# Question 19 - quadratic probility problem

• thomas49th
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.

#### thomas49th

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

b)
i) $$\frac{7}{n+7}$$
ii) Take n to be 8

$$\frac{7}{8+7}$$
$$\frac{7}{15}$$ that DOESN'T round down to $$\frac{2}{5}$$

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

Thanks

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?

$$\frac{7}{n+7}$$ = $$\frac{2}{5}$$

cross multiply!

$$\frac{35}{2n+14}$$

now where?

Um...you're leaving out the equality part of the equation. Solve for n.

Alternatively, you can note that you have 35/(2n + 14) = 1. 35 is odd. 2n + 14 is even. Strange, isn't it?

uh? How does that equal 1?

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?

$$\frac{35}{2n+14}$$ = 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?

Multiply both sides of the equation by 2n + 14, so you end up with:

35 = 2n + 14

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...

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?

you can't have 1/2 a ball...

am I right or am I right

Last edited:
Okay here is the rest of the question

Okay, what are your ideas on part (c)?

(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

Yes, I'd go with that.

I got it down now to $$\frac{14n}{2n^{2}+28n+98}$$ = $$\frac{4}{9}$$

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

$$\frac{14n}{n^{2}+14n+49}$$ = $$\frac{4}{9}$$

got it!

$$\frac{4n^{2} + 56n + 196}{2}$$ = $$\frac{14n * 9}{2}$$
$$\2n^{2} + 28n + 98$$ = $$68n$$

$$\2n^{2} - 35n + 98 = 0$$

and the answer to d must be 1/9
x must be 14 as you can't have 3.5 balls

All sounds good to me, well done

## 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.