Question

In: Advanced Math

4. Suppose there are 99 lockers numbered 1 through 99, and 99 students numbered 1 through...

4. Suppose there are 99 lockers numbered 1 through 99, and 99 students numbered
1 through 99. Initially, all lockers are closed. Now each odd-numbered student
1, 3, 5, 7, · · · , 99, in numerical order from 1 through 99, will open/close all the lockers
that are numbered to be a multiple of the number of the student. For example, student
1 will open/close all the lockers, and student 3 will open/close all the lockers numbered
by 3, 6, 9, 12, · · · , 99, etc. Now find all the lockers that will be open when all students
are done.
Note: An answer containing a computer search only is worth 10 marks. But you can
start a computer search first and see if the results inspire you.

Solutions

Expert Solution


Related Solutions

(Language: c++)Write a program that displays a question and 4 possible answers numbered 1 through 4....
(Language: c++)Write a program that displays a question and 4 possible answers numbered 1 through 4. . The program should ask the user to answer 1, 2, 3, or 4 and tell them if they are correct or not. If the user enters anything besides 1, 2, 3, or 4 the program should return an error message example outout: whats 2+5? 1. 4 2. 7 3. 1 4. 0 // if user inputs anything other then option 2 the screen...
Suppose a 99% CI was provided: (15.2, 16.4), does this means that 99% of students take...
Suppose a 99% CI was provided: (15.2, 16.4), does this means that 99% of students take between 15.2 and 16.4 credits per semester? What was the sample mean used? What was the maximum error of the CI?
A box contains 4 tickets. 1 ticket is numbered 0, 1 ticket is numbered 1, and...
A box contains 4 tickets. 1 ticket is numbered 0, 1 ticket is numbered 1, and 2 tickets are numbered 2. Suppose n draws with replacement are made from this box. Let Sn be the sum of the numbers drawn. a) Approximate the probability P(S100=100)
In a situation where there are 25 students in a class (studentsare numbered from 1...
In a situation where there are 25 students in a class (students are numbered from 1 to 25) and they each have random birthdays so every birthday has a probability of 1/365, there is an event E[a, b] where a and b is each pair of students.1. How many possible events are there and what is the probability of each one?2. What is the expected number of pairs of students who would share a birthday (using linearity of expectation)?3. Would...
(Urn Poker) An urn contains 8 red balls numbered 1 through 8, 8 yellow balls numbered...
(Urn Poker) An urn contains 8 red balls numbered 1 through 8, 8 yellow balls numbered 1 through 8, 8 green balls numbered 1 through 8, and 8 black balls numbered 1 through 8. If 4 balls are randomly selected, find the probability of getting: three of a kind. (Three of a kind is 3 balls of one denomination and a fourth ball of a different denomination. e.g., 5,5,5,2) (c) two pairs. (A pair is two balls of the same...
C++ Primary U.S. interstate highways are numbered 1-99. Odd numbers (like the 5 or 95) go...
C++ Primary U.S. interstate highways are numbered 1-99. Odd numbers (like the 5 or 95) go north/south, and evens (like the 10 or 90) go east/west. Auxiliary highways are numbered 100-999, and service the primary highway indicated by the rightmost two digits. Thus, the 405 services the 5, and the 290 services the 90. Your program will prompt the user to type a highway number ("Please enter a highway number, Ex: 65: "), read in the number typed by the...
There are 7 balls numbered 1 through 7 placed in a bucket. What is the probability...
There are 7 balls numbered 1 through 7 placed in a bucket. What is the probability of reaching into the bucket and randomly drawing two balls numbered 6 and 3 without replacement, in that order? Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.
what is the probability? A jar contains 4 red marbles, numbered 1 to 4, and 12...
what is the probability? A jar contains 4 red marbles, numbered 1 to 4, and 12 blue marbles numbered 1 to 12. a) A marble is chosen at random. If you’re told the marble is blue, what is the probability that it has the number 2 on it? b) The first marble is replaced, and another marble is chosen at random. If you’re told the marble has the number 1 on it, what is the probability the marble is blue?
Consider rolling both a fair four-sided die numbered 1-4 and a fair six-sided die numbered 1-6...
Consider rolling both a fair four-sided die numbered 1-4 and a fair six-sided die numbered 1-6 together. After rolling both dice, let X denote the number appearing on the foursided die and Y the number appearing on the six-sided die. Define W = X +Y . Assume X and Y are independent. (a) Find the moment generating function for W. (b) Use the moment generating function technique to find the expectation. (c) Use the moment generating function technique to find...
Consider a fair four-sided die numbered 1-4 and a fair six-sided die numbered 1-6, where X...
Consider a fair four-sided die numbered 1-4 and a fair six-sided die numbered 1-6, where X is the number appearing on the four-sided die and Y is the number appearing on the six-sided die. Define W=X+Y when they are rolled together. Assuming X and Y are independent, (a) find the moment generating function for W, (b) the expectation E(W), (c) and the variance Var(W). Use the moment generating function technique to find the expectation and variance.
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT