Wednesday
April 1, 2015

Posts by Reiny


Total # Posts: 29,347

Math
prob of grey = 87/100 number of greys in 220 = (87/100)(220) = appr 191
February 20, 2015

Math
number = (1/50)(750) = 15
February 20, 2015

maths
visualize the box cut open and laid out flat on a table. What do you see ? Calculate the area of each of the 5 rectangles and add them up
February 20, 2015

Math
prob of 4 spades = C(13,4)/C(52,4) = 715/270725 = 11/4165
February 19, 2015

Math
original square is x by x cm new rectangle is x by x/2 2( x + x/2) = 24.9 2x + x = 24.9 x = 8.3 the square piece is 8.3 by 8.3 cm
February 19, 2015

Math
volume of similar solids is proportional to the cube of their corresponding sides 240/x = 92^3/23^3 240/x = 778688/12167 778688x = 12167(240) x = 3.75 or 3.8 to the nearest tenth
February 19, 2015

Math (Probability)
You want the 8 of hearts, then an Ace prob = (1/52)(4/51) = 1/663
February 19, 2015

Algebra 2
t3 = ar^2 = -75 t6 = ar^5 = -9375 divide them r^3 = 125 r = 5 in ar^2 = -75 a(25) = -75 a = -3 term(n) = -3(5)^(n-1)
February 19, 2015

Math
I assume the median is 87 z-score = (91-87)/4.01 = ....
February 19, 2015

math
You are basically going through the development of the formula, using a specific example You seem to have a typo your: 3²+3³+3to the power of 6+...to 20 terms makes little sense I will assume we have S(20) = 3^2 + 3^3 + ... + 3^21 multiply both sides by 3 3S(20) = 3^...
February 19, 2015

MATH
Typo: you have Sn=n/2[a+1] clearly should be : Sn=n/2[a+l] let S(n) = a + (a+d) + (a+2d) + ... +(l-2d) + (l-d) + l , for n terms we could just write this turned around S(n) = l + (l-d) + (l-2d) + ... + (a+2d) + (a+d) + a add these two equations 2S(n) = a+l + (a+d+l-d...
February 19, 2015

MATH
I will assume that you are adding the corresponding terms of each sequence, that is .. new sequence: t1 = a+a t2 = a+d + ar t3 = a+2d + ar^2 etc so a+a = 4 a+d + ar = 20 but d=-2 and r=3 2a = 4 a = 2 So all is known t3 = 2 - 4 + 2(9) = 16 check: AS: 2, 0, -2, -4, .. GS: 2, 6, ...
February 19, 2015

math
Use the formulas for both "sum of terms" and "sum of infinite number of terms" Sum to infinity = a/(1-r) a/(1-r) = 243 , ---- #1 ( I recognized 243 as 3^5) a = 243 - 243r sum(5) = a(1 - r^5)/(1-r) 242 = a(1 - r^5)/(1-r) ---- #2 divide #2 by #1 1-r^5 = 242/...
February 19, 2015

Algebra 2
∑ 2n/(n+4) , where n = 1 to 5 write n=1 underneath the sigma symbol and 5 above it
February 18, 2015

Math Help Please
You must mean: (4x^3 + 5x^2 - 12x + 27)/(x + 3) I did a synthetic division and got 4x^2 - 7x + 9 , which is A since none of the answers had a remainder, you knew the division had to be exact, so it had to look like this (4x^3 + 5x^2 - 12x + 27) = (x+3)(4x^2 .... +9) so it had ...
February 18, 2015

math
going to the theatre C = 12.5n, where n is the number of movies seen buying a player, then renting C = 125 + 1.95n 12.5n = 125 + 1.95n 10.55n = 125 n = 11.8 I will let you interpret that decimal answer
February 18, 2015

algebra
let the side parallel to the barn be y yards then the other two sides are x yards each 2x + y = 25 y = 25-2x area = xy = x(25-2x) = 25x - 2x^2 which graphs as a downwards parabola, so the vertex has to be found. quickest way: the x of the vertex is -b/(2a) = -25/-4 = 6.25 then...
February 18, 2015

ALGEBRA
unless [ ] is defined as something special, f(2) = 2*(-1)^2 = 2*(1) = 2
February 18, 2015

math
reflection of P(-3,5) in the x-axis ----> R(-3,-5) which is in quadrant III P(-3,5) reflected in the y-axis---> S(3,5) , which is in quad I
February 18, 2015

Jonie, Pamela, Spartans - math
Why are you changing names, and what could you not understand about my answer here: http://www.jiskha.com/display.cgi?id=1424281591
February 18, 2015

Math
the resultant vector is (9-1 , 3-11) = (8,-8) This is generally considered in component form check with your textbook how they write the vector. Some authors avoid the standard round brackets ( ..., ...) to avoid confusion with a point. Some use this form [8,-8] others use <...
February 18, 2015

Calculus
not an easy problem follow these steps: http://mathworld.wolfram.com/SphericalCap.html or http://en.wikipedia.org/wiki/Spherical_cap or http://keisan.casio.com/has10/SpecExec.cgi?id=system/2006/1223382199
February 18, 2015

math
I hope Mr. Howard put in the closing brackets. 3(20x + 8) = 60x + 24 4(15x)+6) = 60x + 48 so what is your opinion ?
February 18, 2015

Math
so what did your calculator say? remember the angle could have been in quadrant IV also. so 360-(whatever your calculator said)°
February 18, 2015

Algebra 2
sum(7) = (7/2)(2(26) + 6(18)) = 560
February 18, 2015

Algebra 2
so you want 16+20+24+...100 number of terms = ?? you have an AS, where a = 16 , d=4 term(n) = a+(n-1)d 100 = 16 + (n-1)(4) 84 = 4n - 4 88 = 4n n = 22 so we want S(22) = (22/2)(first + last) = 11(16+100) = 1276
February 18, 2015

Algebra not algabra
(3a+2)^3 = (3a+2)(9a^2 + 12a + 4) = 27a^3 + 36a^2 + 12a + 18a^2 + 24a + 8 = 27a^3 + 54a^2 + 36a + 8 or , using the binomial expansion = 1(3a)^3 + 3(3a)^2 (2) + 3(3a)(2^2) = 1(2^3) = 27a^3 + 54a^2 + 36a + 8
February 18, 2015

Math
N = N(M) + N(S) + N(R) - N(M and S) - N(M and R) - N(S and R) + N(M and S and R) = 36+28+12 - 15 - 12 - 8 + 4 = 45 If the question is, How many did not buy any type of book, then it would be 59-45 or 14 You did not state a question. You could draw a Venn diagram and all ...
February 18, 2015

math
sinØ = 4/5 = .8 Your first angle is correct, so the angle in quad II should be 180-53.13 = 126.87° check with a calculator, also check your second answer to see that it is incorrect.
February 17, 2015

math
a + ar = 12 a(1+r) = 12 a = 12/(1+r) ar^2 = 16 a = 16/r^2 then 16/r^2 = 12/(1+r) 12r^2 = 16+16r 12r^2 - 16r - 16 = 0 3r^2 - 4r - 4 = 0 (r-2)(3r+2) = 0 r = 2 or r = -2/3 if r = 2, a = 16/4 = 4 ---> ar = 8, but t1 should be > t2, so, no good if r = -2/3 , a = 16/(4/9) = 36...
February 17, 2015

algebra
area of picture = (4x+3)(3x+5) = 12x^2 + 29x + 15 area of whole thing = (4x+3 +4)(3x+5 + 4) = (4x+7)(3x+9) = 12x^2 + 57x+63 area of border = 12x^2 + 57x+63 - (12x^2 + 29x + 15) = 28x + 48
February 17, 2015

algebra
let the other endpoint be (a,b) by the midpoint method: (a+7)/2 = 3 a+7 = 6 a = -1 (b+4)/2 = 4 b+4 = 8 b = 4 the other point is (-1,4)
February 17, 2015

math
The way you typed it ... -4x + 3 = 0 -4x = -3 x = 3/4 This is a vertical line, so its perpendicular is a horizontal line and this one would be y = 5 so you are correct, even though your statement "x = 4/3 undefined" makes little sense.
February 17, 2015

Pre-calculus
ar^2 + ar^3 = 50 ar^2(1+r) = 50 ---- #1 ar^3 + ar^4 = 100 ar^3(1+r) = 100 --- #2 divide #2 by #1 ar^3/ar^2 = 2 r = 2 in #1: a(4)(3) = 50 12a = 50 a = 50/12 = 25/6 so the first 5 terms are 25/6 , 50/6, 100/6, 200/6, 400/6 check" 3rd + 4th = 50 LS = 100/6 + 200/6 = 300/6 = ...
February 17, 2015

Calculus Chain rule
first write it as f(x) = 2(9x^5 + 1)^-5 now by the chain rule ... f ' (x) = -10(9x^5 + 1)^-6 (45x^4) = -450x^4/(9x^5 + 1)^6
February 17, 2015

algerbra
use the distance between two points formula Distance = √( (6-3)^2 + (4+6)^2 ) = .... carry on
February 17, 2015

math
terms are a , ar, ar^2 ... sum4 = a(r^4 - 1)/(r-1) = 15 sum8 = a(r^8 - 1)/(r-1) = 15 + 240 = 255 divide the 2nd equation by the 1st (r^8-1)/(r^4 - 1) = 255/15 = 17 r^4+1)(r^4-1)/(r^4-1) = 17 r^4+1 = 17 r^4 = 16 r^2 = ±4 , and for reals r = ±2 so the constant ...
February 17, 2015

GEOMETRY
tanØ = 7√3/21 = √3/3 Ø = 30° so the angles are 30°, 60° and 90°
February 17, 2015

algebra
let the short piece be x longer piece is x+7 x + x+7 = 12 2x = 5 x = 2.5 short piece is 2.5 longer piece is 9.5
February 17, 2015

calculus
Here is the area you are finding http://www.wolframalpha.com/input/?i=plot+2y%3D16-x%5E2+%2C+x%2B2y%3D4 Find the intersection of the two graphs, you only really need the x values. take vertical slices. so the height of a slice is (8-x^2/2) - (2 - x/2) = 6 - x^2/2 + x/2 take ...
February 17, 2015

maths
let the number of terms be n last term: a + (n-1)d = 30 a + (n-1)(3) = 30 a + 3n - 3 = 30 a + 3n = 33 or a = 33 -3n sum of n terms = 135 sum of terms = (n/2)(first + last) (n/2)(a + 30) = 135 a + 30 = 270/n subbing in the previous value of a 33-3n + 30 = 270/n -3n^2 + 63n - ...
February 17, 2015

statistics
This is a standard question in binomial distribution. I don't know what your tables in your text look like, but I would do: prob (getting 5 heads in 15 flips) = C(15,5)(1/2)^5 (1/5)^10 = 3003(1/2)^15 = 3003/32768 = appr .0916 or your answer of .092 You are correct
February 17, 2015

analytic geometry
Let's create the equation of your cables using the following data let the vertex be at (0,10) two other points are (300,110) and (-300,110) the equation must be y = a(x-0)^2 + 10 = ax^2 + 10 but (300,110) lies on it 110 = a(90000) + 10 a = 100/90000 = 1/900 y = (1/900)x^2...
February 17, 2015

math
2l + 2w = 18 l + w = 9 could be any two positive numbers that add up to 9 e.g. 5 and 4 7.5 and 1.5 3 2/5 and 4 3/5 6.123 and 2.877 As you can see there would be an infinite number of possibilities.
February 16, 2015

math
6log2^3 √64+ 10log3^5 √243 = 6log(8*8) + 10log(243√243) = log 64^10 + log ( (243√243)^10) = log ( (64^10)(243√243)^10 ) = log ( (64^10)(243^15) ) = log (7.0128 x 10^35) = appr 53.85 I suspect a typo
February 16, 2015

calculus
ds/dt = 64 - 32t , assuming b and d are constants = 0 for a max of s 32t = 64 t = 2 sub back into s s = bd + 128 - 64 = bd + 64
February 16, 2015

Math
See my reply in your previous post for this problem
February 16, 2015

math
nickels --- n dimes ---- d quarters --- (76-n-d) 5n + 10d + 25(76-n-d) = 900 5n + 10d + 1900 - 25n - 25d = 900 -20n - 15d = -1000 4n + 3d = 200 , #1 if nickels = d dimes = n quarters is still 76-n-d 5d + 10n + 25(76-n-d) = 800 5d + 10n + 1900 - 25n - 25d = 800 -15n - 20d = -...
February 16, 2015

math
lavender --- x rose pedals --2x buckwheat --- 10 - 3x 4x + 6(2x) + 3(10-3x) = 3.7(10) 4x + 12x + 30 - 9x = 37 I will let you finish it
February 16, 2015

math
In descending order it would be 7532 you have them in ascending order since the 5 is in the hundreds position, its value is 500
February 16, 2015

Algebra
Ok, now that you figured out which choice is linear and which is quadratic, you only had two to choose from. If you sub x = 0 into your choice, I get y = 0-3 which is NOT -6, so ..... same thing for the next one, this time you seem to have guessed correctly
February 16, 2015

Algebra
#1, correct #2 and #3, both incorrect It asked for a quadratic, you picked a linear each time
February 16, 2015

MAth
clearly the Pen + calculator cost 50-20.45 = 29.55 pen + calc = 29.55 4.5 + calc = 29.55 calc = 25.05 (no tax ? , wow)
February 16, 2015

Math
what you are basically asking is how much is a present value of 200,000 worth in 5 years , and in 10 years, at a rate of 6.8% amount after 5 yrs = 200000(1.068)^5 = 277,898.54 change the exponent 5 to 10 for the 10 year part Note: Normally a reverse mortgage consists of ...
February 16, 2015

math
cost to make the cakes = 200(2.7)= 540 To make a profit of 66% she needs 1.66(540) = 896.40 But she discards 10% of her cakes, so only sells 180 Selling price = 896.4/180 = $ 4.98 check: profit = 4.98(180) - 540 = 356.40 rate of profit = 356.4/540 = .66 or 66%
February 16, 2015

Algebra
-3x^2 - 18x + 15 since 3x^2 + 18x - 15 = 0 does not have any rational roots since b^2 - 4ac is not a perfect square, it does not factor over the rationals
February 15, 2015

math
area of a rhomus = (1/2)(product of its diagonals) let the other diagonal be a (1/2)(15a) = 60 15a= 120 a = 8 So let's find the hypotenuse of one of the right-angled triangles formed by the intersection of its diagonals base = 4, height = 7.5 if h is the hypotenuse, h^2 = ...
February 15, 2015

Calculus
You would now sub those two values into the original equation. The larger answer is your maximum the smaller value is your minimum
February 15, 2015

Algebra 1
I agree. Unless the coeffiecients are relatively small, I usually don't waste too much time trying to factor it. If the x^2 term has a coefficient of 1, and the x term is even I ALWAYS complete the square, it is much faster than the formula. Otherwise, I do a quick ...
February 15, 2015

Math
3^12 /(3x3^6) = 3^12 / 3^7 = 3^5 = 243
February 15, 2015

calc
You must have an idea what the tangent function looks like. As Ø approaches 90° or π/2 from the left, tanØ becomes infinitely large positively. as Ø approaches 90° from the right, it is infinitely negative now look at (x^7 - x^9), as x -->...
February 15, 2015

algebra
expand first , then collect like terms x - 9x + 10 + 11 = 12 - 6x + 1 -8x + 6x = 13 - 21 -2x = -8 x = 4
February 15, 2015

Math
number of quarters --- x number of dimes --- 21-x 25x + 10(21-x) = 345 25x + 210 - 10x = 345 15x = 135 x = 9 He has 9 quarters and 12 dimes check: 9(25) + 12(10) = 345 , check!!
February 15, 2015

math
1.41/100 = 1/x 1.41x = 100 x = 100/1.41 = $70.92 ( your textbook must be from the Clinton era. During the Bush years, it was reversed, the Canadian dollar was worth more. Now under Obama we are slipping again and the US dollar is rising, 1 US = appr 1.18 CND . As you can tell ...
February 15, 2015

math
since you end up with 12 = 4 , which is false, there is no solution
February 15, 2015

maths(urgent answer pls)
Still messing around with #2 #3, ∑ k(k+2)(k+4) , where k = 1 to n if you expand this you will get a cubic , so you will have to have ∑ k^3 for k=1 to n equal to (1/4)n^2(n+1)^2 ( I had to look that one up) for the square and first degree terms use the ones I gave ...
February 15, 2015

maths(urgent answer pls)
I answered the first part in your previous post
February 15, 2015

mathematics
prob(red, black, red) = (3/10)(7/9)(2/8) = 7/120
February 15, 2015

MATHS(sum of series)
yes it will Sum(1) = (4(2)(3) - 12(2) + 6)/6 = 1 sum(2) = (8(3)(5) - 24(3) + 12)/6 = 10 sum(3) = 12(4)(7) - 36(4) + 18)/6 = 35 etc. It works! I am sure!
February 15, 2015

MATHS(sum of series)
I will do the first one We were lucky to have the general term, in most cases you have to find that first Secondly you have to know some basic summation formulas ∑ k ,where k = 1 to n is n(n+1)/2 ∑ k^2 , where k = 1 to n is n(n+1)(2n+1)/6 ∑ c , where k = 1 to...
February 15, 2015

calculus
I will assume you meant: lim (2x + 1 - cosx)/(3x) then ... = lim ( (2x)/(3x) + 1/(3x) - (1/3)(cosx/x) ) as x --> 0 = lim ( 2/3 + 0 - (1/3)(0) ) = 2/3
February 15, 2015

mathematics
let the first 3 terms be a , ar , and ar^2 ar = a + 4 ar - a = 4 a(r-1) = 4 a = 4/(r-1) ar^2 = ar + 9 ar^2 - ar = 9 a = (9/(r^2 - r) so 9/(r^2-r) = 4/(r-1) 4r^2 - 4r = 9r - 9 4r^2 - 13r + 9 = 0 (4r - 9)(r - 1) = 0 r = 9/4 or r = 1 if r = 9/4, a = 4/(9/4 - 1) = 16/5 the first 3...
February 15, 2015

math
.6/1 = 384/x x = 384/.6 = 640 the gas occupies 640 cm^3 in the can volume of can = πr^2 h π(3.2^2)h = 640 h = 640/(10.24π) = 19.89 cm
February 15, 2015

math
let's pick one particular suit, say the hearts to get the above in that order: prob = (1/52)(1/(51)(1/50)(1/49)(1/48) = 1/311875200 but there are 4 such suits prob(of your event) = 4/311875200 = 1/77968800
February 14, 2015

Pythagoras
Hope you made a sketch. In mine I can use the cosine law let the distance from the starting point be x x^2 = 520^2 + 387^2 - 2(520)(387)cos45° = 135572.6627 x = √.... = 368.2 km
February 14, 2015

Algerba
dimes ---- x quarters ---- x+10 nickels ---- 2(x+10) = 2x+20 10x + 25(x+10) + 5(2x+20) = 575 10x + 25x + 250 + 10x + 100 = 575 45x = 225 x = 5 So he has 5 dimes, 15 quarters and 30 nickels check: 5 dimes = 50 cents 15 quarters = 375 cents 30 nickels = 150 cents total = 575 ...
February 14, 2015

Calculus
I took out the highest common factor
February 14, 2015

Calculus
no, you have to use the product rule f(x) = (7^x)(x^7) f ' (x) = (7^x)(7x^6) + (x^7)(ln7)(7^x) = (7^x)(x^6) (7 + x ln7)
February 14, 2015

Calculus
Why are you using days when t was defined in years so t = 1/2 f ' (1/2) = -9 e^(-3(1/2)) = -9 e^(-1.5) = appr -2.008
February 14, 2015

Finance
let the quarterly rate be i then (1+i)^4 = (1+.07/12)^12 take 4th root of both sides 1+i = 1.0058333..^4 1+i = 1.023538 i = .023538 or 2.3538% per quarter times 4, gives us 9.4153% per annum compounded quarterly.
February 14, 2015

Finance
Don't know what EAR is, but I will assume your rate is 11% per annum compounded semi-annually i = .11/2 = .055 PV = 1000(1 - 1.055^-10)/.055 = 7537.63
February 14, 2015

Finance
assuming payments at the end of the day. 100(1 - 1.0006^-n)/.0006 = 27500 1 - 1.0006^-n = .165 1.006^-n = .835 log both sides and use log rules -n(log 1.0006) = log .835 -n = -300.6 300 full daily payments of $100 plus a partial payment on the 301st day.
February 14, 2015

Math
When they "meet" the difference in their travel time is 20 minutes or 1/3 of an hour let the distance from from Tigersville be x x/85 - (154-x)/60 = 1/3 times 1020 , the LCM of 85, 60 and 3 12x - 17(154-x) = 340 12x - 2618 + 17x = 340 29x = 2958 x = 102 time for ...
February 14, 2015

Finance
good question. must find the monthly payment. i = .0675/12 = .005625 (I stored that in my calculator) n = 12x30 = 360 let the payment be p p(1 - 1.005625)^-360)/.005625 = 249000 p = 1615.01 first month interest = .005625(on full amount) = 1400.63 so split-up of first payment: ...
February 14, 2015

Finance
You did not state how each of the rates are compounded, that is critical
February 14, 2015

Math
using de Moivre's Theorem: let z^4 = -46 + 9i changing -46 + 9i to rectangular form r = √46^2+9^2 =√2197 tanØ = 9/-46 Ø = 168.9298° z^4 = √2197(cos168.9298° + i sin 168.9298°) z = ..... so there will be 4 roots, z = √2197^(...
February 14, 2015

Calculus
simplify it ... f(x) = √(sinxcosx) = √( (1/2)(sin(2x) ) = 1/√2 (sin(2x))^(1/2) f ' (x) = (1/√2)(1/2)(sin(2x))^(-1/2)(2cos(2x)) = (1/√2) (cos 2x)/(sin 2x) = 1/√2 cot (2x) or , the way it stands f(x) = (sinxcosx)^(1/2) f ' (x) = (1/2)(...
February 13, 2015

Calculus
1) in that case why not just write the exponent as -5x ? y = 5 e^(-5x) y' = -25 e^(-5x) 3. but your answer resembles the other interpretation, for which I gave you a solution. I stand by that answer.
February 13, 2015

Calculus
1) if you have a function f(x) , what is that 9z doing there in the exponent? 2) yes 3.) is that a stair-case exponent or is it f(x) = (e^x)^-1 ? = e^-x ? on the other hand, Wolfram read your equation as y = e^(1/x) http://www.wolframalpha.com/input/?i=plot+y+%3D+e%5Ex%5E-1 in...
February 13, 2015

Calculus help and please check answer for a)
a) correct b) since you want the rate at a time of t, your derivative is your answer c) you would sub t = 3 into the derivative, the rate of change, that you found in b)
February 13, 2015

math calculus
then go with Steve's suggestion and plot the two curves y = 2^x and y=(1/2)^x to see the result http://www.wolframalpha.com/input/?i=plot+y+%3D+2%5Ex+%2C+y+%3D+%281%2F2%29%5Ex
February 13, 2015

math calculus
the difference between the function 2^x and (1/2)^x = |2^x - (1/2)^x| = | 2^x - 2^-x |
February 13, 2015

algebra
8 + (1/3)(6-p) or to be more specific 8 + (1/3)|6-p|
February 13, 2015

Calculus
So they will need as much in the account to annually generate 10,000 in interest x e^.08 - x = 10000 x(e^.08 - 1) = 10000 x = 10000/(e^.08 - 1) = $120,066.66 Since G is supposed to in thousands G ≥ 120.06666 check: amount of the 120066.66 after 1 year of continuous ...
February 13, 2015

calculus- min value of function
f(x) = sinxcosx = (1/2) sin (2x) by a common identity At this point I have my answer. y = (1/2)sin(2x) has an amplitude of 1/2 that is , its maximum is 1/2 and its minimum is -1/2
February 13, 2015

Algebra 2
.......... D ..R ...T You 60 x+10 60/(x+10) Marley 50 x 50/x 50/x - 60/(x+10) = 2 times x(x+10) 50(x+10 - 60x = 2x(x+10) 50x + 500 - 60x = 2x^2 + 20x 2x^2 + 30x - 500 = 0 x^2 + 15x - 250 = 0 (x+25)(x-10) = 0 x = 10 or x = -25, the latter being silly Marley went 10 mph on a ...
February 13, 2015

pre- calculus
treat the "mother and father" as one entity. So we are arranging 5 around the table which is 5! but we can rotate each particular arrangement 5 times around the table without changing any order, since there is no specified position around the table (e.g. everybody ...
February 13, 2015

GS not AS - maths
in a GS 3rd term = ar^2 = 12 6th term = ar^5 = 96 divide them r^3 = 96/12 = 8 r = 2 then in ar^2 = 12 4a = 12 a = 3 so you have 3 + 6 + 12 + ... +(the last value before 2000) so term(n) = ar^(n-1) < 2000 3(2^(n-1) ) = .. if n = 9, 3(2^8) = 768 n = 10 , 3(2^9) = 1536 n = 11...
February 13, 2015

math
the new equation will differ from the old equation only in the constant so new: x+2y = c , but (5,-2) is on it, so 5-4 = c = 1 x + 2y = 1
February 12, 2015

math
Assume Aaron had x dollars he gave 3/7 x away, so he has 4x/7 left. he gives 1/4 of what he has left to his sister, so he has (3/4)(4x/7) left (3/4)(4x/7) = 120 12x/28 = 120 x = 120(28/12) = $ 280
February 12, 2015

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