The number of ways that 2 female students can be chosen from 7 female students is: 7C2
The number of ways that 3 male students can be chosen from 5 males students is: 5C3
The number of ways that 2 female students can be chosen from 7 females students and 3 male students
can be chosen from 5 male students is: 7C2 x 5C3
The number of ways that 5 students can be chosen from 12 students is: 12C5
The probability will be: 7C2 x 5C3 / 12C5
Notice that CD falls outside the triangle; BA + AD = BD.
In triangle(BDC), BD2 + CD2 = BC2 In triangle(ADC), AD2 + CD2 = AC2
---> (BA + AD)2 + CD2 = BC2 AD2 + CD2 = 82
(17 + AD)2 + CD2 = 202 AD2 + CD2 = 64
289 + 34AD + AD2 + CD2 = 400
34AD + AD2 + CD2 = 111
Combining these two: 34AD + AD2 + CD2 = 111
AD2 + CD2 = 64
Subtracting: 34AD = 47 ---> AD = 47/34
In triangle(ADC), AD2 + CD2 = AC2
(47/34)2 + CD = 82
CD = 7.8796632...
Area of triangle(ACD) = ½·AD·DC = ...
Well.....first.... how many integers between 25 and 250 (inclusive) are there?
then count the # of perfect squares 25 36 49 etc and subtract it.....
subtract the # perfect cubes ( 27 64 etc ) and subtract it....
BUT BE careful to not count numbers twice ( numbers that are perfect squares AND perfect cubes)
What have you done towards solving this for yourself?
Area of square 2 x 2 = 4 units2
Area of circle pi (12) = pi units2
What is the probability that P is within one unit of the origin? pi / 4
The probability is 2/5.
The minimum value is 12.
The slope of the line is 2/5.
{A, A, B}, {A, B, A}, {A, B, B}, {A, B, C}, {A, B, D}, {A, C, B}, {A, D, B}, {B, A, A}, {B, A, B}, {B, A, C}, {B, A, D}, {B, B, A}, {B, C, A}, {B, D, A}, {C, A, B}, {C, B, A}, {D, A, B}, {D, B, A}==18 such permutations.
If a quadratic has one root, it must be a perfect square. Let's say the polynomial factors as (x+m)^2. Then, b = 2m and c = m^2. If 2m = m^2 + 7, m^2-2m+7=0. By vieta's formulas, the product of the solutions is 7. Thus, we square this to get 49.
(as a note, there are imaginary values for b and c, which I'm unsure are allowed here)
See https://web2.0calc.com/questions/need-the-answer-quick for more information.
The locus of points with distance 1 from the origin form a circle with center (0,0), since all of these distances are the circle's radii. Notice that the circle fits inside the square; the square's center is (0,0), and the maximum of the circle, or (0,1), is on the square. The area of the square is 2 * 2 = 4, and the area of the circle is 1^2 * π = π. So, the probability is π/4.
See https://web2.0calc.com/questions/help_73083 for further clarification.
Parallel lines have the same slope.
This means that we will have a 2x+3y term on the left side of the new equation, since this yields a slope of -2/3. If 2x+3y=a, and (2,-9) is a solution, then 2*2 + 3*-9 = a, so a=-23.
Inputting x=j and y=-17 into 2x+3y=-23, we have 2j = -23 + 51 = 28, so j=14.
The sum of all THREE angles in the triangle = 180
so R = 180 - 60 = 120 degrees
(x+4)^2 + (y-2)^2 = 185
\(2 \cdot 5^{-1} + 8 \cdot 11^{-1} \equiv 2 \cdot 37 + 8 \cdot 5 \equiv \boxed{2} \pmod{56}\)
pi ≈ 3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679821480865132823066470938446095505822317253594081284811174502841027019385211055596446229489549303819644288109756659334461284756482337867831652712019091456485669234603486104543266482133936072602491412737245870066063155881748815209209628292540917153643678925903600113305305488204665213841469519415116094330572703657595919530921861173819326117931051185480744623799627495673518857527248912279381830119491298336733624406566430860213949463952247371907021798609437027705392171762931767523846748184676694051320005681271452635608277857713427577896091736371787214684409012249534301465495853710507922796892589235420199561121290219608640344181598136297747713099605187072113499999983729780499510597317328160963185950244594553469083026425223082533446850352619311881710100031378387528865875332083814206171776691473035982534904287554687311595628638823537875937519577818577805321712268066130019278766111959092164201989380952572010654858632788659361533818279682303019520353018529689957736225994138912497217752834791315155748572424541506959508295331168617278558890750983817546374649393192550604009277016711390098488240128583616035637076601047101819429555961989467678374494482553797747268471040475346462080466842590694912933136770289891521047521620569660240580381501935112533824300355876402474964732639141992726042699227967823547816360093417216412199245863150302861829745557067498385054945885869269956909272107975093029553211653449872027559602364806654991198818347977535663698074265425278625518184175746728909777727938000816470600161452491921732172147723501414419735685481613611573525521334757418494684385233239073941433345477624168625189835694855620992192221842725502542568876717904946016534668049886272327917860857843838279679766814541009538837863609506800642251252051173929848960841284886269456042419652850222106611863067442786220391949450471237137869609563643719172874677646575739624138908658326459958133904780275900994657640789512694683983525957098258226205224894077267194782684826014769909026401363944374553050682034962524517493996514314298091906592509372216964615157098583874105978859597729754989301617539284681382686838689427741559918559252459539594310499725246808459872736446958486538367362226260991246080512438843904512441365497627807977156914359977001296160894416
AOD = 180 - BOC
AOD = 3.5 BOC or BOC = AOD/3.5 sub in to top equation
AOD = 180 - AOD/3.5
AOD = 140 DEGREES
12 months is 1 year....he owes the original amount plus 10% interest for a year
$ 11 000 is what he owes
(3/4 * 2 - 1/4 * 2 ) / 2 = 1/2 dollar
pi = 3.1415926535897932......
Difference in speed is 11- 8 = 3 m/hr
to cover 1/4 mile : 1/4 m / 3 m/hr = 1/12 hr = 5 mins.
12 / ( 1/50 + 1/30) = 12/ (8/150) = 225 minutes (as TFH found)
x =1 y = -1
Anytime
The probability is: 5/7 x 4/6 x 3/5 x 2/4==120/840==1/7