For a brief period each year, the rays of the sun are warm enough to melt some of the snows piled a mile deep at the base of the headwalls, and then the pinnacles glisten in the daytime at high noon, and billions of gallons of water begin their slow seepage under the glaciers and across the rockstrewn hanging valleys on their long, meandering journey to the sea -- running east past the sky-carving massifs of Gurla Mandhata and Kemchenjunga, then turning south and curling down through the jungles of Assam, past the Khasi Hills, and into Bengal, past Sirinjani and Madaripur, until the hard water of the melting snows mingles with the soft drainage of fields and at length fans out to meld with the teeming salt depths of the Bay of Bengal.

For centuries the North Atlantic nations dominated the world and as long as they did they could afford the luxury of fighting each other.

For instance -- what about all those people Harold Rhodes went toward unhesitatingly, as if this were the one moment they would ever have together, their one chance of knowing each other??

For each State ( except Puerto Rico, Guam, the Virgin Islands, and, prior to 1962, Alaska and Hawaii ) determine average per capita income based on the last three years.

( For each State, make all computations set forth in items 1 to 8 above, and then add the results obtained for each State in item 8.

For each State ( except the Virgin Islands, Guam, Puerto Rico, and, prior to 1962, Alaska and Hawaii ), determine the average per capita income for the last three years.

For the year 2000 this means servicing ( A ) the protection requirements of a watershed producing at least 200 million acre-feet of water each year, ( B ) recreation and wildlife resources used each year by 635 million visitors, ( C ) a timber resource supporting an annual cut of 21 billion board feet, and ( D ) 60 million acres of rangelands.

For added strength, I also fastened a small block on each side of every frame and batten joint.

Moreland fixed us each another drink, and said, `` For God's sake, tell me something truly amusing ''.

For each mass flow rate the arc voltage was measured.

For each i, let Af.

For an experiment to qualify as a binomial experiment, it must have four properties: ( 1 ) there must be a fixed number of trials, ( 2 ) each trial must result in a `` success '' or a `` failure '' ( a binomial trial ), ( 3 ) all trials must have identical probabilities of success, ( 4 ) the trials must be independent of each other.

For each of these lines meets Q in three points, namely two points on **zg and one point on one of the multiple secants.

For purposes of sample selection only ( individual tests were given later ) we obtained group test scores of reading achievement and intelligence from school records of the entire third-grade population in each school system.

The Wechsler Intelligence Scale For Children was administered to each sample third-grade child by a clinical worker.

For example, one hebephrenic man used to annoy me, month after month, by saying, whenever I got up to leave and made my fairly steoreotyped comment that I would be seeing him on the following day, or whenever, `` You're welcome '', in a notably condescending fashion -- as though it were his due for me to thank him for the privilege of spending the hour with him, and he were thus pointing up my failure to utter a humbly grateful, `` thank you '' to him at the end of each session.

For deserts, puddings and pies are each served once a week.

For easy viewing, the middle 2 beads on each wire ( the 5th and 6th bead ) usually are of a different colour from the other eight beads.

For each picture frame, the 6502 writes graphics commands for the DVG into a defined area of RAM ( the vector RAM ), and then asks the DVG to draw the corresponding vector image on the screen.

For example for any ( even infinite ) collection of pairs of shoes, one can pick out the left shoe from each pair to obtain an appropriate selection, but for an infinite collection of pairs of socks ( assumed to have no distinguishing features ), such a selection can be obtained only by invoking the axiom of choice.

For example, suppose that each member of the collection X is a nonempty subset of the natural numbers.

For any real number the absolute value or modulus of is denoted by ( a vertical bar on each side of the quantity ) and is defined as

For example, the open interval ( 0, 1 ) does not have a least element: if x is in ( 0, 1 ), then so is x / 2, and x / 2 is always strictly smaller than x.

For example, the equation y = x corresponds to the set of all the points on the plane whose x-coordinate and y-coordinate are equal.

For example, using Cartesian coordinates on the plane, the distance between two points ( x < sub > 1 </ sub >, y < sub > 1 </ sub >) and ( x < sub > 2 </ sub >, y < sub > 2 </ sub >) is defined by the formula

For example, the parent function y = 1 / x has a horizontal and a vertical asymptote, and occupies the first and third quadrant, and all of its transformed forms have one horizontal and vertical asymptote, and occupies either the 1st and 3rd or 2nd and 4th quadrant.

For two geometric objects P and Q represented by the relations P ( x, y ) and Q ( x, y ) the intersection is the collection of all points ( x, y ) which are in both relations.

For any system, the following restrictions on measurement results apply, where is the reduced Planck constant and is any direction vector such as x, y, or z:

For curves given by the graph of a function, horizontal asymptotes are horizontal lines that the graph of the function approaches as x tends to Vertical asymptotes are vertical lines near which the function grows without bound.

For example, the graph contains the points ( 1, 1 ), ( 2, 0. 5 ), ( 5, 0. 2 ), ( 10, 0. 1 ), ... As the values of x become larger and larger, say 100, 1000, 10, 000 ..., putting them far to the right of the illustration, the corresponding values of y,. 01,. 001,. 0001, ..., become infinitesimal relative to the scale shown.

For example, the function has a horizontal asymptote at y = 0 when x tends both to −∞ and +∞ because, respectively,

* For all x in L,

* For all x not in L,

For any x ∈ A,

For example, there will only be one term x < sup > n </ sup >, corresponding to choosing x from each binomial.

For non-integer α, the functions J < sub > α </ sub >( x ) and J < sub >− α </ sub >( x ) are linearly independent, and are therefore the two solutions of the differential equation.

For non-integer α, Y < sub > α </ sub >( x ) is related to J < sub > α </ sub >( x ) by:

For any real numbers x, r > 0, one has

For the case of a purely inertial autonavigator consisting of three restrained gyros, a coordinate system is used where the sensitive axis of the X accelerometer is parallel to the east-west direction at the base point, and the Y accelerometer sensitive axis is parallel to the north-south direction at the base point.

: For any set X of nonempty sets, there exists a choice function f defined on X.

For example, after having established that the set X contains only non-empty sets, a mathematician might have said " let F ( s ) be one of the members of s for all s in X.

For finite sets X, the axiom of choice follows from the other axioms of set theory.

For example, suppose that X is the set of all non-empty subsets of the real numbers.

For the graphical user interfaces, AIX v2 came with the X10R3 and later the X10R4 and X11 versions of the X Window System from MIT, together with the Athena widget set.

For example, if K is a field of characteristic p and if X is transcendental over K, is a non-separable algebraic field extension.

For a singly charged hydrogen ion, ionised at 8 kV, the resulting velocity would be X ms < sup >− 1 </ sup >.

For ƒ ∈ C ( X ) ( with a compact Hausdorff space X ), one sees that:

For natural numbers ( taken to include 0 ) n and k, the binomial coefficient can be defined as the coefficient of the monomial X < sup > k </ sup > in the expansion of.

For example " GOOD DOG " can be encrypted as " PLLX XLP " where " L " substitutes for " O ", " P " for " G ", and " X " for " D " in the message.

For example, an " X " is used to indicate a variable group amongst a class of compounds ( though usually a halogen ), while " R " is used for a radical, meaning a compound structure such as a hydrocarbon chain.

For every real number x, the cumulative distribution function of a real-valued random variable X is given by

For any topological space X the ( Alexandroff ) one-point compactification αX of X is obtained by adding one extra point ∞ ( often called a point at infinity ) and defining the open sets of the new space to be the open sets of X together with the sets of the form G < font face =" Arial, Helvetica "> U </ font >

For example, W, a witness, testifies that she saw X drive his automobile into a green car.

For example, books on the English language may be put in X, and books on language in general in a subclass of X, or this can be reversed.

For a given point P, a line is drawn through P perpendicular to the x-axis to meet it at X and second line is drawn through P perpendicular to the y-axis to meet it at Y.

Most of his roles are cameo appearances, as in Into The Night, Jason X, To Die For, Blood_and_Donuts and Alias, but on occasion he has played major roles, as in Nightbreed or Last Night.