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Posts by Reiny

Total # Posts: 38,385

Math
so the odds against the event = 59 : 41

Math
prob(event) = .41 prob(not event) = 1-.41 = .59 odds in favour of the event = .41 : .59 = 41 : 59

math
Let three of the adjacent sides by x, y, and z then the volume is xyz and xy=8 xz=18 yz=25 (xy)(xz)(yz) = 8(18)(25) x^2 y^2 z^2 = 3600 (xyz)^2 = 3600 xyz = 60

Math
Why not type in the regular way like you did here ? http://www.jiskha.com/display.cgi?id=1486616450 I can't read your post the way it was typed.

Math
expected to see an "=" sign in tn-tn-2(n-3)/(n-1) check your spelling and correct. Also use brackets, eg is it : tn = t(n-2)*(n-3)/(n-1) ??

High School Geometry
from 4/ an arc from B to D suggests that the arc passes through A If that is the case, BD is the diameter and your arc is a half-circle. (Any angle subtended by a diameter is 90° ) I am going to guess that half the square lies within the half-circle. If that is the case, ...

Math
Visualize slicing a nice round object such as an apple in the way you described. Try to sketch a 3-D diagram. Your slice will have a circular surface. Sketch a right-angled triangle with hypotenuse of 16 and height of 9 The third side will the the radius of you circular slice...

Math
I did part a) here http://www.jiskha.com/display.cgi?id=1487781971

Math
prob(a 2) = 1/6 prob(not a 2) = 5/6 assuming you want exactly 50 out the 240 to be a 2. prob(50 2's out of 240 throws) = C(240,50)(1/6)^50 (5/6)^190 (my calculator can do the two powers but not the C(240,50) )

business math
No calculations needed. You are earning 12% p.a. vs paying 9% compounded monthly Take the loan e.g. Interest payable for the first month on the loan = 20000(.09/12) = 150 interest earned on fund in first month = 20000(.12)(1/12) = 200

math
From your sketch, join the end of the chord to the centre, drop a height from the centre to the chord. You have a right-angled triangle, with 2 sides known, base is 5, hypotenuse is 13. By Pythagoras, find the height Find the central angle using basic trig. find the ...

mathematics
This is an AS with a = 5, d = 3 and term(n) = 383 your formula for term(n) = a + (n-1)d 383 = 5 + (n-1)(3) solve for n

Math
let the base area of the tank be x cm^2 volume including balls = 15x volume without the balls = 6x volume of the 3 balls = 9x volume of each ball = 3x Unless we know the base dimension of the tank, that is as far as you can go. e.g. if the tank has a base of 40 by 50 and a ...

math
sum = 1/2 + (1/3+2/3) + (1/4+2/4+3/4) + (1/5+2/5+3/5+4/5) + ... (1/9+2/9+... +8/9) = 1/2 + 3/3 + 7/4 + 10/5 + ... 36/9 = 1/2 + 1 + 3/2 + 2 + ... + 4 looks like an arithmetic series with a = 1/2, d = 1/2, and n = 8 sum = (8/2)(2(1/2) + 7(1/2)) = 4( 1 + 7/2) = 4 + 14 = 18

Calculus
so you know: height = -16t^2 + 160t + 0 , zero, since we started at ground level This is a downwards opening parabola, so it has a maximum at its vertex. What method have you learned to find the vertex, there are several ways. simplest way in this case: find the x-intercepts, ...

Math
No equation to solve. you probably meant "evaluate" the expression. (2^8?5^?5?19^0)^?2?(5^-2/ 2^3)^4?2^28 = ( (2^8)(5^-5)(1) )^-2 * ( (5^-2)(2^-3) )^4 * 2^28 = 2^-16 * 5^10 * 5^-8 * 2^-12 * 2^28 = 2^0 * 5^2 = 25 check my arithmetic

math
secA = 12/5 then cosA = 5/12 = .41666... use your calculator, make sure you either have it set in degrees or radians, depending on what you want. let me know what you got.

Math
http://www.wolframalpha.com/input/?i=plot+y%3D-2x+,+-x%5E2

Math/Calculus
For this type of problem , the first thing you should do is to make sure that the given point actually lies on the curve, or else whatever we do would be just gibberish. I did this, and both points satisfy their matching equation. So, we take the derivative, plug in the point ...

Calculus
using: f(x)?f(xo)+f?(xo)(x?xo) <-- should be in your text 1° = 1° - 0° so let xo = 0, then x = 1 we have : f(x) = sinx f'(x) = cosx since we are using Calculus on trig, our x must be in radians 1° = ?/180 f(1°) = sin0 + cos(0)(?/180-0) = 0 + (1)(?/...

precalculus, complex numbers
can 't read it, don't use codes, they don't work here

Math Derivatives
product rule f'(x) = xcos(?/x)(-?/x^2) + sin(?/x) = (-?/x)cos(?/x) + sin((?/x) f''(x) = (-?/x)(-sin(?/x))(-?/x^2) - (?/x^2)(cos(?/x)) + cos(?/x)(-?/x^2) simplify if needed

Math - Related Rates
V = (4/3)? r^3 when V = 36? 36? = (4/3)? r^3 27 = r^3 r = 3 m dV/dt = 4? r^2 dr/dt 2 = 4? (9)dr/dt dr/dt = 2/(36?) m/min = appr .01768 m/min

Algebra I
I would do it this way: Amount of pure water needed --- x gal Amount of the 60% stuff ------ 6-x .6(6-x) + 0x= .5(6) 3.6 - .6x = 3 -.6x = -.6 x = 1 so use 5 gal of the 60% plus 1 gal of pure water your answer of 7.5 gal should have made no sense to you. You want to end up with...

Algebra
Don't use x as a multiplication sign, use * or use brackets, so I see your product as (a)(b)(a)(b) = (ab)^2 or = a^2 b^2 when you say ab^2, it is only the b that is squared.

Derivative-Optimization Problems
side parallel to river --- y m each of other two sides --- x 2x + y = 600 ---> y = 600-2x area = xy = x(600-2x) = -2x^2 + 600x d(area)/dx = -4x + 600 = 0 for a max of area -4x = -600 x = 150 then y = 600-2x = 300 largest area = 150(300) = 45000 m^2

Math
your equation: y = 80 + 10n your brother's equation: y = 275 - 15n b) when does 80+10n = 275-15n ? c) whatever you got for n in b) sub this into "your" equation

Algebra
.125 , .125r, .125r^2, .125r^3, .125r^4, .125r^5, 8 .125r/.125 = 8/.125r^5 r = 64/r^5 r^6 = 64 r = ± 2 set 1: .25, .5, 1, 2, 4 set 2: if r = -2 -.25, .5, -1, 2, -4

maths
make a sketch. draw poles AB and PQ with B and Q on the ground Draw the reflection of AB in the horizontal and call it BA'. Joint A' to P Label the intersection of A'P with BQ as M. let BM = x, then MQ = 20-x Of course the shortest distance between any two points ...

Math word problem
here is your problem: 1.50(x) + 4.00(y) = 712 1.50(x) + (y) = 712/4 you divided the 2 last terms by 4, but not the first one

Maths
Use the formula for the sum of terms (7/2)(2a + 6d) = (13/2)(2a + 12d) times 2, then expand 14a + 42d = 26a + 156d -12a = 114d a = -19/2 d sum(20) = 10(2a + 19d) = 20a + 190d = 20(-19/2 d) + 190d = 0

Algebra
I read your (f of g)(x) as f( g(x) ) By the "Just look at it" theorem, if g(x) = x+3 and f(x) = 1/x^3 then f(g(x)) = f(x+3) = 1/(x+3)^3 , which is h(x)

math
We don't do assignments for students. What part of this do you find difficult? Most are formula-based questions which you must have in your notes.

Math
(4z^2 + 7z – 8)(–z + 3) = -4z^3 + 12z^2 - 7z^2 + 21z + 8z - 24 = -4z^3 + 5z^2 + 29z - 24 matching this with –4z3 + xz2 + yz – 24 5z^2 = xz^2 ----> x = 5 29z = yz -----> y = 29

ss
strongly linked, they are each other's largest trading partner.

maths
Is this translation correct ? A rectangular field is 15 m long and 9 m wide. It has a path 1.5 m wide all around it. Find the area of the path. area of field = 15(9) m^2 =.... area of the whole thing = 18(12) m^2 = ..... (make a sketch to see where the 18 and 12 come from) ...

Math
Ruby now ---- x Pawan now --- 2x 3 years ago: Ruby --- x-3 Pawan -- 2x-3 2x-3 = 3(x-3) carry on

Algebra
Rider: y = .5x + 50 UMove: y = .75x + 45 Just follow the instructions, they are quite clear.

Math
solve: x^3 + 3x + 1 = -3 x^3 + 3x + 4 = 0 let x = 1 ---> 1+3+4 = 0 ? no let x = -1 ---> -1-3+4 = 0 , yeahh x^3 + 3x + 4 = (x+1)(x^2 - x + 4) = 0 so x=-1 or x is a complex number so f^-1 (-3) = -1 check: f(x) = y = x^3 + 3x + 1 f(-1) = -1 -3 + 1 = -3 the inverse is: x = y...

Math
and a rhombus

pre-algebra
1. It said: "The length of a yard is triple the length of the garden" --> so if you let the length of the garden be x then the length of the yard is 3x (we could have used any variable name, you used G, that's fine) It said: "the difference between the ...

Calculus (RATE OF CHANGE)
Make a sketch and use the cosine law: let the rate of the slower car be x mph then the rate of faster car is 2x mph Let the distance covered by the slower car by x then the distance covered by the faster car is 2x let the distance between them be d d^2 = x^2 + 4x^2 -2x(2x)...

Calculus (RATE OF CHANGE)
I assume you want dy/dx y = 1/x + 2 dy/dx = -1/x^2 when x = 2 dy/dx = -1/4

Math
I think you have a typo. You want a 6th added, so there should have been 5 of them given already. You only have four of them

Calculus
see my previous reply, in this case multiply each term by 7, then go from there

Calculus
Some authors consider 18x + y = 13 to be "standard" form , and 18x + y - 13 = 0 to be "general" form Look at your text or notes

calculus
Are there supposed to be exponents in your equation?? I will assume: V = ?aT^3 + bT^2 ? cT + 1 , using the given: dV/dT = -3a T^2 + 2b T - c I assume you plugged in the given values for a, b, and c, used the quadratic equation formula and solved for T Since the coefficient of ...

pre-algebra
number of votes for Michael --- M number of votes for Tina = M - 200 number of votes for Sam = M + 4200 (you had that, good!) Now, just translate: "Samantha plus the number of votes received by Michael minus the number of votes received by Tina (M + 4200) + M - (M-200) = ...

Algebra
You should define your variables, hard to check without knowing what x stands for e.g. let the "other " angle be x then "one" angle is 4x+2 "The third angle is three times the first angle decreased by 6" ---> poor wording. How do we know which ...

Math
certainly not linear, slopes between pairs of points would have to be the same, --- they are not. Took differences in the y values up to the fourth difference columns. No constant so , no polynomial up to 4th degree. Not even Wolfram found an equation, when to least-fit ...

Math, data management
no, you probably meant 10!/(4!,3!,3!) = 4200

Algebra
see http://www.jiskha.com/display.cgi?id=1487716112 this is very similar, except you would have 1/x and 1/2x as the combined rate, and you know that result.

Algebra
look at the solution both Damon and I gave here for a similar question http://www.jiskha.com/display.cgi?id=1487716112 The only difference is that here you are given the combined rate.

Math - Calculus
Make a sketch. Your rock will travel in a circle whose equation is x^2 + y^2= 9 you must release it at a point P(x,y) so that it reaches a point (15,0) Anyway, we have right-angled triangle , (at the point of release, the angle is 90° between radius and tangent. let the ...

Algebra
rate of old machine = 1/170 rate of new machine = 1/119 combined rate = 1/170 + 1/119 time at combined rate = 1/(1/170+1/119) = 1/(1/70) = 70 minutes

Algebra
one number --- x the other ------ x-32 1/(x-32) + 5(1/x) = 1/6 times 6x(x-32) 6x + 30(x-32) = x(x-32) 6x + 30x - 960 = x^2 - 32x x^2 - 68x + 960 = 0 (x-20)(x-48) = 0 x = 20 or x = 48 if x = 20 then the other is negative, but both our numbers are to be positive so x = 48 and ...

Math
v = -32t + 28 Is there a question?

*** Monitor Needed For Banning
Mehdi Moustaoui

algebra
x(500) = .1(200) + .2(300) x = 80/500= .16 change my answer to a percent.

Math
we can find the equation of the line, you have the slope and a given point. Once you have the equation, replace the x with anything you want, then find its matching y value

Algebra
3.18x+2.6+0.9x+x=28 5.08x = 24.4 x = 24.4/5.08 = 5 Hali's equation of 5.1x = 25.4 -->(no idea where that came from ) does not yield the solution of x = 5 as he concluded.

Math
This looks like an assignment or test. I don't see your choices for the answers nor any indication where you had difficulty. You weren't expecting somebody to just do this for you, did you ?

kishore
originial fraction ---- a/b case 1: (a+1)/(b+3) = 1/2 2a +2 = b+3 ----> 2a - b = 1 or b = 2a-1 case 2: (a-1)/(b+2) = 2/5 5a - 5 = 2b+4 5a - 2b = 9 use substitution: 5a - 2(2a-1) = 9 a = 7 , then b = 13 the original fraction was 7/13

math
your height equation must be h = -4.5t^2 + 25t + 50 so you want to solve: 7 = -4.5t^2 + 25t + 50 4.5t^2 - 25t - 43 = 0 use the quadratic formula, discard any negative value of t

Mathematics
What is 1 - (.9)^5 ?

math
right now: 40 people signed up, $120 per person. let the number of additional skiers be m number going : 40+m cost per skier : 120-2m revenue = (40+m)(120-2m) = 4800 + 40m - 2m^2 This is a quadratic, a parabola opens down, so it has a maximum revenue. This is found by finding ...

Maths
I will assume compound interest, i = .06/12 = .005 amount = 12000(1.005)^42 = .... subtract the original 12,000 to find the interest. for interest earned after 2 years = 12000(1.005)^24 - 12000 "How much interest is earned each year " - this would require 42 ...

Math
I made a sketch on a grid, I labeled the point at the anchor (0,2) and the point of atachment at the pole as (x,45) (45-2)/(x-0) = 3/5 3x = 215 x = 215/3 Now , use the formula for the distance between 2 points

Algebra
Your equation should have been 25y^2 - 60y + 324 = 0 by the formula: y = (60 ±?-28800)/50 = (60 ± 120?-2)/50 = (6 ± 12i?2)/5 which is a complex number

maths
speed at remaining distance ---- x km/h (2/3)(450)/75 + (1/3)(450)/x = 13/2 300/75 + 150/x = 13/2 times 2x 8x + 300 = 13x carry on

math
I agree with Bosnian's answer. check your typing of the question. Did you perhaps mean ?15/(9y) < 11/13 ?

Math
At the moment she steps off, her linear velocity equals the rate the arc length is increasing. circumference = 2?(25) = 50? ft 36° = 36/360 = 1/10 of a rotation so the linear velocity of any point is 5? ft/second 5? ft/1 second = (5?/5280) / (1/3600) miles/hour = (5?/(5280...

Algebra
So I assume it is 4x^3 = 16 then: 4x^3 - 16x = 0 4x(x^2 - 4) = 0 4x(x+2)(x-2) = 0 x - 0, ± 2

MATH (POST 2) Need Help Please
I am not familiar with the "average daily balance method " , I don't live in the US. Perhaps one of the other math tutors can help out here.

Algebra
Apparently we are supposed to ignore the loss due to saw-cuts, a bad idea. Looks like we have two verticals and 3 horizontal pieces. let each of the verticals be x and each of the horizontals be y 2x + 3y = 72 inches y = (72-2x)/3 volume = 24(x)(y) = 24x(72-2x)/3 = 576x - 16x^...

Algebra
length ---- x width ----- y 2x+2y = 42 x+y = 21 y = 21 - x printing area: length = x-2 width = y-3 = 21-x - 3 = 18-x area = (x-2)(18-x) = 18x - x^2 - 36 + 2x = -x^2 + 20x - 36 since this is a downwards parabola, the vertex will be the answer to your question. Find the vertex ...

Math
"Guessing" ??? Good grief, this is math. $8 to rent a car for 15 days ????? just plug in your data .... C = 50(15) + .15(475) = ......... I am sure you have a calculator if you can't do it with pencil and paper.

math
(x/50)+(x/25)+(3x/50)+(2x/25)+...+2x = x/50 + 2x/50 + 3x/50 + 4x/50 + ... 100x/50 = (x/50)( 1+2+3+4+ ... + 100) continue

math
slower speed ---- x km/h faster speed ----- x+6 km/h 5x + 4(x+6) = 294 easy to solve....

math
(4xy+2xy)^2 did you notice that you have like terms, so = (6xy)^2 = 36 x^2 y^2

math
P(A or B) = P(A) + P(B) - P(A and B) your data fits that formula

@ penny - math
Penny, it is you who determines if you fail or pass, please don't blame Steve.

Math
Use your formulas ar = -6 ar^4 = 48 divide them: r^3 = -8 r = -2 now find a, then use the formula for the sum(n) terms let me know what you get, so I can check it

math
How many 5's do you see on 1 die ??

Algerba
Well, why don't we solve it, probably faster than subbing in all those values -1.5^2+4x+2.2=0 3x^2 - 8x - 4.4 = 0 x = (8 ± ?116.8)/6 = appr 3.13 or -.5 you are right

maths
list the first prime numbers, add them up, then divide by 10 remember the first prime number is 2, then 3, etc

Algebra I
4p - 2m = 2 ---> 2p - m = 1 or m = 2p-1 3p + 9m = 54 sub in m=2p-1 into the other equation and solve

math
how many kings ? how many hearts ? remember not to count the king of hearts twice, it would be included in both counts.

maths
so you have 2/5 left (2/5)x = 80 2x = 400 x = 200 check: take 3/5 of 200 and subtract it from 200. What do you have left ?

@ Steve - MATH
Nice!!! Well, I always like to take those long detours. I once went from Toronto to Niagara Falls by going all the way around Lake Ontario.

MATH
cos 4A = cos^2 2A - sin^2 2A = (cos 2A - sin 2A)(cos 2A + sin 2A) = (cos^2 A - sin^2 A - 2sinAcosA)(cos^2 A - sin^2 A + 2sinAcosA) from cosA = 1/2 ----> sinA = ?3/2 (A = 60° or ?/3) plug the cos and sin values into my last equation and evaluate, I will leave the ...

math
(1/3)p = 2 p = 6

Geography
The angle between is 150° which is 150/360 or 5/12 of a rotation. 5/12 of 24 hours is 10 hours. so the time would be 5:30 - 5:00 = 19:30 ---> evening of previous day ( that would be 7:30 pm using US notation) time decreases from east to west

algebra 2
my starting equation would be: y-5 = -1(x+3) re-arrange it to see which one fits

Algebra 1
What makes you "think" it is either a or c What did you do to get the answer?

algebra
What are you doing ???? (4275)(4372) = 18,690,300

math
your number ---- x x/4 + 5 - 6 = 6 x/4 = 7 multiply both sides by 7 x = 28 try it.

math
I think that should be 48 done 6 years ago by MathMate http://www.jiskha.com/display.cgi?id=1307634385

math
you have posted 4 disconnected statements 215 = 0.73n ----> false n = 0.73 × 215 ----> does not follow from the previous, but would be correct 0.73 = n × 215 -----> does not follow from the previous 215 = 73n ---> does not follow the previous, but ...

Math
suppose we use an example: e.g. f(x) = (x-5)^2 + 3 , which is a parabola with vertex (5,3), opening upwards f(2-x) = (2-x - 5)^2 + 3 f(2-x) = (-x - 3)^2 + 3 f(2-x) = (x+3)^2 + 3 , (just like (-9)^2 = 9^2 ) -f(2-x) = -(x+3)^2 - 3 so we have a reflection in the x-axis, and a ...

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