James find that his data set has a mean of 75 and a standard deviation of 2. Assuming his data is normally distributed, approxim
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Given:
The compound inequality is:
To find:
The integer solutions for the given compound inequality.
Solution:
We have,
Case 1:
...(i)
Case 2:
...(ii)
Using (i) and (ii), we get
The integer values which satisfy this inequality are only 3 and 4.
Therefore, the integer solutions to the given inequality are 3 and 4.
Answer: UV = 52
Concept:
Additive property of length, or the segment addition postulate, states that given 2 points A and C, a third point B lies on the line segment AC if and only if the distances between the points satisfy the equation AB + BC = AC.
Solve:
<u>Given information</u>
TU = 4x
UV = 2x + 14
TV = 7x - 5
<u>Given expression deducted from the additive property of length</u>
TV = TU + UV
<u>Substitute values into the expression</u>
7x - 5 = 4x + 2x + 14
<u>Combine like terms</u>
7x - 5 = 6x + 14
<u />
<u>Subtract 6x on both sides</u>
7x - 5 - 6x = 6x + 14 - 6x
x - 5 = 14
<u>Add 5 on both sides</u>
x - 5 + 5 = 14 + 5
x = 19
<u>Find UV by substituting the value of x</u>
UV = 2x + 14 = 2 (19) + 14 =
Hope this helps!! :)
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