Standard Math Q+A Thread

[jamonwindeyer]

ok great thanks jamon, for you online HSC holiday video lectures would you be able to do a sction on least sqaure line of best fit ?

I'm not doing the General Math videos, but I'll pass on the suggestion to Steph!

[ca052267]

Hi,

Is anyone able to help me with this question? (attached)

Thank you

[jamonwindeyer]

Hi,

Is anyone able to help me with this question? (attached)

Thank you

Sure! So we've found that \(\frac{20}{110}\) of penguins were tagged on the recapture. That means that, when we initially tagged our penguins, we tagged about \(\frac{20}{110}=\frac{2}{11}\) of the penguins. We initially caught 50 penguins, so our population \(P\) is:



Now we know that this is 13% less than 2012. Meaning, this population is 87% of 2012's population (we'll call this \(X\))!



So, the estimated population in 2012 must have been about 316! You can work it backwards too - Take 13% less than 316 and you get 275, and if you capture 50 out of 275 that is a fraction of 2 out of 11

[ca052267]

Sure! So we've found that \(\frac{20}{110}\) of penguins were tagged on the recapture. That means that, when we initially tagged our penguins, we tagged about \(\frac{20}{110}=\frac{2}{11}\) of the penguins. We initially caught 50 penguins, so our population \(P\) is:



Now we know that this is 13% less than 2012. Meaning, this population is 87% of 2012's population (we'll call this \(X\))!



So, the estimated population in 2012 must have been about 259! You can work it backwards too - Take 13% less than 259 and you get 225, and if you capture 50 out of 225 that is a fraction of 2 out of 11

Thanks soo much.

But I think you may have a carried error, shouldn't the 2013 population come to 275 penguins?

Other than that, everything else makes sense.

[Shadowxo]

Thanks soo much.

But I think you may have a carried error, shouldn't the 2013 population come to 275 penguins?

Other than that, everything else makes sense.

Yep everything else (reasoning and formulas) are right though

[jamonwindeyer]

Thanks soo much.

But I think you may have a carried error, shouldn't the 2013 population come to 275 penguins?

Other than that, everything else makes sense.

Ahh yep you're totally right, sorry about that!! Fixed up the answer - Glad I could help

[morning_sunshine]

So I need help with this question

It's probably easier than what I'm thinking but some guidance would be great

So

What is the product of [8mn/9] and [15/6m] ?

[Eric11267]

So I need help with this question

It's probably easier than what I'm thinking but some guidance would be great

So

What is the product of [8mn/9] and [15/6m] ?

Or you could potentially do

[morning_sunshine]

Thanks so much!

Two more questions i came across

5.83ML is equivalent to ____________ kL

I wrote 5830kL
Is that wrong?

And then

What is the greatest possible error in the measurement 6.3L?

Thanks in advance

[Eric11267]

Thanks so much!

One more question i came across and i just want to make sure i got it right

5.83ML is equivalent to ____________ kL

I wrote 5830kL
Is that wrong?

If that's a conversion from megalitres to kilolitres then it is correct

[morning_sunshine]

Thanks again so so much

Another question because why not

The earth has a mass of 5.9723 x 10 to the power of 24kg. Express this correct to 2 significant figures.

How would I go about it?

[Eric11267]

Thanks again so so much

Another question because why not

The earth has a mass of 5.9723 x 10 to the power of 24kg. Express this correct to 2 significant figures.

How would I go about it?

Since theres only one number before the decimal point, rounding to two significant figures in this case is the same as rounding to one decimal place. Rounding 5.9723 to one decimal place gives you 6.0.

Another way of looking at it is if its asking for two significant figures you look at the third significant figure (in this case 7) and see if it is above or below 5. Then you would change the second significant figure accordingly. So since 7 is greater than five you, the 9 changes to a 0, which changes the 5 to a 6.

Hope this helps

[morning_sunshine]

Since theres only one number before the decimal point, rounding to two significant figures in this case is the same as rounding to one decimal place. Rounding 5.9723 to one decimal place gives you 6.0.

Another way of looking at it is if its asking for two significant figures you look at the third significant figure (in this case 7) and see if it is above or below 5. Then you would change the second significant figure accordingly. So since 7 is greater than five you, the 9 changes to a 0, which changes the 5 to a 6.

Hope this helps

So then would the answer be written as 6.0 x 10 to the power of 24
Or would it just be written as 6.0?

[RuiAce]

So then would the answer be written as 6.0 x 10 to the power of 24
Or would it just be written as 6.0?

You will most certainly need the power of 24

[morning_sunshine]

Thanks so much
Much appreciate the help everyone

next up...

Erica owns 360 shares in a mining company. She paid $2.80 each for the shares and they are valued at $5.40 now. Erica received a dividend of $342
What was the dividend yield on the current market value of the shares?

How would I work out the current market value?