Friday
August 28, 2015

Posts by Reiny


Total # Posts: 30,673

LNU
Use Venn diagrams and this becomes quite easy. Start with the intersection of the three circles and place 3 in that regions. Now working from the inside out, enter the data Make sure you don't count items more than once. e.g. for the 10 taking Math and History, remember ...
July 13, 2015

algebra
if -2(x-3y)-3(x+5y)-(6x-8y) then = -2x + 6y - 3x - 15y - 6x + 8y = -11x - y if -2(x-3y)-(3x+5y)-(6x-8y) . then = -2x + 6y - 3x - 5y - 6x + 8y = -11x + 9y
July 13, 2015

algebra
I see mismatched brackets ... is it -2(x-3y)-3(x+5y)-(6x-8y) or -2(x-3y)-(3x+5y)-(6x-8y) or .... (the brackets going left must have the same count as the brackets to the right)
July 13, 2015

forgot some cases - prob&stat
ok jil, I forgot the case where only one of "swing players" is in the lineup 6. X plays guard, Y does not play GXFCF C(5,1) x 1 x C(4,2) x C(3,1) = 90 7. X plays forward, Y does not play GGXCF C(5,2) x 1 x C(4,1) x C(3,1) = 120 We have the same cases if Y plays, but ...
July 12, 2015

prob&stat
number of ways to choose any 5 of the 14 = C(14,5) = 2002 number of "legitimate" starting lineups Cases: GGFCF 1. X and Y excluded: C(5,2) x C(3,1) x C(4,2) = 180 GXFCF 2. X plays guard, Y included in the forwards C(5,1) x C(5,2) x C(3,1) = 150 GYFCF 3. Y plays guard...
July 12, 2015

math
Best done with a Venn diagram. For the intersection of all three circles which I called F, H, and B, label it x Then fill in the regions of the circle using the given data. e.g. I labeled the part which is only hockey and basketball as 50-x and the part which is only hockey as...
July 12, 2015

math
Looks like Steve answered the same question in the first of the "Related Questions" below http://www.jiskha.com/display.cgi?id=1410269873
July 11, 2015

Math
Not enough information. since volume of a rectangular prism, a plain ol' box, is (length)(width)(height) any 3 numbers that will multiply to give you 256 will work e.g. L = 16 W = 8 H = 2 or L = 32 W = 8 H = 1 or L = 10 W = 6.4 H = 4 etc
July 11, 2015

math probability
Actually looking back at my answer in the Related Question, I see that I made an error The logical connector was OR , so multiples of 3 : 3,6,9,12,15,18 or less than 7: 1,2,3,4,5,6 can't count the 3 and 6 twice, so there are 10 such numbers prob = 10/18 = 5/9
July 11, 2015

Algebra 2
I will assume An is supposed to mean term(n) ?? term(n) = a + (n-1)d 136 = a + 19(7) a = 3 so sum(n) or your Sn = (n/2)(2a + (n-1)d ) = (n/2)(6 + 7(n-1) ) = (n/2)( 7n -1 ) or = (7n^2 - n)/2 or some other variation of that
July 11, 2015

math
from the first: x = 12-3z plug that into the 2nd: -12+3z-2y+z = 10 4z - 2y = 22 2z - y = 11 , #4 plut x = 12-3z into the 3rd 36-9z +5y + 2z = -7 -7z + 5y = -43 , #5 #4 times 5 ---> 10z - 5y = 55 add this to #5 3z = 12 z = 4 in #4: 8-y = 11 y = -3 back in x = 12-3z x = 12-12...
July 10, 2015

changing
s(1) = t(1) = 2+5 = 7 s(2) = 2(2^2) + 5(2) = 18 s(3) = 2(9) + 5(3) = 33 s(4) = 2(16) + 5(4) = 52 .. t(2) = s(2) - s(1) = 18-7 = 11 t(3) = s(3) - s(2) = 33-18 = 15 t(4) = s(4) - s(3) = 52-33 = 19 so we have: 7,11,15,19,... looks like an AP with a = 7 , d = 4 term(n) = a + (n-1)...
July 10, 2015

math-percentage
If that answer is supposed to be correct, then males = 352 , females = 440 percentage of males = 352/792 = appr 44.4% percentage of females = 440/792 = appr 55.6% which is NOT 20% difference. So the choice are clearly all wrong. Since I showed that my answer is correct, what ...
July 10, 2015

math-percentage
let the number of males be x then the number of females = 792-x percentage of males = x/792 percentage of females = (792-x)/792 (792-x)/792 - x/792 = .20 times 792 792-x - x = 158.4 -2x = -663.6 x = 316.8 , can't have partial people So there are 317 males and 475 females ...
July 10, 2015

Math
the primes in that range are: 2,3,5, and 7 Assuming it is a true random generator, the prob would be 4/10 or 2/5
July 10, 2015

Algebra 2
When simplifying, each new line should have an equal sign at the front You are saying: "my next line is equal to the previous line" Don't just make piece-meal statements Here is what I would have expected from my students when I was still teaching: 6x^5/(2x^3...
July 9, 2015

math
geeehhh, math is getting harder all the time.
July 9, 2015

math
I assume your are looking for (√25)x = 12 5x = 12 x = 12/5 Repeat the above for each of the others
July 9, 2015

math
Steve, I was thinking along these lines, can you find a flaw in this? number of 3-person committees that can be formed from the 15 without any restrictions = C(15,3) = 455 number of 3-person committees WITH BOTH John and Mary = C(13,1) = 13 so the number without both John and ...
July 9, 2015

Algebra
I don't think Steve is on line right now, so I will try. Did you notice the the right side of both of Steve's equations are the opposite of yours? Steve's solution would result in s = 4 c = 2 Yours give inadmissible results of s = appr -14 and c = 16.7 Your ...
July 9, 2015

math (algebra)
The x^32 can only come from multiplying the first tems of all those binomials The -1 can only come from multiplying the constants notice that if we multiply the first terms , the x's, in the right side we get (x^16)(x^8)(x^4)(x^2)(x) = x^31 so the missing bracket must be (...
July 8, 2015

Evaluate the difference, and write the result in t
(6- 1/2 I)-(3+ 9/2 I) = 6- 1/2 I - 3- 9/2 I = 3 - 5 l don't know there the t is supposed to come from.
July 8, 2015

math (algebra)
oops, forgot the link to the graph http://www.wolframalpha.com/input/?i=%28x-2%29%5E2%28x-1%29%5E3%28x%2B1%29%5E4%28x%2B2%29%5E5+%3D+0
July 8, 2015

math (algebra)
each factor could be zero, thus x-2 = 0 ---> x = 2 x-1 = 0 ---> x = 1 x+1 = 0 ---> x = -1 x+2 = 0 ---> x = -2 Look how Wolfram graphed it. How many times and where does the graph intersect with the x-axis ?
July 8, 2015

Math
A: true B: true C: false e.g. 0.5 = .499999.... D: true
July 8, 2015

Math
so we are looking at area of base of cylinder + area of sleeve of cylinder + area of cone without its base = π(.29)^2 + 2π(.29)(5) + π(.29)(1) = .... you do the button pushing (surface area of cone = πr^2 + πrs, where s is the slant height of the cone...
July 8, 2015

Calculus
very detailed solution: let 2log4 9 = x log481 = x 4^x = 81 2^(2x) = 81 let log2 3 = y 2^y = 3 2^4y = 3^4 = 81 then 2^(2x) = 2^(4y) ---> 2x = 4y x = 2y So 2log4 9 - log2 3 = x - y = 2y-y = y = log2 3
July 8, 2015

Math
let present amount be x x(1.05)^5 = 50000 x = 50000/1.05^5 = 39176.31
July 8, 2015

Algebra (Normal Distribution)
Here is the perfect website for your problem http://davidmlane.com/hyperstat/z_table.html
July 8, 2015

maths
Did you mean: (√(196/x) )*(√(90/x) ) = 4 or (√196)/x * (√(90)/x = 4 It makes a big difference
July 8, 2015

mathematics
I don't understand your question. You said that the five numbers given were picked, so the probability that five numbers should be selected would be 1 Not sure what you are asking.
July 8, 2015

math
the other is (-28/81) ÷ (14/27) = (-28/81)(27/14) = -2/3
July 8, 2015

Math
"...either a multiple of 3 or a number less than 7" only 2 elements satisfy that condition, namely the 3 and 6 so prob(of your event) = 2/18 = 1/9
July 8, 2015

Maths
If you are studying this, you must know (1+x)^n = 1 + nx + n(n-1)(x^2)/2! + ... valid only for |x| < 1 now let's apply it to your problem of 31^(1/5) = (32 - 1)^(1/5) = 32^(1/5)(1 - 1/32)^(1/5) = 2 (1 - 1/32)^(1/5)) = 2( 1 + (1/5)(-1/32) + (1/5)(-4/5)/2 (-1/32)^2 + (1/5...
July 8, 2015

Algebra
amount of the 20% stuff --- x L amount of the 50% stuff --- 200-x L .2x + .5(200-x) = .3(200) times 10 2x + 5(200-x) = 3(200) 2x + 1000 - 5x = 600 -3x = -400 x = 400/3 The chemist needs 400/3 L of the 20% solution and 200/3 L of the 50% solution
July 7, 2015

Calculus
dy/dx = x(-sinx) + cosx = 0 for a max/min xsinx = cosx sinx/cosx = 1/x tanx = 1/x No direct algebraic method to solve this, so we have to resort to other means let's look at the graph by Wolfram A preliminary look at y = xcosx shows that there would be an infinite number ...
July 7, 2015

Calculus
since v'(t) = a(t), which is the acceleration a(t) = -32 since a(t) is a constant, we get the acceleration due to gravity at -32 ft/s^2 and v'(1) = a(1) = -32 ft/s^2
July 6, 2015

math
Can we expect a question? btw, use 1/2 and 1/8 to show your fractions
July 6, 2015

Algebra
a + s = 598 s = a - 52 sub s = a-52 into the first equation a + a-52 = 598 2a = 650 a = 325 s = 325-52 = 273
July 6, 2015

Math
Let one be x metres long then the other is 150 - x x+40 = 2(150-x) x+40 = 300 - 2x 3x = 260 x = 260/3 m one is 260/3 m, the other is 150-260/3 or 190/3 m or in decimals, appr 86.67 m and 63.33 m. check: one is 86.67 twice the other is 126.67 which is 40 m more
July 6, 2015

mathematics : intergration
S = 4t - (1/2)t^2 + c "given that S=S when t=0" ????? I will assume you meant: given that S=0 when t=0 0 = 0 - 0 + c ---> c = 0 S = 4t - (1/2)t^2
July 6, 2015

maths
original --- x after first increase --- x + 1200 now decrease of 11% -- 89% are left .89(x+1200) = x-32 .89x + 1068 = x - 32 1100 = .11x x = 10,000
July 6, 2015

Algebra
The equation would be: n(t) = 5 (2^(t/20) , where t is in minutes (note that t/20 = (1/20)t = .05t) So they want the count after 4 hrs or 240 minutes n(240) = 5 (2^(240/20)) = 5 (2^12) = 5(4096) = 20480 you could do this the long way: now --- 5 after 20 min -- 10 after 40 min...
July 5, 2015

maths
start with a sketch of the finished product Let the triangle be ABC, so that angle B = 120°, angle BCA = 40° and angle CAB = 180-40-120 = 20° the centre of the triangle, O, lies on the right-bisectors of BC and AB, so that CO = AO = BO = 3 cm remember that the ...
July 4, 2015

St jonhs high school/mathamatics
√5 is obviously greater than √3 And you have 4 of the √5's vs 3 of the smaller value ! I really can't believe you asked this question.
July 4, 2015

MATH
" ..... find the polynomial whose zeroes are root 3 and -root 3" y = (x-√3)(x+√3) = x^2 - 3 What does the fact that alpha and beta are zeros of the the polynomial x^2 - 5x + 6 have to do with it? other than alpha = 2 and beta = 3
July 4, 2015

Algebra
(fog)(-2) = f(g(-2)) g(-2) = (-(-2))^3 + 1 = 10 f(10) = 3(10)+7 = 37 so (fog)(-2) = 37
July 4, 2015

trigonometry
did you make a sketch? If so you will see that sinØ = 30/40 = .75 Ø = appr 48.6° also: x^2 + 30^2 = 40^2 x^2 = 700 x = 7√10 or appr 22.1 ft
July 4, 2015

Math
children --- x grandkids --- 7-x children got (1/3)(6,000,000) = 2,000,000 so grandkids got 4,000,000 each grandkid got 4000000/(7-x) kids got 2000000/x each "200,000 more a piece than what each of the grandchildren" ---> 2000000/x - 200000 = 4000000/(7-x) times x...
July 4, 2015

math
thousandth digit --- t tens digit --------- 2t hundredth digit ---- t + 2t = 3t well, digits can only range from 0 to 9 let's rule out t = 0 , since that would not be a sensible number then tenth digit is obviously an even number so it could be 2,4,6,8 which means that t ...
July 4, 2015

Applied Mathematics ( Mechanices
your distance equation: height = -4.9t^2 + 14t + 29.4 at ground, height = 0 -4.9t^2 + 14t + 29.4 = 0 divide by -7 .7t^2 - 2t - 4.2=0 times 10 7t^2 - 20t - 42 = 0 t = (20 ± √1576)/14 = appr 4.26 seconds (or a negative)
July 2, 2015

linear equations in two variable
let the speed of the current be x km/h time against the current = 40/(5-x) time with the current = 40/(5+x) 40/(5-x) = 3(40)/(5+x) 1/(5-x) = 3(5+x) 15-3x = 5+x -4x=-10 x=2.5 the speed of the stream is 2.5 km/h check: time against the current = 40/2.5 = 16 hrs time withe the ...
July 2, 2015

trigonometry26
1 + sin^2 Ø = 3sinØcosØ divide by cosØ 1/cosØ + tanØsinØ = 3sinØ secØ + tanØsinØ = 3sinØ tanØ = (3sinØ - secØ)/sinØ = 3 - secØ/sinØ let's stop here...
July 2, 2015

trigonometry 28
This basic proof should be found in your textbook or in your notes. If not, just Google it, you will found many proofs.
July 2, 2015

calculus
the largest area of course is contained within a circle. So if the perimeter is 15 m then 2πr = 15 r = 15/(2π) area = π(15/(2π))^2 = 225/(4π) m^2 or appr 17.9 m^2
July 2, 2015

calculus
Ok, I will go with that assumption. As I made my diagram, I also noticed that you did not state the speed of the car B. I will also assume that the speeds are the same. At a time of t hrs, let the distance between them be x miles so by the cosine law: x^2 = (30+30t)^2 + (30t)^...
July 2, 2015

calculus
How are the two cars positioned relative to each other ? e.g. is car A directly west of car B ? is car A north of car B ?
July 2, 2015

trigonometry
use the fact that cos Ø = sin (90° - Ø) cos(3x - 10) = sin(90 - (3x-10) ) cos(3x - 10) = sin(100 - 3x) so sin(x-20) = sin(100 - 3x) then: x-20 = 100-3x 4x = 120 x = 30 check with your calculator
July 2, 2015

trigonometry
given: sinØ = a/b so y = a , x = ? r = b r^2 = x^2 + y^2 b^2 = x^2 + a^2 since we are in quad I, x = +√(b^2 - a^2) now use your definitions to state the trig ratios
July 2, 2015

Math
#1 is the interesting question Since the annuity payments become your "salary", I will assume they are made at the beginning of the year. IF x is the first payment made now , the Present Value is: PV = 8,503.05 + (1.03)(1.075)^-1 (8,503.05) + (1.03)^2 (1.075)^-2 (8,...
July 2, 2015

Math
I did this one yesterday http://www.jiskha.com/display.cgi?id=1435760969
July 2, 2015

Math
done yesterday http://www.jiskha.com/display.cgi?id=1435761181 why did you repeat the question?
July 2, 2015

Math
did you mean a = (√5 + 1)/(√5 - 1) and b = (√5-1)/(√5 + 1) ?? or the way you typed it
July 1, 2015

Math
27x^3+8y^3 --- the difference of cubes = (3x + 2y)(9x^2 - 6xy + 4y^2) = 12(9x^2 - 6xy + 4y^2) but 9x^2 - 6xy + 4y^2 = (9x^2 + 12xy + 4y^2) - 18xy = (3x+2y)^2 - 18xy = 144 - 108 = 36 so 27x^3 + 8y^3 = 12(36) = 4320 or: y = 6/x back in the first: 3x + 2(6/x) = 12 times x 3x^2 + ...
July 1, 2015

Maths
You will have 2 congruent triangles, so we need to find only the area of one of them Heron's formula: Area = √(s(s-a)(s-b)(s-c)) , were a, b, and c are the sides and s= half the perimeter s = (26+28+30)/2 = 42 s-a = 16 s-b = 14 s-c = 12 area = √(42x16x14x12...
July 1, 2015

math in distress
the second oldest could be either 9, 10, 11, or 12 All of the following satisfy the given conditons: 5 5 9 9 12 5 5 9 10 12 5 5 9 11 12 5 5 9 12 12
July 1, 2015

math in distress
one book weighs 2.5 lbs so 5 books weigh 5(2.5) or 12.5 lbs one notebook weighs 4 ounces 5 notebooks weigh 20 ounces = 1 lbs and 4 ounces , (if I recall the non-metric stuff) total = 12.5 lbs + 1 lb + 4 ounces, you were correct here = 13.5 lbs + .25 lbs = 13.75 lbs or 13 lbs ...
July 1, 2015

math
set up a simple ratio ... 1/x = (3/4) / 4 (3/4)x = 4 3x = 16 x = 16/3 I will take 5 1/3 quarts You will need to buy 6 quarts, (best bought as 1 gallon and 2 quarts) or, (by the 3 step process) 3/4 wall takes 1 quart one wall takes 1 / (3/4) quarts or 4/3 quarts 4 walls take 4(...
July 1, 2015

correction - maths
logx (1/8) = -3/2 means: x^(-3/2) = 1/8 x^(3/2) = 8 (√x)^3 = 8 √x = 2 x = 4 check: log4 (1/8) = log41 - log48 = 0 - 3/2 , (since 4^(3/2) = 8) = -3/2
July 1, 2015

mathematics :geometric progression
If geometric, then (2k-4)/(k-3) = (4k-3)/(2k-4) (2k-4)^2 = (k-3)(4k-3) 4k^2 - 16k + 16 = 4k^2 -15k + 9 -k = -7 k = 7 so the first 3 terms are: 4, 10, 25 a = 4, r = 2.5 sum(8) = a(r^8 - 1)/(r-1) = 4(2.5^8 - 1)/(2.5-1) = 4(390625/256 - 1)/(3/2) = 4(390369/256)(2/3) =4(130123/128...
June 30, 2015

Tupper
Never heard of a subject called Tupper. anyhow.... let the number of Katies truffles be x after first gifting: Katie had (3/4)x left she gave 1/2 of those away leaving her with (1/2)(3/4)x or (3/8)x truffles (3/8)x = 18 3x = 144 x = 48 So she started with 48 check: she gave 1/...
June 30, 2015

math
actually it is 1/18 since we are counting all 36 possible outcomes, our desired event could be 1,2 or 2,1 so 2/36 = 1/18
June 30, 2015

math
we have 1 - 7/9 + (7/9)^2 - (7/9)^3 + ... a = 1 , r = -7/9 sum∞ = a/(1-r) = 1/(1 - (-7/9) ) = 9/16
June 30, 2015

MRGS SCHOOL.
It says that any whole number greater than 1 is either prime itself or can be expressed as a product of two or more primes. e.g. 600 = 2x2x3x5 247 = 13x19 the factors in both examples are all made up of primes
June 30, 2015

Math
I know, I know, 6+2+5 ≠ 15, but maybe in the far distant past it was. That's what happens when you have to switch to the second hand to count, I always get confused if I have to count a finger as a carry.
June 29, 2015

Math
prob = (2/15)(5/12) = ...
June 29, 2015

Mah
prob of 2 nickels = (4/12)(4/12) = 1/9 so prob of not picking 2 nickels = 8/9 odds in favour of 2 nickels = (1/9) / (8/9) = 1 : 8 none of the choices are correct for the ODDS if you wanted the probability of getting 2 nickels it would be 1/9 the odds of an event is NOT the ...
June 29, 2015

calc
Maybe I should become a politician. Never actually answer the question, rather give an answer to some other question. Thanks for the catch Steve, that is two for one evening, I should get more sleep.
June 29, 2015

calc
slope = x/y = 3/1 = 3 so the equation of the tangent at the point (3,1) is y-1 = 3(x-3) y = 3x -8 or 3x - y - 8 = 0
June 29, 2015

Calculus
let the piece of paper be x inches wide and y inches long area of printed part = (x-4)(y-8) = xy - 8x - 4y + 32 but that equals 72 xy - 8x - 4y + 32 = 72 y(x-4) = 8x + 40 y = (8x+40)/(x-4) , clearly x > 4 amount of paper used = A A = xy = x(8x+40)/x-4) = (8x^2 + 40x)/(x-4) ...
June 29, 2015

Cycle geometry
So the exterior angle = 180-162 = 18° sum of exterior angles = 360° so 18n = 360 n = 20 It is a 20-gon
June 29, 2015

Physics
let's assume that for the first 1.95 seconds, the given acceleration of 44.3 m/s^2 includes the effect of gravity, and for any time thereafter the effects of gravity of -4.9 m/s^2 takes over for the first part: a = 44.3 v = 44.3t + c but when t = 0 (at the start) v = 0...
June 29, 2015

Algebra
amount of 15% juice --- x amount of 5% juice ---- 10-x .15x + .05(10-x) = .12(10) solve for x
June 29, 2015

algebra
Steve answered a similar question: http://www.jiskha.com/display.cgi?id=1435406901
June 28, 2015

math
the way you typed it, it is not a quadratic but a cubic e.g. 10x^2 - 1/x = 3 times x, 10x^3 - 1 = 3x 10x^3 - 3x - 1 = 0 , which is a cubic equation appr x = .67023 if you meant: (10x^2 - 1)/x = 3 then 10x^2 - 1 = 3x 10x^2 - 3x - 1 = 0 (2x - 1)(5x + 1) = 0 x = 1/2 or x = -1/5 ...
June 28, 2015

Math
I assume you are rounding to the nearest thousand since it rounds to 4000, the hundreds digit could only be 0,1,2,3, or 4 if the number starts with a 4 or only 5,6,7,8,9 if it starts with a 3 but the hundreds digit is twice the tens, so the hundreds digit must be even so cases...
June 28, 2015

MATH
number of 5RS coins --- x number of 2RS coins = .15x 5x + 2(.15x) = 1272 5.3x = 1272 x = 240 so 240 of the 5 RS coins, and 36 of the 2 RS coins
June 28, 2015

Maths
let the number of cookies be x let the number of friends by y x - 5y = 0 x - 3y = 36 subtract them: -2y = -36 y = 18 x - 5(18) = 0 x = 90 John has 90 cookies.
June 28, 2015

Math
starts with x spends half, so amount left = (1/2)x Spends 1/3 of that, so left with (2/3)of (1/2)x thus amount left = (2/6)x or (1/3)x but (1/3)x = 20 x = 60
June 28, 2015

Geometry
no, one other piece of information , such as one of the angles or one of the diagonals must be given. Many years back on Sesame Street, Oscar the Grouch took a rectangle and squished it, so its angles were no longer 90°. He then called it a wrecked-angle. Notice that if ...
June 27, 2015

ahhh #2 - Math
looks like our replies crossed. So there was an actual direction to your problem. Now you state: "Write each expression as a single logarithm" Why didn't you say that at the beginning and avoid all this confusion.?
June 27, 2015

ahhh - Math
Just thought I would play some "Jeopardy" with your post Alex Trebek : log3 (3x^2) me: What is 1 + log3 (x^2) simplified expanation: log3 (3x^2) = log3 3 + log3 (x^2) = 1 + log3 (x^2) so the two expressions are the same.
June 27, 2015

Math
1 + log3(x^2) is not a question 1 + log3(x^2) is an algebraic expression What do you want to do with it ? Do you want to solve something like 1 + log3(x^2) = 0 ? Do you want to colour it blue? Do you want to sent it to Donald Trump as a campaign slogan? etc The way it stands, ...
June 27, 2015

Math
just replace y with x, since it says y = x 2x^2 - x^2 = 1 x^2 = 1 x = ±1 if x = 1, then y = 1 if x = -1, then y = -1
June 27, 2015

Maths
arrangements in a line = 5! = 120 around a circle, with no specified position around the table = 5! / 5 = 4! = 24 e.g. for any arrangement of the 5 people around the table, everybody could get up, move once to the left, and the arrangement would not change, etc . We could do ...
June 27, 2015

Math
A: x > 14 , so NO B: x > 77/2 , so NO C: x = -8 , so NO D: x ≤ 26/3 or x ≤ 8 2/3 , YEAH, since 8 ≤ 8 2/3
June 26, 2015

Geometry
Just use ordinary keyboard keys According to the properties of tangents to circles, AO is perpendicular to PA making angle PAO = 90°, thus angle angle POA = 90-32 = 58° The same property is true for angle POB since PA = PB , angle POB = 58° Then angle AOB = 116°...
June 26, 2015

math
possible numbers: 111111 222222 .... 999999 largest such number: 999999 number from above with a sum of 6 : 111111 999999 - x = 111111 x = 888888
June 26, 2015

Probability
sounds like conditional probabilty Prog(A|B) , (read as the prob of A, given B) = prob(A AND B)/prob(B) prob(A and B) = 1/15 prob(B) = 7/15 prob( as stated) = (1/15) / (7/15) = 1/7 (of course, since the 4 is one of the 7 even numbers from 1 - 15)
June 25, 2015

Algebra
I agree with Ms Sue To show us that you are not merely sponging off us, for the question above, I would be interested in your thinking to solve the problem So you want whole numbers m and n so that 3^m + 2^n ≤ 999
June 25, 2015

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