A youth club has introduced three new activities badminton (B), cookery (C) and drama (D). Each of the 75 members of the youth club is asked to say in which of these activities they have participated. Their answers showed that of the 75 members all have participated in at least one of these activities 27 have participated in badminton and drama 31 have participated in badminton and cookery 23 have participated in cookery and drama 48 have participated in badminton B PC 49 have participated in cookery 40 have participated in drama. Let x be the number of members of the youth club who have participated in all three activities. (a) Using all this information, complete the Venn diagram opposite to show, in terms of x, the number of elements in each appropriate subset. (b) Find the value of x. (2. (c) Find (i) n(BnC) (ii) n

Q: a. Wendy’s but not the other two?   b. Only one of them?   c. None of these three?

A: Here define events and draw venn diagram

Q: An undergraduate math course gives all the usual letter grades of A, B, C, D, or F. The department…

A: An undergraduate math course gives all the usual letter grades of A, B, C, D or F.

Q: 3. A group of 20 people consisting of 6 women and 14 men will give a tea invitation. For the…

A:

Q: In a bucket of tacos, we have 4 spicy beef tacos, 6 spicy chicken tacos, and 6 mild beef tacos. If…

A: Given data: In a bucket of tacos, we have ; 4 spicy beef tacos, 6 spicy chicken tacos, and 6 mild…

Q: A company surveyed 36 people at an Italian restaurant and asked if they ordered the following pizza…

A:

Q: Assume that there is a group of 8 students making presentations on 4 issues: recreational sports…

A:

Q: Customer center operator Raaj works at the customerservice call center of a major credit card bank.…

A:

Q: The public health authorities of a small town have divided the population into three categories:…

A: Given: The population of a small town has been divided into three categories: covid-negative,…

Q: The Department of Foreign Languages of a liberal arts college conducted a survey of its recent…

A: Let, F=French for at least one year, G=German for at least one year, S=Spanish for at least one…

Q: The public health authorities of a small town have divided the population into three categories:…

A: Note: There are multiple sub questions. No specific question has been asked. So, We will solve the…

Q: 68. In a city three daily newspapers X, Y, Z are published, 40% of the people of the city read X,…

A: Let the number of people in the city be 100x (where x=0, a constant). Furher assume that A,B and C…

Q: A research Development department at Oda manufacturing company determines that 20% of people who…

A:

Q: 3) A restaurant offers 4 choices of appetizer, 9 choices of main meal and 3 choices of dessert. A…

A: If the customer wants to eat a 1 course meal, then the number of possible meals offered by the…

Q: At the Sports JD Club, 35 people play basketball, 30 play soccer, and 31 play badminton.  Of these…

A: Let B be the event representing Basketball. Let S be the event representing Soccer. Let N be the…

Q: search Development department at Oda manufacturing company determines that 20% of people who…

A: Given problem is : A research Development department at Oda manufacturing company determines that…

Q: In a survey of 80 people, it was found that 35 people read newspaper H, 20 read newspaper T, 15 read…

A: From the given data, In a survey of 80 people, 35 people read newspaper H 20 people read newspaper T…

Q: A rent a car company has 14 available cars on its lot and 3 customers waiting in the office. Assume…

A: The formula for combination is C(n, r) = n! / [r! (n – r)!] = [n (n – 1) … (n – r + 1)] / r!.…

Q: A mobile phone manufacturer purchases microchips from three suppliers, namely: Samsung, Nokia, and…

A:

Q: Hospital records show that 425 of the 850 patients who contracted a strain of influenza recovered…

A:

Q: A company is deciding between a blue logo and a gold logo. Suppose 50 out of 160 adultsapprove of…

A: Approval rate among adults for blue logo= 50/160 = 0.3125 = 31.25% Approval rate among adults for…

Q: In a survey, 1000 individuals were asked how often they took exercise in the form of cycling. There…

A:

Q: One semester in a chemistry class, 14 students failed due to poor attendance, 23 failed due to not…

A: LetA→ Set of students failed due topoor attendance.B→ Set of students failed due tonot…

Q: In a survey of 100 ​resorts, it was found that   30 had a spa. 58 had a fitness center. 41 had a​…

A: A Venn diagram is a mathematical representation of mathematical or logical sets as circles or closed…

Q: 4. In a class of 60 students, 40 students like math, 36 like science, 24 like both the subjects.…

A: In a class of 60 students, 40 students like maths, 36 students like science, 24 like both the…

Q: Consider three different classes at a small college; a mathematics class with 32 students, an…

A:

Q: After representing the population in a given week as a column vector v=[n;p;h], where n,p, and h…

A: Given information:- Among those who are negative, 95% remain so, 4% become positive, and 1% need to…

Q: 2. At an eSports tournament, m American, n Canadian, and k Korean League of Legends players sit in a…

A: Given information: Number of American players = m Number of Canadian players = n Number of Korean…

Q: A rental car company offers three types of vehicles (compact, mid-size, and full-size).Based on…

A: Given:Percentage of customers choose a compact vehicle = 35%Percentage of customers choose a…

Q: The Department of Foreign Languages of a liberal arts college conducted a survey of its recent…

A:

Q: Keep in Shape Club has 73 members. 35 members swim, 24 play basketball, and 27 jogs. Of these…

A:

Q: In a survey of restaurant customers, 63 customers ordered french fries or a salad, 38 ordered french…

A: Given that In a survey of restaurant customers, 63 customers ordered french fries or a salad, 38…

Q: 8. A woman has 10 close friends. Find the number of ways in which she can invite 4 of them dinner if…

A: 18) A woman has 10 close friends. To find the number of ways in which she can invite 4 of them to…

Q: 7. In a chess competition involving some men and women, every player needs to play exactly one game…

A:

Q: The public health authorities of a small town have divided the population into three categories:…

A: The entire population has been divided into categories: negative, positive and hospitalised. 1.…

Q: a) Felicia is deciding on her schedule for next semester. She must take each of the following…

A: a) There are no conflicts between the classes which means any class from one group can be scheduled…

Q: 6. I I have to invite 7 out of my 14 friends to a party. In how many ways can I do that if a. Both…

A:

Q: A survey of 1,200 tourists visiting Orlando was taken. Of those surveyed: 255 tourists had visited…

A: The set is a collection of well defined objects, which are visualized using the Venn diagrams. That…

Q: A car rental company has three locations in Mexico City: the International Airport, Oficina Vallejo,…

A:

Q: A survey of non healthy habits of 80 sophomore students of a certain seminary showed the following…

A: In this question, By using the given data to find (1) How many drink alcohol only? (2) How many…

Q: In a certain group of 50 students at Hogwarts School of Wizardry, only 15 students are wearing caps…

A: Let C be the group of students who are wearing caps and N be the group of students who are wearing…

Q: In a survey of 120 consumers conducted in a shopping mall, 82 consumers indicated that they buy…

A: Let A be the set of people by product A B be the set of people buy product B U be the universal set…

Q: A pharmaceutical company recently hired 5 biologists, 3 chemists, 4 environmental scientists, and 3…

A:

Q: In the 75th Congress (1937-1939) there were in the Senate 75 Democrats, 17 Republicans, and 4…

A: Since you have asked multiple questions, we will solve the first Question for you. If you want any…

Q: A vendor specializing in outdoor gear offers customers three wWays telephone using a catalog. Of the…

A: The formula for Probability is as follows: Probability=Number of favourable casesTotal number of…

Q: In a survey of 1000 households, 275 owned a home computer. 455 a video, 405 two cars, and 265…

A: Answer 3 :

Q: 2. A research Development department at Oda manufacturing company determines that 20% of people who…

A:

Q: ) At least one of the two games?   members (b) Exactly one of the games?  members (c) The Summer…

A: Concept:   The number of ways of achieving success that is the total number of possible outcomes is…

Q: n a certain city, with a population of 1,000,000 people, 17 people have been infected with a…

A:

Q: In a survey of 500 students in a university, 200 are enrolled in Psych 101, 180 are enrolled in…

A: Given that, In a survey of 500 students in a university, 200 are enrolled in Psych 101, 180 are…

Q: In the 1990s, significant numbers of tourists traveled from North America and Asia to Australia and…

A: Given that, Number of people visited Australia  n( Australia) = 2,231,000 Number of people visited…

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.