Saturday

February 28, 2015

February 28, 2015

Total # Posts: 29,207

**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*

**linear algebra**

and we both called the variables a, b, and c What's that old saying, something about great minds, lol
*February 12, 2015*

**linear algebra**

I will use a, b, and c, instead of c1, c2 and c3 a(3,3,-1) + b(1,2,-3) + c(-11,-13,9) = (0,0,0) 3a + 2b - 11c = 0 3a + 2b - 13c = 0 -a - 3b + 9c = 0 subtract 2nd from 1st 2c = 0 c = 0 sub into 2nd and 3rd 3a + 2b = 0 -a - 3b = 0 triple the 3rd: -3a - 9b = 0 3a + 2b = 0 -7b = 0...
*February 12, 2015*

**math**

The only tricky part in this question is to ignore data which is irrelevant, like the 6 ft girl's initial mirror placement. The only fact we care about is that we have two similar right-angled triangles, formed by the second student and the mirror, and the tree and the ...
*February 12, 2015*

**math**

current price of ticket = $2.00 number of sales = 600 let the number of 50 cent increases be n price per ticket = 2 +.5n number of sales = 600-30n income = (2+.5n)(600-30n) = 1200 - 60n + 300n - 15n^2 = 1200 + 240n - 15n^2 not sure if you know Calculus, so I will not use that ...
*February 12, 2015*

**Calculus**

did you mean something like y = √( (x^2 + 5x)/(5x) ) original form derivative: dy/dx= (1/2)((x^2+5)/(5x))^(-1/2) ( 5x(2x) - (x^2+5)(5))/(25x^2) etc , but still has to be simplified using logs first: take ln of both sides: ln y = ln((x^+5)/(5x))^(1/2) = (1/2)(ln (x^2+5...
*February 12, 2015*

**math**

ahh, I see you corrected it 1st: length -- 3x width ---2x area = 6x^2 2nd : lenth : width = 3y : 2y area = 6y^2 but length of larger : length of smaller = 7:5 3y : 3x = 7 : 5 y/x = 7/5 y = 7x/5 so area of 2nd = 6(7x/5) = 294x^2/25 larger area / smaller area = (294x^2/25) / 6x^...
*February 11, 2015*

**Find the domain of the function**

remember we can't divide by zero so anything goes for the x, except 0 Write that up in the format that you have learned.
*February 11, 2015*

**math**

first: length -- 3x width --- 2x area = 6x^2 2nd: ??? "The ratio of the length of the larger is 7:5" don't know what that means
*February 11, 2015*

**Math**

a) you would simply choose 3 of the 11 = C(11,3) = 165 b) 3 men of 5, 4 women of 6 = C(5,3) x C(6,4) = 10x15 = 150
*February 11, 2015*

**Math (Interest)**

yes, it would be 18.6387 since the time is so short, it is no surprise that the two answers are the same
*February 11, 2015*

**Math (Interest)**

don't make it look so complicated i = .025/12 = .00208333.. (I use my calculator's memory to store such numbers, don't round them off yet) amount = 18.6(1.00208333...)^1 , for 1 month = 18.6(1.00208333.. = $ 18.64 Wow, we gained 4 cents interest !
*February 11, 2015*

**Algebra**

let x^(1/4) = k then we have k^2 - 7k + 12 = 0 (k-3)(k-4) = 0 k = 3 or k = 4 x^(1/4) = 3 or x^(1/4) = 4 x = 81 or x = 256
*February 11, 2015*

**perpendicular vectors**

Nice !
*February 11, 2015*

**linear algebra**

I will read that as [(a -b) -3] = [7 (a+b)] then a-b=7 a+b=-3 add them 2a = 4 a = 2 and then 2+b=-3 b = -5
*February 11, 2015*

**MATH**

100^2 ÷ 10^-5 = 10^4/10^-5 = 10^9 , which is 1 billion times as large
*February 11, 2015*

**math**

width -- x length -- 2x+1 x+x + 2x+1 + 2x+1 = 29 6x+2=29 take over Just realized I used x instead of w, no big deal.
*February 11, 2015*

**Algebra 1**

width --- x length --- 2x+4 (17)(x)(2x+4) = 2720 x(2x+4) = 160 2x^2 + 4x - 160=0 x^2 + 2x - 80 = 0 (x+10)(x-8) = 0 x = -10 , which would make no sense or x = 8 The box is 8 inches wide check: w=8 l= 20 h=17 V = 8x20x17=2720 All looks good
*February 11, 2015*

**Algebra**

I suggest googling "factoring trinomials" or "factoring quadratic trinomials" Also there are many good youtubes and Khanacademy has many clips to show you how.
*February 11, 2015*

**Algebra**

if you mean factored form, then = (2x+1)(3x+2)
*February 11, 2015*

**Algebra 1**

there is no solution in the set of real numbers, but there are two complex number solutions. see: http://www.jiskha.com/display.cgi?id=1362104847
*February 11, 2015*

**Algebra 1**

there are two solutions x^2 + 6x + 5 = 0 (x+1)(x+5) = 0 x = -1 , you had that one or x = -5
*February 11, 2015*

**Algebra 1**

take 1/2 of the middle term coefficient and square that number (1/2)(11 = 11/2 squared gives us 121/4 so x^2 + 11x + 121/4 = (x+11/2)^2 so n = 121/4 or 30.25 if you want a decimal
*February 11, 2015*

**algebra**

let her initial speed be x mph time for first trip = 320/x new speed = x+10 mph time for second part of trip = 500/(x+10) so.. 500/(x+10) - 320/x = 2 times x(x+10) 500x - 320(x+10) = 2x(x+10) 500x - 320x - 3200 = 2x^2 + 20x 2x^2 - 160x + 3200 = 0 x^2 - 80x + 1600 = 0 (x-40^2...
*February 11, 2015*

**math**

.342 = 342/1000 so its reciprocal is 1000/342 = 500/171
*February 11, 2015*

**Math - Answer Check**

all your answers are correct
*February 11, 2015*

**Algebra**

suppose something costs $x and you increase it by 5% doing it your ways: increase = .05x end result = x + .05x = x(1 + .05) = 1.05x so you get the result after anything is increased by 5% , just multiply by 1.05 or to get the result after anything is increased by 16% , just ...
*February 11, 2015*

**maths**

The LCM of 2, 3, 5, 7, and 12 is 420 So they will all fire together again 420 minutes, or 7 hours from now
*February 11, 2015*

**math**

Ok, I made a sketch and concluded that the angle at X is 150° Is there another question?
*February 11, 2015*

**Andrew , Meg, Sarah - math**

We are not going to do your assignment/homework for you. What have you learned from my previous answers so far?
*February 11, 2015*

**math**

same stuff (any reason why you switched names ?)
*February 11, 2015*

**math**

use the concepts I used in my previous answer to your similar question.
*February 11, 2015*

**math**

how about y = 3x^2/( (x-3)(x-6) )
*February 11, 2015*

**math**

Did you mean y = (3x+6)/(x-7) ?? Vertical asymptotes: What happens when the denominator is zero? For what value of x does this happen ? horizontal : Which terms fall by the wayside as x→∞ ? what remains of y = (3x ...)/(x ....) ?
*February 11, 2015*

**math**

by the "just look at it" theorem lim x→∞ sqrt(x^2+9) = x , so there is no limit e.g. let x = 1,000,000 ,using my calculator I got 1,000,000
*February 11, 2015*

**math**

I am sure you meant: lim (2- e^x)/(2+9e^x) divide each by e^x = Lim (2/e^x - 1)/(2/e^x + 9) now as x→∞ , e^x ---> 0 and we approach the value (0-1)/(0+9) = -1/9
*February 11, 2015*

**math**

area of original = 40(20) =800 cm^2 after cutoff, new size is 32 by 12 area of that = 32(12) = 384 cm^2 area of strip cut out = 800-384 = 416 cm^2
*February 11, 2015*

**maths(Probability)**

There are 36 ways for the 2 dice to fall (make yourself a 6by6 matrix) a) there is only one way to get a sum of 2 ---> 1,1 prob (a sum of 2) = 1/36 b) a sum of 7: 1 6, 2 5, 3 4, 4 3, 5 2, 6 1, so 6 ways prob(a sum of 7) = 6/36 = 1/6 c) a prime: the primes are 2, 3, 5, 7, or...
*February 11, 2015*

**math**

actually it should be -2 notice that x ---> negative infinity, so the x^3 is negative
*February 11, 2015*

**Calc**

There is no "formal" way to do this. One method is Newton's Method if you know Calculus Another way is to have a good calculator, and finetune your values of x e.g. let x = 1 LS = e^1 = 2.71828.. Rs = 4 let x = 2 LS = e^2 = 738 RS = 6 , ahh, I went too high let x...
*February 11, 2015*

**Algebra 1**

teams left after 1 week = 64 = 128(1/2) teams left after 2 weeks = 32 = 128(1/2)^2 .. teams left after 6 weeks = 128(1/2)6 = 2
*February 11, 2015*

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