Monday

June 27, 2016
Total # Posts: 35,087

**Math**

#1 I will interpret that as: 2log (squarerootx) -log (4/3x^2) + log(4x^3)/log(100) = 2log x^(1/2) - (log4 - log3 - 2logx) + (log4 + 3logx)/2 = logx - log4 + log3 + 2logx + (1/2)log4 + (3/2)logx = (9/2)logx - (1/2)log4 = (1/2)(9logx - log4) or, = (1/2) log(x^9/4) = log [x^9/4...
*April 2, 2016*

**math**

p=log(squareroot8)/log(2) = log 8^(1/2) / log2 = (1/2)log 2^3 / log2 = (3/2) log2/log2 p = 3/2 log(31+log(16)/log(x))/log(9)=log(squareroot8/log(2) I see "mismatched brackets" on the right side. Where does p = 3/2 enter the picture?
*April 2, 2016*

**Maths**

area of whole circle = Pi(20)^2 = 400Pi Using a simple ratio: A/400Pi = 120/360 A = 400Pi/3 cm^2 = ....
*April 2, 2016*

**math( pls help me out)**

I disagree The probs that Bob found would each have 4 children, not three prob(of 3 children, two are girls) = C(3,2)(1/2)^2 (1/2) = 3/8 illustration: BBB BBG BGB GBB GGG GGB -- 2 GIRLS GBG -- 2 GIRLS BGG -- 2 GIRLS So there are 3 cases of 2 girls prob(2 girls) = 3/8 prob(3 ...
*April 2, 2016*

**another approach - math**

Ok, how about this approach sinA = x + cosA x = sinA - cosA let's change sinA - cosA into a single sinusoidal expression: Let sinA - cosA = a sin(A + k) a sin(A+k) = a(sinAcosk + cosAsink_ = asinAcosk + acosAsink then asinAcosk = sinA acosk = 1 cosk = 1/a acosAsink = -cosA...
*April 2, 2016*

**math**

I did this yesterday http://www.jiskha.com/display.cgi?id=1459511832
*April 2, 2016*

**Maths**

A 45 degree sector is 1/8 of the circle So find (1/8)(pi)(14^2)
*April 2, 2016*

**math**

prob(get money) = .3 prob(not get money) = .7 prob(at least 3 of 5 get money) = C(5,3)(.3)^3 (.7)^2 + C(5,4)(.3)^4 (.7) + .3^5 = .. you do the button-pushing
*April 2, 2016*

**Math**

by simple observation, the x's increase by 2 , so 20+p = 21 thus p=1 which lets the y's increase nicely by 1
*April 2, 2016*

**math**

prob(buy) = .4 prob(not buy) = .6 prob(5 of 10 will buy) = C(10,5) (.4)^5 (.6)^5 = 252(.000796..) = appr .2007
*April 2, 2016*

**Algebra**

in the first, replace x with -3 and solve for y in the second, replace y with 1 and solve for x
*April 1, 2016*

**Math**

distance from (3,4) to (-1,0) = sqrt(4^2 + 4^2) = sqrt(32) = appr 5.7 where you just guessing?
*April 1, 2016*

**Math- quadratic equation**

width of pathway = x m width of whole thing = 12+2x m length of whole thing = 16+2x (12+2x)(16+2x) = 258 192 + 56x + 4x^2 = 258 2x^2 + 28x - 33 = 0 x = (-28 +- sqrt(1048))/4 = 1.093 or a negative the path should be appr 1.09 m wide all around check: (12+ 2.18)(16+2.18) = 14.18...
*April 1, 2016*

**Math**

looks like for every increase of 1 in the x, our y decreases by 5 so it must be y = -5x + c all we need is to find c pick one of the data values: 0 = 0, y = -1 -1 = 0 + c c = -1 y = -5x - 1
*April 1, 2016*

**trigonomentry out of ideal help ah!crying**

cute problem recall that cos x = - cos(180 - x) that is cos(1) = - cos(179) cos(3) = - cos(177) .. cos(89) = - cos(91) cos(91) = - cos(89) ... cos(177) = - cos(3) cos(179) = - cos(1) so : cos1 + cos3 + ... + cos 177 + cos 179 = (cos1+cos179) + (cos3+cos177) + ...+ (cos89+cos91...
*April 1, 2016*

**typo - Math**

I did this on paper first, but then messed up when I typed it. the first few lines in the equations should have been: (x+1)(x - (1+i))(x - (1-i)) = 0 (x+1)(x-1-i)(x-1+i) = 0 (x+1)(x^2 - x + xi -x +1 -i -xi + i - i^2) = 0 the rest is fine
*April 1, 2016*

**Math**

complex roots always come in conjugate pairs, so if one is 1+i, you must have another as 1-i so we know the equation is (x+1)(x - (1+i))(x + 1+i) = 0 (x+1)(x-1-i)(x+1+i) = 0 (x+1)(x^2 + x + xi -x -x -i -xi - i - x^2) = 0 (x+1)(x^2 - 2x + 2) = 0 x^3 - x^2 + 2x + x^2 - 2x + 2 = ...
*April 1, 2016*

**Mathematics**

trying your choice: for (2,-1) in y = 2x - 1 -1 = 2(2) - 1 -1 = 3 ???? not every likely. try the others the same way.
*April 1, 2016*

**Math**

Since the sine is negative and the tangent is positive, the angle is in quadrant III from sin theta = -4/9, r = 9 and y = -4 x^2 + y^2 = r^2 x^2 + 16 = 81 x = -sqrt(65) , in III the x is negativ Then cos theta = -sqrt(65)/9 sec theta = -9/sqrt(65) or -9sqrt(65)/65
*April 1, 2016*

**math**

let sinA = x + cosA x = sinA - cosA x^2 = sin^2 A - 2sinAcosA + cos^2 A x^2 = 1 - 2sinAcosA x^2 = 1 - sin 2A x = +/- sqrt(1-sin(2A)), |sin 2A| <= 1 not sure if that is what you want. Since I squared the equation, any (A,x) would have to be verified
*April 1, 2016*

**math**

Since no letters repeat, this is straightforward. number of "words" = 9! = 362880
*April 1, 2016*

**Math**

4 queens or 4 fives prob(of stated event) = 8/52 = 2/13
*April 1, 2016*

**Math**

In any of these kind of problems , n has to be a whole number, that is n = 1,2,3, .... My choice would be term(n) = 5n - 1 , which is the only one that makes term(1) = 5(1) - 1 = 4 your choice would produce a first term of 9, which is the second term, not the first your ...
*March 31, 2016*

**Algebra 2**

interpretation: the division must be excact, that is, there cannot be a remainder. Arrange the terms in the proper order and do a synthetic division: -1 | -2 1 -1 1 ....... 2..-3..4 .... -2 3..-4..5 so we should have had a 0 instead of a 5 at the end of our algorithm, that ...
*March 31, 2016*

**Math**

A is the only one that works our pattern.
*March 31, 2016*

**Math**

#1 notice that the terms keep getting smaller, so we clearly are adding a -6 What number did we start with? #2 the correct choice would be -64, -128, -256 which I don't see, unless you have a typo
*March 31, 2016*

**Pre cal 11**

let 5b-3 = x, then we have 4x^2 + 10x - 6 = 2(2x^2 + 5x - 3) = 2(x+3)(2x-1) replace x with 5b-3 within each bracket , then simplify
*March 31, 2016*

**Calculus**

If your function contains terms of the type ax^2, ay^2, ax, and ay along with some constant terms , and where a is a rational number, then you have a conic if it contains terms such as xy , it could be a conic that has been rotated, and is no longer parallel or perpendicular ...
*March 31, 2016*

**Maths**

What the question does not say, but what I will assume is true to have your answer of 10, is that the dimensions must be whole numbers. Otherwise there would be an infinite number of cases So we need 3 multipliers (LWH) to get 28 the factors of 28 in triples are 1 1 28 1 2 14 ...
*March 31, 2016*

**math**

For the 10 K race in 58 minutes the runner would take 5.8 minutes per km or 5 minutes and 48 seconds to run 1 km The equivalent race of 6.2 miles would have a time of 58/6.2 minutes per mile or 9.3548.. minutes per mile = 9 minutes, 21 seconds (A real runner doing a 10 K race ...
*March 31, 2016*

**math**

the average of 200 and 160 is 180 so the speed of the plane with no wind is 180 mph, and the wind speed is 20 mph check: going against the wind = 180-20 = 160 going with the wind = 180 + 20 = 200
*March 31, 2016*

**@ AMANSANDHUWILLDIE - pr calc 11**

You might have noticed that Steve did not reply to your question. You may talk in a disrespectful way to your peers the way you did, but calling a distinguished professor "dude" is not the smartest thing to do. I am sure one of your fellow dudes might suggest that ...
*March 31, 2016*

**Math**

hearts OR ten = 13 + 4 - 1 = 16 (can't count the 10 of hearts twice) continue
*March 31, 2016*

**Geometry**

Oh my goodness! What has happened to each of the coordiates of the two points? Why was 6 your choice? How can you "feel" an answer to be right?
*March 31, 2016*

**Math**

I was able to see your diagram. Since the band circle must have a total of 25, and we have already (11+7+3) or 21 entered in the Venn diagram, the missing part of Band and Choir must be 4 So label the math-only part 9 and the intersection of Math and Choir as x (only the part ...
*March 31, 2016*

**Math**

Look at the previous post and simply change the numbers
*March 31, 2016*

**Math**

The number of ways to select 7 from 1 to 45 = C(45,7) = 45,379,620
*March 31, 2016*

**math**

The HCF of 64 and 124 is 4 The LCM of 64 and 124 is 1984 so what is 1984/4 ?
*March 31, 2016*

**business math**

100(r)(2/52) = 2.50 r = (2.5/100)(52/2) = .65 = 65% The equivalent annual rate is 65% (In the middle ages they would have been burned at the stake for usury.)
*March 31, 2016*

**Math**

wins --- x ties --- y x+y= 18 2x+y= 30 subtract them: x = 12 then y = 6 wins: 12 losses: 10 ties: 6 check: 2(12) + 0(10) + 1(6) = 30
*March 31, 2016*

**Trig**

make sketches of two right angles triangles in the third quadrants since tanA = 3/4, the terminal arm of angle A ends at (-4,-3) , and r = 5 so sinA = -3/5, and cosA = -4/5 (you have a 3-4-5 right-angled triangle) since cosB = -5/13 , the terminal arm of angle B ends at (-5,-...
*March 31, 2016*

**Math**

term(n) = -3n + 27
*March 31, 2016*

**math**

.05(3000) + .08x = .075(3000+x) 150 + .08x = 225 + .075x .005x = 75 x = 15,000 check: total invested = 3000+15000 = 18000 .075(18000) = 1350 interest at partial investments = .05(3000) + .08(15000) = 150 + 1200 = 1350 How did you possible get $279,375 ??? Did that sound ...
*March 31, 2016*

**Algebra**

x + (1/7)x = 88 hint: multiply each term by 7 to clean up the fraction, and solve for x
*March 31, 2016*

**Algebra 1-Factoring Help!**

Somebody had the same question earlier today. http://www.jiskha.com/display.cgi?id=1459354736
*March 30, 2016*

**math**

correct, 10% of 80 is 8 so prob of fail = 8/80 = 1/10 so for 400 units, prob = (1/10(400) =
*March 30, 2016*

**math**

what is 10% of 80 ?
*March 30, 2016*

**Math**

looks like a simple typo here actually 4/52 = .0769... = .08 correct to 2 decimals
*March 30, 2016*

**NO - Math**

no The order in which the cards are drawn should not matter. They even used the word "combination", which implies that the order does not matter. So you are simply choosing 2 of the 9 cards = C(9,2) = 9!/(2!7!) = 36 The answer of 72 would be correct if the order in ...
*March 30, 2016*

**Math**

cylinder1: height = h radius = r volume = pi r^2 h = pi r^2h cylinder2: height = h radius = 2r volume = pi (2r)^2 h = 4pi r^2h or ratio is 1 : 4 so the volume is 4 times as large
*March 30, 2016*

**Trigonometry**

correct conclusion
*March 30, 2016*

**Trigonometry**

Your probably made a sketch and have learned the sine law If not, go to the construction part of my reply using the sine law: sinA/30 = sin54/20 sinA = 1.2135.... but that is not possible , since the sine of any angle has to be between -1 and 1 So there is no such triangle ...
*March 30, 2016*

**math (ms sue)**

Note that your 3 probabilities do not add up to 1, thus other parties must also have received votes Your want the prob(CP OR L) = .36+.23 = .59
*March 30, 2016*

**algebra**

frame = (3+2x) by (5+2x) (3+2x)(5+2x)= 35 15 + 16x + 4x^2 = 35 4x^2 + 16x - 20 = 0 x^2 + 4x - 5 = 0 (x-1)(x+5) = 0 x = 1 or x = -5 , the last one is not possible the frame is 5 cm by 7 cm
*March 30, 2016*

**Algebra 1-HELP!**

small typo should have said: step2: look for 2 factors which multiply to get -18, and whose sum is the middle term coefficient But you probably figured that out anyway.
*March 30, 2016*

**Algebra 1-HELP!**

first arrange them in the standard order 18x^2 + 21x - 9 look for a common factor, in this case 3 18x^2 + 21x - 9 = 3(6x^2 + 7x - 3) A method which seems to be popular these days is "decomposition", (not my personal favourite) Step1: multiply the (a)(c) (6)(-3) = -18...
*March 30, 2016*

**mathd**

Make a sketch, label the top of the building P and its bottom Q. On the ground, label angle A = 20 and mark point B as 23 degrees then angle ABP = 180-23 = 157 degrees angle A = 20 and angle APB = 3 degrees by the sine law BP/sin20 = 80/sin3 BP = 80sin20/sin3 = .... then in ...
*March 29, 2016*

**Math**

number of club members --- x girls ---- 3x/8 number of 6th grader girls = (2/5)(3x/8) = 3x/20 fraction of 6th grade girls = (3x/20) / x = 3/20
*March 29, 2016*

**algebra**

You used the word "combination" which implies that the order does not matter. We will also assume that flavours cannot be repeated, e.g. no double-vanilla Number of combinations = C(38,3) = 38!/(3!35!) = 8436
*March 29, 2016*

**math**

All I did is to translate the English into Math Let Sandy's age be x "Jay is as twice as old as Sandy " ----> Jay's age is 2x "Jay is 2 years younger than Mike" ---> Mike's age is 2x+2 "Mike is 7 years older than Sandy" ---> ...
*March 29, 2016*

**math**

Sandy --- x Jay------- 2x mike ----- 2x+2 "Mike is 7 years older than Sandy " ---> 2x+2 = x+7 x=5 check: Sandy is 5 Jay = 10 Mike is 12 Is Mike 7 years older than Sandy? YES
*March 29, 2016*

**Algebra**

since both say y = we equate: x^2+2x=3x+20 x^2 - x - 20 = 0 (x-5)(x+4)=0 x=5 or x=-4 for x=5, y = 35 for x=-4, y = 8
*March 29, 2016*

**math**

ramus age --- 3x sister's age --- 4x but 4x = 36 x = ... carry on.
*March 29, 2016*

**math**

The number of ways to select 7 from 1 to 45 = C(45,7) = 45,379,620
*March 28, 2016*

**math**

any 3 positive numbers which have a product of 64 There would be an infinite number of ways, one of them is 4 cm by 8 cm by 2 cm , another is 2.25 by 7 by 256/35
*March 28, 2016*

**Math**

you already know the equation must be y = a(x+2)^2 - 3 All that is missing is the value of a To find a, plug in the given point and solve for a. Rewrite my equation and you are all done.
*March 28, 2016*

**math**

Wow! - slop is something they feed to pigs. - you have the same point listed twice - "undefied" ??? , probably meant undefined.
*March 28, 2016*

**Math**

no, you cant add them notice you would have a probability equal to 1, which means the event you want will always happen. prob(yellow, black, then white) = (5/10)(3/9)(2/8) = 1/24 notice that each time a sock is pulled there is one less to choose from, hence the decreasing ...
*March 28, 2016*

**Math**

part 1 No idea, since you didn't tell us what he paid for them part 2 So he had 35% of the 500 oranges left or 175 of those 8% went bad so he still had 92% of the 175 to sell or 161 return per orange = 24.15/161 = .15 he sold them at 15 cents each ( good price, must be an ...
*March 28, 2016*

**Algebra**

(5√2 − √5)(5√2 − 5√5) = 50 - 25√10 - 5√10 + 25 collect your like terms and simplify
*March 28, 2016*

**Math**

The third angle of triangle RST is 180-38-75 = 67 which is one of the given angle of the second triangle. So both triangles have the same angles and the sides are proportional. The two triangles are similar, therefore one is a dilation of the other.
*March 28, 2016*

**Pre calc aesthetic quadratic stuff**

let the two numbers be x and y so we have: x+y = 9 --->y = 9-x and xy = 20 x(9-x) = 20 9x - x^2 - 20 = 0 the equation you want is: x^2 - 9x + 20 = 0 easily solved, it even factors nicely.
*March 28, 2016*

**math**

card > 2 AND < 7 must be 3,4,5, or 6 there are 16 in that group prob(of your event) = 16/52 = 4/13
*March 28, 2016*

**math**

don't know how detailed your "unit circle" is , but you should easily read off that sin30° = 1/2 cosπ = -1 sin 11π/6 = sin 330° = - sin30° = -1/2 cos 135 = -cos 45 = -√2/2
*March 28, 2016*

**EASY Math**

14000 = -2000t + 20000 2000t = 60000 carry on
*March 28, 2016*

**Math please help**

let the angle be x then its supplement is 180-x 180-x = 2x + 30 150 = 3x x = 50 the angle is 50°, the supplement is 130° check: Its supplement would be 130 is that 30 more than twice 50 ? YES!
*March 28, 2016*

**Math**

Good job
*March 28, 2016*

**maths**

number of rows --- x number of students in a row --- y Then the number of students = xy case1: 4 students added to each row --- y+4 rows is reduced by 2 ----- x-2 (x-2)(y+4) = xy case2: 4 student taken off each row --- y-4 number of rows is now --- x+3 (x+3)(y-4) = n so (x-2)(...
*March 28, 2016*

**Maths**

simplest way is using vectors. resultant vector = (4cos38,4sin38) + (5cos67,5sin67) = (3.152.., 2.4626..) + (1.9536..., 4.6025..) = (5.1056.., 7.065...) distance = √(5.1056..^2 + 7.065.^2) = appr 8.717 correct to 3 decimals bearing: tanØ = 7.065../5.1056.. Ø...
*March 28, 2016*

**Math**

What kind of cup? A coffee cup, a cup o' tea? There is such a thing as the "metric cup" where 1 cup = 250 ml In that case 1 cup would cost 31 cents 1 U.S. customary cup = appr 236.588 ml In that case 1 cup would cost $1.25 ÷ (1000/236.588) = $.295 or 30 ...
*March 28, 2016*

**Maths**

ratio of correct to wrong = 6 : 2 = 3 : 1 = 3x : x total questions = 4x given: 3x = 54 x = 18 so there were 4(18) or 72 questions percentage correct = 54/72 = .75 or 75% we could have seen that from the top correct = 3x, total = 4x percentage correct = 3x/4x = 3/4 = .75
*March 28, 2016*

**Math**

let the width be x m let the length be y m So we need 2 widths and 1 length given: xy= 448 y = 448/x 2x + y = 60 2x + 448/x = 60 times x 2x^2 + 448 = 60x x^2 - 30x + 224 = 0 (x-16)(x-14) = 0 x = 16 or x = 14 then y = 448/16 or y = 448/14 y = 28 or y = 32 The field could be 16 ...
*March 28, 2016*

**Algebra**

so you have the points: (-2,1), (0,5), and (4,-59) let the function be y = ax^2 + bx + c for (0,5) 5 = 0 + 0 + c -----> c = 5 so we could reduce our equation to y = ax^2 + bx + 5 for (-2,1) 1 = 4a - 2b + 5 4a - 2b = -4 2a - b = -2 *** for (4, -59) -59 = 16a + 4b + 5 16a + ...
*March 28, 2016*

**Math**

Sal Khan does an excellent job of this topic in this video. https://www.khanacademy.org/math/cc-sixth-grade-math/cc-6th-data-statistics/cc-6-mad/v/mean-absolute-deviation He goes through two different cases
*March 28, 2016*

**math**

8 red 3 white 9 blue total = 20 at least one is white ---- exclude case of all non-white prob(that 3 of 19 are all non-white) = C(17,3) x C(3,0)/C(20,3) = 680/1140 = 34/57 prob(at least one white) = 1 - 34/57 = 23/57 one of each colour = C(8,1) x C(3,1) x C(9,1)/c(20,3) = 216/...
*March 28, 2016*

**math**

look at the first of the Related Questions below
*March 28, 2016*

**math**

prob(fail) = .2 prob(not fail) = .8 prob(exactly 2 of 10 will fail) = C(10,2) .2^2 .8^8 = appr .302 2 or more defective ---> exclude 0 not fail and 1 not fail = 1 - C(10,0) .8^0 .2^10 - C(10,1) (.8)( .2^9) = .... more than 5 = prob(exactly 6) + prob(exactly 7) + ... + prob(...
*March 28, 2016*

**Algebra**

just plug in ... a(15) = -4(15) + 1 = ...
*March 27, 2016*

**Calculus Urgent**

I see what you mean, the two curves appear to coincide form -1 to 1 http://www.wolframalpha.com/input/?i=y%3Dcos(pi*x%2F2),+y%3D1-x%5E2 Because of the symmetry, I looked closer from 0 to 1 and it shows that the parabolo lies above the cosine curve for that domain, and of ...
*March 27, 2016*

**College Algebra 1**

Again first look for a common factor in the constants which is -4 -36a^2-96ab-64b^2 = -4(9a^2 + 24ab + 16b^2) the 9a^2 and 16b^2 are both perfect squares, could we perhaps have (3a + 4b)^2 ? A quick mental expansion shows this is indeed the case, so -36a^2-96ab-64b^2 = -4(9a^2...
*March 27, 2016*

**College Algebra 1**

HCF of -36, -96, and -54 is -6 I see no same variable in all 3 terms -36a^2-96ab-54b^2 = -6(6a^2 + 16ab + 9b^2) the trinomial does not factor further over the rationals. Mentally expand to check the answer.
*March 27, 2016*

**Math**

A picture is worth a thousand words, (groan) Draw a vertical line and mark it 120 inches the centre must be 76 inches from the floor or 44 inches from the ceiling. Since the picture is 34 inches high and you want its centre, just add half of 34 or 17 inches to 76. So the top ...
*March 27, 2016*

**math**

Cannot read your last two posts.
*March 27, 2016*

**math**

so you want y = a csc (2/3)x where a is whatever your (−‡,−2]¾[2,‡) means well, y = csc (2x/3) looks like this: http://www.wolframalpha.com/input/?i=plot+y+%3D+csc+(2x%2F3) the vertical lines are asymptotes at x = 0, ±3&#...
*March 27, 2016*

**Calculus**

the graph of f(x) = x/(x-4) looks like this: http://www.wolframalpha.com/input/?i=plot+y+%3D+x%2F(x+-+4)+for+0+to+10 the vertical line x=4 is the asymptote
*March 27, 2016*

**Calculus**

For f^-1(10), 10 = x^3 + x by quick inspection, x = 2 so f^-1(10) = 2 similarly for f-1(2), 2 = x^3 + x --> x=1 so f^-1(2) = 1
*March 27, 2016*

**Pre calc 11**

term(20)=186 ---> a+19d = 186 a = 186-19d sum(12) = 6(2a + 11d) = 186 2a + 11d = 31 2(186-19d) + 11d = 31 -27d = -341 d = 341/27 a = 186-19(341/27) = -1457/27 sum(40) = 20(-1467/27+ 39(341/27) = -16041/27 better check my arithmetic, did not expect such weird numbers
*March 27, 2016*

**math**

prob = C(8,3)xC(5,0)xC(2,0)/C(15,3) = 56/455 = 8/65 prob(both homeowners plus one of the others) = C(2,2) x (13,1)/C(15,3) = 13/455 = 1/35 one of each: C(8,1) x C(5,1) x C(2,1)/C(15,3) = 80/455 = 19/91
*March 27, 2016*

**math**

4 NDC 3 NPP 3 others total = 10 i) one of each party: C(4,1) x C(3,1) x C(3,1)/C(10,3) = 36/120 = 3/10 ii) C(3,2) x (7,1)/C(10,3) = 21/120 = 7/40 iii) follow my steps of ii)
*March 27, 2016*

**Algebra**

speed of raft ---- x km/h speed of boat ----12 km/h when the boat caught up with the raft, they both had gone 20 km time for raft = 20/x time for boat = 20/12 20/x - 20/12 = 5 hrs, 20 min = 16/3 times 12x 240 - 20x = 64x 240 = 84x x = 240/84 km/h = 20/7 km/h check" time ...
*March 27, 2016*