Theories, Problems, Solutions

Replacement

Crazy Horse — Fri, 09 Sep 2005 21:58:43 -0400

A box contains 10 light bulbs. Find the number of n of ordered samples of (a) size 5 with replacement, and (b) size 5 without replacement.

Photon Energies

Crazy Horse — Wed, 07 Sep 2005 23:13:55 -0400

Einstein's Logic Problem

Crazy Horse — Fri, 02 Sep 2005 17:19:42 -0400

Given:

(a) There are 5 houses in 5 different colors.
(b) In each house lives a person with a different nationality.
(c) These 5 people drink a certain drink, smoke a certain cigar and have a particular pet.
(d) None of the people have the same pet, smoke the same cigar nor drink the same drink.

From the following statements, determine who will Keep the Fish

1: The Brit lives in a red house.
2: The Swede keeps dogs as pets.
3: The Dane drinks tea.
4: The green house is on the left of the white house.
5: The green house owner drinks coffee.
6: The person who smokes Pall Mall rears birds.
7: The owner of the yellow house smokes Dunhill.
8: The man living in the house right in the centre drinks milk.
9: The Norwegian lives in the first house.
10: The man who smokes Blend lives next to the one who keeps cats.
11: The man who keeps horses lives next to the man who smokes Dunhill.
12: The owner who smokes Blue Master drinks beer.
13: The German smokes Prince.
14: The Norwegian lives next to the blue house.
15: The man who smokes Blend has a neighbor who drinks water.

Positive Integers

Crazy Horse — Fri, 02 Sep 2005 17:10:45 -0400

How many positive integers can be formed from the digits 1, 2, 3, and 4 if no digit is repeated in any one integer?

Biological Classifications

Crazy Horse — Thu, 25 Aug 2005 16:00:00 -0400

Which of the following biological groups has the fewest members:

(1) Species

(2) Genus

(3) Family

(4) Class

Genetic Info

Crazy Horse — Sat, 20 Aug 2005 09:00:00 -0400

What structures carry the most genetic information for a leaf cell:

(1) chromosomes

(2) ribosomes

(3) centrioles

(4) chloroplasts

More resources

BOTW Plants
Berkeley - Plant Photos

Karyotypes

Crazy Horse — Fri, 12 Aug 2005 16:00:00 -0400

A karyotype would be least useful in determining whether a person had:

(1) a missing 23rd chromosome

(2) more than one X chromosome

(3) a recessive gene on the Y chromosome

(4) an extra copy of chromosome 21

SUVs

Crazy Horse — Thu, 11 Aug 2005 16:00:00 -0400

A recent survey of 80 auto owners indicated that 24 owned SUVs and 62 owned cars which are not SUVs. Find the number of q people who owned both an SUV and some other car.

Additional resources:

BOTW Number Theory
Stanford - Set Theory
Chaos, Fractals, and Arcadia

NOT Gates

Crazy Horse — Wed, 10 Aug 2005 11:00:00 -0400

How would a NOT gate process each of the following:

(1) 110001

(2) 10010111

(3) 1000111010

Cold and Snow

Crazy Horse — Tue, 09 Aug 2005 15:00:00 -0400

Let x be "it is cold" and let y be "it is snowing". Describe each of the following:

(1) ~x

(2) x ^ y

(3) ~x ^ ~y

(4) ~(~y)

Executive Committee

Crazy Horse — Mon, 08 Aug 2005 07:00:00 -0400

Find the number of n ways that a company consisting of 30 members can elect a president, vice-president, and secretary (assuming that no one person can be elected to more than one position).

Balls on a Shelf

Crazy Horse — Sun, 07 Aug 2005 10:00:00 -0400

Two balls lie on next to each other on a shelf. If one ball has a radius of 8 inches and the point of contact is 10 inches above the shelf, what is the radius of the second ball?

Relations

Crazy Horse — Sat, 06 Aug 2005 11:00:00 -0400

Let R be the relation on A = {4,5,6,7}defined by "x is less than y", that is, R is the relation < . Write R as a set of ordered pairs.

Derivatives

Crazy Horse — Fri, 05 Aug 2005 17:00:00 -0400

Find the derivative for the following:

f(x) = 3x6 + 5x - 4

Jelly Beans

Crazy Horse — Fri, 05 Aug 2005 09:00:00 -0400

You have a large glass jar filled with Jelly Belly jelly beans. Some are green, some are yellow, some pink, some blue, and some are orange. With your eyes closed, pick out 2 of a like color. How many do you have to grab to be sure you have 2 of the same?

Hot Water

Crazy Horse — Thu, 04 Aug 2005 14:00:00 -0400

How much energy is required (in Joules) when the temperature of 3.6 grams of liquid water increases by 4 °C ?

More chemistry:

Yahoo Chemistry
BOTW Chemistry
DMOZ Chemistry

Radiated Energy

Crazy Horse — Wed, 03 Aug 2005 07:00:00 -0400

If the absolute temperature of a blackbody is increased by a factor of three, the energy radiated per second, per unit area:

(1) decreases by a factor of 9

(2) increrases by a factor of 9

(3) increases by a factor of 27

(4) decreases by a factor of 81

(5) increases by a factor of 81

Set Fractal

Crazy Horse — Tue, 02 Aug 2005 16:25:57 -0400

Set fractal provided by "Chaos Theory and Fractals" by Jonathan Mendelson and Elana Blumenthal

Pretty cool stuff. They have plenty more, and fine examples of chaos theory and fractals. Definitely worth a look-see.

Set Theory

Crazy Horse — Tue, 02 Aug 2005 13:32:42 -0400

Given:

V = { M,W,F}
W = {S,SU}
X = {M,T,W,TH,F}
Y = {W,TH,F,S}

Find:

(V \ W)^c

Destructive Interference

Crazy Horse — Sun, 31 Jul 2005 10:00:00 -0400

Two idenical speakers driven by the same signal produce 680 Hz soundwaves. The speakers are different distances away from you. What must be the difference in distances to result in destructive interference?

(1) 0.85 m

(2) 1.3 m

(3) .30 m

(4) .25 m

Niches

Crazy Horse — Sat, 30 Jul 2005 19:00:00 -0400

Areas with a vast amount of varied niches will invariably contain:

(1) great diversity among the organisms

(2) little diversity among the organisms

(3) no organisms that risk extinction

(4) large numbers of organisms that risk extinction

Oxidation Reduction

Crazy Horse — Sat, 30 Jul 2005 16:28:03 -0400

Balance the following oxidation-reduction equation:

NaHSO₄ + Al + NaOH ---> Na₂S + Al₂O₃ + H₂O

Boolean algebra

Crazy Horse — Tue, 26 Jul 2005 14:22:31 -0400

Let D₇₀= {1, 2, 5, 7, 10, 14, 35, 70}, the divisors of 70. Show how D₇₀ is made into a Boolean algebra.

Best of the Web Algebra
Algebra.com
Equation Solver

Propositions

Crazy Horse — Tue, 26 Jul 2005 14:14:04 -0400

Verify that the proposition (p ^ q) ^ ~ (p v q) is a contradiction.

Half Life

Crazy Horse — Tue, 26 Jul 2005 11:00:41 -0400

If an enriched radioactive isotope has a half-life of 8 minutes, what proportion would be left after 24 minutes?

(1) .083

(2) .125

(3) .166

(4) .25

(5) .5

Dream Girl

Crazy Horse — Mon, 25 Jul 2005 22:12:22 -0400

One-half of Lily's age two years from now plus one-third of her age three years ago is twenty years. How old is she now?

Related Rates

Crazy Horse — Sat, 23 Jul 2005 14:14:35 -0400

As a last ditch attempt to destroy a meteor propelling towards Earth, NASA scientists decide to launch a nuclear warhead. As the two converge, the missile and the meteor are at right angles to each other. The nuke is 700 miles away from the point of impact and traveling at 900 MPH; the meteor is 500 miles from impact and traveling at 1100 MPH.

(1) At what rate is the distance between the two decreasing?

(2) How much time until they converge?

(3) Since the beginning of the war in Iraq, how many people have died in the US due to inflated defense budgets in lieu of increased health department budgets?

Permutations

Crazy Horse — Fri, 22 Jul 2005 23:06:24 -0400

How many ways can a judge award first, second, and third places in a contest with 20 contestants?

Blow my Horn

Crazy Horse — Thu, 21 Jul 2005 22:02:09 -0400

An engineer in a moving train blows the train's horn while the train is moving away from a woman standing on a nearby platform. Compared to the frequency of the sound that the engineer hears, the lady standing on the platform hears a sound with:

(1) the same wavelength

(2) more variation in tone

(3) greater amplitude

(4) a lower frequency

Combinatorial Analysis

Crazy Horse — Thu, 21 Jul 2005 11:25:34 -0400

There are twelve children in a kindergarten class. Find the number of ways that the twelve children play three different games if four children are to play each game.

For more resources related to combinatorial analysis and discrete mathematics, check out

Best Book Buys - for some books relating to combinatorial analysis

Best of the Web Math Category - lists quality sites relating to all aspects of mathematics

Combinatorics Problems - a collection of problems in combinatorics

Generating Functions - interactive introduction to generating functions