Friday
September 4, 2015

Posts by Reiny


Total # Posts: 30,720

stadistic
for any question, prob(correct guess) = 1/4 prob(wrong guess) = 3/4 To have exactly 7 of 15 correct, prob = C(15,7)((1/4)^7 (3/4)^8 = 6435 (1/16384)(6561/65536) = appr .039
August 2, 2015

gnmps
let their ages be 6x and 7x (6x+12)/(7x+12) = 12/13 78x + 156 = 84x + 144 -6x = -12 x = 2 they are now 12 and 14
August 2, 2015

Math ho.
You have not indicated if the given number has any repeating decimals. The way you typed it, it appears to terminate. Thus it would be rational. An irrational number has decimals than neither repeat nor terminate. The way you typed it, we can't tell.
August 2, 2015

Math ho.
nope, each length is 25/2 m which is a rational number.
August 2, 2015

Algebra
I will read that as: 4/(x^2 - 4x + 1) + 2/(x^2 - 1) We usually "solve" equations, but you have no equation. Are you simplifying? If so, I was expecting the first denominator to factor like the second one, so we can find the LCD. The way it stands, the simplification ...
August 1, 2015

MATH
I agree with Bosnian that the question contains a typo. If the sum of n terms is 225 as stated we could solve for r = 2.309.. but then the solution for n is not a whole number. Bosnian assumed correctly that sum(8) = 255
August 1, 2015

alpha
secØ = x - tanØ for a trivial solution, but .... If you want secØ in terms of x, then you have a mess Secø + tanø=x 1/cosØ + sinØ/cosØ = x (1+sinØ)/cosØ = x 1 + sinØ = xcosØ square both sides 1...
August 1, 2015

MTH 157
x(1.04)^5 = 50000
July 31, 2015

Math
first get you results to sine and cosine of x since you are in II, from your diagram, sinx = 15/17 tanx = -15/8 use the formula for tan(3x) you just found in your other post. then apply the formula for tan(A/2) actually that is a nice one: tan (A/2) = (1 - cosA)/sinA good luck
July 31, 2015

Math
easy to look up, here is one such page http://www.trans4mind.com/personal_development/mathematics/trigonometry/multipleAnglesTangent.htm If you have to actually develop it, use tan(A+B) = (tanA + tanB)/(1 - tanAtanB) on tan(3x) = tan(2x+1) after doing tan2x first.
July 31, 2015

math
let his income be x after food expenses he is left with (2/3)x he then spends (1/4+1/5)(2x/3) = (3/10)x which leaves him with 2x/3 - 3x/10 or 11x/30 (11/30)x = 1760 x = 4800 which is choice c)
July 31, 2015

math
so you want: √a + √b = √c just take any two perfect squares, add their square roots and square that to get c e.g. a = 1 , b=1, c = 4 ----> √1 + √1 = √4 a = 1 , b = 4, c = 9 a = 4, b = 9, c = 25 ---> √4 + √9 = √25 ...
July 30, 2015

math
amount of the 30% alloy to be added --- x ounces .3x + .05(10) = .2(10+x) .3x + .5 = 2 + .2x .1x = 1.5 x = 15
July 30, 2015

math
let the side of the square be x let d be the diagonal, d^2 = x^2+x^2 = 2x^2 d = √2 x "the sum of the squares of the four sides plus the sum of the squares of the two diagonals is 400" x^2+x^2+x^2+x^2 + 2(2x^2) = 400 8x^2 = 400 x^2 = 50 x = 5√2 area of ...
July 30, 2015

Probability
Is the password case sensitive ? It usually is, so number of ways to arrange 5 letters = 52^5 also assuming that letters can be repeated only one of these is correct prob(getting it right) = 1/52^5 = 1/380204032
July 30, 2015

Probability
prob(A/C) = 1/2 prob(not A/C) = 1/2 prob(that 5 out of 10 have A/C) = C(10,5)(1/2)^5 (1/2)^5 = 252 (1/2)^10 =252/1024 = 63/256 or appr .246
July 30, 2015

Probability
So he already has 1 penny, which means he can only draw another penny or another nickel Prob(as stated) = 3/8 + 2/8 = 5/8
July 30, 2015

Cones
V = (1/3)π r^2 h = 36π r^2 h = 108 Now if we cut the height in half, then the radius is also cut in half new volume = (1/3)π(r/2)^2 (h/2) = (1/24)π r^2 h = (1/24)π(108) = 9π/2 or the volume of similar solids is proportional to the cube of their ...
July 30, 2015

Math
b men earning D dollars = bD remaining men = m-b each earning D/2 so they earn D/2(m - b) = mD/2 - bD/2 total = bD + mD/2 - bD/2 = 2bD/2 + mD/2 - bD/2 , using a common denominator = bD/2 + mD/2 = D/2(b+m) , using a common factor of D/2 which is B D/2 is the same as (1/2)D
July 30, 2015

Math
It would be a good idea if you familiarize yourself with Pascal's Triangle, the 4th row has values 1 4 6 4 1 so (2x-1)^4 = (2x)^4 + 4(2x)^3 (-1) + 6(2x)^2 (-1)^2 + 4(2x) (-1)^3 + (-1)^4 the term that will yield x^2 is 6(2x)^2(-1)^2 = 24x^2 confirmed by Wolfram: http://www....
July 30, 2015

GCF
pick out the factor with the lowest exponent for each variable e.g. for the b's it would be b^5 etc
July 30, 2015

What did I did wrong MATH
number of $1 coins --- 3x number of half-dollars --- 4x Your second sentence does not make any sense to me taking your equation ... cross-multiply 9x - 18 = 4x+6 5x = 24 x = ???? , x must be a whole number Fix your second sentence.
July 30, 2015

math
I find it odd that you made the same typo in this question as somebody else did back in Nov 2014. http://www.jiskha.com/display.cgi?id=1416116940
July 30, 2015

Math
You will need brackets to establish the correct order of operations. The way you typed it, the +1 -1 would cancel and you are left with 4 /X^2 – 4x + 2/ x^2 = 4/x^2 - 4x^3/x^2 + 2/x^2 = (6 - 4x^3)/x^2 I have a strong feeling that is not what you meant.
July 30, 2015

math
I started it as a simple calculus question ... first number: x 2nd number : 48/x sum = x + 48/x d(sum)/dx = 1 - 48/x^2 = 0 for a min of sum x^2 = 48 x = √48 = appr 9 but you want the numbers to be whole numbers so possible ordered pairs: (1,48) (2,24) (3,16) (4,12) (6,8...
July 30, 2015

maths
Why not just say: the volume equals the surface area (4/3)πr^3 = 4πr^2 times 3/π 4r^3 - 12r^2 = 0 r^3 - 4r^2 = 0 r^2(r - 4) = 0 r = 0 (trivial solution) or r = 4 or the diameter is 8 Your actual question is strangely worded.
July 30, 2015

Mathematics
The zeroes of a function indicate where the corresponding graph touches or crosses the x-axis.
July 30, 2015

math
check your typing, right now your post makes no sense. "... find the length if its worth (16x^2y^2) dm ?? " did you mean , if it width is .... ? In that case just divide 256x^4y^4-169c^4y^4 by 16x^2 y^2 to get 16x^2 y^2 - 169c^4 y^2/(16x^2) btw, the units for the ...
July 30, 2015

Math
you must mean "simplify" ((1/x)-(1/y))/(y^2-x^2) = ( (y-x)/(xy) ) / ((y-x)(y+x) ) = (y-x)/( (xy)(y+x)(y-x) ) = 1/(xy(y+x) ) , y≠x
July 29, 2015

Math
or for #3 you have 1*(1+2+3+...+9+10) + 2*)1+2+3+...+9+10) + ... 10*(1+2+3+...+9+10) add them: (1+2+3+...+9+10)(1+2+3+...+9+10) = 55*55 = 3025
July 29, 2015

Maths
In your first case , there were 4 children and the answer was 4! or 24 So if there are 5 children .... ??
July 29, 2015

Math
width --- x length --- 3x x^2 + (3x)^2 = (8√10)^2 10x^2 = 640 x^2 = 64 x = 8 width = 8 length = 24 area = (8)(24) = 192
July 29, 2015

College Algebra
I am sure you meant: m(t) = 9 e^(-.012t) so if t = 0 , remember that anything^0 = 1 so m(0) = 9
July 29, 2015

Data management
my interpretation of a face card is either Jack, Queen, or King number(spade or face) = number(spade) + number(face) - number(spade AND face) = 13 + 12 - 3 = 22 prob(spade or face) = 22/52 = 11/26
July 29, 2015

rd. math
I will assume that by the "division method" you are referring to what is generally call Euclid's Algorithm find the HCF of the first two numbers by following this Youtube clip, then use that answer with the third number https://www.youtube.com/watch?v=AJn843kplDw...
July 29, 2015

Math
present age of Joy --- x present age of Drew --- 2x five years ago: Joy = x-5 Drew = 2x-5 (x-5)(2x-5) = x-7 2x^2 -15x + 25 = x-7 2x^2 - 16x + 32 = 0 x^2 - 8x + 16 = 0 (x-4)^2 = 0 x = 4 Joy is now 4, and Drew is 8 check: 5 years ago: Joy = -1 ?? Drew = 3 product of their ages...
July 29, 2015

Math
amount spent = 1/12 + 1/4 = 1/3 So (2/3) of his money is left (2/3)x = 240 x = 240(3/2) = 360 so he spent (1/4)(360) or $90 on books
July 29, 2015

Algebra
Really? Then what does this mean ? "How in the world do I solve for x without using a calculator?"
July 28, 2015

Algebra
If the question says to solve without a calculator, then admittedly this is a very unreasonable question. Not even in my olden days, (you know when we had to rely on slide rules and log tables) would they have expected a solution. I ran it through Wolfram and it shows that you...
July 28, 2015

Algebra 2 CP
100000(1+i)^11 = 196000 (1+i)^11 = 1.96 take 11th root of both sides 1+i = 1.96^(1/11) = 1.06309 i = .06309 or appr 6.3% check: 100000(1.06309)^11 = 196006 , not bad
July 28, 2015

math
I don't understand the question √1000000 = 1000 why express 1000 as a square root did you mean? = 1*√1000000 = √10*√100000 = √100*√10000 = √1000*√1000
July 28, 2015

math
the last term in the expansion of (2x^2+3x+2)^n is 2^10 and .... we know 2^10 = 1024 (1 kb = 1024, recall your computer science stuff) so n = 10
July 28, 2015

math
I think you have a typo and meant 1 - 2 + 3 - 4 + ... + 1997 - 1998 + 1999 - 2000 (all odds are positive and all evens are negative) take them in pairs: 1-2 = -1 3-4 = -1 5-6 = -1 .. 1999-2000=-1 so you have 1000 of these pairs, and the sum is -1000
July 28, 2015

math
slope RS = (-d-b)/(-c+a) or (d+b)/(c-a) test for slope going through T slope TA = (b+d)/(c-a) ----> that is correct slope TB = (b+d)/(-c-a) slope TC = (-b+d)/(c-a) slope TD = (-b+d)/(-c-a) use an actual example to illustrate: a=3, b=4, c=2 , d=5 let R be (-3,4) and S be ( -...
July 28, 2015

Math
from the 2nd, y = x-8 now sub that into the 1st: -3x - 2(x-8) = 16 -3x - 2x + 16 = 16 -5x = 0 x = 0 y = 0 - 8 = -8
July 28, 2015

Math
H -- hit M -- miss possible outcomes HH -- (.6)(.8) = .48 HM -- (.6)(.2) = .12 MH -- (.4)(.4) = .16 MM -- (.4)(.6) = .24 notice the sum = 1 , as expected
July 28, 2015

Maths
volume = (1.4)(.8)(.5) m^3 = .56 m^3 = 560 L of water , 1 m^3 holds 1000 L leak is 40 cl or .4 L/min ( 100 cl = 1 L) number of minutes to drain = 560/.4 =1400 minutes or 23 hrs, and 20 minutes
July 28, 2015

maths
same problem four times! and still typed incorrectly .... Don't you read previous replies to this question??
July 28, 2015

Geometry
Since it is isosceles, we can construct a right-angled triangle with an altitude to the base of 3 then cosØ = 1.5/√3 = 3/2√3 = 3/2√3 * √3/√3 = √3 /2 ahhh, do you recognize the 30-60-90° triangle (if not, use your calculator) &...
July 28, 2015

mathematics
Other than changing the "subject" heading, you have not answered any of my concerns, and posted the problem in the same confusing way. http://www.jiskha.com/display.cgi?id=1438088880
July 28, 2015

Physics
The circumference of the wheel is 50π cm = π/2 m 1 rotation covers π/2 m x rotations cover 26 m x/1 = 26/(π/2) x = 52/π = appr 16.55 the wheel is turning at 16.55 rotations/second or appr 993 rpm
July 28, 2015

government secondary school abuja
Wow, before I start, some clarification: I will assume that you meant: (x^4+3x-2)/( (x^2+1)^3 (x-4) ) My second concern: In your break-down your last term is h/(x-4)^2, yet the original denominator showed only (x-4) Besides that, if the denominator did contain (x-4)^2, then ...
July 28, 2015

math
volume = (9)(16)(√25) = 720 cubic units none of your choices are correct unless your dimensions are √9, √16, and √25 Then the volume would be 60 cubic units, but that is not what you said.
July 27, 2015

algebra
ok up to 50-100+5 which is -45
July 27, 2015

Maths
let then number of sugar bags be x then the number of salt bags is 100-x now for the cost: 2x + 5(100-x) = 380 2x + 500 - 5x = 380 -3x = -120 x = 40 so he bought 40 bags of sugar and 60 bags of salt or, using two variables sugar bags --- x salt bags ----- y x + y = 100 2x + 5y...
July 27, 2015

Maths Problem
When the car catches up with the van, they would have both traveled the same distance let the time from 7:30 am to the catch-up time be t hrs. distance covered by car = 80t distance covered by van = 60t + (1/2)(60) = 60t + 30 80t = 60t + 30 20t = 30 t = 3/2 3/2 hours added to ...
July 27, 2015

math
Make a sketch of your finished quad and enter all the information. Notice that adjacent angles add up to 180°, so AT || MH, and it is easy to see that MAH must be an equilateral triangle. You should see that MATH must be a rhombus, with all sides equal to 8 cm I assume you...
July 27, 2015

Maths
time for first part = d/15 time for 2nd part = d/30 total time = d/15 + d/30 = d/10 avg speed = total distance/total time = 2d/(d/10) = 20 km/h notice we can't just average the two speeds.
July 27, 2015

Maths
speed of slower train --- x km/h speed of faster train ---- x+20 km/h 6 minutes = 6/60 or 1/10 hour (1/10)x + (1/10)(x+20) = 11 times 10 x + x+20 = 110 2x = 90 x = 45 the slower train goes at 45 km/h the faster at 65 km/h
July 27, 2015

Maths
Let the length and width be x and y, both x and y positive xy = 6 and x^2 + y^2 = (2√5)^2 from xy=6, y = 6/x x^2 + (6/x)^2 = 20 x^2 + 36/x^2 = 20 x^4 + 36 = 20x^2 x^4 - 20x^2 + 36 = 0 (x^2 - 18)(x^2 - 2) = 0 x^2 = 18 x = √18 = 3√2, and y = 6/√18 = &#...
July 27, 2015

Math
I assume you made a sketch In mine, 36/x = tan30° x = 36/tan30 , but I know from my basic 30-60-90 triangle that tan30 = 1/√3 x = 36/(1/√3) = 36√3 m or appr 62.35 m
July 27, 2015

math
I will assume your expression is a complex number of the form a + bi , let me know if you give it a different meaning. (2+j4)*(-3-j4) = -6 - 8j - 12j - 16j^2 = -6 - 20j + 16 = 10 - 20j tanØ = -20/10 = -2, with Ø in quad IV Ø = 5.176 argument = √(10^2...
July 27, 2015

College Algebra
If 4i is a zero, then -4i must also be a zero, since complex zeros come in conjugate pairs. a possible polynomial is f(x) = (x-4i)(x+4i)(x+1)^2 a general solution would be f(x) = a(x-4i)(x+4i)(x+1)^2 , where a is a non-zero integer. If necessary, your can expand this.
July 27, 2015

Algebra
The way you typed it , we would get 5m + 7/m^2 - 21 I have a feeling you meant: (m+7)/(m^2+4m-21) = (m+7)/( (m+7)(m-3) ) = 1/(m-3) , m ≠ -7 See how extremely important those brackets are ??
July 26, 2015

math
The way you typed it ..... -8/15 a = 9/10 would mean: (-8/15) a = 9/10 , by the order of operation -80a = 135 a = -135/80 = - 27/16 = - 1.6875 Ms Sue interpreted it as the way you probably meant it ... -8/(15a) = 9/10 a = -16/27 = -.59259259.. (the 592 is repeated) See how ...
July 26, 2015

math- partial fractions
What you typed is really just (s^2 +2s +3)/s^2 which is = 1 + 2/s + 3/s^2 I don't know if this is what you needed.
July 26, 2015

algebra
My name is Billy vs Billy is my name If I recall, it is called the transitive property
July 26, 2015

Data management
prob(getting a six) = 1/6 prob(not getting a six) = 5/6 a) prob (at least 1 six in 6 tries) ---> we don't want all non-sixes prob(no six in 6 tries) = C(6,0)(1/6)^0 (5/6)^6 = .3349 so prob of at least 1 six = 1 - .3349 = .6651 b) this time we exclude the case of no ...
July 26, 2015

Math
let m be the number of minutes cost1 = .20m + 14 cost2 = .15m + 18 When is .20m + 14 = .15m + 18 ? .05m = 4 m = 4/.05 = 80
July 25, 2015

maths
ahhh, see http://www.jiskha.com/display.cgi?id=1437880873 Looks like I assumed correctly
July 25, 2015

circle
You are missing an operator in your line equation, I will assume you mean 5x + 12y = 1 or 5x + 12y - 1 = 0 we know that the equation must be (x-3)^2 + (y-4)^2 = r^2 , so the only thing missing is the value of r using the distance from a point to a line method, r = |5(3) + 12(4...
July 25, 2015

11th maths
I read that as log3 243 - log2 64 - log√3 3 notice that 3^5 = 243 , 2^6 = 64 and (√3)^2 = 3 then: log3 243 - log2 64 - log√3 3 = 5 - 6 - 2 = -3
July 25, 2015

math
let the longest side be x shortest side = (1/3)x + 2 other side = x-5 x + (1/3)x + 2 + x - 5 = 53 times 3 3x + x + 6 + 3x - 15 = 159 7x = 168 x = 24 longest side = 24 shortest = 10 other = 19 check: 24+10+19 = 53
July 25, 2015

Deogiri
1 mile = 1.60934 km so 150 miles = appr 241.4 km 150 mph = 241 km/h
July 24, 2015

Algebra
divide each term by 81 to get (x+1)^2/9 + (y-1)^2/3 = 1 so a = 3, and b = √3, which means that the major axis is parallel to the x-axis (since a > b)
July 24, 2015

maths
argggghhh! go with Steve's method, I'm going back to bed
July 24, 2015

maths
speed of boat --- x km/h speed of current -- y km/h case1: 30/(x-y) + 44/(x+y) = 10 times (x+y)(x-y) .... 30(x+y) + 44(x-y) = 10(x+y)(x-y) 30x + 30y + 44x - 44y = 10x^2 - 10y^2 10x^2 - 10y^2 = 74x - 14y ----> #1 case2: 40/(x-y) + 55(x + y) = 13 40(x+y) + 55(x-y) = 13(x+y)(x...
July 24, 2015

sets
Make a Venn diagram, and enter your data. Let the number of people who like only tennis be x x + 10 + 30 = 65 x = 25 so number who like tennis = 10+25 = 35 check: N(C or T) = N(C) + N(T) - N(C and T) LS = 65 RS = 40 + 35 - 10 = 65 = LS All is good!
July 23, 2015

statistics
What is (3/10)^5 ??
July 23, 2015

Trigonometry
You would be correct if you had x^2+y^2-7x+5y = 0 remember, you want an equation, not just an expression.
July 23, 2015

Math quadratic function
Your vertex is indeed (70,17) Other points would be (142,0) and (0,1.2) Since the vertex must lie midway between the two intercepts and the distance between 70 and 142 is 72, the other intercept must be (-2,0) h(x) = a(x-70)^2 + 17 must be the equation use (142,0) to find a 0...
July 23, 2015

Math
"My ten thousand digit is the highest odd number" What is the highest odd number ?
July 20, 2015

Math
Didn't it say that your unit digit is zero ?
July 20, 2015

Math
"My thousand digit is the second odd number. " 2 is not an odd number.
July 20, 2015

Math
Did you check if your answer matches all the conditions ?
July 20, 2015

Math
yes, see http://www.jiskha.com/display.cgi?id=1435211710
July 20, 2015

math
Of course all sides are the same let the side be x given: "the sum of the cubes of two sides is equal to the square of the third side" ... just translate into math 2x^3 = x^2 2x^3 - x^2 = 0 x^2(2x - 1) = 0 x = 0 , which would make an interesting triangle or x = 1/2 ...
July 19, 2015

math
When it reaches the ground, h(t) = 0 -4.9t^2 + 9.5t + 1.2 = 0 don't think it will factor, so let's use the formula I got t = 2.0578 or a negative, the latter does not make sense It will hit the ground after appr 2.06 seconds
July 19, 2015

math
Then tan is +, and the cos is -, so you must be in quadrant III tan a = 15/8 = y/x so y = -15 , x = -8, and r = 17 [sin(-a)-cosa]/[tan(-a)+sec(-a)] = (-sina - cosa)/(-tana + seca) = (15/17 + 8/17)/(-15/8 - 17/8) = (23/17)(-8/32) = -23/68
July 19, 2015

@ Nick - calculus
Nick, with a little effort on your part to complete the solution I gave you and some small adjustment for this question, you could have saved the duplication of this solution by Damon.
July 19, 2015

math
We could extend the terminal arm to (12,5) without changing the angles. Ahhh, now you should recognize the 5-12-13 right-angled triangle values x=12 y=5 r=13 You just have to memorize the definition of the basic trig functions in terms of the x,y, and r values that is, sin&...
July 19, 2015

Math
Never heard of a term in math called bcm complementary angles add up to 90° , so ... let one of them be x then the other is 90-x 4x + 20 = 90-x 5x = 70 x = 14 State your conclusion
July 19, 2015

maths
Use standard keyboard keys to type your expresssion. Use ^ to indicate exponents, e.g. x^2 is "x squared"
July 19, 2015

Math
Steve explained to you yesterday, (before you posted the question above), what the meaning of '' and ' is in the US system of measurement. He also answered your question which is very similar to the above problem http://www.jiskha.com/display.cgi?id=1437257316
July 19, 2015

math
I will assume you mean that the whole property is 80 m by 60 m, and the swimming pool lies within. area of whole thing = 4800 m^2 area of pool = 120 m^2 area of lawn = 4800-120 = .... multiply that by Rs 30 to get the cost.
July 18, 2015

Algebra
3^m goes over 3 digits at 3^7 so m<7 let m = 6 to get 3^6 = 729 so that leaves 270 for 2^n I know 2^8 = 256 , using 2^9 would put me over. 3^6 + 2^8 = 729+256 = 985
July 18, 2015

Calculus
use implicit differentiation, .... 2y^3 + y^2 - y^5 = x^4 -2x^3 +x^2 6y^2 (dy/dx) + 2y (dy/dx) - 5y^4 (dy/dx) = 4x^3 - 6x^2 + 2x dy/dx = (4x^3 - 6x^2 + 2x)/(6y^2 + 2y - 5y^4) for a horizontal tangent, dy/dx = 0 ---> the numerator is zero 5x^3 - 6x^2 + 2x = 0 x(5x^2 - 6x + 2...
July 18, 2015

Mathematics
so the new equation must be y = (-1/52)x + b with (-4,0) lying on it 0 = (-1/52)(-4) + b b = -1/13 new line: y = (-1/52)x - 1/13
July 18, 2015

calculus
Good grief ! You changed one of your equations from y = 12x to y = .5x and you can't make the necessary changes in my solution ??
July 18, 2015

calculus
intersection of y = 6/x with y = 2x 2x = 6/x x^2 = 3 x = √3 intersection of y = 6/x with y = 12x 12x = 6/x x^2 = 1/2 x = √2/2 According to my sketch I would find the area of the triangle from x = 0 to √2/2 with a height of 12x - 2x or ∫10x dx from 0 to...
July 18, 2015

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