For an engine speed of 5000 rpm, a gear ratio of 4.00 to 1, and a tire radius of 13 inches, the equation would look like this: Af

For example, on the basis of the regression equation, a child with an I.Q. of 120 in this sample would be expected to earn an achievement test score of 4.8 ( grade equivalent ).

For example, the number of solutions of an equation over a finite field reflects the topological nature of its solutions over the complex numbers.

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 flow through a tube with one inlet ( state 1 ) and exit ( state 2 ) as shown in the figure in this section, the continuity equation may be written and solved as:

; Associativity: For all a, b and c in A, the equation ( a • b ) • c = a • ( b • c ) holds.

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 example, most ab initio calculations make the Born – Oppenheimer approximation, which greatly simplifies the underlying Schrödinger equation by assuming that the nuclei remain in place during the calculation.

For a steady flow of charge through a surface, the current I ( in amperes ) can be calculated with the following equation:

For a fully relativistic treatment, the equation of state used will interpolate between the equations for small ρ and for large ρ.

For an axially loaded straight column with any end support conditions, the equation of static equilibrium, in the form of a differential equation, can be solved for the deflected shape and critical load of the column.

For example, the condition number associated with the linear equation

For example, a circle of radius 2 may be described as the set of all points whose coordinates x and y satisfy the equation x < sup > 2 </ sup > + y < sup > 2 </ sup > = 4.

For other initial conditions, the equation of motion is given by the exponential of a matrix: for an initial point x < sub > 0 </ sub >,

For an ellipse in canonical position ( center at origin, major axis along the X-axis ), the equation simplifies to

For example, the equation has 2 sets of solutions: ( with any x ) and ( with any y ).

For example, one can use it to determine, for any polynomial equation, whether it has a solution by radicals.

For current cryptographic purposes, an elliptic curve is a plane curve which consists of the points satisfying the equation

For example, the Cobb-Douglas equation — often used in economics — is nonlinear:

For an economic model described by more than one equation, simultaneous-equation methods may be used to remedy similar problems, including two IV variants, Two-Stage Least Squares ( 2SLS ), and Three-Stage Least Squares ( 3SLS ).

For example, if is uncorrelated with years of education, then the equation can be estimated with ordinary least squares.

For the diffusion equation this formula gives

For the inhomogeneous anisotropic media these two forms of the diffusion equation should be combined in

For example, the giant elliptical galaxy M87 has an absolute magnitude of − 22 ( i. e. as bright as about 60, 000 stars of magnitude − 10 ).

For example, if the array has five elements, indexed 1 through 5, and the base address B is replaced by B − 30c, then the indices of those same elements will be 31 to 35.

For example, an 8-bit integer allows the numbers − 128 to + 127.

For about three decades immediately before 1902 it was negative, reaching − 6. 64 s. Then it increased to + 63. 83 s at 2000.

For example, the first pair emitted by the source might be "(+ z, − x ) to Alice and (− z, + x ) to Bob ", the next pair "(− z, − x ) to Alice and (+ z, + x ) to Bob ", and so forth.

For if k, m, and n are integers, and k is a common factor of two integers A and B, then A = nk and B = mk implies A − B = ( n − m ) k, therefore k is also a common factor of the difference.

For example, 21 is the GCD of 252 and 105 ( 252 = 12 × 21 ; 105 = 5 × 21 ); since 252 − 105 = ( 12 − 5 ) × 21 = 147, the GCD of 147 and 105 is also 21.

: For every a in F, there exists an element − a in F, such that a + (− a ) = 0.

For instance, suppose that each input is an integer z in the range 0 to N − 1, and the output must be an integer h in the range 0 to n − 1, where N is much larger than n. Then the hash function could be h

For example, if N is the number ( 2 < sup > 521 </ sup > − 1 ) × ( 2 < sup > 607 </ sup > − 1 ), then trial division will quickly factor 10N as 2 × 5 × N, but will not quickly factor N into its factors.

For this reason, the list he compiled contains only objects found in the sky area he could observe: from the north celestial pole to a celestial latitude of about − 35. 7 °.

For Sydney, the highest temperature ever recorded was 36. 7 ° C ( 98 ° F ) on August 18, 1935, and the lowest was − 31. 7 ° C (− 25 ° F ) on January 31, 1873, and January 29, 1877

For instance, the distribution of their absolute magnitude is bimodal, with a main peak at magnitude − 8. 8, and a lesser one at − 7. 5.

* For UT: at 1 January 2000, ΔT (= TT − UT ) was + 63. 83 s ; hence the correction for the clock time UT = TT − ΔT of the conjunction is:

For every fission that is induced in the system, an average total of 1 /( 1 − k ) fissions occur.

For any luminosity from a given distance L ( r ) N ( r ) proportional to r < sup > a </ sup >, is infinite for a ≥ − 1 but finite for a < − 1.

For example: 1.

( 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 continuous control, feed 1 part phenothiazine to 9 parts minerals or salts.

For the albumin method, equal volumes of 30% bovine albumin, sample and 2% cells suspended in saline were allowed to stand at room temperature for 1 hr and then were centrifuged at 1000 rpm for 1 Aj.

For preparative ultracentrifugation, fractions from the column were concentrated by negative pressure dialysis to volumes of 1 ml or less, transferred to cellulose tubes and diluted to 12 ml with isotonic saline.

For example, the marked susceptibility of the monkey to respiratory infection might be related to its delicate, long alveolar ducts and short, large bronchioles situated within a parenchyma entirely lacking in protective supportive tissue barriers such as those found in types 1, and 3.

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 example, the marksman gets 5 shots, but we take his score to be the number of shots before his first bull's-eye, that is, 0, 1, 2, 3, 4 ( or 5, if he gets no bull's-eye ).

For Yokuts, I tabulated these 71 items in five columns, according as they were expressed by 1, 2, 3, 4, and more than 4 stems.

For Athabascan, with a greater range of stems, the first two of five corresponding columns were identical, 1 and 2 stems ; ;

For the initial development an oxidation pond was constructed as shown in Figure 1.

For example Test 3, E 1 refers to a specimen which has been washed by procedure `` 3 ( '' ( at 160-degrees-F ) for a total of 60 minutes in the machine, has been dried in a tumble dryer by procedure `` E '' and has been subjected to restorative forces on the Tension Presser by procedure `` 1 ''.

For hundreds of years, the evidence available consisted of ( 1 ) the captain's fragmentary journal, ( 2 ) a highly prejudiced account by one of the survivors, ( 3 ) a note found in a dead man's desk on board, and ( 4 ) several second-hand reports.

For example, the 2nd Academy Awards presented on April 3, 1930, recognized films that were released between August 1, 1928 and July 31, 1929.

For example Connecticut applies the following standard to review unpreserved claims: 1. the record is adequate to review the alleged claim of error ; 2. the claim is of constitutional magnitude alleging the violation of a fundamental right ; 3. the alleged constitutional violation clearly exists and clearly deprived the defendant of a fair trial ; 4. if subject to harmless error analysis, the state has failed to demonstrate harmlessness of the alleged constitutional violation beyond a reasonable doubt.

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 analysis of the debris at the testing site of the first U. S. hydrogen bomb, Ivy Mike, ( 1 November 1952, Enewetak Atoll ), revealed high concentrations of various actinides including americium ; due to military secrecy, this result was published only in 1956.

For each element a of a group G, conjugation by a is the operation φ < sub > a </ sub >: G → G given by ( or a < sup >− 1 </ sup > ga ; usage varies ).

For a 256-bit block, the first row is unchanged and the shifting for the second, third and fourth row is 1 byte, 3 bytes and 4 bytes respectively — this change only applies for the Rijndael cipher when used with a 256-bit block, as AES does not use 256-bit blocks.

For example, the prime number theorem states that the number of prime numbers less than or equal to N is asymptotically equal to N / ln N. Therefore the proportion of prime integers is roughly 1 / ln N, which tends to 0.

For example, if the water is 25 ft ( 8 m ) deep, and the anchor roller is 3 ft ( 1 m ) above the water, the scope is the ratio between the amount of cable let out and 28 ft ( 9 m ).