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

Balance the following oxidation-reduction equation:

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

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

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

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

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?

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?

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

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

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

A college soccer star runs towards the opposing goal and kicks a 0.5 kg stationary inflated ball with a total force of 50 newtons.  What is the force on the athlete's foot?

(1) 0 N

(2) 25 N

(3) 50 N

(4) 100 N

Dictator a is planning to slaughter the people of province q and province q anticipates the attack. Dictator a can either attack by air or by sea. Province q can either prepare for an aerial defense or a defense againt an assault by sea. Both sides must choose either an all air or all sea strategy, and they can't divide their armed forces. Given:

* If Dictator a attacks by sea and q defends by sea, the probability of massive slaughter is 80%.
* If Dictator a attacks by sea and q defends by land, the probability of massive slaughter is 100%.
* If Dictator a attacks by land and q defends by land, the probability of massive slaughter is 60%.
* If Dictator a attacks by land and q defends by sea, the probability of massive slaughter is 100%.

What should the strategy of Dictator a be, assuming the goal is to slaughter as many people of Province q as possible? Assume the goal of Province q to be to minimize the probability of mass slaughter. What is the final probability of mass slaughter assuming both utilize an the best strategy?

A 3 microfarad capacitor is connected with a 6 microfarad capacitor. When a 300 volt potential difference is applied across this combination, the total energy stored in the two capacitors is:

(1) 0.41 J

(2) 0.27 J

(3) 0.09 J

(4) 0.81 J

(5) 0.18 J

When a duck dives into cold water, the capillaries in its skin constrict and move deeper below the surface of the skin. This reaction is an example of:

(1) homeostasis

(2) synthesis

(3) respiration

(4) excretion

Balance the oxidation-reduction equation below:

Cr₂O₃ + Na₂CO₃ + KNO₃ ---> Na₂CrO₄ + CO₂ + KNO₂

To the nearest tenth, find the circumference. Use 3.14 for



VZ = 43.85 inches

Suppose that you have two jars, one with 50 red marbles and the other containing 50 blue marbles. First, a jar is picked at random, and then a marble will be picked from the corresponding jar. Placing all of the marbles in the jars, how can you maximize the chances of a red marble being picked? What are the exact odds of getting a red marble using your scheme?

Each toss of a quarter will produce either a head or a tail. Let A = {Q, T} denote the set of outcomes. Find A³, n(A³), and explain what A³ represents.

Draw a labeled graph that represents the following scenario:

Three sisters, Rachel, Lily, and Jenn, each regularly call their mother Agnes, though Agnes only calls Lily. Jenn will not call Lily, though Lily continues to call Jenn. Rachel and Jenn will call each other, as will Rachel and Lily.

A snowball rolls down a hill gathering snow as it rolls and keeping perfectly spherical shape as it goes.   more »