company pays the sales tax amount that is due when filing the form. The company does not use a third-party designee, and prepares the sales tax forms on its own. The forms are signed by Alton Thompson, the CEO of the company (phone number: 631-555-8476, no e-mail address), and are filed on the due date for the form.

Based on the instructions that have been provided for Form ST-100, complete Form ST-100 of Ping-Pong Industries for the 2^ndquarter of the year.

1. Prove ├(∀x)A ∨ (∀x)B → (∀x)(A ∨ B).

2. Use the ∃ elimination technique —and ping-pong if/where needed— to show ├(∃x)A → (∃x)(B → A).

Appreciate you.

describe the effects of

mixed inhibition

Substrate inhibition

Product inhibition

Mechanism based/suicide inhibitors

Covalent intermediates

Ping Pong Mechanisms

Burst Kinetics

Allosteric Inhibitors