mm-311

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Subject:
: Re: Problem on Mensa page-a-day calender.>
Question: If eight winkles and nine wonkles cost $118, and
nine> winkles and eight wonkles cost $120, how much will five
winkles and> five wonkles cost?ANSWER: $70 (winkles, $8;
wonkles, $6) > problem with the calendar is that it doesn't
show how to set up the> problem. Could someone tell me how to
set up this problem?Use algebra. Let A stand for winkles and B
stand for wonkles. Now you have:8A + 9B = 1189A + 8B =
120Simply solve for A and B, then plug your answers into the
equation 5A+5B=?-- tml===
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Subject:
: Re: Problem on Mensa
page-a-day calender.Could you please explain how to solve for
A and B?> Question: If eight winkles and nine wonkles cost
$118, and nine> winkles and eight wonkles cost $120, how much
will five winkles and> five wonkles cost?ANSWER: $70 (winkles,
$8; wonkles, $6) > problem with the calendar is that it doesn't
show how to set up the> problem. Could someone tell me how to
set up this problem?Use algebra. Let A stand for winkles and B
stand for wonkles. Now you > have:8A + 9B = 118> 9A + 8B =
120Simply solve for A and B, then plug your answers into the
equation 5A+5B=?-- tml===
===
Subject:
: Re: Problem on Mensa
page-a-day calender.<< Question: If eight winkles and nine
wonkles cost $118, and nine winkles and eight wonkles cost
$120, how much will five winkles and five wonkles cost?
ANSWER: $70 (winkles, $8; wonkles, $6) problem with the
calendar is that it doesn't show how to set up the problem.
Could someone tell me how to set up this problem? >>W/o
algebra recognize that if we substitute one winkle for a
wonkle the total is $2 more, the wonkles are 2 dollars less
expensive than the winkles. Substituting back to the first
condition the total for 17 wonkle wouldbe 118 - 8*2 = 102, so
one wonkle is 102/17 = 6-- tml===
===
Subject:
: Re: Problem on Mensa
page-a-day calender.>> Question: If eight winkles and nine
wonkles cost $118, and nine>> winkles and eight wonkles cost
$120, how much will five winkles and>> five wonkles cost?
ANSWER: $70 (winkles, $8; wonkles, $6) >> problem with the
calendar is that it doesn't show how to set up the>> problem.
Could someone tell me how to set up this problem?Use algebra.
Let A stand for winkles and B stand for wonkles. Now you >
have:8A + 9B = 118> 9A + 8B = 120Simply solve for A and B,
then plug your answers into the equation 5A+5B=?Too compica.
Just add the information given: 17 winkles + 17wonkles = $238
, so 1 pair is $238/17 = $14, so 5 pairs=$70. Whocases what a
single winkle or wonkle costs, it wasn't asked for!-- Kevin
Karplus karplus@soe.ucsc.edu
http://www.soe.ucsc.edu/~karpluslife member (LAB, Adventure
Cycling, American Youth Hostels)Effective Cycling Instructor
#218-ck (lapsed)Professor of Computer Engineering, University
of California, Santa CruzUndergraduate and Graduate Director,
BioinformaticsAffiliations for identification only.--
tml===
===
Subject:
: Re: Problem on Mensa page-a-day
calender.triumpht5@yahoo.com discusses and asks:>Question: If
eight winkles and nine wonkles cost $118, and nine>winkles and
eight wonkles cost $120, how much will five winkles and>five
wonkles cost?>ANSWER: $70 (winkles, $8; wonkles, $6) >problem
with the calendar is that it doesn't show how to set up
the>problem. Could someone tell me how to set up this
problem?>p8oust7eh+This is too simple. Two linear equations
with two unknowns. x=winkle price per piece, dollarsy=wonkle
price per piece8*x+9*y=1189*x+8*y=120The asterisk (*) means
multiplication operation.G C-- tml===
===
Subject:
: Statistical
Variance. Is it n or n-1 in the denominator?The cute Problem
on a Mensa page-a-day calendar pos by D. Buck,together wih a
recent thread on statistics inspires :) me to ask:1. Why is it
that when we want to compute the population variance, we usea
formula with N in the denominator, where N is the size of
thepopulation, but when we want to compute a sample variance,
we use asimilar formula with n-1 in the denominator where n is
the size of thesample?2. Being math orien, we can also get a
little extreme, for the sake offurther understanding, and
ask:What if the population size is N, and we obtain a *sample*
of size N, thatis, the same size as the population. Should we
use N or N-1 to calculatethe variance? What variance
would/should we get this way, the samplevariance or the
population variance?According to a recent post: The reason
that there are two differentformulas for variance is that when
you have a small sample, the varianceof the sample is smaller
than the variance of the whole population, justbecause you
have a small sample. Is that correct?--- Joe-- tml===
===
Subject:
:
Re: Statistical Variance. Is it n or n-1 in the denominator?>
1. Why is it that when we want to compute the population
variance,> we use a formula with N in the denominator, where N
is the size> of the population, but when we want to compute a
sample variance,> we use a similar formula with n-1 in the
denominator where n is> the size of the sample?By using n-1 in
calculating the sample variance, we obtain anunbiased estimator
for the population variance, which means: Theexpec value of the
sample variance equals the population variance.Dom Rosa--
tml===
===
Subject:
: Re: Statistical Variance. Is it n or n-1 in the
denominator?Here is a less mathematically sophistica way of
viewing this n-1 versus Nchoice:One of the measurements for a
small sample may be equal to or very close tothe true average
value; therefore, the count of values used for the
calculationof Average should be 1 less than the count of
samples or items measured.>Should we use N or N-1 to
calculate>the variance? What variance would/should we get this
way, the sample>variance or the population variance?>According
to a recent post: The reason that there are two
different>formulas for variance is that when you have a small
sample, the variance>of the sample is smaller than the
variance of the whole population, just>because you have a
small sample. >Is that correct?>--- JoeG C-- tml===
===
Subject:
:
Re: Statistical Variance. Is it n or n-1 in the denominator?>
The cute Problem on a Mensa page-a-day calendar pos by D.
Buck,> together wih a recent thread on statistics inspires :)
me to ask:1. Why is it that when we want to compute the
population variance, we use> a formula with N in the
denominator, where N is the size of the> population, but when
we want to compute a sample variance, we use a> similar
formula with n-1 in the denominator where n is the size of
the> sample?See below.> 2. Being math orien, we can also get a
little extreme, for the sake of> further understanding, and
ask:> What if the population size is N, and we obtain a
*sample* of size N, that> is, the same size as the population.
Should we use N or N-1 to calculate> the variance? What
variance would/should we get this way, the sample> variance or
the population variance?If you are sampling without
replacement, then you've seen the wholepopulation each exactly
once and can use the population formula forthe variance. If you
are sampling WITH replacement, then you may ormay not have seen
the whole population (most likely not, unless N=1),and the
sample variance formula is still the one to use.> According to
a repcent post: The reason that there are two different>
formulas for variance is that when you have a small sample,
the variance> of the sample is smaller than the variance of
the whole population, just> because you have a small sample.
Is that correct?Yes. (But then I was the one who said it the
first time, so of courseI think so.) Here is some simple
reasoning to help convince you. Fora sample of size zero, the
sample variance cannot be compu (0/0),but the population
variance is zero---no samples differ from the mean.If you have
the entire population, and there is only one value in it,then
indeed the variance is zero, but if you have taken one sample
froma population of unknown size, then you have no idea what
the varianceis. The reasoning that shows that changing n to
n-1 in the denominator isthe right correction to make is a bit
subtle, and I won't try todredge it out of my memory at this
time of night. As I recall, thischange produces the best
estimate of the true variance (under someappropriate
definition of best).-- Kevin Karplus karplus@soe.ucsc.edu
http://www.soe.ucsc.edu/~karpluslife member (LAB, Adventure
Cycling, American Youth Hostels)Effective Cycling Instructor
#218-ck (lapsed)Professor of Computer Engineering, University
of California, Santa CruzUndergraduate and Graduate Director,
BioinformaticsAffiliations for identification only.--
tml===
===
Subject:
: Re: Statistical Variance. Is it n or n-1 in the
denominator?See my responses between the rows of **********
below> The cute Problem on a Mensa page-a-day calendar pos by
D. Buck,> together wih a recent thread on statistics inspires
:) me to ask:1. Why is it that when we want to compute the
population variance, we use> a formula with N in the
denominator, where N is the size of the> population, but when
we want to compute a sample variance, we use a> similar
formula with n-1 in the denominator where n is the size of
the> sample?See below.2. Being math orien, we can also get a
little extreme, for the sake of> further understanding, and
ask:> What if the population size is N, and we obtain a
*sample* of size N, that> is, the same size as the population.
Should we use N or N-1 to calculate> the variance? What
variance would/should we get this way, the sample> variance or
the population variance?If you are sampling without
replacement, then you've seen the whole> population each
exactly once and can use the population formula for> the
variance. If you are sampling WITH replacement, then you may
or> may not have seen the whole population (most likely not,
unless N=1),> and the sample variance formula is still the one
to use.> ********************************JJS: Yes, you pass the
test so far.********************************> According to a
repcent post: The reason that there are two different>
formulas for variance is that when you have a small sample,
the variance> of the sample is smaller than the variance of
the whole population, just> because you have a small sample.
Is that correct?Yes. (But then I was the one who said it the
first time, so of course> I think so.) Here is some simple
reasoning to help convince you. For> a sample of size zero,
the sample variance cannot be compu (0/0),> but the population
variance is zero---no samples differ from the mean.> If you
have the entire population, and there is only one value in
it,> then indeed the variance is zero, but if you have taken
one sample from> a population of unknown size, then you have
no idea what the variance>
is.*********************************************JJS: Even if I
correct an obvious typo of yours, all I get from the aboveis
that a) If we use the denominator n, in an attempt to
calculate the samplevariance of a sample of size n=1, then we
*always* would get zero for the(proposed) sample variance.
(Statistically, of no help).b) If we attempt to use the n-1
denominator, this would result in ameaningless expression
(0/0).And I agree, the attempt to calculate the variance of a
sample of size n=1is statistically of no help, or worse,
algebraic nonsense.This in no way explains why two formulas
are used to calculate variance,one for a sample, and one for
the entire population. You have merelyshown that *both*
proposed formulas for the case n=1 are mathematically ofno
real use. But we already knew that.Maybe.. you can use n=2 to
make your point (?) n=3 (?)---
Joe********************************************** The
reasoning that shows that changing n to n-1 in the denominator
is> the right correction to make is a bit subtle, and I won't
try to> dredge it out of my memory at this time of night. As I
recall, this> change produces the best estimate of the true
variance (under some> appropriate definition of best).-- >
Kevin Karplus karplus@soe.ucsc.edu
http://www.soe.ucsc.edu/~karplus> life member (LAB, Adventure
Cycling, American Youth Hostels)> Effective Cycling Instructor
#218-ck (lapsed)> Professor of Computer Engineering, University
of California, Santa Cruz> Undergraduate and Graduate Director,
Bioinformatics> Affiliations for identification only.-- Delete
the second o to e-mail me.-- tml===
===
Subject:
: Re: order of
operations> [5(9-6)+7]*7For the sake of conceptual
understanding, try to go beyond a roteapplication of memorized
procedures. (Don't get me wrong. I ampro-memorization. It's
just that we have to think about what we wantto memorize and
apply.)Parentheses create inner and outer parts of the whole
expression.These inner parts are intended by the parentheses
to be givenprecedence. Seeing the form a(b + c) or (b + c)a
helps us to findthese inner parts that can be nes deeper and
deeper.Look at your expression, [5(9-6)+7]*7. Do you see here
the form (b +c)a? (Here, b is 5(9-6) and c is the 7 inside the
bracket.) Look atthe left addend of this sum inside the
brackets, this addend being theproduct 5*(9-6). Do you see
here the form a(b + c)? (Here, b is 9 andc is -6.)So, starting
from an inmost part working out, combined with
givingmultiplication precedence over addition: Perform 9-6,
then multiply by5, then add 7, then multiply by 7. Do you see
the pattern of inner toouter, combined with giving
multiplication precedence over addition?Always be on the
lookout for the form a(b + c) or (b + c)a. When youhave an
expression that involves both addition and
multiplication,you're going to have either a sum where at
least one addend is aproduct or a product where at least one
factor is a sum (like a(b + c)or (b + c)a). Always be on the
lookout for these forms, so you can SEEthem in these
expressions.Try to transfer this way of thinking out to other
examples.Paul-- tml===
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Subject:
: Re: order of operations>
[5(9-6)+7]*7For the sake of conceptual understanding, try to
go beyond a rote> application of memorized procedures. (Don't
get me wrong. I am> pro-memorization. It's just that we have
to think about what we want> to memorize and apply.)> Here is
an example:Take the example given by Anna, where we have only
multiplication anddivision:This is a problem concerning the
Order of Operations that has nearlystumped everyone I've
asked, and I still do not have an answer:12/3(4)=? Is it 1 or
16?To promote a conceptual understanding of order of
operations incontexts where there is only multiplication and
division, apply thedefinition of division. This is
multiplication by the multiplicativeinverse: a/b = a*(1/b) =
(1/b)*a. This means that whether we use thesolidus or obelus
or horizontal line to denote division, we replace/b with
*(1/b) where 1/b is viewed not as a fraction but as
adenotation of the multiplicative inverse of b.This means that
to understand an expression involving division
andmultiplication, we can reduce it to an expression involving
onlymultiplication and thus free ourselves from having to
blindly rely onthe left-to-right rule and thus understand what
is really going onmathematically by applying the definition of
division andcommutativity of multiplication:12/3(4) =
12*(1/3)*4 = 12*4*(1/3) = (1/3)*4*12, etc.We have here
therefore just one operation, multiplication, with 3factors
that we can order in any way we wish.For exactly the same type
of reasons, the above applies to expressionsinvolving only
addition and subtraction. The analogue here to theabove
is12-3+4. We can reduce this to an expression involving only
one operation,addition, and by commutativity of addition, we
have an expressioninvolving 3 addends that we can order in any
way that we wish:12-3+4 = 12+(-3)+4 = 12+4+(-3) = (-3)+4+12,
etc.Internalizing the ability to see this condensation or
simplificationfrom two operations to one is a must for
understanding and beingfluent in algebra. It's an opportunity
to turn teaching order ofoperations as a rote exercise of
applying rote-memorized rules to aconceptual exercise in
peeling away some layers to see some realmathematics and thus
prepare the way for future deeper understanding.(This
condensation also shows that if we want to still have
memorizedrules in acronym form, then we can have a set of
rules that is tighterand more compact. It shows how PEMDAS in
conjunction with theleft-to-right rule can be reduced to PEMA
with no left to right rule.)Paul-- tml===
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Subject:
: Re: order of
operations>> (1) Innermost bracke or parenthesized expressions
first>> (2) exponentiation>> (3) multiplication>> (4)
division>> (5) addition and subtraction>Try again:>(1)
Innermost bracke or parenthesized expressions first>(2)
exponentiation>(3) multiplication and division>(4) addition
and subtraction>It gets more complica when you add comparison
operations and>Boolean operations into the same
expression:>(5) comparison operations (>, <, =)>(6) logical
negation>(7) and>(8) or>Also, unary operators like numeric
negation generally come after>exponentiation, and function
evaluation causes some confusion.>For example, sin(x)^2, which
means (sin(x))^2, is sometimes>confusingly written as sin^2(x),
but sin^(-1)(x) usually means>arcsin(x), not (sin(x))^-1.>(1)
Innermost bracke or parenthesized expressions first>(2)
function evaluation>(3) exponentiation>(4) multiplication,
division, numeric negation>(5) addition and subtraction>(6)
comparison operations (>, <, =)>(7) logical negation>(8)
and>(9) or>I've only used the most common operators in
computer languages, not>including ternary ones like (a? b: c)
and computer-specific ones like>bit-wise logical operators.
I've also not included dot products,>cross products, matrix
multiplication, and quantifiers, all of which>can mess up the
precedence of operators.>-- >Kevin Karplus
tkarplus@soe.ucsc.eduhttp://www.soe.ucsc.edu/~karplus>life
member (LAB, Adventure Cycling, American Youth
Hostels)>Effective Cycling Instructor #218-ck
(lapsed)>Professor of Computer Engineering, University of
California, Santa Cruz>Undergraduate and Graduate Director,
Bioinformatics>Affiliations for identification only.This gets
very intricate, but the innermost grouping symbols are what is
mostimportant as long as this does not violate grouping symbols
showing functioninput values....Outside of dealing with
machines, many mathematical people intuitively handleorder of
operations extremely well using only a slight bit of
consciousanalysis. Many years ago first studying introductory
algebra, I internalizedthese rules and never lost this. I
never figured out if it is a greatdifficulty for other
algebra+ students, but it often is an area of difficultyfor
less-than-algebra students.G C-- tml===
===
Subject:
: Re: order of
operationsX-No-Archive: yes>Many years ago first studying
introductory algebra, I internalized>these rules and never
lost this. I never figured out if it is a great>difficulty for
other algebra+ students, but it often is an area of
difficulty>for less-than-algebra students.My experience with
beginning algebra students tells me thatinternalizing the
order of ops in it's basic form, PEMDAS, is a must.If this is
done, then solving one-variable linear equations is
nothingmore than reversing the order and inverting the
operations that resulin the corresponding linear function
output in question.3x+5=14Three times input plus five yields
an output of fourteen, so the inputcan be found by subtracting
five then dividing this result by three.This is the fundamental
approach taken by the learning materialsprovided withing
Cognitive Tutor Algebra 1, from Carnegie Learning.-- --
tml===
===
Subject:
: parabolasI need help on figuring out how to get
the equation from the givengraphed parabola.-- tml===
===
Subject:
:
Re: parabolas> I need help on figuring out how to get the
equation from the given> graphed parabola.If you know some of
the points it passes through, you can use a system
ofequations.-- tml===
===
Subject:
: Re: parabolas<<I need help on
figuring out how to get the equation from the givengraphed
parabola. >>If axis of the the parabola is parallel w/ y axis
:http://lzkiss.netfirms.com/cgi-bin/igperl/igp.pl?dir=test&
name=parabola3Click on prin output or Program tab for the
algorithm-- tml===
===
Subject:
: recurrence relationmay you help me
to solve the recurrence relation below? / | ( nabla^{k+1} f )
(Y_1, ...,Y_{k+1}) = | = Y_{k+1} (nabla^k f (Y_1, ...,Y_{k}) )
| - sum_{i=1}^k nabla^k f (Y_1, .,nabla_{Y_{k+1}}Y_i ,..,Y_k)/
| nabla^1 f (X)= df X | | Y_i denotes a tangent vector field
over a differentiable manifold M,f is a real valued function
over M, f: M--> R, nabla denotes a linear (affine) connession;
nabla^{k+1} f := nabla (nabla^k f).Thank you very much , i need
an help to succede in solving this recurrence relation, please,
helpme.. Tern-- tml===
===
Subject:
: 3 digit number combinationsI
need to generate a list of all possible 1, 2, and 3 number
setsfor the numbers 0 through 9. This will be very time
consuming to dowith a paper and pencil seeing that there are
1000 possiblecombinations and I was wondering if anyone could
help come up with amore efficient strategy. Thanks.--
tml===
===
Subject:
: Is there a free study guide online for the
GED?I had to drop out of high school, and now I am trying to
get my GED. But I dont think I know enough to pass the test so
I am going to needto find a study guide.... If anyone out there
can give me a site thathas a study guide, it would be most
appreciative.-- tml===
===
Subject:
: Re: Is there a free study guide
online for the GED?Unclebuddy420@yahoo.com states and wants to
know:>I had to drop out of high school, and now I am trying to
get my GED. >But I dont think I know enough to pass the test so
I am going to need>to find a study guide.... If anyone out
there can give me a site that>has a study guide, it would be
most appreciative.Go to a bookstore and find a study guide.
OR, go to a used book sale and tryto find one. OR, go to any
local adult school and attend either GED Testpreparation
course or study for a high school diploma which essentially
willalso prepare you for the GED test. G C-- tml===
===
Subject:
:
Re: Is there a free study guide online for the GEDHi Adam.I
found a couple sites you might want to check
out:http://www.free-ed.net/fr10/http://www.4tests.com/exams/
examdetail.asp?eid=38http://www.nwlincs.org/NWLINCSWEB/
gedclass.htmI would also suggest getting a book to study
from.Here is one such book (not very expensive):
http://www.4tests.com/main/fr_main.asp?l=http%3A%2F%2Fwww%
2Eamazon%2Ecom%2Fexec%2Fobidos%2FASIN%2F0743215559%2F4testscom
&returl=%2Fexams%2Fexamdetail%2Easp%3Feid%3D38&retname=Return&
i=72&t=p&ccat=1There should also be free classes in your
areayou can attend for preparing for the GED. You cancall the
GED hotline to get information about these classes:
1-800-626-9433 Good luck!Jon MarlanFront Range Tutoring --
tml===
===
Subject:
: Re: Is there a free study guide online for the
GED?>I had to drop out of high school, and now I am trying to
get my GED. >But I dont think I know enough to pass the test
so I am going to need>to find a study guide.... If anyone out
there can give me a site that>has a study guide, it would be
most appreciative.Contact the GED folks. Also contact your
local high school. Many have GED prep courses. Inany case,
they should have GED info.bob-- tml===
===
Subject:
: System of
equationsI have a problem if somebody can please help me.You
are planning a party and want to have 2 hot
snacks:Stuffedmushroom and cheese sticks. Each stuffed
mushroom costs $0.25 to makeand each cheese stick costs $0.15
to make. You want to have enough sothat each person can have
at least two stuffed mushroom and at leastthree cheese sticks.
There are going to be at most 40 people at theparty and you do
not want to spend more than $45. Write a system oflinear
inequalities that shows the various numbers of
stuffedmushrooms and cheese sticks that you could make.--
tml===
===
Subject:
: Everyday Math and Low Achievers:
suitability?Our son's school is moving to the U Chicago
Everyday Math curriculum.Reviewing their web site I saw this
reference [1]. It fit my suspicionthat Everyday Math would
improve the test scores of high achieverstudents and many
average students, but lower the test scores of lowachiever,
LD, or sub-25 percentile IQ students.curriculum or sub-25
percentile IQ learners? For students who arelower IQ, or who
have focal cognitive impairment impactingmathematical concepts
(see Geary [2]), is their data pointing to amore effective
approach? Clearly these students are unlikely to dowell on
standardized test; the goal is to provide the foundations
for(ironically) everyday arithmetic
operations.thanks!johnjfaughnan@spamcop.netwww.faughnan.com[1]
Baxter, J. A., Woodward, J., & Olson, D. (2001). Effects
ofreform-based mathematics instruction on low achievers in
fivethird-grade classrooms. Elementary School Journal, 101(5),
529547.[Eth] This paper extends an earlier study of learning
disabled childrenusing the first edition of thirdgrade EM
(Woodward & Baxter, 1997). The earlier study used the IowaTest
of Basic Skills andthe Informal Mathematics Assessment, a test
of problem solvingabilities, and found that EMwas effective
for average- and high-ability students, but lesseffective for
lower-ability students.[Eth] The study used surveys,
interviews, and classroom observations toexamine the
difficulties lowachieving students face when working
withcurricula such as EM, and identified the formation ofa
community of learners and the cognitive load as key features
of thecurriculum that need to beconsidered in relation to low
achievers.to conclude from our work thatreform-based
mathematics should be abandoned when teaching lowachievers;
however, ourwork does suggest that many of these students may
be struggling andneed additional support.meta: jfaughnan,
jgfaughnan, 040128, education, curriculum,elementary, k12,
mathematics, arithmetic, performance, cognition, LD,autism,
retardation, lower IQ, low performer, low achiever-- tml