Mathematics Question Thread

[Fahim486]

Hey need help with this question. Thanks!!!

[kiwiberry]

Hey need help with this question. Thanks!!!

Given that population is growing at a rate proportional to the population:

then

Where \(P_o\) is the initial population. When the population increases by 20%, it will be 1.2 times the initial population. Therefore, when \(t=3, P=1.2P_o\)

Similarly, when the population has doubled, \(P=2P_o\). Sub this in and solve to find t

[julia_warren13]

Hey need help with this question. Thanks!!!

Hopefully this makes sense! Let me know if you need me to explain it

P = Ae^kt

120% x A = Ae^3k
1.2 = e^3k
ln1.2 = lne^3k
ln1.2 = 3k
k = 0.060773... (save in calculator memory!!)

200% x A = Ae^kt
2 = e^kt
ln2 = lne^kt
ln2 = kt
substituting in k = 0.060773...
t = 11.4 days

[jamonwindeyer]

Great stuff above guys

[katnisschung]

hi i have 3 qs on probability

14) in a particular game of chance, the probability of winning the only prize in any draw is 1 in 50.
ii) if it is to be 99% certain that the prize will have been won, how many consecutive draws must
be made?

so i already saw the fallacy of my reasoning when trying to prove it but i don't understand why u take the probability of not winning...
my reasoning
p(winning)=0.02
(0.02)^n=0.99
and used logs to solve but i could already see before doing it i would get a very small number (below 1) for the number
of draws which obviously doesn't make sense.

Answers:
p(not winning)=49/50 = 0.98
(0.98)^n ≤ 0.01
so could someone explain why we use the values for not winning to solve this question? I'm so lost

19) a game involving a single dice has the following rules
a player throws two ordinary dice repeatedly until the sum of the two numbers is either
a 6 or a 8. If the sum is a 8, the player wins. If the sum is 6, the player loses.
If the sum is any other number, the player continues to throw until it is 6 or 8.

i) Show the probability that the player wins on the first throw of the dice is 5/36
so i don't understand why it is 5/36.
technically isnt the probability= probability he throws an 8 and doesn't throw a 6 for every throw

so for the first throw isn't it 5/36 x 31/36

15) A local high school has a student population comprising of 52% female and 48% male.
a survey is carried out and two students are randomly selected to take part.
i) find the probability both students are male

so considering that one student is picked and another is picked without replacement
would this not affect the probability for the gender of the second student?
(becos one is removed so the percentage of females would increase and the males would decrease....
its probably incorrect but i was thinking in terms of fractions assuming the student body had 100 people or is it too large that taking one student out would have a minute effect on the percentages?)

thanksss

[_____]

Could you guys confirm whether differentiation and integration of a^x (a is any integer so not e) is in the 2 unit syllabus or not? The Cambridge math textbook covers it but it's not on the formula sheet and we didn't do it in class. Thanks.

[MisterNeo]

Could you guys confirm whether differentiation and integration of a^x (a is any integer so not e) is in the 2 unit syllabus or not? The Cambridge math textbook covers it but it's not on the formula sheet and we didn't do it in class. Thanks.

I'm pretty sure it is since we did it in class a few weeks ago.

The easy way to do it is by taking log to both sides, then getting it as an exponential.






The same applies with integration:

[RuiAce]

Could you guys confirm whether differentiation and integration of a^x (a is any integer so not e) is in the 2 unit syllabus or not? The Cambridge math textbook covers it but it's not on the formula sheet and we didn't do it in class. Thanks.

[_____]

Thanks guys.

So Rui you can quote x = e^lnx and then move to say 2^x = e^(xln2), correct? Just want to make sure I'm using that result correctly.

[RuiAce]

Thanks guys.

So Rui you can quote x = e^lnx and then move to say 2^x = e^(xln2), correct? Just want to make sure I'm using that result correctly.

[RuiAce]

hi i have 3 qs on probability

14) in a particular game of chance, the probability of winning the only prize in any draw is 1 in 50.
ii) if it is to be 99% certain that the prize will have been won, how many consecutive draws must
be made?

so i already saw the fallacy of my reasoning when trying to prove it but i don't understand why u take the probability of not winning...
my reasoning
p(winning)=0.02
(0.02)^n=0.99
and used logs to solve but i could already see before doing it i would get a very small number (below 1) for the number
of draws which obviously doesn't make sense.

Answers:
p(not winning)=49/50 = 0.98
(0.98)^n ≤ 0.01
so could someone explain why we use the values for not winning to solve this question? I'm so lost

19) a game involving a single dice has the following rules
a player throws two ordinary dice repeatedly until the sum of the two numbers is either
a 6 or a 8. If the sum is a 8, the player wins. If the sum is 6, the player loses.
If the sum is any other number, the player continues to throw until it is 6 or 8.

i) Show the probability that the player wins on the first throw of the dice is 5/36
so i don't understand why it is 5/36.
technically isnt the probability= probability he throws an 8 and doesn't throw a 6 for every throw

so for the first throw isn't it 5/36 x 31/36

15) A local high school has a student population comprising of 52% female and 48% male.
a survey is carried out and two students are randomly selected to take part.
i) find the probability both students are male

so considering that one student is picked and another is picked without replacement
would this not affect the probability for the gender of the second student?
(becos one is removed so the percentage of females would increase and the males would decrease....
its probably incorrect but i was thinking in terms of fractions assuming the student body had 100 people or is it too large that taking one student out would have a minute effect on the percentages?)

thanksss

The prize may have been won on the first, second, third, fourth or fifth and so on (basically n-th) draw. We don't know what that is.

So a direct approach would mean we'd have to add the probability of winning on the first draw, and on the second, AND on the third AND keep going until we finally get there. This is too much effort.

Hence we consider the complementary event. This is the probability that given n draws, the prize hasn't been won yet at all. Unlike the above, the one and ONLY way this can happen is if it doesn't get won, and doesn't get won again, and doesn't get won again and so on. Because we want a 99% confidence that the prize has been won, we want the (complement) probability of not winning the prize at all to be less than 1%.
Hence \(0.98^n \le 0.01\)
_____________________________________

He throws two dice at once, and the numbers shown must add up to 8. I'm not sure what you mean here because it appears as though you're implying that the two numbers can sum to both 8 and 6 at once, which obviously it can not.

Listing out the outcomes, the number sum to 8 only when you roll (6,2), (5,3), (4,4), (3,5) or (2,6) i.e. 5 possible ways. Hence 5/36.
_____________________________________

Yes. Always assume that the population size is too large so that taking one out affects the percentage only negligibly, so we ignore it. Only when the populations are given in proportions (or here, percentages) do we do this.

[laurenf58]

Hey,
Can I please have help with these two questions? I know how to do them but keep getting the wrong answers and want to see where i'm going wrong.

1) A sum of $1000 is invested at the end of each year for 22 years, at 9% pa. Find the amount of superannuation available at the end of 22 years.

2) What is the interest rate if a $5000 investment is worth $6511.30 after 6 years?

Thanks!

[jamonwindeyer]

Hey,
Can I please have help with these two questions? I know how to do them but keep getting the wrong answers and want to see where i'm going wrong.

1) A sum of $1000 is invested at the end of each year for 22 years, at 9% pa. Find the amount of superannuation available at the end of 22 years.

2) What is the interest rate if a $5000 investment is worth $6511.30 after 6 years?

Thanks!

Hey Lauren! Just on the way home ATM so can't do any LaTex, could you post a pic of your working for them? I reckon it is probably a really little thing, I'll try and spot the error for you!

[MisterNeo]

Hey,
Can I please have help with these two questions? I know how to do them but keep getting the wrong answers and want to see where i'm going wrong.

1) A sum of $1000 is invested at the end of each year for 22 years, at 9% pa. Find the amount of superannuation available at the end of 22 years.

2) What is the interest rate if a $5000 investment is worth $6511.30 after 6 years?

Thanks!

For Question 2...

[laurenf58]

Hey Lauren! Just on the way home ATM so can't do any LaTex, could you post a pic of your working for them? I reckon it is probably a really little thing, I'll try and spot the error for you!

So far, i have a = 1000 x 1.09, r=1.09 and n=22

Not sure if i've got my numbers mixed up or if the textbook has the wrong answer!

Thanks!