Question 19 - quadratic probility problem

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In summary, the conversation discusses solving for the value of x in the equation (x-14)(2x-7) and determining the value of n in the equation 7/(n+7) = 2/5. The conversation also touches on probability calculations and solving for n in the equation (probability of taking white x probability of taking yellow) + (probability of taking yellow x probality of taking white). Ultimately, it is determined that the value of n is 1/9 and the value of x is 14.
  • #1
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img021.jpg


a) (i) (x-14)(2x-7)
(ii) x = 14 or x = 3.5

b)
i) [tex]\frac{7}{n+7}[/tex]
ii) Take n to be 8

[tex]\frac{7}{8+7}[/tex]
[tex]\frac{7}{15}[/tex] that DOESN'T round down to [tex]\frac{2}{5}[/tex]

Is that all correct so far?
If so I will post the next (really hard) question)...

Thanks
 
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  • #2
Why take n to be 8? Nothing is said about any value for n.
If 7/(n+7)= 2/5, SOLVE for n. What happens?
 
  • #3
[tex]\frac{7}{n+7}[/tex] = [tex]\frac{2}{5}[/tex]

cross multiply!

[tex]\frac{35}{2n+14}[/tex]

now where?
 
  • #4
Um...you're leaving out the equality part of the equation. Solve for n.
 
  • #5
Alternatively, you can note that you have 35/(2n + 14) = 1. 35 is odd. 2n + 14 is even. Strange, isn't it?
 
  • #6
uh? How does that equal 1?
 
  • #7
Look, you're essentially supposed to say, "Suppose Bill is right. Suppose 7/(n + 7) = 2/5. Then such and such would follow." Why would the conclusion be a problem?
 
  • #8
[tex]\frac{35}{2n+14}[/tex] = 1

now I need to get N on it's own (don't know how- please show). But I am guessing that n is greater than 3/5 so it CANT be right?
 
  • #9
Multiply both sides of the equation by 2n + 14, so you end up with:

35 = 2n + 14
 
  • #10
silly me...

2n = 35-14
n = 10.5
EDIT: Which as a fraction is 10/1/2 which DOESN'T equal 2/5...am i right yet. I doubt that's right...
 
  • #11
You're getting there. What's the problem with n being 10.5. Look at your original assumptions. What are you tacitly assuming about the original n balls?
 
  • #12
you can't have 1/2 a ball... :bugeye:

am I right or am I right
 
Last edited:
  • #13
Okay here is the rest of the question

img022.jpg
 
  • #14
Okay, what are your ideas on part (c)?
 
  • #15
(probability of taking white x probability of taking yellow) + (probability of taking yellow x probality of taking white)

Is that somthing to go from?

Thanks
 
  • #16
Yes, I'd go with that.
 
  • #17
I got it down now to [tex]\frac{14n}{2n^{2}+28n+98}[/tex] = [tex]\frac{4}{9}[/tex]

is that right so far?

EDIT: is the question is says -28n but I've got +28n


EDIT 2: O no it must be this so far

[tex]\frac{14n}{n^{2}+14n+49}[/tex] = [tex]\frac{4}{9}[/tex]
 
  • #18
got it!

[tex]\frac{4n^{2} + 56n + 196}{2}[/tex] = [tex]\frac{14n * 9}{2}[/tex]
[tex]\2n^{2} + 28n + 98[/tex] = [tex]68n[/tex]


[tex]\2n^{2} - 35n + 98 = 0[/tex]
 
  • #19
and the answer to d must be 1/9
x must be 14 as you can't have 3.5 balls
 
  • #20
All sounds good to me, well done :approve:
 

What is Question 19 - quadratic probability problem?

Question 19 - quadratic probability problem is a mathematical problem that involves finding the probability of an event occurring when there are multiple independent variables involved. It is typically solved by using quadratic equations and probability rules.

How is Question 19 - quadratic probability problem solved?

Question 19 - quadratic probability problem is solved by first identifying the independent variables and then using quadratic equations and probability rules to calculate the probability of the event occurring.

What are the key concepts involved in solving Question 19 - quadratic probability problem?

The key concepts involved in solving Question 19 - quadratic probability problem include understanding probability rules, identifying independent variables, and using quadratic equations to calculate the probability.

What are some common applications of Question 19 - quadratic probability problem?

Question 19 - quadratic probability problem is commonly used in fields such as statistics, economics, and physics to calculate the probability of events occurring in complex systems.

How can I improve my understanding and skills in solving Question 19 - quadratic probability problem?

To improve your understanding and skills in solving Question 19 - quadratic probability problem, you can practice solving similar problems, study probability rules and quadratic equations, and seek help from a tutor or instructor if needed.

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