Tutors Answer Your Questions about Finite-and-infinite-sets (FREE)
Question 564074: the set of multiples of 6 between 0 and 90
Answer by stanbon(48546)  (Show Source):
Question 555263: 26th term: 3,8,13,18
Answer by jim_thompson5910(21682) (Show Source):
Question 550149: Look at the series : 53,53,40,40,27,27,... what number should come next
Answer by fcabanski(385) (Show Source):
You can put this solution on YOUR website!A number is repeated, then it is reduced by 13 and the result is repeated. The next number is 27-13=14.
If you need help understanding math so you can solve these problems yourself, then one on one online tutoring is the answer ($30/hr). If you need faster solutions with guaranteed detailed answers, then go with personal problem solving ($3.50-$5.50 per problem). Contact me at fcabanski@hotmail.com
Question 542288:
Suppose that how a voter choses to vote (Democrat, Independent, or Republican) is a stochastic process determined by how she voted in the previous election and that the process is described by the following transition matrix.
D I R
D 0.45 0.15 0.4
I 0.4 0.35 0.25
R 0.55 0.1 0.35
Further, suppose that the voters are evenly split among the three parties in the first election. How will the voters be distributed in the second election? (give 4 decimal places)
Answer by stanbon(48546) (Show Source):
Question 515378: could any one help me in my homework please =)
suppose that S and T both are sets such that T subset of S then show that :
a) if S is a finite set ,then T is also finite set.
b) if T is an infint set, then S is an infinites set.
waiting your help <3 <3
Answer by drcole(72) (Show Source):
You can put this solution on YOUR website!We'll prove (b) first. If T is an infinite set, and T is a subset of S, then S contains an infinite set, and therefore must be an infinite set itself. There are more sophisticated ways to show this, but this is a perfectly reasonable proof.
Now notice that (a) is the contrapositive of (b). Recall that the contrapositive of a statement "if p is true, then q is true" is "if q is not true, then p is not true." Another way to state (a) is "if S is not an infinite set, then T is not an infinite set." So (a) is the contrapositive of (b). Now, we know that if an implication like (b) is true, then its contrapositive is also true, and vice versa. So by proving (b) and showing that (a) is its contrapositive, we have proven (a).
Question 504726: An urn contains 4 red, 5 white, and 4 blue marbles. In how many ways can three marbles be selected so that at least one of them is blue?
I've tried C(4,1) x C(9,2) + C(4,2) x C(9,1) = 198. I'm getting an "incorrect" response when I click submit.
Answer by stanbon(48546) (Show Source):
You can put this solution on YOUR website!An urn contains 4 red, 5 white, and 4 blue marbles. In how many ways can three marbles be selected so that at least one of them is blue?
I've tried C(4,1) x C(9,2) + C(4,2) x C(9,1) = 198. I'm getting an "incorrect" response when I click submit.
----------------
#(at least one blue) = #(all sets of 3) - #(no blue)
---
#(at least one blue) = 13C3 - 9C3
---
#(at least one blue) = 286-84 = 202 ways
=============================================
Cheers,
Stan H.
=======================
Question 483556: Could someone help me with this problem:
Let p represent a true statement, while q and r represent false statements. Find the truth value of the compound statement.
(p V ~q) Λ r
1. True
2. False
Answer by Tatiana_Stebko(1060)  (Show Source):
You can put this solution on YOUR website!p is T, q and r are F
1. ~q is T (because ~F is T)
2. p V ~q is T, (because T V T is T)
3 (p V ~q) Λ r is F (because T Λ F is F)
Answer: 2. False
Question 483259: Could you please help with this?
Use De Morgan’s laws to determine whether the two statements are equivalent:
∼p ∨ ∼q, ∼(p ∧ q)
Answer by Theo(2973)  (Show Source):
You can put this solution on YOUR website!you want to test for equivalency of the 2 statements.
the statements are:
(not p) or (not q)
not (p and q)
if the statements are equivalent, then they will have the same truth table.
we'll construct a table and see what happens.
here's a reference you can look at later if you're interested.
http://www.bookrags.com/research/demorgans-laws-wom/
our truth table looks like this:
p q ~p ~q (p ^ q) (~p v ~q) (~(p ^ q)) (~p v ~q) <-> (~(p ^ q))
T T F F T F F T
T F F T F T T T
F T T F F T T T
F F T T F T T T
you start with the basic variables and create your truth table from that.
first column is p (truth table for p)
second column is q (truth table for q)
third column is ~p (truth table for not p - this is the negation of p)
fourth column is ~q (truth table for not q - this is the negation of q)
fifth column is (p ^ q) truth table for (p and q)
sixth column is (~p v ~q) truth table for (not p or not q)
seventh column is (~(p v q) truth table for (not (p and q) - this is the negation of (p and q)
eighth column is (~p v ~q) <-> (~(p ^ q))
this is the equivalency statement for (not p or not q) and (not (p and q)).
as seen from this table:
if p is true, then not p is false.
if p is false, then not p is true.
if q is true, then not q is false.
if q is false, then not q is true.
(p ^ q) is true only if p and q are both true. If they are mixed or both false, then (p ^ q) is false.
~(p^q) is the negation of (p ^ q).
if (p ^ q) is true, then ~(p ^ q) is false.
if (p ^ q) is false, then ~(p ^ q) is true.
(~p v ~q) is true if ~p or ~q is true.
only 1 of them is required to be true.
(~p v ~q) is false only if ~p and ~q are both false. If they are mixed or both true, then (~p v ~q) is true.
(~p or ~q) <-> (~(p ^ q)) is the equivalency statement.
it has the form of A if and only if B.
in this statement, A is equal to (~p or ~q) and B is equal to (~(p ^ q)).
since (~p or ~q) <-> (~(p ^ q)) is true under all conditions, then the 2 statements are equivalent.
Question 483261: Will someone help with this?
Determine the truth value of the statement when p is T, q is F, and r is F:
(p ∨ q) ↔ (∼r ∧ p)
Answer by jim_thompson5910(21682) (Show Source):
You can put this solution on YOUR website!(p ∨ q) ↔ (∼r ∧ p)
(T ∨ F) ↔ (∼F ∧ T)
(T ∨ F) ↔ (T ∧ T)
(T) ↔ (T ∧ T)
(T) ↔ (T)
T
So (p ∨ q) ↔ (∼r ∧ p) is T when p is T, q is F, and r is F.
Question 476974: If two cards are drawn from a 52-card deck without replacement, in how many different ways is it possible to obtain a king on the first draw and a king on the second?
Answer by robertb(4012)  (Show Source):
Question 476965: Find the number of different subsets of the set {8, 9, 10}.
Answer by mananth(10549)  (Show Source):
Question 473421: Using correct mathematical notation and symbols, express the following in set-builder notation: Z = {10, 11, 12, 13, 14, 15, 16, 17}
Answer by jim_thompson5910(21682) (Show Source):
Question 473182: what is trainagle
Answer by Alan3354(21596)  (Show Source):
Question 465832: Let U = {x│x is an American}
C = {x│x is a smoker}
D = {x│x has a health problem}
E = {x│x is a male}
Describe in words a member of each of the following:
(a) ¯C¯
(b) ¯C¯ ∩ ¯D¯
(c) C ∩ D
(d) D - C
(e) D U C
NOTE: U denotes “union” , ∩ denotes “intersection” and ¯ ¯ denotes “negation”,
for example, ¯ C¯ = is not a smoker
Stumped unable to start.
Answer by solver91311(12126)  (Show Source):
Question 459087: Let A and B be subsets of U={a,b,c,d,1,2,3,4} A={a,2}
A ∩ B = {2} and A ∪ B = {a,c,d,2,4}. Find B
Answer by Edwin McCravy(6936)  (Show Source):
You can put this solution on YOUR website!Let A and B be subsets of U={a,b,c,d,1,2,3,4} A={a,2}
A ∩ B = {2} and A ∪ B = {a,c,d,2,4}. Find B
First draw a big rectangle for the universal set U:
Next draw a circle and label it A:
Next draw a circle overlapping the first circle and
label it B.
The overlapping part is the set A ∩ B which is given
to be {2}.
So we put "2" in the overlapping part, the sort
of football-shaped area in the middle, shaped sort
of like this: "()".
Now we are told that A={a,2}. A is the entire
left circle. Since we already have the "2" as
the only element of A ∩ B, then the "a" must go
in the leftmost part of circle A, which is sort of a
moon-shaped region part of the circle
We are told that A ∪ B = {a,c,d,2,4} which is the
whole figure 8 part, consisting of both circles
together, and "2" is the only element in the "()" part,
and a is the only element in the left "moon" part.
so all the rest of the elements of A ∪ B must go in the
right part of B, the moon-shaped part of the
circle on the far right, so we will put the other elements
of A ∪ B, which are "c", "d", and "4", over there, like
this:
We can stop there because we have placed all the
elements in both sets A and B. B consists of
all the elements in the right circle, so the
answer is B = {c,d,2,4}
However let's finish the Venn diagram. All the rest
of the elements "b","1",and "3" of the universal
set U go outside of both circles, so we will put
them outside the circles:
Edwin
Question 458504: A pair of dice is rolled and the product of the two numbers showing is noted. How many products are possible?
Answer by Edwin McCravy(6936) (Show Source):
You can put this solution on YOUR website!A pair of dice is rolled and the product of the two numbers showing is noted. How many products are possible?
Here are all 36 ways to roll a pair of dice:
(1,1)(1,2)(1,3)(1,4)(1,5)(1,6)
(2,1)(2,2)(2,3)(2,4)(2,5)(2,6)
(3,1)(3,2)(3,3)(3,4)(3,5)(3,6)
(4,1)(4,2)(4,3)(4,4)(4,5)(4,6)
(5,1)(5,2)(5,3)(5,4)(5,5)(5,6)
(6,1)(6,2)(6,3)(6,4)(6,5)(6,6)
Multiplying each pair we get this
1 2 3 4 5 6
2 4 6 8 10 12
3 6 9 12 15 18
4 8 12 16 20 24
5 10 15 20 25 30
6 12 18 24 30 36
The products are
1,2,3,4,5,6,8,9,10,12,15,16,18,20,24,25,30,36
That's 18 different products.
Edwin
Question 458505: Construct all subsets of {a,b,c}. How many subsets are there?
Answer by richard1234(4796)  (Show Source):
Question 458353: What is the solution to the infinite geometric series... the lower limit is = to 1. The upper limit is the infinite symbol. 0.8(0.2)^(n-1).
Found 2 solutions by Edwin McCravy, robertb:
Answer by Edwin McCravy(6936) (Show Source):
Answer by robertb(4012) (Show Source):
Question 458354: What is the solution to the infinite geometric series... the lower limit is = to 1. The upper limit is the infinite symbol. (-2/3)^(n-1)
Answer by robertb(4012) (Show Source):
Question 420405: if some smaugs are thors and some thors are thrains, then some smaugs are definitly thrains.! this statement is true false or neither?
Answer by josmiceli(6784)  (Show Source):
Question 414142: what is every number 5 combonation that can be made with numbers 1 through 99
Answer by Alan3354(21596) (Show Source):
Question 412051: Use the De Morgan's laws to simplify the expression:
(S'union T')'
Answer by Edwin McCravy(6936) (Show Source):
You can put this solution on YOUR website!(S'U T')'
DeMorgan's Laws are:
1. (A ᑌ B)' = A' ᑎ B'
and
2. (A ᑎ B)' = A' ᑌ B'
To do your problem we need the first one:
(A ᑌ B)' = A' ᑎ B'
Substitute (S') for A
Substitute (T') for B
Substitute [ for (
Substitute ] for )
[(S') ᑌ (T')]'
becomes
(S')' ᑎ (T')'
Substitute S for (S')' and T for (T')'
S ᑎ T
Edwin
Question 407323: {All multiples of 5 greater than 29}
Answer by MathLover1(3376)  (Show Source):
You can put this solution on YOUR website!remember: multiples of  always end in  or
all of the multiples of you can find using a formula  where  is any negative or positive number,
the multiples of are every  number in multiplication table
you need all greater than  , so you will start with  , the first number greater than
30, 35,40,45,50,55,60,65,70,75,80,85............... 
Question 385701: what is infinity*infinity
Found 2 solutions by richard1234, user_dude2008:
Answer by richard1234(4796) (Show Source):
Answer by user_dude2008(1825) (Show Source):
Question 348244: Identify n(S) for the given set: S={f, h, n, t}
Answer by jim_thompson5910(21682) (Show Source):
Question 344969: The difference of two integers is 46.If the larger integer is twice the smaller.Find the integers
Answer by jsmallt9(2063) (Show Source):
You can put this solution on YOUR website!Let x = one integer and let y = the other integer. Then
x - y = 46
and
x = 2y
There are several ways to solve systems of equation like this. Since the second equation is already solved for x, the Substitution Method looks easiest. So we'll substitute the expression for x, 2y, in the second equation for the x in the first equation:
(2y) - y = 46.
(Note the use of parentheses. It is an extremely good habit to use parentheses like this whenever you substitute one expression for another. In this problem it doesn't make much difference but in many problems it is critical.)
Subtracting we get:
y = 46
Now that we have y we can find x. We can use x = 2y with y = 46:
x = 2(46) = 92
So the two integers are 46 and 92.
Question 315210: If 300 jellybeans cost you x dollars. How many jellybeans can you purchase for 50 cents at the same rate?
Answer by malaydassharma(59)  (Show Source):
Question 305771: the base of a swimming pool is a circle of radius of 3 m
find its area correct to two decimal place
Answer by themathtutor2009(81) (Show Source):
Question 303205: I am not sure if I am asking the right person (or section), but I posted my question on an image hosting site: http://i39.tinypic.com/2n7154w.jpg . It has something to do with "catenary" stuff. Can you help, please?
Answer by Fombitz(13823)  (Show Source):
You can put this solution on YOUR website!Wow, you're in the wrong location.
You need to find the arc length.
You need to find the derivative of f(x).
The formula for arc length is
.
.
.
.
.
.
.
.
.
Now you have the arc length based on "a".
Use the values given in the problem to find "a" and "C" and you'll have the arc length.
Question 300874: A credit card company classifies its consumers in a given month in three groups; nonusers, light users, and heavy users. The transition matrix for these states is
Nonuser Light Heavy
Suppose the initial distribution for the three states is [0.4 0.4 0.2]. Find the distribution after each of the following periods.
(a) 1 month
(b) 2 months
(c) 3 months
(d) What is the long-range prediction for the distribution of users?
Answer by Fombitz(13823) (Show Source):
Question 279325: what set is a subset of every set?
Answer by jim_thompson5910(21682) (Show Source):
Question 274180: If each score in a set of test scores is divided by 10, describe the effect of the division on the mean, median, mode, range, and standard deviation of the set.
Answer by solver91311(12126) (Show Source):
You can put this solution on YOUR website!
The mean:
The mean of every data element divided by 10:
Factor out 
\left(\frac{\sum_{i=1}^n{x_i}}{n}\right))
Hence 
The median is either an actual data element, in the case of an odd number of data elements, or it is the average of two data elements, in the case of an even number of data elements. In the first case, if all of the data elements have been divided by 10, the one selected for the median would also be divided by 10. In the second case, the mean of two data elements divided by 10 would also be divided by 10 (see discussion of the mean, above).
The mode is, in all cases, one of the data elements. If all of the data elements have been divided by 10, then the mode must be divided by 10 as compared to the original.
The range:
With the data elements divided by 10:
Factor out
\left(x_{max}\ -\ x_{min}\right))
Hence 
Standard Deviation:
\sum_{i=1}^n{\left(x_i\,-\,\overline{x}\right)^2})
The mean of every data element divided by 10 and every instance of the mean divided by 10 as demonstrated earlier:
\sum_{i=1}^n{\left(\frac{x_i}{10}\,-\,\frac{\overline{x}}{10}\right)^2})
Factor out
\sum_{i=1}^n{\left(\left(\frac{1}{10}\right)\left(x_i\,-\,\overline{x}\right)\right)^2})
\left(\frac{1}{100}\right)\sum_{i=1}^n{\left(\right)\left(x_i\,-\,\overline{x}\right)^2})
\sqrt{\left(\frac{1}{n}\right)\sum_{i=1}^n{\left(\right)\left(x_i\,-\,\overline{x}\right)^2})
Hence 
John
Question 258083: What is the set builder notation for the following?
D = (5, 10, 15, 20, . . .)
Express in set builder notation.
Answer by drk(1908) (Show Source):
Question 251233: In a sample of size n=50 and the proportion that responded favorably is .4. Find the standard error.
Answer by drk(1908) (Show Source):
Question 251235: A marketing advisory service wants to estimate the proportion of the population that responds favorably to a new product. It wants the estimate to be correct within 4% at the 95% confidence level. How big of a sample should they take?
Answer by Theo(2973) (Show Source):
You can put this solution on YOUR website!you need three pieces of information to determine that, based on the following link.
http://www.custominsight.com/articles/random-sampling.asp
those pieces of information are:
population size
desired accuracy
confidence level.
you have 2 out of the 3.
you are missing the population size.
it matters.
if a small population, then you will need a proportionally larger sample size to get the same accuracy.
as the population size gets larger, the percentage of the population that needs to be samples is relatively smaller.
example:
if the population is 1,000 people, then you need to get 375 people to provide data in order to get 4% accuracy at the 95% confidence level./
if the population is 10,000 people, then you need to get 566.
if the population is 100,000 people, then you need to get 597.
The percentage of the population required for 4% accuracy at 95% confidence level is progressively smaller as the population gets larger.
The above mentioned article doesn't give you the formula to calculate the right percentages, but it does provide a calculator that provides you with the answer.
the following link uses a similar calculator that provides the same answer.
http://www.surveysystem.com/sscalc.htm
the following link shows the formula they use.
http://www.surveysystem.com/sample-size-formula.htm
there is an additional factor called percent. the default value for this is .5 (50%). this would be a worst case scenario where only 50% of the respondents answer yes to a question and 50% of the respondents answer no. if all answered yes, then the sample size could be smaller. the safe bet is to assume the worst case which is why 50% is the default percent.
An example of how the formula works is as follows:
The formula is:
pss = preliminary sample size. there is an adjustment to this value shown below which will result in fss (final sample size).
p = proportion of the sample respondents that picked the desired answer. the worst case is .5 and that is the typical default value used. a value of .5 requires the largest sample size for a desired accuracy level.
c = confidence interval which is the desired accuracy level you want to achieve. if you want your answer to be +/- 4%, you would make c = .04
z is the z-score. for 95% accuracy, a z-score of 1.96 would be required. this is rounded to the nearest one hundredth.
example:
the following statement is extracted from above.
"if the population is 100,000 people, then you need to get 597."
this means that a sample size of 597 would be required for a population of 100,000 at a 95% confidence level with a 4% confidence interval and a default worst case percent of 50%.
the calculator provided that answer.
the formula that the calcultor used is:
pss is the preliminary value for what we want to find (sample size)
z = 1.96 (95% confidence level)
p = .5 (default value for worst case percent)
c = .04 (confidence interval)
the formula becomes:
this becomes pss = 600.25
there is an adjustment to this answer for population size based on the following formula:
fss is the sample size we are looking for.
pss is the preliminary sample size we derived above.
ps is the population size.
in our example, we have the following values for this formula.
fss = what we want to find.
pss = 600.25
ps = 100,000
the formula becomes:
this becomes:
this becomes fss = 596.6744285 which rounds to fss = 597.
we set sample size equal to fss and we get:
sample size = 597 for a population of 100,000 with a desired confidence interval of 4% at a 95% confidence level with a default percent of 50%.
the question you asked can't be answered because you are missing a very important ingredient. that's the sample size.
include that and you should be able to find the required sample size using the information and tools provided in the references.
Question 251238: A teacher gives a test and gets normally distributed results with a mean of 50 and a standard deviation of 10. If the top 10% will receive an A and the bottom 10% will receive an F, find the minimum score for a letter grade of A and the maximum score fo the letter grade of F.
Answer by Theo(2973) (Show Source):
You can put this solution on YOUR website!mean is 50.
Standard Deviation is 10.
Top 10% get an A.
Bottom 10% get an F.
Based on normal distribution, you can use the Z-Table Calculator to find the percentages of the population that fall under each category.
Any score below 37.1845 will get an F.
Any score above 62.8155 will get an A.
Select the following link to access the z-table calculator.
http://davidmlane.com/hyperstat/z_table.html
you select the bottom graph.
enter a mean of 50
enter a standard deviation of 10
enter a shaded area of .1
select below to get the bottom 10%
select above to get the top 10%
the graph will show you the area you picked.
Question 251231: The heights of American men aged 18 to 24 are approximately normally distributed with mean 68 inches and standard deviation 2.5 inches. Only about 5% of young men have heights outside which range?
Answer by edjones(7311)  (Show Source):
Question 230930: In how many ways can 5 people be chosen and arranged in a straight line, if there are 11 people from whom to chose?
I tried 11 x 5 to get the answer 55 but I am thinking that is the wrong way to solve this problem. Thank you.
Answer by Alan3354(21596) (Show Source):
Question 218968: find the greatest common factor of 16 and 20
Answer by stanbon(48546) (Show Source):
You can put this solution on YOUR website!find the greatest common factor of 16 and 20
-------
Convert to prime factor form:
16 = 2^4
20 = 2^2*5
------------------
The greatest common factor is 2^2 = 4
=========================================
Cheers,
Stan H.
Question 209133: is the greates two diget number an odd number or an even number how do you know?
Found 2 solutions by stanbon, Alan3354:
Answer by stanbon(48546) (Show Source):
You can put this solution on YOUR website!is the greates two diget number an odd number or an even number how do you know?
The greatest 2-digit number is 99 which is odd.
Cheers,
Stan H.
Reply to stanbon@comcast.net or algebra.com
Answer by Alan3354(21596) (Show Source):
Question 208033: Find the sum of each of the following infinite series. If a series does not have a sum write "no sum" as the answer.
1/2+1+2+4
I know that to solve thisyou just put S=A/1-R (A= first term, R= ratio) yet I dont get how I should do it with the fraction 1/2 (I know it sounds stupid but I dont get how to solve it when it starts with a fraction =/)
Answer by rapaljer(4551)  (Show Source):
Question 206370: 20 The population of a small country increases according to the function B=900,000e0.03t, where T is measured in years. How many people will the country have after 4 years
a.828,737
b.1,014,747
c.1,186,431
d.1,908,237
Answer by stanbon(48546) (Show Source):
You can put this solution on YOUR website!The population of a small country increases according to the function B=900,000e^0.03t, where T is measured in years. How many people will the country have after 4 years
---
900,000*e^(0.03*4) = 1,014,747
-----------------------
Cheers,
Stan H.
==============================
a.828,737
b.1,014,747
c.1,186,431
d.1,908,237
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Older solutions: 1..45, 46..90, 91..135
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