Sunday
May 29, 2016

Posts by Reiny

Total # Posts: 34,822

math
So first you want to know how many pairs I can form from the 7 horses , then arranging the other 5 That would be C(7,2) or 21 for the first part - the remaining 5 horses can be arranged in 5! or 120 ways So there are 21(120) or 2520 ways to finish the race
May 6, 2016

math
games won by Lee --- 15 games won by ---- 2(15) + 3 = 33 total games = 48 prob(Tasha wins) = 33/48 = 11/16
May 5, 2016

Math
h^2 = 5^2 + 6^2 = 61 h = √61 = .....
May 5, 2016

Trigonomentry
Steve did this for earlier http://www.jiskha.com/display.cgi?id=1462459298
May 5, 2016

Algebra
Did you switch names? http://www.wolframalpha.com/input/?i=xy-x%2By%3D0
May 5, 2016

math
use your definitions fourth term = ar^3 = 9(-1/3)^3 = 9(-1/27) = -1/3 or simply list the first 4 terms to see the 4th term 9, -3, 1, -1/3, ...
May 5, 2016

Algebra
before you even start, did you notice the two equations have the same slope, but have different y-intercepts. Thus they will never meet, and therefore there can't be a solution. If you try it anyway .... first equation: y = 2x+3 sub in the second 2x-2 = 2x + 3 -2= 3 , ...
May 5, 2016

math- geometry
Correct me if I am wrong in the understanding of the question. Round table, we don't know its radius, I eventually let it be r Smaller circle lies on the table, the radius of the smaller table is 1/2 or .5 m The area outside the circle is shaded and you said the area of ...
May 5, 2016

math- geometry
You started well , but it collapsed on you in the second part. I would not have rounded off intermediate answer, only round off your final answer. I assume you used a calculator, get into the habit of using the memories of the calculator to store intermediate answers. for area...
May 5, 2016

math
-2 9 -1 4 0 -1 1 -6 2 -11 looks like we are dropping the y by 5 for each increase of 1 in the x y = -5x - 1 , ----> I noticed that (0,-1) was the y-intercept
May 5, 2016

Math
find all pairs of factors of 72 72 = 1 x 72 = 2 x 36 = 3 x 24 = .... etc count them up, but I would not count the duplicates such as .... 24 x 3 36 x 2 72 x 1
May 5, 2016

Math
let the other side be x case 1: x/3.7 = 1.618 x = = 5.9866 or 6.0 inches to the nearest tenth case 2: 3.7/x = 1.618 x = 3.7/1.618 = 2.286.. or appr 2.3 inches
May 5, 2016

math 21
What is your question? the graph looks like this http://www.wolframalpha.com/input/?i=xy-x%2By%3D0
May 5, 2016

math
a^5/a^3 = a^2 x^9/x^5 = x^4 you do the others by simply using the division rule of powers.
May 5, 2016

math
yes check it by taking 1.8% of it
May 5, 2016

math
.018x = 72 solve for x
May 5, 2016

MATH HELP PLZ!
looks like the same as this http://www.jiskha.com/display.cgi?id=1462291500
May 5, 2016

math
earning in first year --- x earining in 2nd year = 5.5x earning in 3rd year = 5.5^2 x earning in 4th year = 5.5^3 x x(1 + 5.5 + 5.5^2 + 5.5^3) = 29250 inside the bracket is a GP, but since there are only 4 times, we might as well just add them up x(203.125) = 29250 x = 144 so ...
May 5, 2016

math
neighbour's age --- x (4x+7)/3 - 9 = 20 times 3 4x+7 - 27 = 60 4x = 80 x=20 The neighbour is 20 years old check: times 4 --->80 add 7 ---->87 divide by 3 --> 29 subtract 9 ---> 20
May 5, 2016

Geography
20°N, 80°E ----> right smack in the middle of India 20°S, 80° E --> you better be in a boat
May 5, 2016

Math
Confusing wording: "he first pyramid has a height of 6 inches and a base area of 10 inches" since you tell us the volume is 20 inches^2 , the base are must be 10 inches^2 I also will assume that the base does not change volume of 1st pyramid = (1/3)(10)(6) = 20 ...
May 5, 2016

math
The first 3 are correct. You check by making sure you subbed correctly in the formula and performed the arithmetic correctly. For the last one about Lucia I have no idea since we can't see your diagram.
May 5, 2016

math
whole circumference = 12π so your arc is 105/360 or 7/24 of that
May 5, 2016

Algebra
amount of cheaper mix --- x kg amount of expensive mix -- 18-x solve for x and sub into my definitions 5x + 10(18-x) = 7(18)
May 5, 2016

Math ---HELP!!!!!
I got .1587, which matches 16% or D Did you take 1 - ...., since it asked for "above" ?
May 5, 2016

Math ---HELP!!!!!
I got .6538 , so yours is close enough
May 5, 2016

Math ---HELP!!!!!
according to the chart I am using, I ge 43.26 , so I agree with your choice
May 5, 2016

math
Billions and billions of them ... here are just two of them: (0,-3) , (75.2 , 147.4)
May 5, 2016

math
base --- b height = b+5 (1/2)(b)(b+5) = 45 b^2 + 5b = 90 b^2 + 5b - 90 = 0 b = (-5 ±√385)/2 = appr 7.311 or some negative base = 7.311 , height = 12.311 check area = (1/2)(7.311)(12.311) = 45.0028.. not bad, my answer is correct
May 5, 2016

Math
I pasted your original post, so I don't have to scroll up and down. I have inserted the corrections. If nothing is shown , then the question was correct 1. Simplify. 3x^2+ 5x-5x^2-4x+5-2 A.-8x^2-9x+3 B.2x^2+x+3 C.-2x^2-9x+3*** D.-2x^2+x+3 ****** 3x^2+ 5x-5x^2-4x+5-2 = -2x^...
May 5, 2016

Math
do you not have a calculator? just watch the order of operation, should be [2cos(45)] - [tan(45)/90.5] - 64
May 5, 2016

math
Just translate into Math using your definitions of an AP a+5d = 7 ** a+ 3d = 2(a+d) - 1 a + 3d = 2a + 2d - 1 -a + d = -1 *** add ** and *** 6d = 6 d = 1 back in ** a + 5=7 a = 2 the first term is 2 check: sequence is 2,3,4,5,6,7,8, ... Is the fourth term less than twice the ...
May 5, 2016

error in data - Trigonometry
error in data if B is in quad III, then cosB must be negative I will assume you meant: cos B = -12/13 make sketches of triangles in the two quadrants for sinA = 1/2, y = 1, r = 2 x^2 + 1^2 = 2^2 x = √3 so tanA = y/x = 1/√3 for cosB = -12/13 in III x = -12 , r = 13 ...
May 5, 2016

Math
I assumed you made a sketch. On mine, I labeled the position of Ms Hunt as H on top of the tall building, its base J For the shorter building, I labeled its top as P and its bottom as Q I drew a horizontal from H to meet QP extended at R All kinds of right-angled triangles! ...
May 5, 2016

Math
you will need the vertex of this parabola the x of the vertex is -b/2a = 192.1/32.4 = 5.929 so add 5.9 or appr 6 years to 1925 to get the year 1931
May 4, 2016

algebra
x+y=4 or y = 4-x , and xy=6 sub in the first part x(4-x) = 6 4x - x^2 - 6 = 0 x^2 - 4x + 6 = 0 x = (4 ± √-8)/2 = 2 ± √2 If you are dealing with real numbers, there are no numbers to fit your condition. If you allow complex numbers, the two numbers are...
May 4, 2016

Math
I answered it in your previous post of this question
May 4, 2016

Math
let the number of chairs over 400 be x now: number of chairs = 400 price per chair = 120 Revenue = 48000 after production increase: number of chairs = 400+x price per chair = 120 - .25x Revenue = R = (400+x)(120-.25x) = 48000 + 20x - .25x^2 which is a downwards opening ...
May 4, 2016

math
log(2+x)-log(x-3)=log2 log( (2+x)/(x-3) ) = log2 "unlog" it (2+x)/(x-3) = 2 2x - 6 = 2+x x = 8 check it with your calculator
May 4, 2016

Math
correct
May 4, 2016

Math
correct, I use http://davidmlane.com/normal.html
May 4, 2016

Math
I used the actual normal distribution and got .9973 http://davidmlane.com/normal.html
May 4, 2016

Math
I used the actual normal distribution and got .9973 http://davidmlane.com/normal.html
May 4, 2016

Math
the largest rectangle would be the square 2W + 2L = 8 W+L=4 for a square each side is 2 cm, and the maximum area is 4 cm^2 There is no such thing as a smallest rectangle. We can make one of the sides very very small, but there would still be an area. e.g. suppose W = .001 then...
May 4, 2016

math
Since it asked for an estimate and and Dπ = C I would approximate 270/3 = 90 so the diameter is about 90, making the radius about 45 Since they wanted an estimated answer, giving answers with those kind of decimals makes no sense. Using 3.14 for π is not estimating.
May 4, 2016

math
Unfinished sentence .... Does your keyboard not have any capital letters? Whatever is missing in your sentence , the probability is 1/9
May 4, 2016

Geometric Sequence
you want: .95^n = .25 take log of both sides nlog.95 = log.25 n = log.25/log.95 = 27.0268.. = appr 27 washings or start with 100% colour after 1 washing ---- 95% left after 2 washings --- .95(.95) left after 3 washings --- .95(.95)^2 left .... after n washings ------ .95(.95)(...
May 4, 2016

Maths
boys --- b girls --- g b+g = 150 (3/4)b = (1/7)g 3b/4 = g/7 4g = 21b g = 21b/4 sub into the first b+g = 150 b + 21b/4 = 150 times 4 4b + 21b = 600 25b=600 b = 24 then g = 21(24/4) = 126 24 boys and 126 girls went to the concert check: is 24+126 = 150 ? , YES is (3/4)(24) = (1/...
May 4, 2016

Algebra
number of adult tickets ---- x number of children tickets -- 2000-x solve: 4x + 2(2000-x) = 6400 solve the value of x into my definitions
May 4, 2016

math
i = .0475/12 = .00395833.. n = 12(10) = 120 PV = 20,000(1.00395833..)^-120 = $12,449.37
May 4, 2016

math
Formulas are equations that contain an = sign you have an expression, not an equation, so... ???
May 4, 2016

PLEASE HELP ASAP ALGEBRA
Yes, 3 numbers are divisible by 3 so prob = 3/10
May 3, 2016

mathematics
GP ar^2 = 4a ----> r^2 = 4 r = ±2 ar^5 = 3ar^3 + 32 if r = +2 32a = 24a + 32 8a =32 a = 4 the sequence is 4,8,16,32,64, 128, ... if r = -2 -32a = -24a + 32 -8a = 32 a = -4 the sequence is -4, 8, -16, 32, -64, 128, ...
May 3, 2016

Calculus 3
starting with the 4th term, we have a definite pattern and the general term from that point is 1/(3^n + √(n+1) ) , where n starts with 1 Since you wanted to "write the series", why don't we just add the first 3 terms and begin the serious stuff with term 4 ...
May 3, 2016

MATH
let the number of gigs used be g Runfast: cost = 25 + 10g BA&D: cost = 18+15g let's see for how many g's the plans are the same cost of one = cost of the other 18+15g = 25+10g 5g = 7 g = 7/5 = 1.4 gigs so for 0 gigs over, BA&D would cost $18 vs $25 for Runfast, so BA&D...
May 3, 2016

Analytic Geometry
http://www.wolframalpha.com/input/?i=plot+x%5E2-xy%2By%5E2-3%3D0 nice rotated ellipse. This is a good equation for you to use in studying or reviewing the topic of rotation of conics. Obviously I could not possible teach you that on here in one post. When I last taught this ...
May 3, 2016

calculus
Sketch a right angles triangle with a base of 400 m, a height of h m , (the balloon), and an angle of Ø opposite the height. tan Ø = h/400 h = 400 tanØ dh/dt = 400 sec^2 Ø (dØ/dt) given: when Ø = 10° or 10(π/180) radians d&...
May 3, 2016

math 1324
Solve using matrices ??? What can be easier than the following? : amount borrowed at 9.5% ---- x amount borrowed at 8.5% ---- 4x amount borrowed at 7% = 2,000,000 - 5x .095x + .085(4x) + .07(2000000-5x) = 169750 solve for x , and sub back in my definitions
May 3, 2016

Analytic Geometry
factor it y(x+1) = x y = x/(x+1) a rotated hyperbola , with asymptote at x = -1 http://www.wolframalpha.com/input/?i=plot+y+%3D+x%2F(x%2B1)
May 3, 2016

Maths
So it would take 20 man-hours to paint the house, (or "person-hours to be politically correct) No distribute those 20 hours needed among 3 painters, so it would take 20/3 hours = 6 2/3 hours = 6 hours and 40 minutes
May 3, 2016

Nath
work backwards, 2:30 pm ---- 44° noon -------- 41° 7:00 am ----- 29°
May 3, 2016

math
So many questions: are the circles touching each other? are the circles the same size ? are each of the circles touching the length and width of the rectangle? ... etc
May 3, 2016

Math
If you want L/hr, then rate = (4/5) / (1/4) L/h = (4/5)(4/1) L/h = 16/5 L/h Daniel is correct
May 2, 2016

Yup! - Math
-- stands in corner with dunce cap --- looks like I had another "old-timer's " moment.
May 2, 2016

Math
I would have it as 90° < d < 180° think of it as: d is between 90 and 180
May 2, 2016

Pre-calculus
width = 8.5-2x length = 11 - 2x height = x V = x(8.5-2x)(11-2x) domain: 0 < x < 4.25
May 2, 2016

correction - math
use A^3 + B^3 = (A+B)(A^2 - AB + B^2) (memorize it) We call it the sum of cubes, we can also factor the difference of cubes. 8x^3 is a perfect cube and so is 1, so the expression fits the formula 8x^3+ 1 = (2x + 1)(4x^2 - 2x + 1)
May 2, 2016

algebra
first speed --- x mph return speed -- x+16 mph 6/x + 6/(x+16) = 1 times each term by x(x+16) 6(x+16) + 6x = x(x+16) x^2 + 4x - 96 = 0 (x-8)(x+12) = 0 x = 8 or x is a negative her first speed was 8 mph her return speed was 24 mph check: 6/8 + 6/24 = 1 , that's good!
May 2, 2016

Math
smallest angle --- x the other is ------ x+45 third ------ 2x - 5 solve for x: x + x+45 + 2x-5 = 180
May 2, 2016

Trigonometry
easier than it looks: cos^-1(radical3/2), means you want the angle Ø so that cosØ = √3/2 of course you should recognize that as a ratio form our 30-60-90 triangle, and Ø = 30° for tan^-1 (-√11/√5), construct a triangle in quadrant II ...
May 2, 2016

Probability and statistics
prob(choosing child) = 6/12 = 1/2 prob(non-child) = 1- 1/2 = 1/2 prob(exactly one child in choosing two) = C(2,1) (1/2)(1/2) = 1/2 or If C stands for choosing child and N stands for non-child we have these cases: CC -- prob = (1/2)(1/2) = 1/4 CN -- 1/4 NC --1/4 NN -- 1/4 so ...
May 2, 2016

Math
The least perimeter is obtained when you have a square let the side be s s^2 = 32 s = √32 = 4√2 so the least perimeter is 8√2 by Calculus: let the width be x then the length is 32/x P = 2x + 2y = 2x + 64/x P' = 2 - 64/x^2 = 0 for a min of P 2 = 64/x^2 x^2...
May 2, 2016

Math
Well, your homework is poorly stated. Here is an example of what Steve is saying: suppose the width is .1 ft then the length = 39/.1 or 390 ft perimeter = 2(390) + 2(.1) = 780.2 ft check: area = .1(390) = 39 suppose the width is .001 ft then the length is 39/.001 or 39000 ft ...
May 2, 2016

Geometry
3 small ones of 5 in diameter v = 3((4/3)π(2.5)^3) = 125π/2 = 62.5π = appr 196.35 one of diameter 8 v = (4/3)π(4^3) = 256π/3 = appr 268.08 hemisphere of radius 5 = (1/2)(4/3)π(5^3) = 250π/3 = appr 261.8
May 2, 2016

Probability and statistics
we can build our 5 digit number using 5 different numerals all possible numbers = 5! or 120 In all of these, the lead digit, the 10-thousand digit, can be occupied by the "9" 24 times, the "8" 24 times, etc. The value of those 24 9's would be 24(90000...
May 2, 2016

Gr 11 Functions
(1+tanx)^2 ≠ (1-sinx)(1+sinx) RS = 1 - sin^2 x = cos^2 x and cos^2 x is certainly not equal to (1+tanx)^2 try x = 45° (1+tan45)^2 = (1+1)^2 = 4 cos^2 (45°) = (1/√2)^2 = 1/4 no wonder you got nowhere with your work. check the question, or check your typing.
May 2, 2016

Correcion - math
Sarim's solution above makes absolutely no sense consider this one: http://www.jiskha.com/display.cgi?id=1462219074
May 2, 2016

maths
I know that the cost of coffee has gone up, but $2000 per kg ???? I will assume that you meant $22.00, (even that is too high) anyway..... let the cost of the mix be $x per kg 8(20) + 12(22) = x(8+12) 20x = 424 x = $21.20
May 2, 2016

math
looks for every increase of 1 unit in the x's the corresponding y decreases by 5 so slope = -5 y = -5x + b at x = -2, y = 9 9 = -5(-2) + b b = -1 function rule: y = -5x - 1
May 2, 2016

Math
I have no idea what your line 42pi C=pi*d=pi.pi*42=42pi. is supposed to say or mean. Are you saying the C = 42π ?? in that case the radius would be 21 units and the answer is in exact form now if we use the approximation of 22/7 for π we get C = 42(22/7) = 132 42&#...
May 2, 2016

Algebra
yes, the new vertex will be (4,-1) proof: f(x-2) = (x-2)^2 - 4(x-2) + 3 = x^2 - 4x + 4 - 4x + 8 + 3 = x^2 - 8x + 15 = g(x) vertex of g(x) = -b/(2a) = 8/2 = 4 g(4) = 4^2 - 8(4) + 15 = -1 vertex is (4,-1)
May 2, 2016

calculus
a) let the top right vertex be (x,y) then the area = 2xy A = 2xy = 2x(16-x^2) = 32x - 2x^3 dA/dx = 32 - 6x^2 = 0 for a max of A 6x^2 = 32 3x^2 = 16 x^2 = 16/3 x = 4/√3 , then y = 16 - 16/3 = 32/3 so the rectangle has a base of 2(4/√3) = 8/√3 and a height of ...
May 2, 2016

calculus
sum(1) = 1^3/1^4 = 1 or 4/4 sum(2) = (1 + 8)/16 = 9/16 sum(3) = (1+8+27)/81 = 36/81 = 4/9 or 16/36 sum(4) = (1+8+27+64)/256 = (1+8+27+64)/256 = 100/256 = 25/64 sum(5) = (1+8+27+64+125)/625 = 225/625 = 9/25 = 36/100 I noticed I can change my numerator to (n+1)^2 for sum(n) and ...
May 2, 2016

calculus
recall that tan^2 A +1 = sec^2 A and d(tanA)/dA = sec^2 A so ∫ tan² x/3 dx = ∫ sec^2 (x/3) - 1 dx form 0 to π = [3 tan (x/3) - x] from 0 to π = 3tan π/3 - π -(3tan 0 - 0) = 3 √3 - π
May 2, 2016

maths
volume of cube = (5.5 cm)^3 = 166.375 cm^3 then our cylinder's height would increase by h , such that π(49)h = 166.375 h = 1.081 cm (note that the 9 cm depth of water did not enter the picture)
May 2, 2016

Calculus
let the water level have a radius of r ft let the height of the water be h ft by ratio: r/h = 5/12 12r = 5h ---> r = 5h/12 V = (1/3)π r^2 h = (1/3)π(25h^2/144)(h) = (25/432)π h^3 dV/dt = (25/144)π h^2 dh/dt plug in our given stuff 1 = (25/144)π(64) ...
May 2, 2016

Calculus
dy/dt = 2ax dx/dt + dx/dt dy/dt = dx/dt(2ax + 1) but dy/dt = dx/dt , so 1 = 2ax + 1 2ax = 0 x = 0 then y = b at the point (0,b)
May 2, 2016

Calculus
did you make your sketch ?? let the length of the man's shadow be x ft let the distance he is from the lightpost be y by ratios: 6/x = 15(x+y) 6x + 6y = 15x 6y = 9x 2y = 3x 2dy/dt = 3dx/dt but dy/dt = 3 so 6 = 3 dx/dt dx/dt = 2 His shadow is lengthening at 2 ft/s but he is...
May 2, 2016

Math
your def: a*b= a+b-ab = first + last - product of first times last (a*b)*c = (a+b-ab)*c = a+b-ab + c - ac - bc + abc = a+b+c - ac - ab - bc + abc a*(b*c) = a*(b+c - bc) = a+b+c-bc - ab - ac + abc = a+b+c - ac - ab - bc + abc = (a*b)*c so the operation is associative -5*8 = -5+...
May 2, 2016

calculus too hard help
let's try this: let y = x^x lny = xlnx y'/y = x(1/x) + lnx dy/dx = y(1 + lnx) = x^x + x^x(lnx) let u = x^x^x , the x's are staggered ln u = x ln(x^x) u'/u = x(x^x + x^x(lnx))/x^x) + ln(x^x) argghhhh!! I was looking for a pattern. What am I not seeing ????
May 2, 2016

calculus too hard help
second last line should have been 532 = 5^9 = 1953125
May 2, 2016

calculus too hard help
y=x^x^x^x... take ln of both sides ln y = ln(x^x^x^x... ) ln y = x ln(x^x^x^x... ) lny = x ln(y) 1 = x well, that got me nowhere. are the x's staggered upwards or on the same level? e.g 532 = 5^8 = 390625 but (5^3)^2 = 5^6 ≠ 5^8
May 2, 2016

maths
r = 50 volume of full tank = (4/3)π(50)^3 = ... so half of that is .....
May 2, 2016

Math
with no restrictions, number of 4 digit permutations are 10x10x10x10 = 10,000 as you stated but , if we exclude the 9, we have only 9 numerals to play with number of 4 digit phone number endings = 9x9x9x9 = 6561 (now, a nicer question would have been: of those 4 digit endings...
May 2, 2016

Maths
sin(2Ø + π/3) = 1/2 we know sin (π/6) = 1/2 , (sin 30° = 1/2) so 2Ø + π/3 = π/6 OR 2Ø + π/3 = 5π/6 (sin30° = 1/2 and sin150° = 1/2) case1: 2Ø + π/3 = π/6 2Ø = π/6 - π/3 = -π/6...
May 2, 2016

Math
do you want something like this ? RR --> (4/12)(3/11) = 1/11 RG --> (4/12)(8/11) = 8/33 GR --> (8/12)(4/11) = 8/33 GG --> (8/12)(7/11) = 14/33 note that 1/11 + 8/33 + 8/33 + 14/33 = 1
May 2, 2016

Math
We have similar triangles Juan is 6' 1" = 73 inches so we can say: 73 inches/5 m = x inches/12 m notice we have the same units in each ratio, so 73/5 = x/12 5x = 12(73) x = 175.2 inches x = 14.6 ft = 14 ft and 7.2 inches
May 2, 2016

MATH
1 m^2 = 1.1959905 yards^2 so 76000 m^2 = 90895.278 yards^2 cost = 80(90895.278) = $7,271,622.24 (In reality, the cost would be found in terms of Euros/m^2. )
May 2, 2016

Math
A marathon is 42.195 km = 42,195 m time = 42195/1.8 = 23441.666.. seconds = 6.5116 hrs or 6 hours and 31 minutes or 1.8 m/s = 64800 m/h = 6.48 km/h rate = 42.195/6.48 hours = 6.5116 hrs as above or 1.8 m/s = 180 cm/s = 70.866.. inches/s = 5.90551... ft/s ,(stored in calculator...
May 2, 2016

maths
"u" is not an English word, however "you" is one. let the number of bikes be b let the number of tricycles be t 2b + 3t = 19 integer solutions (b,t) are (8,1) , (5,3) , (2,5) for 2b + 3t = 23 integer solutions are: (10,1) , (7,3) , (4, 5) , (1, 7)
May 2, 2016

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