how do you solve pythagerom therom

Suppose you are playing a game of Yahtzee. You know that you play with 5 dice, each with 6 sides. Since the dice are all rolled at the same time, let the roll (5, 4, 3, 2, 1) to be equal to (2, 4, 5, 1, 3). Assume for this question that we will only be rolling the dice once.  (i) How many ways can you roll all the dice? (ii) To win 50 points you would need all the dice to roll the same number (ex. (1, 1, 1, 1, 1)). How many ways can you win the 50 points? (iii) Suppose you are trying to get your dice to roll only consecutive numbers (ex. (1, 2, 3, 4, 5) or (2, 3, 4, 5, 6)) How many different ways are there to do this? (iv) Suppose instead you are trying to get your dice to roll 4 consecutive numbers (ex. (1, 2, 3, 4, 1) or (2, 3, 4, 5, 3)) How many different ways are there to do this? (make sure to not count any only consecutive numbers) This is a combinatorics math counting problem.

In a gambling game, I roll two dice and win $1 if the sum of my two rolls is largerthan 7. I lose $1 if the sum of my two rolls is smaller than 7. In any other cases, Idon’t lose or win anything. I am going to repeat this game 72 times.  c) Now make a box model for the number of times I win, including the values onthe tickets, the number of repeats of each ticket, and how many draws we willmake with replacement from the box.     The average of the tickets in the box from (c) is ___________ and the SD is___________.

You have worked for the Department of Administrative Affairs (DAA) for 27 years, and you still have little or no idea exactly what your job entails. To make your life a little more interesting, you have decided on the following course of action. Every Friday afternoon, you will use your desktop computer to generate a random digit from 0 to 4 (inclusive). If the digit is a zero, you will immediately quit your job, never to return. Otherwise, you will return to work the following Monday. (a) Use the states (1) employed by the DAA and (2) not employed by the DAA to set up the transition matrix P for the system with decimal entries.         Calculate P2.         Calculate P3.         (b) What is the probability that you will still be employed by the DAA after each of the next three weeks? one week       two weeks       three weeks       (c) What are your long-term prospects for employment at the DAA?  a. Eventually, you will quit your job. b. You…

7.) Several years ago, the US began running out of telephone numbers. Telephone companies introduced new area codes and numbers were used up, and eventually almost all area codes were used up. (a) Until recently, all area codes had a 0 or 1 as the middle digit, and the first digit could not be 0 or 1. How many such area codes are possible? (b) The actual number of area codes under this system was 152. What could be the cause of the discrepancy between this number and your answer to part (a)?

In a certain year, a state switched from a 6/45 lottery to a 6/49 lottery. Later, the state switched again to a 6/47 lottery. How much more probable is it that one will win the 6/45 lottery than the 6/49 lottery? (Round your answer to the nearest whole number.)

An industrial engineer has found that when she takes a sample of size 5 of a product, 90% of the time there are no defectives in the sample, 3% of the time there is 1 defective, 2% of the time there are 2 defectives, 2% of the time there are 3 defectives, 2% of the time there are 4 defectives, and 1% of the time there are 5 defectives. What is the robability of taking a sample that has at least 3 defectives in the 5? O 7% O 5% O 9% O 15%

Suppose that we roll three (six-sided) dice 600 times. Find an approximation for theprobability that we obtain the “triple-one” combination (each dice showing the value 1)at most 3 times.

Question 11 P(BA)= Be sure to give probability as a decimal to two decimal places. Question 12 C en P(AB9)= SEPERATE Be sure to give probability as a decimal to two decimal places.

21 The Ebola virus has an infection rate of 11% per day as compared to the SARS virus, which has a rate of 4% per day. If there were one case of Ebola and 30 cases of SARS initially reported to authorities and cases are reported each day, which statement is true? At day 10 and day 53 there are more Ebola cases. (2) At day 10 and day 53 there are more SARS cases. (3) At day 10 there are more SARS cases, but at day 53 there are more Ebola cases. (4) At day 10 there are more Ebola cases, but at day 53 there are more SARS cases.