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A set of five distinct positive integers has a mean of 1000 and a median of 100 What is the largest possible integer that could be included in the set?
median = 100, mean = 1000 set of numbers = {a,b,100,c,d} a+b+100+c+d = 5000 As the set contains distinct numbers, and there is no range that is given in the problem, we can consider the set of numbers as {1,2,100,101,4796} So the largest possible integer can be 4796.
What does an integer plus another integer equal?
an integer plus and integer will always be an integer. We say integers are closed under addition.
When you subtract a positive integer by a positive integer do you get a positive integer?
If the integer subtracted is smaller than or equal to the first integer, then the answer is positive. Otherwise, if the integer subtracted is larger, then the answer is negative.
What is 0.1 as an integer?
It is not an integer, nor can it ever be an integer. It can, however, be rounded to the nearest integer, in which case 0.1 will round to 0 to the nearest integer.
Is square of 6 an integer?
Yes; the square of any integer is also an integer.Yes; the square of any integer is also an integer.Yes; the square of any integer is also an integer.Yes; the square of any integer is also an integer.
How many triangles are there with a perimeter of 12?
To find the number of triangles with a perimeter of 12, we can use the triangle inequality theorem, which states that the sum of the lengths of any two sides must be greater than the length of the third side. By letting the sides be (a), (b), and (c) such that (a + b + c = 12) and applying the inequalities, we can determine valid combinations of side lengths. After considering the integer solutions and applying the inequalities, we find that there are 8 distinct triangles with integer side lengths that satisfy the conditions.
How many integer sided triangles can be formed having a perimeter of 12?
Three: 2, 5, 5 3, 4, 5 and 4, 4, 4
How many triangles with integer sides are there where its perimeter is 9cm's?
Only 3: [1,4,4], [2,3,4] and [3,3,3] Remeber that the sum of the lengths of any two sides MUST be greater than the third side. So triangles like [1,2,6] cannot exist.
What is a distinct integer?
Distinct integer is a number with non fraction or decimal.
Which measure is closest to the area of an equilateral triangle with a perimeter of 12 centimeters?
It is: 0.5*4*4*sin(60 degrees) = 7 square cm rounded to nearest integer
Is the perimeter of a square an integer?
Not always
What is the largest integer that is not a sum of distinct power?
the largest integer of distinct power is 28
How many unique triangles can have all sides of integer length one side of length 5 cm and a perimeter less than or equal to 16 cm.?
To find the number of unique triangles with one side of length 5 cm and a perimeter less than or equal to 16 cm, we can denote the other two sides as (a) and (b). The perimeter condition gives us (5 + a + b \leq 16), or (a + b \leq 11). Additionally, the triangle inequality requires (a + b > 5). Thus, (6 \leq a + b \leq 11). The integer pairs ((a, b)) that satisfy these conditions can be systematically counted, leading to a total of 15 unique triangles.
How many different isosceles have integers side lengths and perimeter 23?
To find the number of different isosceles triangles with integer side lengths and a perimeter of 23, we can denote the equal sides as ( a ) and the base as ( b ). The equation for the perimeter gives us ( 2a + b = 23 ), or ( b = 23 - 2a ). For the triangle inequality to hold, ( 2a > b ) must be satisfied, which translates to ( 2a > 23 - 2a ), leading to ( 4a > 23 ) or ( a > 5.75 ). Since ( a ) must be an integer, ( a ) can take values from 6 to 11, giving the valid pairs: (6, 11), (7, 9), (8, 7), (9, 5), (10, 3), and (11, 1). Therefore, there are 6 different isosceles triangles with integer side lengths and a perimeter of 23.
What is the perimeter of an equilateral triangle whose area is 97.428 square cm showing work and answer to the nearest integer?
Let the sides be s:- If: 0.5*s squared*sin(60 degrees) = 97.428 Then: s = square root of 97.428*2/sin(60 degrees) => 15.00001094 Perimeter: 3*15 = 45 cm
The largest integer that is not a sum of distinct powers?
30 distinct powers are 13,14, and 1523
What types of right triangle have all integer values for their sides?
isosceles right triangles
