What is the Correct Value of X in the Histogram Study?

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AI Thread Summary
The discussion revolves around determining the value of X in a histogram study where 75% of students sent X or fewer messages out of a maximum of 80 calls. The initial calculation suggests that X should be 60, but the book states it as 62. Upon further review, it is clarified that the book indicates 75% sent less than 62 messages, not that 62 is the value of X. The confusion stemmed from a misinterpretation of the wording in the book. Ultimately, the issue was resolved, confirming that there was no error in the book's answer.
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Homework Statement



There was study made, with a histogram shown below where the maximum number of calls made were 80, of the students who sent messages, 75% sent X or less, determine X.

Homework Equations



X/80= 0.75

The Attempt at a Solution



Now unless I'm missing something (which I'll proceed to lash myself if that's true) the answer should be 60, yet the book says 62.

Is this a misprint or am i missing something?
 
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Are you able to upload the histogram you were provided?
 
I should have read the book answer more clearly, i just read it and it says 75% sent LESS than 62 messages, it didn't say 62 was the answer (i.e X)

Sorry folks false alarm, nothing to see here.
 
I tried to combine those 2 formulas but it didn't work. I tried using another case where there are 2 red balls and 2 blue balls only so when combining the formula I got ##\frac{(4-1)!}{2!2!}=\frac{3}{2}## which does not make sense. Is there any formula to calculate cyclic permutation of identical objects or I have to do it by listing all the possibilities? Thanks
Since ##px^9+q## is the factor, then ##x^9=\frac{-q}{p}## will be one of the roots. Let ##f(x)=27x^{18}+bx^9+70##, then: $$27\left(\frac{-q}{p}\right)^2+b\left(\frac{-q}{p}\right)+70=0$$ $$b=27 \frac{q}{p}+70 \frac{p}{q}$$ $$b=\frac{27q^2+70p^2}{pq}$$ From this expression, it looks like there is no greatest value of ##b## because increasing the value of ##p## and ##q## will also increase the value of ##b##. How to find the greatest value of ##b##? Thanks

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