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#201 Re: Help Me ! » Systematic Listing / Product Rule for Counting » 2024-06-24 22:33:14

paulb203

Thanks, Bob, thanks, Phil.

I think I've got it.

The possible outcomes for;

1 flip = 2^1 (H or T)

2 flips = 2^2 (HH, HT, TT, TH)

3 flips = 2^3 (HHH, etc)

and,

4 flips = 2^4 (16 possible outcomes; HHHH, etc)

5 flips = 2^5

etc, etc?

#202 Help Me ! » Mean, median, mode » 2024-06-24 22:13:05

paulb203
Replies: 2

I came across a problem which began with;

"Mark ran a mean distance of 13.2km in 5 days"

Is this badly worded?

#203 Re: Help Me ! » Systematic Listing / Product Rule for Counting » 2024-06-22 11:24:37

paulb203

Thanks, Phil.

But why does 2^3 give us our answer?

I get that there are 2 possible outcomes, and we flip 3 times, so I can see the 2 and the 3, but don't get why 2^3 works.

#204 Help Me ! » Systematic Listing / Product Rule for Counting » 2024-06-20 21:44:41

paulb203
Replies: 6

Bob is going to flip a coin 3 times

List all the possible outcomes

*

I did this 'systematically' as the topic heading suggested, and got HHH HHT etc (8 possible outcomes).

But what is the product rule (I think that's the correct term?) for working out the possible outcomes?

#205 Re: Help Me ! » L.C. Denominator for several values » 2024-06-17 03:34:01

paulb203

Ah, ingenious.

Thanks, Bob.

About your Galileo quote; has he borrowed/developed that from Socrates/Plato. I think Socrates, or Plato putting words in Socrates' mouth, said something similar. Socrates would try to help his interlocutor 'give birth' to insights. Socrates was sometimes known as the midwife due to this. Also, his mother might have actually been a midwife.

#206 Re: Help Me ! » Subtracting in Columns » 2024-06-16 06:37:29

paulb203

Thanks, Bob.

I agree that understanding the method is so important, for both enjoyment, and for remembering how to do it when you've forgotten the rote method.

I also get the approach; stick to the method you know. But, if a student has time, and the inclination, to learn a different method can be enlightening, as certain pennies can drop in various ways.

P.S. I tried the MathsGenie way. It was interesting, but could be messy, sometimes crossing out and replacing several numbers in several coloumns

P.P.S. I think some students are not taught, or not reminded enough after they are taught, that with the add one ten to the top, one ten to the bottom method, they are adding, for example, ten UNITS to the top in the units column, which amounts to one TEN for the tens column. Some think, 'Why does adding 1 to the top, and 1 to the bottom work? (1 as in 1 unit).

#207 Help Me ! » L.C. Denominator for several values » 2024-06-16 06:23:17

paulb203
Replies: 6

Lowest common denominator for;

1/3  2/9  1/4  3/16  3/10 ?

Where do you start if you don’t see it immediately?
I know I can multiply all the denominators together to get a common denominator (but not necessarily the lowest one)
3*9*4*16*10=17,280

But how do I get the lowest one?

#208 Help Me ! » PEMDAS etc » 2024-06-16 02:45:36

paulb203
Replies: 1

8÷2(2+2)=?

I've Googled this one but don't know who to believe.

#209 Help Me ! » Difference between divided by, and shared evenly between » 2024-06-15 07:17:21

paulb203
Replies: 1

Is there one?

*

Divided by/shared evenly between
Does 10÷ 2 mean both;
10 divided by 2
and;
10 shared evenly between 2
*
Also, can you give an example of 10 divided by 2?
I can grasp, for example, 10 sweets, shared evenly between 2 children (each child getting 5 sweets).
But 10 sweets divided by 2 children doesn’t sound right, to me.
*
Does 10 divided by 2 simply mean; 10 split into 2 equal lots?

#210 Help Me ! » Subtracting in Columns » 2024-06-14 23:24:48

paulb203
Replies: 5

I was taught the “add one ten to the top, one ten to the bottom,” method.

I just discovered another method on MathsGenie. When necessary you borrow 1 from the column to your left, e.g, you're subtracting in the units column but the answer would be negative so you borrow one of the tens from the column to your left which gives you ten units for your units column number.

Which did/do you use, and why?

And in either did/do you understand what's going on, or were/are you just following the method?

#211 Re: Help Me ! » Truncation » 2024-06-01 12:03:28

paulb203

smile

#212 Re: Help Me ! » Prime Numbers » 2024-06-01 12:01:34

paulb203

2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97

#213 Re: Exercises » Determine Which Are Right Triangles » 2024-05-31 11:35:40

paulb203
mathxyz wrote:

The lengths of the sides of a triangle are given. Determine which are right triangles. For those that are, identify the hypotenuse.



A. 6, 8, 10


B. 2, 2, 3


C. 10, 24, 26


D. 5, 4, 7

6 8 10 is a scaled up 3 4 5 so that's a right triangle.

2 2 3 ; no, as c would be root 8 (a and b being 2 and 2)

10 24 26; yes

5 4 7 ; no, as c would be root 41 (a and b being 4 and 5)

And the hypotenuse would always be the largest of the 3 values

#214 Re: Help Me ! » Truncation » 2024-05-31 11:24:21

paulb203
KerimF wrote:

This is how I understand truncation:
6.20 to 6.2499999 gives 6.2
6.25 to 6.2999999 gives 6.3

Therefore, my answer is:
6.2 ≤ x < 6.25

For instance, the answer [ 6.2 ≤ x < 6.3 ] refers to int(x).

Kerim

Thanks, KerimF, but I'm not sure what your first two lines mean.

6.20 to 6.2499999 gives 6.2?

What does that mean?

As I understand it, to truncate means to chop off all the numbers after a certain decimal place, but without rounding.

#215 Re: Help Me ! » Truncation » 2024-05-31 11:20:28

paulb203
Bob wrote:

Whoever wrote that answer needs to check the meaning of truncated. I'm with you on this one.

Doubt it'll come up in an exam but if it does I'm sure you'd get full marks.

Bob

Thanks, Bob.
That was MathsGenie (which I like a lot).
And it wasn't just one answer; there were a lot of questions with similar set ups, and similar answers.

#216 Re: Help Me ! » Rearranging formulae » 2024-05-31 11:17:32

paulb203
Bob wrote:

We want /x^2 so factorise on the left and also take the 4 across to the RHS

Divide by x^2 and add 3

Bob

Thanks, Bob.

That's the way I did it, but MathsGenie did it as follows;

Added 3x^2 to both sides
Added 4 to both sides
Then divided both sides by x^2

#217 Help Me ! » Truncation » 2024-05-30 22:12:37

paulb203
Replies: 7

A number x is truncated to 1 decimal place
The result is 6.2
Write down the error interval for x
Answer;
6.2 ≤ x < 6.3

*

Why less than or equal to 6.2? Why the equal to 6.2 part? If x had been 6.2 no truncation would have taken place; nothing would have taken place. The 6.2 just stays the same, no?
We haven’t shortened it. We haven’t chopped off any numbers beyond 1 decimal place; there were no numbers after 1 decimal place.

So why isn’t the answer;
6.2 < x < 6.3 ?
That way we could infer that x was something like 6.21, or 6.2999999999999998, no?

#218 Help Me ! » Rearranging formulae » 2024-05-29 22:49:24

paulb203
Replies: 2

Rearrange;

x^3-3x^2-4=0

to;

x=3+4/(x^2)

#219 Re: Help Me ! » Rounding up or down » 2024-05-29 08:24:12

paulb203
Bob wrote:

Mostly .5 is rounded up but as its exactly halfway between the options you could make a case for rounding down.

Why is round up preferred?

(1) there only has to be one non zero digit after the 5 to tip the number over to round up.

(2) if you round down when the tenths digit is 0 1,2 3 or 4 and up if it's 6, 7 , 8, or 9 then that's 5:4 so choosing up for .5 gives even ups and downs. In a company such as an electric supplier this means bills are rounded up as often as down so the regulator is kept happy.

Example of rounding down. Various cupboards have to be pushed through a narrow gap.  We know the gap is 50cm.  Each cupboard is measured for width to see if it will fit through the gap. Round the widths down to the nearest cm
Why?

Bob
.

Thanks, Bob. I hear you regards rounding up is only preferred, not written in stone, and a case can be made for rounding down; but I'm surprised that at GCSE level, where you're taught to round up for .5, that this answer (from MathsGenie) is given without an explanation.
Also, what might the case be here for saying that the bag could have been  15.5kg, i.e, that rounding down is appropriate?

Regards your cupboards example; I'm not sure. If a cupboard was 50.5, and it was rounded down to 50 (instead of the usual rounding up to 51) it would be deemed acceptable, only for someone to be frustrated later (with a cupboard that doesn't fit in the gap), no?

#220 Help Me ! » Rounding up or down » 2024-05-27 21:49:41

paulb203
Replies: 6

Error Intervals (Bounds)

The weight of a bag of potatoes is 15kg to nearest kg.
a)Write down the smallest possible weight of the bag of potatoes
Answer; 14.5kg (any smaller, e.g, 14.499999999998kg would be rounded DOWN to 14kg.
14.5kg is correctly rounded UP to 15kg

b)Write down the largest possible weight of the bag of potatoes
My answer; Greater than 14.5kg but less than 15.5kg; but a specific weight can't be given.
Their answer; 15.5kg
My question; How can it be 15.5kg? If it was 15.5kg it would have been rounded UP to 16kg (?).

#221 Re: Help Me ! » Simplifying Algebraic Fractions » 2024-05-26 03:24:09

paulb203

Thanks. I thought that. But the answer given implied otherwise. I'll try to dig out the question and post it. One of those moments where you think, "darn! How can I do this when I'm forgetting basic algebra."

#222 Re: Help Me ! » Inequalities on Graphs » 2024-05-26 03:21:12

paulb203

Thanks, Bob.

#223 Re: Help Me ! » Edexcel Maths GCSE Higher Tier » 2024-05-26 03:14:50

paulb203

Thanks, Bob. And will do.

#224 Re: Help Me ! » Error Intervals » 2024-05-26 03:12:22

paulb203
phrontister wrote:

I suspect that rounding might come into this...

I've never heard of error intervals, but rounding is uppermost in my mind atm because I'm working on a tricky problem where rounding is critical in finding solutions.

Thanks. Ah, they are related to Bounds (upper bound/lower bound). Must be a UK thing. Rounding is the significant feature, but truncation is also a part of it.

#225 Re: Help Me ! » Error Intervals » 2024-05-26 03:10:13

paulb203
Bob wrote:

I think you've arrived at the right answer.

What is 8.27685 doing in your list?

Bob

Thanks. Oh yeah, I forgot it began with 8.3! 8.999999.... shouldn't be there either!

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