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What is the Maximum number of node at height h of a binary tree?

It is ((2^h) -1)/(2-1) generally for an m-tree is: ((m^h)-1)/(m-1)


What is the degree of freedom when the number of component and number of phase are both equal to 2?

df = (n-1)*(m-1) = (2-1)*(2-1) = 1*1 = 1


How would you prove that the sum of an even number and an odd number is always an odd number?

Suppose x is an even number and y is an odd number. Then x = 2*n for some integer n and y = 2*m + 1 for some integer m Therefore x + y = 2*n + 2*m + 1 = 2*(n + m) +1 Now, since n and m are integers, (n + m) is also an integer [by the closure of integers under addition]. Thus, x + y = 2*p + 1 where p = n + m is an integer. ie x + y is an odd integer.


When was kenmore serial number M 31803091 built?

2 1/2 tons


What is m-2 over m plus 2 times m over m-1?

(m-2)/(m+2) * m/(m-1) = [(m-2)*m]/[(m+2)*(m-1)] = (m2 - 2m)/m2 + m - 2)


What is the average of all the integer's of 13 to 37?

To find the (mean) average, add all the numbers and divide by the number of numbers. The sum of a series of digits (in arithmetic progression, like 13, 14, 15, ... 37) is sum = (first + last) x number_of_digits / 2 So their average is: average = ((first + last) x number_of_digits / 2) / number_of_digits = (first + last) / 2 = average of first and last digits! So the average of the numbers 13, 14, 15, ..., 37 is: average = (13 + 37) / 2 = 50 / 2 = 25 To find the sum of n digits starting with m: Sum = m + (m+1) + ... + (m+n-2) + (m+n-1) Rewrite the sum in reverse order: Sum2 = Sum = (m+n-1) + (m+n-2) + ... + (m+1) + m Add the two sums, term by term: Sum + Sum2 = 2 Sum = (m + (m+n-1)) + (m + (m+n-1)) + ... + (m + (m+n-1)) + (m + (m+n-1)) There are n terms, all (m + (m+n-1)), so: 2 Sum = (m + m+n-1) x n Sum = (m + m+n-1) x n / 2 But n is the number of digits, m is the first number and (m+n-1) is the last, so: Sum = (first + last) x number_of_digits / 2


Why does an even number subtract to odd number is equal to odd number?

Suppose x is an odd number, then x leaves a remainder when divided by 2. That is, x = 2m+1 (for some integer m). Suppose y is an even number, then y is a multiple of 2 so suppose y = 2n (for some integer n). Then x-y = 2m+1 - 2n = 2m-2n + 1 =2(m-n) + 1 Since m and n are integers, then m+n is an integer so that the sum gives 1 more than a multiple of 2. And that is what an odd number is!


What 2 number you can mutiply to 80 but subtract to get -79?

mn = 80 m -n = -79 Substitute m - 80/m = -79 m^2 - 80 = -79m m^2 + 79m = 80 (NB Notice change of signs) Quadratic Eq'n m = { - 79 +/- sqrt[)79)^2 - 4(1)(-80)}] / 2(1) m = { - 79 +/- sqrt[6241 + 320}]/ 2 m = { -79 +/- sqrt[6561]} / 2 m = { - 79 +/- 81}/2 m = -160 / 2 = -80 or m = 2/2 = 1 Hence n = 1 + 79 = 80


What are the possible values of the quantum numbers n l m s for the second shell?

Possible values of quantum numbers in order of n,l,m,s in the second shell:2,0,0,-1/22,0,0,+1/22,1,-1,-1/22,1,-1,+1/22,1,0,-1/22,1,0,+1/22,1,1,-1/22,1,1,+1/2


What are 3 consecutive numbers?

They are numbers of the form m, m+1 and m+2 where m is an integer. However, sometimes it can be easier - particularly with an odd number of consecutive integers - to write them as n-1, n and n+1 where n is an integer (= m+1).


What are the factors of the quadratic function -m2 3m-2?

-m2+3m-2 -m2+2m+m-2 -m(m -2)+1(m-2) (-m+1)(m-2) or


What is the multiplicative inverse of a whole number?

Let m be a whole number, then the multiplicative inverse of m is a number n such that mn=1 since 1 is the multiplicative identity. There is only one choice for n, it is 1/m since m(1/m)=1