*· Given a set (x, x+3, x+6, x+9, x+12} where xE2*, show there exists at minimum 1 of the numbers in the set is composite (has more than 2 factors).

Q: A pencil case has 400 colored markers: 200 blue, 120 red, 50 green, and 30 yellow. What is the least…

A: Given problem Given that   A pencil case has 400 colored markers . 200 blue 120 red 50 green 30…

Q: does not exist

A: Given that:  The limit   lim(x,y)→(0, 0 ) x2 + yx2 + y2   .

Q: Suppose that you know that a golfer plays the first hole of a golf course with an infinite number of…

A: To prove that the golfer plays every hole on the course when given that a golfer plays the first…

Q: schedule is to be made with football teams. Suppose that 7 teams need to play with three other teams…

A: It's clear from the given problem that 7 teams play against three other teams. This leads to 7…

Q: What two nonnegative real numbers a and b whose sum is 23maximize a2 + b2? Minimize a2 + b2?

A: Given that real number a and b whose sum is 23ie   a+b=23⇒b=23-a-1Let S be the sum of their…

Q: Q6. Comment on Pigeonhole principle. On the basis of Pigeonhole principle find minimum number of…

A:

Q: A finite sequence of numbers is called AWESOME if each subsequent member of the sequence, except the…

A: Given: To determine the natural number of x and y.

Q: Considerthreemappingsα,β,γ:Z→Zdefined by α(n)=2n−1, β(n)=(n−1)^2, γ(n)=(n−1)^3

A:

Q: Two distinct numbers are selected from the set (1,2,3,4,...,36,37) so that the sum of the remaining…

A: Given two distinct numbers are selected from the set 1,2,3,4,…,36,37 and The sum of remaining 35…

Q: 10. Show that the interval (0, 1) is covered by the open intervals In (1/n, 1- 1/n), n 2 3, but (0,…

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Q: There are n = 50 students registered for the course 08TI2. It is well known that two students are…

A:

Q: A point on a number line is at least 13.4 units from the point with coordinate 2. What are all the…

A: Definition used -             Distance between a point x on the number line from a given point a on…

Q: In a town with two districts A and B an administrative committee of 7 people is to be formed. There…

A: Given:  In district A, there are 204 eligible candidates…

Q: A football club has 15Players. Find the possible number of team with 11Players which can be formed…

A: Given Data: Number of players=15   Number of players in a team=11

Q: Two different lines can intersect in at most one point. Three different lines can intersect at most…

A: To find the maximum number of intersection for six different lines n = 6

Q: Find integers x and y such that 3220x + 6006y = gcd(3220,6006).

A:

Q: How many strings of length 12 have at least three y's if the strings have. x's or y's?

A: The solution is given as follows

Q: Suppose I choose two numbers from the set {1, 2, 3,... 100}. How many have an even sum? Show all…

A: Hello. Since your question has multiple parts, we will solve first question for you. If you want…

Q: {u1, u2, u3} is an orthonormal set and x = c1u1 + c2u2 + c3u3. ||x|| = 5, = 4 , x ㅗ u2 , find…

A:

Q: witness to a hit-and-run accident told the police that the license number contained the letters RQLH…

A: Answer:72 Explanation: First digit=2 No.of digits=10 ie, (0,1,2,3,4,5,6,7,8,9) Now possibilities…

Q: A 3 × 7 rectangle is divided into 21 squares each of which is colored red or black. Prove that the…

A: Solution: let suppose the board is a 3 × 7 rectangle.

Q: Assume that there are 13 pairs of black socks (çorap) and 8 pairs of blue socks in your drawer What…

A: In a single pair, there are two socks. In order to form a pair, at least 2 socks must be drawn.…

Q: Suppose that Hilbert’s Grand Hotel is fully occupied on the day the hotel expands to a second…

A: We know, Hilbert's Grand Hotel is a thought experiment which gives counterintuitive property of…

Q: In a city each person earns at most $5000 per month and every house is occupied by at most five…

A: HERE Given  Maximum earnings of of person = $5000 Maximum person in one one house= 5

Q: When I arrange the members of a marching band in rows of 2, 3, or 4, there is always 1 person left…

A: To solve the given problem

Q: How many bijective functions have [10] as both the domain and codomain

A: Given, 10

Q: 6) The product of two numbers is equal to 192. Find values for these numbers such that the sum is…

A:

Q: Express (4, 10) as a set {x:|x−a|<cx:|x−a|<c} for suitable a and c.

A: give domain of xx∈(4,10)i.e4&lt;x&lt;10

Q: Find the set of all positive integers n with the property that the set  M={n,n+1,n+2,n+3,n+4,n+5}…

A: A very good problem based on a nice application of quadratic residues

Q: A bag contains 10 red marbles, 10 white marbles, and 10 blue marbles. What is the minimum number of…

A: From provided information; A bag contains 10 red marbles, 10 white marbles and 10 blue marbles. The…

Q: From a group of 7 men and 6 women, five persons are to be selected to form a committee so that there…

A:

Q: 名7 Find fen(x)if fx)=ュ-ズ 2-X

A:

Q: The set of elements common to both (-0, 9) and (-∞, 12) is

A:

Q: 5. It is required to seat 5 men and 4 women in a row so that the women occupy the even places. How…

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

Q: Show that you can make four distinct lists of books so that the total number of pages in the books…

A: Given: 15 text books is available and each with between 200 and 600 pages

Q: Propose a partial order on a non-empty finite set so that it has 3 maximal elements and two minimal…

A:

Q: 3. Discuss about the Completeness Axiom.

A: The Completeness Axiom or Least Upper Bound Property, is one of the fundamental properties of the…

Q: A course has 30 students and four possible letter grades A, B, C, D. What is the maximum number of…

A:

Q: GIve a simple example of the Well Ordering Principle of Integers

A: We have to explain the Well Ordering Principle of Integers using an example.

Q: Specify the sets by roster, (a) (Even counting numbers less than 14) (b) (Positive muitiples of 7)…

A: To simply the sets in roaster form

Q: {xlx is a whole number less than 6} if U is the set of all whole numbers

A:

Q: Suppose 7 female and 6 male applicants have been successfully screened for 5 positions. In how many…

A:

Q: In a country, there are n farms and in each farm, there are at most 15 types of fruit trees. For any…

A: Use the data given to determine the answer. Use simple mathematics to determine the minimum number…

Q: 1. Write the interval of points that are less than -4: 2. Write the set of points from -5 to 2 but…

A: To find-  Write the interval of points that are less than -4. Write the set of points from -5 to 2…

Q: Four consecutive positive integers are such that the smallest is a multiple of 5, the second is a…

A:

Q: The technique of boxing in a triangle and determing its area by using rectangle and right triangle…

A: Let ABC is triangle with vertices, Ax1,y1,Bx2,y2,Cx3,y3. WhereDx1,0, Ex2,0, Fx3,0 are points on…

Q: Suppose that all the pages are black and white, but each group of 25 consecutivepages (1-25, 26-50,…

A: To determine the number of ways for the 125 pages to assign to the 5 printers. Given that, the total…