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March 23, 2017

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Posts by Reiny

Total # Posts: 38,061

math
a = 16 ar^4 = 9 sub in a = 16 16r^4 = 9 4r = ± 3 r = ± 3/4 7th term = ar^6 = 16(±3/4) = 16(729/4096) = 729/256
January 4, 2017

Math
length of BC = ?( (5-1)^2 + (1-3)^2) = ?(16+4) = ?20 = 2?5 since BM = (1/2)BC BM = ?5
January 4, 2017

Statistics
number of two-digit numbers: 10, 11, ... , 99, ----> 90 of them (1 - 9 are missing) smaller than 20: 10,11, ... , 19 ----> 10 of them prob( < 20) = 10/90 = 1/9 use the same type of analysis for the two other parts, let me know what you get.
January 4, 2017

Maths
solve: 4x - 23 = (1/3)(54)
January 4, 2017

Maths
looks like your standard: x = my + b case1: y = 2 when x = 15 15 = 2m + b ** case2: y = 4 when x = 27 27 = 4m + b *** subtract ** from *** 12 = 2m m=6 from ** 15 = 12+b ---> b=3 x = 6y + 3 when y = 7 x = 42+3 = 45
January 4, 2017

Math
new length = 1.15(8) = ... new width = ....
January 4, 2017

maths
original dimensions ---- w by l original area = wl new width = 9w/10 new length = L L(9w/10) = lw L = lw/(9w/10) = (10/9)l = 1.111.. so the length would have to increase, not be reduced, as your question stated. The increase is 10/9 of the original or appr 11.1% check: if wl ...
January 4, 2017

Maths
(4/3) ? r^3 = 250?/3 4?r^3 = 250? r^3 = 250/4 or 500/8 r = 500^(1/3) / 2 SA = 4? r^2 = 4? (500)^(2/3) / 8 = (1/2)(500)^(2/3) ?
January 3, 2017

Algerbra
The two areas of similar objects are proportional to the square of their corresponding sides. The two volumes of similar objects are proportional to the cubes of their corresponding sides. sides of model^2 : sides of statue^2 = 6 : 253.5 side of model : side of statue = ?6 : ?...
January 3, 2017

Maths
looks like your base is x-2 and the height is x, so (1/2)(x)(x-2) = 2.5 x(x-2) = 5 x^2 - 2x - 5 = 0 solve for x and take it from there
January 3, 2017

Mathmatics
Just re-arrange it .... 3x^2 - x^3 + 3 = 0 -x^3 = -3x^2 - 3 x^3 = 3x^2 + 3 divide both sides by x^2 x = 3 + 3/x^2 let x = 3.2 RS = 3+ 3/10.24 = 3.29296875 sub that into the RS RS = 3 + 3/(3.2929...)^2 = 3.276659... new RS = 3.279420685 new RS = 3.278950402 new RS = 3.279030424...
January 3, 2017

Maths
your sequence has a = 7, d = 6 term(n) = a+(n-1)d = 7 + 6(n-1) = 7 + 6n - 6 = 6n + 1 term(n+1) = a + (n-2)d = 7 + 6(n-2) = 7 + 6n - 12 = 6n - 5 (6n+1)^2 - (6n-5)^2 = 36n^2 + 12n + 1 - (36n^2 - 60n + 25) = 72n - 24 = 24(3n - 1) which is clearly a multiple of 24 (anything ...
January 3, 2017

Math
make a sketch and use a simple ratio: h/55 = 8/11 solve for h
January 3, 2017

Math
f (g(x) ) = (1 + g(x) )/(1 - g(x) ) = (1 + x/(1-x) / (1 - x/(1-x) ) multiply top and bottom by (1-x) = (1 - x + x) / (1 - x - x) = 1/(1 - 2x) check: let x = 2 g(2) = 2/(1-2) = -2 f(g(2)) = f(-2) = (1-2)/(1+2) = -1/3 in mine f(g(2)) = 1/(1-4) = -1/3 it is "highly likely&...
January 3, 2017

geometry
Follow similar steps I used in your previous post. Make sure you use the definition of supplement of an angle.
January 3, 2017

geometry
let the angle be x then its complement is 90-x 90-x = x + 18 -2x = -72 x = 36 check: the angle is 36° and its complement is 54° which is 18° more than 36°
January 3, 2017

Geometry
first transformation: (x,y) ---> (x+5,y) (-3,-3) ----> (2,-3) second transformation: reflection in y = 1 (x,y) ---> (x, 2-y) (2,-3) ----> (2, 5) A' is (2,5)
January 2, 2017

Kudos for Steve
What a splendid observation ! Ignore my gibberish, it must contain an error somewhere anyhow.
January 2, 2017

maths
tanx - ?3 + tan2x + ?3tanx tan2x = 0 tanx - ?3 + tan 2x(1 + ?3tanx) = 0 recall tan 2x = 2tanx/(1 - tan^2 x) tanx - ?3 + 2tanx/(1 - tan^2 x)(1 + ?3tanx) = 0 times (1 - tan^2 x) tanx - tan^3 x - ?3 + ?3tan^2 x + 2tanx(1 + ?3tanx) = 0 let tanx = y for easier typing y - y^3 - ?3...
January 2, 2017

algebra
Can you think of 2 numbers which have a sum of 11 and when multiplied give a product of -42 ? how about -3 and +14 ? Now form the factors
January 2, 2017

algebra
Steve answered this same question for you over a week ago http://www.jiskha.com/display.cgi?id=1482520904
January 2, 2017

math
looks like you defined the larger as x and the smaller as y so x - y = 26 is correct then.... "one number is three times the other " ---> x = 3y now sub that into the first equation: x - y = 26 3y - y = 26 2y = 26 y = 13 then x = 3y = 3(13) = 39
January 2, 2017

Algebra
Why not follow the same steps I showed you for the questions similar to this one. Let me know how you make out.
January 2, 2017

Math :)
It helps to make a sketch in this case, I assume you did that (-2,-1) ---reflect in y=-5 ---> (-2,-9) notice the midpoint of these points lies on y = -5 (-2,-9) ---reflect in x = 1)---> (4,-9) again, notice the midpoint of these two points lies on the line x = 1
January 2, 2017

trigonomentry
looks like your equation to solve is incomplete.
January 2, 2017

Math
Just like in trigonometry, a counterclockwise rotation is considered positive.
January 2, 2017

Algebra
Start with what I gave you here: http://www.jiskha.com/display.cgi?id=1483383485 Pick any two points on y = ?x e.g. (9,3) and some other point find the equation of the straight line passing through two points, and you are done
January 2, 2017

math
"the fifth term of an arithmetic progression is 19" ----> a+4d = 19 " the fourteenth term is 55" ----> a+13d=55 subtract the two equations: 9d = 36 d = 4 in a+13d = 55 a + 13(4) = 55 a = 3
January 2, 2017

Algebra
try y = ?x and y = (1/4)x + 1 see: http://www.wolframalpha.com/input/?i=y+%3D+%E2%88%9Ax+,+y+%3D+(1%2F4)x+%2B+1
January 2, 2017

Math
15 metres is 1500 cm. So what is 1500/75 ? This is a silly question. The snowball would have hit the ground long before it traveled 15 m due to gravity. The speed of 75 cm/s is way too slow.
January 2, 2017

Math
What a sucker you would be to play this game! the expected winnings on one play is 15 cents. You are playing this 30 times, so your can expect to win $4.50 , but you spent $30 to play those games.
January 2, 2017

@ R
Why did you repost this question ?? Just noticed that Steve answered it for you several days ago http://www.jiskha.com/display.cgi?id=1483135842
January 2, 2017

Math
Assuming you meant: f(x)=?x^3 ?x^2 +16x+16 f ' (x) = -3x^2 - 2x + 16 f ''(x) = -6x - 2 If you are studying Calculus or Pre-Calculus, you MUST know how to do this. if f(x) = 0 ?x^3 ?x^2 +16x+16 = 0 x^3 + x^2 - 16x - 16 = 0 by grouping, x^2(x+1) - 16(x+1) = 0 (x+1)(x...
January 2, 2017

Math
No idea what a "tape diagram" is, but the question is easy to solve in the traditional way: number of adults ---- 45 number of students ---- 90 Just noticed that there is NO question in your post. If you want the return for the museum Return = 25(45) + 12(90) = $2205
January 2, 2017

math C2 sequences and series
8th term of AS = a+7d 4th term of AS = a+3d 2nd term of AS = a+d then, if they form the first three terms of a GS (a+3d)/(a+7d) = (a+d)/(a+3d) (a+3d)^2 = (a+7d)(a+d) a^2 + 6ad + 9d^2 = a^2 + 8ad + 7d^2 2d^2 - 2ad = 0 d(d-a) = 0 d = 0 or d = a but we are told that d ? 0 , so d...
January 2, 2017

Math
what is 100000(.95)^2 ?
January 1, 2017

Math
let the number be x 1/(x-4) = 2(1/x) solve for x
January 1, 2017

Geometry
Did you know that the slope of a line equals the tangent of the angle that the line makes with the x-axis ? so tan45° = 1 so we know the slope of the line is 1 (-5-5)/(a-4) = 1 a - 4 = -10 a = -6 Check with a quick sketch of the situation.
January 1, 2017

math
Even though with only 3 terms, 20 + 12 + 36/5 + .... seems to be the sum of an infinite series with a = 20 and r = .6 Sum(all terms) = a/(1-r) = 20/(1-.6) = 20/.4 = 50 btw, " ---tend as n" makes no sense.
January 1, 2017

Math
4d^2= (d+4)(-d+12) 4d^2 = -d^2 + 12d - 4d + 48 5d^2 - 8dd = 48 d^2 - (8/5)d = 48/5 d^2 - (8/5)d + 16/25 = 48/5 + 16/25 (d - 4/5)^2 = 256/25 d - 4/5 = ± 16/5 d = 4/5 + 16/5 OR d = 4/5 - 16/5 d = 4 or d = -12/5
January 1, 2017

math
Well, did you use your graph as instructed? What did you get?
January 1, 2017

Math
let the tens digit be x, and the unit digit be y So the number is 10x + y, the number reversed is 10y + x 10x+y - (10y+x) = 9 9x - 9y = 9 x - y = 1 or x = y+1 ** 2x = 7y-8 sub in ** 2(y+1) = 7y - 8 2y + 2 = 7y - 8 -5y = -10 y = 2 The number is 32 check: the number reversed is ...
January 1, 2017

math(geometric series)
2nd term is 3/2 --- ar = 3/2 sum of all terms is 8 a/(1-r) = 8 divide the first equation by the 2nd equation: (ar) / (a/(1-r)) = (3/2) / 8 r(1-r) = 3/16 r - r^2 = 3/16 3 = 16r - 16r^2 16r^2 - 16r + 3 = 0 (4r - 1)(4r - 3) = 0 r = 1/4 or r = 3/4 check for r = 1/4 a(1/4) = 3/2 a...
December 31, 2016

math(A.P/G.P)
Shall I assume that 2% p.a C.I means 2% per annum compounded instantaneously ? the amount = 55 e^.02t if 2005 ---> t = 0 then 2015 --- t = 10 amount = 55 e^(.02(10)) = 67.177 crores (is 1 crore equal to 10 million? I see one answer as 6700, but that would not match your ...
December 31, 2016

Algebra
for 1st series: first term is a, common difference is d sum(n) = (n/2)(2a + d(n-1)) for 2nd series: first term is b, common difference is e sum(n) = (n/2)(2b + e(n-1)) (n/2)(2a + d(n-1)) / (n/2)(2b + e(n-1)) = (7n+1)/(4n+27) (2a + dn - d)/ (2b + en- e) = (7n+1)/(4n+27) 8an + ...
December 31, 2016

Math
The way you typed it, and following the order of operation ... 100-100/100-100 = 100 - 1 - 100 = -1
December 29, 2016

mathematics
look at the second part of this post http://www.jiskha.com/display.cgi?id=1482579345
December 24, 2016

maths
No zero in single digit numbers For double digit numbers: 10, 20 .. , 90 ---> 9 of them triple digits: using 2 zeroes: 100, 200, 300, 400, 500 --- 10 of them using 1 zero: case 1: the zero in 2nd place = 5 x 1 x 9 = 45 case 2: the zero in 3rd place = 5 x 9 x 1 = 45 total = ...
December 24, 2016

MATH
The change is caused by the term -3x Since you are "decreasing" x by 2 we sub in x = -2 so y = 42 - 3(-2) = 42 + 6 thus the change is 6
December 24, 2016

ellipse
alternate solution for B: let's "move" everything to standard position using (x,y) ---> (x+1, y-2) centre (-1,2) ---> centre (0,0) F(-1,5) ----> focus( 0, 3) , so c = 3 P(5,6) -----> P' (6, 4) b^2 = a^2 + c^2 = a^2 + 9 starting equation: x^2 /a^2...
December 24, 2016

ellipse
A) centre at (-2,3) --> (x+2)^2 /a^2 + (y-3)^2 / b^2 = 1 focus at (-2,7) implies the ellipse is vertical and c = 7-3 = 4 vertex is (-2,10) , so a = 10=3 = 7 and a^2 + c^2 = b^2 7^2 + 4^2 = b^2 = 65 (x+2)^2 /49 + (y-3)^2 / 65 = 1 B) centre (-1,2) ---> (x+1)^2/a^2 + (y-2)^...
December 24, 2016

algebra
I see 2c^3 as a common factor = 2c^3(a^2 - 7b + 16d^2)
December 22, 2016

math
a1 = 13 a2 = 15 = a1 + 2 a3 = 17 = a2 + 2 ... an = an-1 + 2 , n > 1
December 22, 2016

small correction - QUADRILATERAL MATHS
For the last method, I meant to say : " list the coordinates of the quadrilateral counter-clockwise starting with any point in a column. "
December 22, 2016

QUADRILATERAL MATHS
There are several ways to do this: 1. If you join AC, you have a right-angled triangle ABC. Find the length of AB and BC and use area = (1/2)base x height for its area. Find angle D by using the slopes of AD and CD, find the lengths of CD and AD , then area of triangle ACD = (...
December 22, 2016

math
look at the last 4 answers below under Related Questions.
December 22, 2016

math
Sketch your three intersecting circles, V, B, and T place 20, 10 and 6 in the "only" part of the circles. Place 4 in the intersection of all circles. Place x in the remaining parts of the circle. Add up all the parts: x + x + x + 4 + 20 + 10 + 6 = 70 3x + 40 = 70 3x...
December 22, 2016

calculus
looks like a homework dump. Five questions without showing us any of your starting steps or any indication where your problems lie with these questions.
December 21, 2016

calculus
find the derivative, set that equal to zero and solve for x sub back into original f(x) to find the matching y values. also find the end values of f(-2) and f(4) , then decide which are your max/mins.
December 21, 2016

calculus
let the two numbers be x and y xy = 16 y = 16/x Let S be the sum of their squares S = x^2 + y^2 = x^2 + 256/x^2 = x^2 + 256x^-2 dS/dx = 2x - 512x^-3 = 2x - 512/x^3 = 0 for a min of S 2x = 512/x^3 2x^4 = 512 x^4 = 256 x = ±4 then 16/±4 = ±4 the two numbers ...
December 21, 2016

math
Or did you notice that each of the given numbers is one more than the perfect square, that is 2 = 1^2 + 1 5 = 2^2 +1 10 = 3^2 + 1 17 = 4^2 + 1 thus: term(n) = n^2 + 1
December 21, 2016

math connections
solve -4n + 7 + 2n=1 ---> -2n = -6 n = 3 solve 4(y-4)=8 divide by 4 y-4 = 2 y = 6
December 21, 2016

Math
let the distance traveled by car X be x km let the distance traveled by car Y by y km their paths form a right-angled triangle. Let the distance between them be D km D^2 = x^2 + y^2 2D dD/dt = 2x dx/dt + 2y dy/dt dD/dt = (x dx/dt + y dy/dt)/D at the given case: x = 60, y = 80...
December 20, 2016

math
effectively he gains 10 m every 2 minutes but for the last 10 m he does not have to rest 1 minute to reach his goal. That is, at the end of 2 minutes, he has gone 10 m 4 minutes, he has gone 20 m ... 36 minutes, he has gone 180 m Since he can swim 20 m per minute, he will ...
December 20, 2016

pre calculus
Ok, Meredith, after doing this one for you http://www.jiskha.com/display.cgi?id=1482199382 surely you can follow the same steps for this one.
December 19, 2016

Business Finance
ummmhhh, for 5 years, for 2 years, for 20 years ??? The question is incomplete.
December 19, 2016

Business Finance
You did not state the time period
December 19, 2016

math
Prob(sum of 2) = 1/36 prob(sum of 3 ) = 2/36 prob(sum of 4) = 3/36 prob(sum of 5) = 4/36 prob(sum of 6) = 5/36 prob(sum of 7) = 6/36 ... sum of 8 = 5/36 ... sum of 9 = 4/36 ... sum of 10 = 3/26 ... sum of 11 = 2/36 ... sum of 12 = 1/36 notice the sum of these prob's is 1 ...
December 19, 2016

Maths
I will do the first one, you do the other two in the same way. let the width be x let the length be 2x, notice x : 2x = 1 : 2 2(x) + 2(2x) = 30 5x = 30 x = 6 sides are 6 cm and 12 cm, with an area of 72 cm^2
December 19, 2016

business math
i = .055/365 = .000150684 amount after 21 days = 6000(1.000150684)^21= 6019.01 So what interest did she earn ?
December 19, 2016

Write the system of equations as an augmented matr
-4 -1 | -6 -8 -5 | -6
December 19, 2016

Pre calculus
recall: sinØ = y/r and cosØ = x/r so: r= 5/(sin theta +2cos theta) r = 5/(y/r + 2x/r) r = 5/((2x+ y)/r) r = 5r/(2x + y) 1 = 5/(2x+y) 2x + y = 5 <----- a straight line proof: http://www.wolframalpha.com/input/?i=polar+plot+r%3D+5%2F(sin+theta+%2B2cos+theta)
December 19, 2016

data management gr.12
Your question is perfectly suited for this applet http://davidmlane.com/normal.html Just enter your data
December 19, 2016

pre calculus
Steve has the correct equation. I don't know why my 8 was dropped in my 3rd last line, just careless.
December 19, 2016

pre calculus
from your previous question, recall sinØ = y/r --> y = rsinØ cosØ = x/r --> x = rcosØ (x-4)^2+y^2=16 (rcosØ -4)^2 + r^2sinØ = 16 r^2 cos^2 - 8rcosØ + 16 + r^2sin^2 Ø = 16 r^2 (cos^2 Ø + sin^2 Ø) - rcos...
December 19, 2016

data management gr.12
See the webpage I gave you in your other post
December 19, 2016

Trigonometry
tan(Ø - 30) = -5 we know tan 78.69° = +5 and since the tangent of our given angle of Ø-30 is negative it must be quadrants II or IV Ø-30 = 180-78.69 = 101.31 Ø = 101.31+30 = 131.3° ir Ø-30 = 360 - 78.69 = 281.3 Ø = 311.3°
December 19, 2016

Engineering Mathematics-I
First you need the intersection (2x^2)^2 = 4x 4x^4 - 4x = 0 x(x^3 - 1) = 0 x=0 or x = 1 see: http://www.wolframalpha.com/input/?i=y%3D2x%5E2+,+y%5E2%3D4x effective height = ?(4x) - 2x^2 = 2 x^(1/2) - 2x^2 area = ?(2 x^(1/2) - 2x^2) dx from x = 0 to 1 = [ (4/3)x^(3/2) - (2/3)x^...
December 17, 2016

Maths
original fraction ----- 5x/2x new fraction: (5x+5)/(2x-2) I can't make out what 15 4 is supposed to be. Once you have decided, set that equal to (5x+5)/(2x-2) , looks like you would just cross-multiply to solve
December 17, 2016

Math
width --- 5x length ---8x (5x)(8x) = 169 40x^2 = 169 x^2 = 169/40 x = 13/?40 width is 65/?40 = appr 10.28 length is 104?40 = appr 16.44 check: area = (65/?40)(104/?40) = 6760/40 = 169 ratio = (65/?40) : 104/?40) = 65 : 104 = 5 : 8
December 16, 2016

math-circles
The areas of two circles are proportional to the square of their raddi so r1^2 / r2^2 = 9/4 r1/r2 = 3/2 r1 = 3r2/2 also r1 = r2 + 2 Thus: 3r2/2 = r2 + 2 3r2 = 2r2 + 4 r2 = 4 then r1 = 6 the larger radius is 6 units check: area of larger = 36? area of smaller is 16? ratio of ...
December 16, 2016

Math
sequence is : 3/4 , 1/4, 1/12, 1/36 = 27/36 , 9/36, 3/36, 1/36, ... = (1/36){ 27, 9, 3, 1, ......} can you see the pattern in 27, 9, 3, 1, .... ??
December 16, 2016

maths
volume of original sphere = (4/3)? R^3 volume of each of the 1000 smaller ones = (4/3000)? R^3 = (1/750) ? R^3 let the radius of the smaller be r 4/3 ? r^3 = (1/750) ? R^3 r^3 = (1/1000) R^3 r = R/10 surface area of smaller = 4? r^2 = 4? R^2/100 = ? R^2/25
December 16, 2016

Math
first number ---- x 2nd number ----- x+5 x + x+5 = 57 carry on
December 16, 2016

Math algebra
A quick check with your notes or textbook would have shown this to be a clear case of the distributive property.
December 16, 2016

precalculus
#1 term(5) = C(8,4) (2x)^4 (-4)^4 = 70(16x^4)(256) = 286720 x^4 <-------- B general term of (a+b)^n: term (k+1) = C(n,k) * (a)^(k-1) * b^k #2, correct
December 16, 2016

math
4/9 b^6 = (2/3 b^3)^2
December 16, 2016

calc
x/8 - (2/9)y dy/dx = 0 dy/dx = (x/8) / (2y/9) = 9x/(16y) at (4?2,3), dy/dx = 36?2/(48) = 3?2/4 equation: y - 3 = (3?2/4)(x - 4?2) clean it up to whatever form is needed. Proof: http://www.wolframalpha.com/input/?i=plot+(x%5E2%2F16)-(y%5E2%2F9)%3D1+,+y+-+3+%3D+(3%E2%88%9A2%2F4...
December 15, 2016

Physics- Car moving with speed of 22 m/s...
acceleration --- (-a) velocity = -at + c when t = 0, v = 22 22= 0+c ---> c = 0 v = -at + 22 when t = 6.5, v = 0 0 = -6.5a + 22 a = 22/6.5 = 44/13 distance = d = (-1/2)a t^2 + 22t + k d = (-22/13)t^2 + 22t + k when t = 0, d = 0, so k = 0 when t = 0 , d = 0 when t = 6.5, d...
December 15, 2016

algebra
(4.2*10^2)(4.2*10^5) = 17.64 x 10^7 = 1.764 x 10^8
December 15, 2016

algerbra
h(t) = -16t^2 + 96t 144 = -16t^2 + 96t t^2 - 6t + 9 = 0 (t-3)(t-3) = 0 t = 3
December 15, 2016

math
After giving .3x of the flowers to her sister Fariza has .7x of them left over giving (4/7) to her brother leaves her with (3/7)(.7x) (3/7)(.7x) = 45 .3x = 45 x = 150 she kept 45/150 or 30% of them for herself She had 150 of them the sister got (.3)(150) or 45 the brother got...
December 15, 2016

math
What Ms Sue is saying is .... y = 3x + 3
December 15, 2016

Calculus
Ok, so the second derivative is negative and you know that if the 2nd derivative is negative the function is concave downwards. Of course you should recognize that we are dealing with a quadratic function, a parabola, which opens downwards for all values of x
December 15, 2016

MATH HELP PLEASE
For any number to be divisible by 9, the sum of its digits must be divisible by 9 So far we have a sum of 16, so we need a 2 21258 is divisible by 9 Surely you know how to do the other two questions.
December 15, 2016

Zee school , math subject.
What is the area of the original sheet ? What is the area of one of the squares to be cut out? How many of those cut-out squares are there? What is left over after we cut them out? ... etc. I'll wait for your reply and check your answers.
December 15, 2016

Math grade 6, ratio
number of oranges --- x after give-away number of oranges = x-10 number of pears = 24 and he had twice as many pears as oranges 24 = 2(x-1) 2x - 2 = 24 x = 13 ratio of oranges : pears = 13 : 24
December 15, 2016

Math grade 6, ratio
current count: boys --- 4x girls ---- 3x 4x = 3x + 6 x = 6 there were 24 boys and 18 girls after 2 girls are added, new ratio is 24 : 20 = 6 : 5
December 15, 2016

math
let the 3 numbers be x, x+1, and x+2 2(x+2) + x = 4(x+1) - 15 solve for x, then sub into my definitions
December 15, 2016

Math grade 6, ratio
Number of stamps for david -- 4 x number of stamps for Tim = 3x after give-away, Tim has 1.5x David has 5.5x ratio of Tim : David = 1.5x : 5.5x = 1.5 : 5.5 = 15 : 55 = 3 : 11
December 15, 2016

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