Given bags are labelled to any or all the coins in every bag have an equivalent weight. Some bags have coins of weight ten g, others have coins of weight eleven gm. I choose some random coins severally from bags five to 1 Their total weight comes bent on 323 gm. Then the merchandise of the labels of the baggage having 11 gm coins is toilet
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- A drawer contains 7 pair of socks where 8 socks are white, and 6 are red. In how many ways we can take 14 random socks out of the drawer so each sock is next to its matching pair. a. 441 ways b. 42 ways c. 1225 ways d. 70 waysConsider a tournament between N teams, each team playing each of the other teams. Show (by example) there is a tournament that might occur, where every team is beaten by some team.A high school has 1000 students and 1000 lockers, one locker for each student. On the first day of school, theprincipal plays the following game: She asks the first student to open all the lockers. She then asks the secondstudent to close all the even-numbered lockers. The third student is asked to check every third locker. If it isopen, the student closes it; if it is closed, the student opens it. The fourth student is asked to check every fourthlocker. If it is open, the student closes it; if it is closed, the student opens it. The remaining students continuethis game. In general, the nth student checks every nth locker. If it is open, the student closes it; if it is closed,the student opens it. After all the students have taken turns, some of the lockers are open and some are closed.The program below, when ran, will prompt the user to enter the number of lockers in the school. After thegame is over, the program will output the number of lockers and the lockers numbers of the lockers…
- A hallway has 100 locked lockers. A guy begins by opening each of the 100 lockers.He then shuts every other locker. Then, on his third pass, he toggles every third locker (closes if open, opens if closed). This method is repeated for 100 passes, such that the man toggles every ith locker on each pass i. How many lockers are open after his 100th journey along the corridor, in which he toggles just locker #100?Suppose that the only currency were 3-dollar bills and 10-dollar bills. Show that every amount greater than 17 dollars could be made from a combination of these bills.Imagine there are N teams competing in a tournament, and that each team plays each of the other teams once. If a tournament were to take place, it should be demonstrated (using an example) that every team would lose to at least one other team in the tournament.
- In a high school, 111 students are surveyed and asked which of the foreign languages they learn. 49 students learn Spanish, 58 learn French, and 53 learn Chinese. 23 students learn Spanish and French, 16 learn Spanish and Chinese, and 21 learn French and Chinese. 6 students learn no foreign language a.)Number taking all three subjects b.)Find the cardinality of those taking Chinese language only c.)If S, F and C is the set of those who take Spanish, French and Chinese languages respectively, What is n(S∩F∩C)′n(S∩F∩C)′=Solve it and provide the 100% correct answer with covering of all test cases.There is an upcoming football tournament, and the n participating teams are labelled from 1 to n. Each pair of teams will play against each other exactly once. Thus, a total of matches will be held, and each team will compete in n − 1 of these matches. There are only two possible outcomes of a match: 1. The match ends in a draw, in which case both teams will get 1 point. 2. One team wins the match, in which case the winning team gets 3 points and the losing team gets 0 points. Design an algorithm which runs in O(n2 ) time and provides a list of results in all matches which: (a) ensures that all n teams finish with the same points total, and (b) includes the fewest drawn matches among all lists satisfying (a). Do not write the code, give steps and methods. Explain the steps of algorithm, and the logic behind these steps in plain English.Please give time complexity. list of results mean Any combination of wins, losses and draws. You may wish to view this as a mapping from the set of…
- A safe is locked by a combination of of four binary digits (that is, 0 or 1), but theowner has forgotten the combination. The safe is designed in such a way that nomatter how many digits have been pressed, if the correct combination of three digitsis pressed at any point, then the safe automatically opens (there is no ”enter” key).Our goal is to find the minimum number of digits that one needs to key in in order toguarantee that the safe opens. In other words, we wish to find the smallest possiblelength of a binary sequence containing every four-digit sequence in it.(a) Create a digraph whose vertex set consists of three-digit binary sequences. Fromeach vertex labelled xyz, there is one outgoing edge (labelled 0) leading to vertexyz0, and another outgoing edge (labelled 1) leading to vertex yz1.(b) Explain why every edge represents a four digit sequence and why an Euleriantour of this graph represents the desired sequence of keystrokes.(c) Find the minimum number of digits that one…There are four medals (Gold, Silver, Bronze and Wood) on a table, but they are all wrapped with dark wrapping paper, such that it is impossible to distinguish them. You would like to find the gold medal.The game starts as follows. You pick one medal without unwrapping it, and then the game host unwraps one of the remaining medals and reveals that it is a silver medal. (Assume here that the host unwraps a medal with equal probability, but knowing where the gold medal was and avoiding unwrapping the gold medal if still on the table, to keep the game interesting to watch until the end.)You have now three medals left to unwrap (one in your hand, two on the table). At this point, the host gives you the option to change your mind and swap your medal for one of the two left on the table. What would you do at this point? Would you keep your medal, or swap it with one of the two medals left on the table? If so, which one? Hints: Find the solution by using Bayes’ theorem, calculating all the…Roots of the equation 9x² - 9x + 1 = 0 areGroup of answer choices imaginary real and unequal real and equal irrational