Sunday

December 21, 2014

December 21, 2014

Total # Posts: 28,261

**Math help**

Since the angle of incidence is equal to the angle of reflection in the mirror you have tow similar right-angled triangles. Thus we can use our good ol' fashioned ratios x/7.5 = 5.5/3 3x = 41.25 x = 13.75 or 13.8 ft to the nearest tenth of a foot
*December 6, 2014*

**Algebra**

I don't think you are using the concept of the "inverse of a function" in the proper way, you are just solving the equation for c d = .15c - 1.5 .15c = d + 1.5 c = (d+1.5)/.15 now plug in d = 18 c = (18+1.5)/.15 = 130 We could have just plugged in d = 18 in the ...
*December 6, 2014*

**calculus**

you had ∫ e^(8x) (e^(8x) + e^(-8x) )/2 dx which is = ∫ ( e^(16x) + e^0 )/2 dx = (1/2)(1/16)e^(16x) + (1/2)x | from 0 to 1/16 = (1/2)(1/16) e^1 + 1/32 - (1/2)(1/16)e^0 - 0 = (1/32)e or = e/32
*December 6, 2014*

**capacity problems**

ummmh, what is 2 x 80 ??
*December 6, 2014*

**7th grade math**

#4 There are only 6 students, so just take (5/6)(120) = 100 so 100 prefer pepperoni #6. Taylor/Kate = 3/2 Taylor/120 = 3/2 2 Taylor = 360 Taylor = 180 #9 d) (-2/5) / (-1/5) = (-2/5)(-5/1) = 10/5 = 2 The others are correct
*December 6, 2014*

**algebra**

let the speed of the plane in still air be x mph let the speed of the wind be y mph then 570/(x+y) = 3 --->3x + 3y = 570 x + y = 190 570/(x-y) = 5 ---> 5x - 5y = 570 x - y = 114 add them 2x = 304 x = 152 back in the first: 152 + y = 190 y = 38
*December 6, 2014*

**algebra**

If you are taking Calculus .... E ' (v) = -.032v + 1.408 = 0 for max of E .032v = 1.408 v = 44 E(44) = ....just sub in
*December 6, 2014*

**maths**

Please proof-read your post before sending it route = root squre = square i/3 = 1/3 ?? So if 1/3 of the diagonal is 3√2, then the diagonal is 9√2 let the side of the square be x x^2 + x^2 = (9√2)^2 2x^2 = 162 x^2 = 81 x = √81 = 9
*December 6, 2014*

**Algebra**

notice you can take out r^2 as a common factor r^2(15.64 + 4.16) = 235.619 19.8 r^2 = 235.619 r^2 = 11.899945... r = appr 3.45 to the nearest hundredth
*December 6, 2014*

**Math Trig**

sec Ø = -13/5 in quad II so cosØ = -5/13 x = -5, r = 13 and y = +12 sinØ = 12/13 cotØ = -5/12
*December 5, 2014*

**math**

let the number of days be x let the rate per mile be $ y 4x + 450y = 244.5 3x + 200y = 149 1st times 3 ---> 12x + 1350y = 733.5 2nd times 4 --> 12x + 800y = 596 subtract them: 550y = 137.5 y = .25 sub back into 2nd 3x+200(.25) = 149 3x + 50=149 3x = 99 x = 33 The daily ...
*December 5, 2014*

**math help**

just replace you x with -7 and evaluate. you appear to have a typo
*December 5, 2014*

**Calculous Finding K, using zeros**

since as x ---> ± infinity, y --> + infinitey, the function must be of even exponent, so one of the roots must be a double root, as you have f(x) = k(x-3)(x+3)(x-5) but we are also told that the y-intercept is 17, so we have the point (0,17) on our polynomial. 17...
*December 5, 2014*

**Math Calculous**

so we have x-intercepts of 0 and 3 thus f(x) = kx(x-3) but (5,30) also lies on f(x), so ... 30 = k(5)(2) 10k = 30 k = 3 f(x) = 3x(x-3) or f(x) = 3x^2 - 9x
*December 5, 2014*

**Calculous (Finding Zeros!)**

Oh no, don't expand, then we would be in a real mess y = (x^2 + 2x - 5) (x^3 + 3x^2 - 40x) the first factor does not factor any more, so we use the quadratic equation to find two roots from there. x^2 + 2x - 5 = 0 x = (-2 ± √24)/2 = (-2 ± 2√6)/2...
*December 5, 2014*

**Pre-Calc/Trig...**

A poorly worded question, we would not use logs to expand this perhaps you meant: if y = [(x+3)^4(x-5)^7] then log y = log (x+3)^4 + log (x-5)^7 = 4log(x+3) + 7log(x-5) btw, here are the 12 simplified terms of the expansion. http://www.wolframalpha.com/input/?i=expand+%28x%2B3...
*December 5, 2014*

**intermediate algebra**

√(40x^3) = √4*√10*√x^2*√x = 2x√(10x)
*December 5, 2014*

**math**

36 cm : 9 dm = 36 cm : 90 cm = 36 : 90 = 2 : 5
*December 5, 2014*

**Precalc/Trig**

looks like a direct case of the cosine law d^2 = 434^2 + 525^2 - 2(434)(525)cos 60° = 188356 + 275625 - 227850 = 236131 d =√236131 = 485.933
*December 4, 2014*

**Algebra**

after subbing .... -5(16) / 8^-1 = -80 (8) = -640 8^-1 = 1/8^1 so 1/8^-1 = 8^1 = 8
*December 4, 2014*

**Algebra**

5/√20 - 2√45 = 5/(2√5) - 6√5 = 5/(2√5) *√5/√5 - 6√5 = 5√5/10 - 6√5 = √5/2 - 12√5/2 = -(11√5)/2 I have a strong feeling you meant 3/(y+2) + 2/y = (5y-4)/(y^2-4) do you know why we would multiply by y(...
*December 4, 2014*

**algebra 1**

Just noticed a typo in my conclusion statement, should have read: The chemist will need 80 L of the 30%, and 120 L of the 50% solution. notice I did use 120L in my check
*December 4, 2014*

**algebra 1**

amount of 30% solution needed ---- x L amount of 50% solution needed ---- 200-x L .3x + .5(200-x) = .42(200) .3x + 100 - .5x = 84 -.2x = -16 x = -16/-.2 = 80 The chemist will need 80 L of the 30%, and 20 L of the 50% solution. check: .3(80) + .5(120) = 84 or , using the 2 ...
*December 4, 2014*

**calculus**

sec x = -3 then cos x = -1/3, and x is in the 2nd quadrant the triangle with angle x is in quad II and has a hypotenuse of 3 and an adjacent of 1, so the opposite is √(9-1) = √8 or 2√2 cot x = adjacent/opposite = -1/√8 or -√8/8 = -2√2/8...
*December 4, 2014*

**Help math**

let the two pieces be 3x and 7x , then 3x + 7x = v+4 10x = v+4 x = (v+4)/10 The longer piece was 7x or 7(v+4)/10
*December 4, 2014*

**Math**

|x-4| ≤ 10 - |x+4| x-4 ≤ 10-|x+4| AND -x+4 ≤ 10 - |x+4) |x+4 ≤ 14-x AND |x+4| ≤ 6 + x x+4≤14-x AND -x-4 ≤ 14-x AND x+4 ≤ 6+x AND -x-4 ≤ 6+x 2x ≤ 10 AND -4 ≤ 14 AND 4 ≤ 6 AND -2x ≤ 10 x ≤ 5 AND ...
*December 4, 2014*

**Math**

cube both sides 4 - x^(2/3) = -8 -x^(2/3) = -12 (x^2)^(1/3) = 12 x^2 = 1728 x = ± √1728 = ±24√3 so the difference between the two roots is 48√3
*December 4, 2014*

**math**

didn't Steve do this for you on Tuesday ? http://www.jiskha.com/display.cgi?id=1417568391 Always check back before posting the same question again.
*December 4, 2014*

**Math: Reiny**

In that case we need the intersection of y = x and y = -x+3 x = -x+3 2x = 3 x = 1.5 so area = ∫(upper y - lowery) dx from 0 to 1.5 = ∫(-x+3 - x)dx from 0 to 1.5 = ∫ 3 dx from 0 to 1.5 = 3x | 0 to 1.5 = 3(1.5) - 3(0) = 4.5
*December 3, 2014*

**math**

https://www.youtube.com/watch?v=GDLZYp2U9g8
*December 3, 2014*

**math**

First of all, here is a graph of the curve http://www.wolframalpha.com/input/?i=plot+x+%3D+t%5E3+%2B+6t%2C++y+%3D+4t+-+t%5E2+ As you can see, when t = 0 , x = 0, y = 0 when t = 4, x = 88, y = 0 so our parameter will run form t = 0 to t = 4 in general the area would be integral...
*December 3, 2014*

**Math**

let log1/4 32^-18 = x (1/4)^x = 32^-18 (2^-2)^x = (2^5)^-18 2^(-2x) = 2^-90 -2x = -90 x = 45
*December 3, 2014*

**Math**

I will assume it is 64^(1/3) which would be 4 , so your problem is log4 4^x = 1 x logb4/sub>4 = 1 x(1) = 1 x = 1
*December 3, 2014*

**Math**

yes 10/3 < √x < 24/5 square it 100/9 ≤ x ≤ 576/25 11.111.. < x < 23.04 so with whole numbers ... { 12, 13, ... 22, 23} count them up (just realized I used x instead of h, no big deal, eh)
*December 3, 2014*

**math**

not linear in real life, but .... so you have two points (0,18) and (5,9) slope = (9-18)/(5-0) = -9/5 so y-18 = (-9/5)(x - 0) y = (-9/5)x + 18 so when x = 11 y = (-9/5)(11) + 18 = -1.8 Now do you see how silly it is to label this linear ? (after 10 years there would be nothing...
*December 3, 2014*

**math**

Is the decay exponential, is it linear ? It must be stated
*December 3, 2014*

**Math**

y ≥ x is the region above and including y = x y ≤ -x + 3 is the region below and including y = -x + 3 I see a region open at the left, so we can't find the area. We need to close it up on the left. Are we looking at the little triangle between the two lines and...
*December 3, 2014*

**math**

cost per photo --- x cost = 2x + 20 = 55 2x = 35 x = 17.5 I will let you determine what I did and what I found
*December 3, 2014*

**Math 120**

4logb(X)-1/3logb(y)+2logb(z) = logb (x^4) - logb (y(1/3)) + logb (z^2) = logb (x^4 z^2)/y^(1/3)
*December 3, 2014*

**math - pls check!!!**

29. 4k-1 ≥ -3 4k ≥ -2 k ≥ -1/2 30. 6(c-1) ≤ -18 6c - 6 ≤ -18 6c ≤ -12 c ≤ -2 31. 3t > 5t + 12 -2t > 12 t < -6 , yeahhh you got it right 32. -6/7y - 6 ≥ 42 multiply be 7 -6y - 42 ≥ 294 -6y ≥ 336 y ≤ -56...
*December 3, 2014*

**Math**

You should learn to do this until you can do it in one step, it is essential to know. (p+3)(p-7) = p^2 - 7p + 3p - 21 = p^2 - 4p - 21 with practice you can get to the last line in one step
*December 3, 2014*

**Calculus**

Let his position in the lake be b, let A be the point on shore closest to him, let S be the store so AS = 2, AB = 3 Let P be the point between A and S. So triangle ABP is right angled and BP^2 = x^2 + 9 BP = (x^2+9)^(1/2) recall that Time = Distance/Rate Total Time = T = ((1/5...
*December 3, 2014*

**Math**

Assume that none of the couples knew each other, but hopefully each of the married people would be acquainted with their spouse so Sir John's wife would shake hands with 8 other people (not with Sir John) (My question to you: How many different handshakes took place ? )
*December 3, 2014*

**MAth**

correct
*December 3, 2014*

**maths**

area = 2.1(.39) m^2 = .819 m^2
*December 3, 2014*

**Math**

There exists an infinite number of fractions between any two fractions
*December 3, 2014*

**math**

Since Taryn earns 122.50 to mow 7 lawns he charges 122.5/7 or $ 17.50 to mow a lawn. Since Alastair earns 112.50 to mow 9 lawns he charges 112.5/9 or $ 12.50 to mow a lawn. The number of hours he spends mowing does not enter this part of the question. Earning of Taryn per hour...
*December 3, 2014*

**Algebra 1**

usually we write your point in the form (12,9) direct variation ---> y = kx so 9 = 12k k = 9/12 = 3/4 constant of variation is 3/4
*December 3, 2014*

**algebra**

x^3 + 3x^2 - 9x - 27 = 0 looks like grouping will work x^2(x+3) - 9(x+3) = 0 (x+3)(x^2 - 9) = 0 (x+3)(x+3)(x-3) = 0 x = ± 3 (x = -3 is a double root)
*December 3, 2014*

**Algebra 1**

y = kx , where k is a constant for the given: 14 = k(-4) k = -7/2 or -3.5 y = -3.5x when x = -6 y = -3.5(-6) = 21
*December 3, 2014*

**Maths**

sin(2Ø+30°) = cos(3Ø + 40°) we know that sin x = cos (90-x) so sin(2Ø-30) = cos(90 - 2Ø + 30) = cos(120 - 2Ø) then cos(120-2Ø)=cos(3Ø+40) 3Ø+40 = 120-2Ø 5Ø = 80 Ø = 16° or cos(3Ø + ...
*December 3, 2014*

**Pre-Calc/Trig...**

t(1) = (1/4)4^1 - 1 = 1 - 1= 0 t(2) = (1/4)(4^2 - 1 = 4 - 1 = 3 t(3) = (1/4)4^3 - 1 = 4^2 - 1 = 15 t(4) = (1/4)4^4 - 1 = 4^3 - 1 = 63 t(5) = ........ = 255 however, if you meant (1/4)4^(n-1) .....? just sub in and evaluate
*December 3, 2014*

**math**

You want the vertex of this parabola. the x of the vertex is -b/2a = -36/-32 = 1.125 seconds plug that in h = - 16(1.125)^2 + 36(1.125) + 9 = ....
*December 2, 2014*

**algebra**

e^(.07t) = 2 .07t lne = ln2 t = ln2/.07 = appr 9.9 years
*December 1, 2014*

**Math**

let each side be x we have 6 sides of area x^2 6x^2 = 6534 x^2 = 1089 x = √1089 = 33 ft so volume = 33^3 ft^3 or 35937 ft^3
*December 1, 2014*

**math**

18 1/5 is the exact answer, so you did not "estimate" in estimation they expect something like this 7 4/5 is appr 8 2 1/3 is appr 2 and 8x2 = 16 so my estimated answer would have been 16
*December 1, 2014*

**calculus**

the inner-most brackets are not needed, so f(x)=3ln(x^2 + 2) - 2x you should know how to differentiate a log function, so f ' (x) = 3(2x)/(x^2 + 2) - 2 = 0 for max/min 6x/(x^2 + 2) = 2 3x = x^2 + 2 x^2 - 3x + 2 = 0 (x-2)(x-1) = 0 x = 2 or x = 1 when x = 2, f(2) = 3 ln(6...
*December 1, 2014*

**mathematics**

Re-type in English please.
*December 1, 2014*

**Algebra**

You want f(x) to be zero, so -x^2 + 7x + 8x = 0 I suspect a type, why would you not just add 7x and 8x ? waiting for your correction.....
*December 1, 2014*

**algebra**

since your divisor is a monomial, just divide it into each term of the numerator = (1/2)x^3 - 2x^2 - 7/2
*December 1, 2014*

**Algebra**

You have a typo, there is no exponent on the first term anyway ... max when E ' (v) = 0 E ' (v) = ..... then set that equal to zero and solve for v for b) sub in your v from a) into the original equation
*December 1, 2014*

**math**

arhghh, should have said: so the number is indeed 27/5 or 5.4
*December 1, 2014*

**math**

I interpreted that as 5(x-2) = 17 5x - 10 = 17 5x = 27 x = 27/5 check: 2 less than 27/5 = 27/5 - 2= 17/5 and 5(17/5) = 17 so the number is indeed 17/5 or 3.4
*December 1, 2014*

**math**

Since distance = rate x time the rate is in m/s but the time is in hours so 1.5 hr = 1.5(3600) seconds = 5400 seconds we have distance = 5.9(5400) m = 31860 m = 31.86 km
*December 1, 2014*

**Math**

let's first solve it .... 4 = -2(4.5p + 25) 4 = -9p - 50 9p = -54 p = -54/9 check: LS (for left side) = 4 RS = -2(4.5(-54/9) + 25) = -2(-27 + 25) = -2(-2) = 4 = LS since LS = RS, my solution is correct
*December 1, 2014*

**algerbra**

did you mean ... 4^y = 64 ? I will assume such 4^y = 64 <-----> log4 64 = y
*November 30, 2014*

**Calculus**

Use implicit differentiation x^2 + y^2 = 2xy 2x + 2y dy/dx = 2x dy/dx + 2y 2y dy/dx - 2x dy/dx = 2y - 2x dy/dx(2y - 2x) = 2y-2x dy/dx = (2y - 2x)/(2y - 2x) = 1 well, that was weird let's see why .... x^2+y^2=2xy x^2 - 2xy + y^2 = 0 (x - y)^2 = 0 x - y = 0 y = x ahhhh!, ...
*November 30, 2014*

**Sixth Grade Math**

good job
*November 30, 2014*

**Math PLEASE HELP ME**

invested at 12% ---- x invested at 8% ----- 2x invested at 10% -----210000- x - 2x = 210000-3x .12x + .08(2x) + .10(210000-3x) = 20100 times 100 12x + 16x + 10(210000-3x) = 2010000 -2x = -90000 x = 45000 so 45000 at 12% ---> 5400 90000 at 8% -------> 7200 75000 at 10...
*November 30, 2014*

**Geometry**

I painted the courthouse blue, but now my screen is all smudgy. How do I get the paint off my monitor?
*November 30, 2014*

**algebra**

1. I got 180.8 which would round to 181 2. yup 3. 172.3356 4. 87.5 Were you rounding off before you got to the last answers?
*November 30, 2014*

**Algebra word problem**

Robert's current age --- x Mary's current age ---- x+2 x + x+2 = 28 take it from there
*November 30, 2014*

**AP Calculus**

huh? they don't come any easier f(x) = -x^2 + x f ' (x) = -2x + 1
*November 30, 2014*

**Calculus**

Step 1 of any limit question for me is to sub in the approach value. I that turns out to be a real number, that is your answer, all done! so when x = -1 your expression = (1-2+3)/(1+1) = 2/2 = 1 looks like B to me
*November 30, 2014*

**Calc**

L(x) = f(a) + f ' (a) (x-a) , where x = a f(x) = cosx - sin 2x f ' (x) = -sinx - 2cos 2x L(x) = f(0) + f ' (0) (x-0) = 1-0 + (0-2)(x-0) = 1 - 2x
*November 30, 2014*

**AP Calculus**

f(x)=(x^2-3x)/x^2 you could use the quotient rule, but .... f(x)=(x^2-3x)/x^2 = 1 - 3/x = 1 - 3x^-1 f'(x) = 3x^-2 = 3/x^2
*November 30, 2014*

**Algebra**

(7.8*10 to the 12th power)*800 = 7.8*800* 10^12 = 62400 * 10^12 = 6.24 * 10^15 (7.8*10 to the 10th power)*80,000 = 624000 * 10^10 = 6.24 * 10^14 so what do you think ?
*November 30, 2014*

**SIXTH GRADE MATH**

correct Did you notice that your thinking was along the same lines as that in your previous problem?
*November 30, 2014*

**SIXTH GRADE MATH**

yes, you are correct (they signed up 6 volunteers in 3 weeks, so in 1 week they would sign up 1/3 of 6 , which is 2)
*November 30, 2014*

**SIXTH GRADE MATH**

You are welcome
*November 30, 2014*

**SIXTH GRADE MATH**

Your ratio is 2:3, which means that the total number of games must be a multiple of 5 the only number I see to fit that is 25 e.g. we can split 25 into 2 parts 10:15 = 2:3 but we could not do that with 26 games and still have whole numbers
*November 30, 2014*

**math**

17.4 L + 376 ml = 17.4 L + .376 L = 17.776 L (compare the simplicity of the metric system to the complication of the Imperial system in the 2 previous posts)
*November 29, 2014*

**Math**

let (5x^3 - x^2 + 20x - 8)/(x^2+4)^2 = (Ax + B)/(x^2 + 4) + C/(x^2+4)^2 or = ( (Ax+b)(x^2+4) + C )/(x^2=4)^2 = ( Ax^3 + 4Ax + Bx^2 + 4B+C)/(x^2+4)^2 matching up coefficients of the original numerator ... A = 5 B = -1 4A = 20 ---> confirms A=5 4B+C = -8 -4+C = -8 C = -4 so ...
*November 28, 2014*

**Math**

s^3 = 50653 s = 37 surface area = 6s^2 = 8214
*November 28, 2014*

**math**

3√7 is the best you can do
*November 28, 2014*

**maths**

area = x(x+12.8) , where x is the width more data needed to continue
*November 28, 2014*

**MATH**

√63 = √9 √7 = 3√7
*November 28, 2014*

**math**

i = .07/4 = .0175 n = 7(4) = 28 x(1.0175)^28 = 30000 x = 30000/1.0175^28 = $ 18456.85
*November 28, 2014*

**Math**

#2 , (without expanding) y - 1.5 = a(x+2)^2 a = (y-1)/(x+2)^2 to get x: (y-1.5)/a = (x+2)^2 x+2 = ± √( (y-1/5)/a ) x = -2 ± √( (y-1/5)/a ) follow the same steps for #1, which is easier
*November 28, 2014*

**math**

I think you have a typo Your statement is only true for n = 1 http://www.wolframalpha.com/input/?i=evaluate+3n+%2B+7n+-+2+for+n+%3D+1%2C2%2C3%2C4 Is there supposed to be a power somewhere?
*November 28, 2014*

**calculus**

a = -9.8 then v = -9.8t + c when t = 0 , v = 5 m/s 5 = 0 + c, ----> c = 5 v = -9.8t + 5 s = -4.9t^2 + 5t + k when t = 0, s =442 442 = 0 + 0 + k s = -4.8t^2 + 5t + 442 b) highest point when v = 0 0 = -9.8t + 5 t = 5/9.8 = appr .51 sec when t = .51 s = -4.9(.51)^2 + 5(.51) + ...
*November 28, 2014*

**maths**

Since the distance covered by the belt depends on the circumference of the circles , ... 150(2π(15)) = 300(2πr) 15π = 2πr r = 15/2 = 7.5 cm or the speed of the pulleys is inversely proportional to the their radii r/15 = 300/150 r/15 = 2 2r = 15 r = 7.5
*November 28, 2014*

**Algebra**

I assume you want her pay to be a function of the number of hourse worked let the number of hours worked be h Pay ≥ 10h + 7.5h pay ≥ 17.5 h
*November 28, 2014*

**Math**

I did a similar question last night just change the numbers http://www.jiskha.com/display.cgi?id=1417144323
*November 28, 2014*

**math**

number correct ---- x number incorrect ---- 200 - x number left unanswered--- 0 2x - (1/2)(200 - x) = 360 4x - 200 + x = 720 5x = 920 x = 184 so on his test he got 184 correct and 16 wrong. check: 184(2) - 16(1/2) = 368 - 8 = 360 with the new scoring system: score = 184/2 - 2(...
*November 28, 2014*

**MATH 100**

let the light be situated x ft from one light and 9-x from the other. Let the power be P, where P is a constant let I be the total illumination. I = P/x^2 + 10P/(9-x)^2 = Px^-2 + 10P(9-x)^-2 dI/dx = -2Px^-3 - 10P(9-x)^-3 (-1) = 0 for a min of I 10P/(9-x)^3 = P/x^2 divide by P...
*November 27, 2014*

**math**

happens to everybody
*November 27, 2014*

**math**

let the original fraction be x/y (x+1)/(y+1) = 2/3 3x + 3 = 2y + 2 ----> 3x - 2y = -1 , #1 (x-2)/(y-2) = 3/5 5x - 10 = 3y - 6 ----> 5x - 3y = 4 , #2 #1 times 3 ---> 9x - 6y = -3 #2 times 2 ---> 10x - 6y = 8 subtract them: x = 11 in #1: 33 - 2y = -1 -2y = -34 y = 17...
*November 27, 2014*

**math**

number of 20 paisa coins --- x number of 25 paisa coins --- 50-x 20x + 25(50-x) = 1150 20x + 1250 - 25x = 1150 -5x = -100 x = 20 so she has 20 of the 20paisa and 30 of the 25 paisa coins check: 20+30 = 50 , check! 20(20) + 25(30) = 1150 , check!
*November 27, 2014*

**Algebra**

n+d = 45 5n + 10d = 360 or n + 2d = 72 so... n+d = 45 n + 2d = 72 subtract them to eliminate the n , then solve for d sub d back into the first and all is easy.
*November 27, 2014*

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