VCE Methods Question Thread!

[lastminute]

Hi!
How would I do this? Would I do a tree diagram? the solutions did a table but i don't understand what they're doing...
Thanks in advance

[Pineapple66]

For the circular functions questions:
1) You would find the solutions between [π,2π] because you change the domain to whatever is being done to x in the equation (in this case x is being divided by 2)
2) For negative values (eg. -1/2) I write the base angle as π/6 and the find solutions of sine where it is negative and I don't think they find solutions in quadrants where sine is negative, I would need to see an example

ohh okay, so if it was sin(2x), you'd have to multiply the domain by 2?

Hm.. how about this one? Solve 2cos(2x) = - square root 3 for x, where [0,pi]
I ended up getting pi/12 and 11pi/12 since cos of a negative = a positive so I found solutions in quadrants where cos is positive?  But the answer is 5pi/12 and 7pi/12 .. 

[paendeo]

Hi can i get some help with this question?
For two events A and B, Pr(A)=1/3 and pr(B)=1/2
Find Pr(A U B') if
a) A and B are mutually exclusive
b) A and B are independent events

i'm having trouble figuring out the difference

[MB_]

Hi!
How would I do this? Would I do a tree diagram? the solutions did a table but i don't understand what they're doing...
Thanks in advance

Working attached, hopefully it makes sense

[MB_]

ohh okay, so if it was sin(2x), you'd have to multiply the domain by 2?

Hm.. how about this one? Solve 2cos(2x) = - square root 3 for x, where [0,pi]
I ended up getting pi/12 and 11pi/12 since cos of a negative = a positive so I found solutions in quadrants where cos is positive?  But the answer is 5pi/12 and 7pi/12 ..

I don't think you're meant to use "cos of a negative = a positive" when solving trigonometric equations which is maybe why you are getting the questions wrong. Working is attached

[blacksanta62]

Can someone tell me the main difference between a population porportion, p, and a sample porportion, p(hat)?
Can seem to distinguish between them
Thanks

[Syndicate]

Hi can i get some help with this question?
For two events A and B, Pr(A)=1/3 and pr(B)=1/2
Find Pr(A U B') if
a) A and B are mutually exclusive
b) A and B are independent events

i'm having trouble figuring out the difference

Pr(AUB') = Pr(A) - \(Pr(A\cap B) \)


a) If two event are mutually exclusive then \(Pr(A\cap B) \) = null. If \(Pr(A\cap B) \) =0, then Pr(AUB) = Pr(A) + Pr(B).

So Pr(AUB') = Pr(A) = 1/3


b) If two event are independent, then \(Pr(A\cap B) \) = Pr(A) x Pr(B)

\(Pr(A\cup B) \) = 1/3 x 1/2 = 1/6

Therefore Pr(AUB') = 1/3 - 1/6 = 1/6

Can you please check if the answers are right?

[FallingStar]

Can someone tell me the main difference between a population porportion, p, and a sample porportion, p(hat)?
Can seem to distinguish between them
Thanks

I have a population of Xs. They can be red, or black. The population of 30 is shown below:

XXXXXXXXXX
XXXXXXXXXX
XXXXXXXXXX

Now from that population, I take a sample of 5 Xs.

XXXXX
Here, the proportion of red Xs is different to the proportion of red Xs in the population of 30, as I have only taken a sample of what the population is.

So the sample proportion is the proportion of a particular characteristic of a sample such as the sample of 5 from a population of 30 as above. The population proportion on the other hand, is the proportion of the particular characteristic of the whole population, in this case of all 30.

Please note that samples can differ depending on where you take it. Like the above is only one sample of the 30 Xs. Another sample may have 2,3,4 or even all five of the red Xs.

I hope I make sense here.

[halo]

Hi is combinatorics in the study design? And can we be expected to them by hand? I just came across a company exam 1 that required you to evaluate them by hand and I have no idea how to 

[exit]

Hi is combinatorics in the study design? And can we be expected to them by hand? I just came across a company exam 1 that required you to evaluate them by hand and I have no idea how to 

Yes, you should be able to do them by hand. You need them for binominal also.

[halo]

Yes, you should be able to do them by hand. You need them for binominal also.

Oh ok thanks... my tutor and teacher didn't go over it though so I just thought we didn't need it >.< So sorry but would you mind explaining how to do them by hand? Thank you so much!

[qwertyu1234567]

Are we expected to know general solutions off the top of our heads?
If so, does anyone have any tips for remembering them??

[MB_]

Oh ok thanks... my tutor and teacher didn't go over it though so I just thought we didn't need it >.< So sorry but would you mind explaining how to do them by hand? Thank you so much!

Hopefully this helps ...

[eforlano]

I've been trying to do this question for like a week and I keep returning to it but I just can't seem to work it out! Could someone help me out please? ><

[bedigursimran]

Hey guys, this is probably simple. But how would I integrate this?