The diagram below shows ten circles joined by six lines with three circles each. Place all the integers from 1 to 10 in the circles, one in each circle, such that each line has the

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A: Let us say there are n students and n desks.  Number of ways in which n desks can be assigned to n…

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A: Given that for a segment of a radio show a disc jockey can play 5 records.  Total number of records…

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A: Here it is given that the order is of no importance, we will use the combination rule here where we…

Q: Find the sum of n terms of an AP whose nth term is given by an=5-6n

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Q: If m and p are positive integers, which expression must be negative?

A: Let m and p are positive integers ,

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Q: Prove that the sum of any three consecutive numbers is divisible by 3

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Q: Identify the property of integers being illustrated in 1[2( 4)] = (1 • 2)(¯ 4).

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Q: A class consists of 12 students ​(six boys and six ​girls) and one teacher. In how many ways can the…

A: Here there is a class consists of 12 students where there is 6 boys and 6 girls and 1 teacher We…

Q: Every seventh customer entering a shopping mall is asked to select his/her favorite store.

A: Cluster sampling - It involves the process of sampling intact groups not individuals, within the…

Q: How many integers will there be on the number line between the numbers 2.09 and 15.3?

A: There will be 13 integers between 2.09 and 15.3 on the number line.

Q: Set C is the set of positive two-digit even numbers less than 56 that are divisible by 5.

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Q: ou are to form a 4-digit number from the digits 1, 2, 3, 4, 6, and 8, using each at most once. How…

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Q: If X ~ N(80, 144) then find (90< x<100).

A: GivenX~N(80,144)Mean(μ)=80variance(σ2)=144standard deviation(σ)=144=12

Q: If the decimals 0.4721, 0.4722, and 0.48 are arranged on a typical horizontal number line, which is…

A: given numbers are -  0.4721, 0.4722, 0.48

Q: find all possible three-digit numbers that are of the form 75_ and are divisible by both 3 and 2

A: Since the number is divisible by 2 and 3, it must be divisible by 6.

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

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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: (b) Find the sum of the first 110 positive odd integers.

A: Our Aim is to find the sum of the first 110 positive odd integers.

Q: From the digits 4,3,6,1,5 and 7. How many 4 digit numbers can be made w/o repetition that are more…

A: The number of permutations of n objects taken r at a time is determined by the following formula:…

Q: Find the sum of all integers that are multiples of 3 from 4 to 100.

A: We have to find the sum of all integers that are multiples of 3 from 4 to 100 Then, If A denotes the…

Q: 7. Circle all the expre-

A: INTRODUCTION: To make it less hard or difficult; to make it simpler or easier To condense an…

Q: Express O in each figure in terms of x. (a) = (b) 4

A: a) In the right angle triagle opposite side is x and adjacent side is 7 angle is θ.b) In the right…

Q: Find the sum of all the integers from 1 to 1000. Select one: a. 505,000 b. 5,000,000 C. 500,500 d.…

A: We have find out sum

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

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Q: How many irrational numbers are there?

A: How many irrational numbers are there?

Q: Suppose that B and C are points on the number line. If BC = 10 and B lies at - 4 , where could C be…

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Q: that if 3 divides the sum of the digits of n, then 3|n

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Q: A lock uses 3 numbers as an unlock code, each of which can be 0 to 40. If there are no restrictions…

A: From 0 to 40, there are 41 integers.  Since there are no restrictions  so we can pick the first…

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Q: Suppose that one selects some subset of integers from the set {1, 2, ., 47). What is the smallest…

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Q: a. On each of four consecutive plays in a football​ game, a team lost 8 yards. If lost yardage is…

A: On each of  four consecutive Plays in football gane team lost 8 yards

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Q: Find the largest eight-digit number made up of the digits 1, 1, 2, 2, 3, 3, 4, and 4 such that the…

A: Given digits are 1,2, 3, 4.Given conditions is 1s are seperated by one digit,2s are seperated by two…

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Q: How many distinct integers do we have to pick in order to have two that have the same remainder when…

A: To find - How many distinct integers do we have to pick in order to have two that have the same…

Q: Find all integers that leaves the reminders 5,1, and 4 when divided by 8,5, and 9 respectively.

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Q: Find the sum of the integers from −20 to 256.

A: It is required to calculate the sum of integers from -20 to 256 that is:

Q: Where did the numbers 12 and 14 come from?

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Q: Find the next two terms in (an)n20 beginning

A: Given,             3,  5, 11, 21, 43, 85, . . .

Q: be a positive number. Determine the values of p for which

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Q: How many blocks would be needed to build a stack like the one shown In the figure If the bottom row…

A: Given that bottom row has 21 blocks. On going from bottom to top, number of blocks are reduced by 1.…

Q: If n EN and n < 2000, how many numbers n have the property that the sum of the digits of n and the…

A: Given: n∈ℕ And n&lt;2000

Q: Find for the sum of the first 50 negative even integers.

A: Negative even integers :-    -2,-4,-6,-8, ....... This is AP series with a=-2, d=-2

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Q: Find the least natural number a with the property that the sum a + 2ā + 3a + ...+ 9a is the number…

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