You are given 3  ropes and   a lighter.The  time required  to burn through rope 1  with a  single  flame is 20 minutes.Time required  to burn through rope 2  with   single  flame  is 30 minutes . Time required to burn rope 3 with a sinlge flame is 60 minutes.The burn rates  in differnet  sections in the  rope are  unknown  and vary. For how many integers M  in the  set{5,10,15,20...........100,105,110}is  it NOT possible to measure  out exactly M minutes  using the  3  ropes  and the  lighter?

Q: what integer is closer to 6

A: given: the integer is six.

Q: c) Given A {1,2,3,4,5,6,7,8,9,10}, show that if you pick 5 number from A, the sum of two of them is…

A: Permutation -every  possible ways in which a set or number of things can be  arranged.

Q: If A={a,b}, what is A times A?

A:

Q: How many integers from 1 through 1000 are multiples of 7 or multiples of 4?

A: Let A be the set of integers that are multiples of 7 and B be the set of integers that are multiples…

Q: Determine how many eight-digit positive integers you can make if the integers must include at least…

A: Let us assume there are three persons A, B and C sitting beside each other. The different ways in…

Q: A man has seven shirts and ten ties. Assuming that they all match, how many different shirt-and-tie…

A: Given data 7 shirts10 tiesall match with each otherno. of combinations possible = ?

Q: There are nine different marbles in a bag. A student reaches in and randomly draws one marble at a…

A: Given there are nine different marbles in a bag. A student reaches in and randomly draws one marble…

Q: Suppose you want to get a license plate. The license plate has to have 3 letters without repetition,…

A:

Q: How many numbers greater than 3000 can be form with the digits 0,2,3,4 a.  if repetition is not…

A:

Q: A team composed of two grade 11 and two grade 10 students is to be sent to a debate contest. If…

A: The provided information is  There are Two grade 11 and two grade 10 students  There are also 60…

Q: A time traveler can take 4 books with him, and he has 54 books to choose from. How many different…

A: The objective of this question is to find out the number of ways the time traveler can select 4…

Q: If a men working 6hours a day can do a work in 88days, then 6men working 8hours a day can do it in…

A: Given that men working 6 hours a day can do work in 88 days

Q: a five-person committee is created by randomly selecting members from a group of 3 faculty and 5…

A: 3 Faculty5 students___________8 total peopleselect five person committee by selecting members at…

Q: c) List vertically all the ways each number 0-35 can be represented as a sum of two or more…

A: Assume that limiting the numbers to integers. Let's try a few and see if we can find a pattern:…

Q: An ATM pin consists of 6 digits. Each digit can be numbers 0-9. The PIN should not be a birthdate…

A: Given: Number of digits in ATM pin is, N=6. The possible numbers from 0 to 9 are, n=10. The first…

Q: Find 1000 consecutive composite integers, without writing them out.

A: Let m be a positive integer then m consecutive comoposite positive integers is given by  (m+1)! + 2,…

Q: How many integers must you pick in order to be sure that at last two of them have the same remainder…

A: To Find: Number of integers that must be picked in order to be sure that at least two of them have…

Q: Find the number of different ways that a family of 9 can be seated around a circular table with 9…

A:

Q: Any n consecutive integers will include a number that is divisible by n.

A:

Q: How many 3-digit number can be formed from the digits 0,1,2,3  a. if no two digits are to be the…

A: * SOLUTION :-  from the given information the calculation is given below

Q: Write the following in terms of factorials. 1. number of arrangements in a row of 8 objects taken 6…

A:

Q: Suppose that the number of students in a class increase by 2, the number of ways they may be…

A:

Q: How many distinct ways are there to arrange 3 clear marbles, 4 yellow marbles, and 2 orange marbles…

A: Given problem:- How many distinct ways are there to arrange 3 clear marbles, 4 yellow marbles, and 2…

Q: A musician knows 10 songs is only going to play 4 of them at a concert. In how many different ways…

A: A musician knows 10 songs is only going to play 4 of them at a concert.  In how many different ways…

Q: can you show how you got 625 for k and L? and how did you get them at $375

A:

Q: Five students (one is named Fer) and their best friends (one of whom is named Stan) all live in an…

A: Solution: The given clues are Carol’s best friend is Dette who was assigned to gets the eggs on…

Q: ind the pattern when every other Fibonacci number is added, starting with the second. F2=1 F2+F4=1+3…

A: We will use the basic knowledge of Fibonacci numbers to answer this question properly, in detail.

Q: A student is told to work any 8 out of 15 questions on an exam. In how   many different ways can he…

A: He will pick a group of questions. The arrangement will not matter, so we will use the combination…

Q: A survey of 100 people showed that 25 own a car, 58 own a bicycle, and 17 own both a car and a…

A: Solution-: We have Number of people showed that own a car =25               Number of people showed…

Q: Compute P9,2. (Enter an exact number.)

A:

Q: 11. Five people each write a positive integer on a piece of paper. If the average of these five…

A: Given,  Average of 5 integers is 8  So, sum of all integers is 40

Fundamentals of Trigonometric Identities

Trigonometric Identities are the equalities that involve trigonometry functions and hold for all the values of variables given in the equation.