Tuesday
October 21, 2014

Posts by Reiny


Total # Posts: 27,495

math (1)
Just drop in the values and stir. e.g. c) x = 2, y=1 h(2,1) = (4+8)/(2-1) = 12 That's all there is to it.
April 28, 2014

Math
(3√8 + 4√9)^2 = (3√8 + 12)^2 = 72 + 72√8 + 144 = 216 + 72(2√2) = 216 + 144√2 or appr 419.65
April 28, 2014

math
2x+8=3x+2 2x - 3x = 2 - 8 -x = -6 x = 6
April 28, 2014

math
5x-2(x+4)=3(2x+1) 5x - 2x - 8 = 6x + 3 5x - 2x - 6x = 3 + 8 -3x = 12 x = -4
April 28, 2014

Physics waves- check answers please
agree with all of them
April 28, 2014

Integrated Trig
if compounded annually 1.03^t = 2 t ln1.03 = ln2 t = ln2/ln1.03 = appr 23.45 years
April 28, 2014

Integrated Trig
5000 e^(.03t) = 10000 e^(.03t) = 2 take ln of both sides , and use rules of logs .03t = ln 2 t = ln 2/.03 = appr 23.1 years
April 28, 2014

math
solve for x 2x + 2(3x) = 64
April 28, 2014

Math 1314
width of pond --- x length of pond --- 3x width of whole thing = x+6 , (3 feet on each end) length = 3x + 6 2(x+6) + 2(3x+6) = 100 2x + 12 + 6x + 12 = 100 8x = 76 x = 9.5 ft the pond is 9.5 ft wide and 28.5 ft long
April 28, 2014

Math 120
d = -16t^2 , if we have to consider direction or d = 16t^2 if all we care about is distance when t = 17 d = 16(17)^2 = 4624 ft some deep well !!
April 27, 2014

Math HELP HELP
use Venn diagrams, fill in your data starting with the intersection of all three, then the intersection of two at a time, etc.
April 27, 2014

Maths
check your previous post for this
April 27, 2014

math/ratio
let the number of apples, oranges, and pears be 3x, 5x, and x respectively. 5x+x - 3x = 12 3x = 12 x = 4 so 12 apples, 20 oranges and 4 pears check: oranges + pears = 24 apples = 12 is 24 more than 12 by 12 ?? YES
April 27, 2014

Calculus
area = integral ( e^-x) from 0 to infinitiy = [ - e^-x] from 0 to infinity = [-1/e^x] from 0 to infinity now clearly as x ---> ∞ , 1/e^x --> 0 so we have ( 0 - (-1/1) = 1
April 27, 2014

Math
Do you want the probability of drawing 2 green balls? = (3/5)(2/4) = 3/10
April 27, 2014

Maths
the 17 would cancel, leaving you with 93/97
April 27, 2014

Math
The way you typed it: 5x/6 = 15 5x = 90 x = 18
April 27, 2014

Precalculus
A = {2,3,5,7,11,13} B = {1,2,3,4,6,9,12} c= {4,8,12,16} Just noticed that in your listing of C you don't have the 16 Does that result in your difficulties? A intersect B = {2,3) (A intersect B)' = {1,4,5,6,7,8,9,10,11,12,13,14,15,16} which in "union" with C...
April 27, 2014

Math
18 ft / 2 seconds = 9 ft/sec = (9/5280) miles / (1/3600) hours = (9/5280)(3600/1) m/h = (135/22) mph = appr 6.1 mph or 18 ft in 2 seconds = 9 ft in 1 second = 540 ft in 1 minute = 32400 ft in 1 hour = 6.1 mph
April 27, 2014

algebra
tried: ±1 , ±2 and found x = 2 to be a triple root. successive synthetic divisions shows x^5−8x^4+28x^3−56x^2+64x−32=0 (notice how we show exponents) x=2 to be triple root so x^5−8x^4+28x^3−56x^2+64x−32=0 (x-2)^3 (x^2 - 2x + 4...
April 27, 2014

Math - Trigonomety
What a silly and unrealistic problem, anyway .... I made a sketch the main working triangle has the height of the tree, its opposite angle as 10°, and the other angles as 105° and 65° The side opposite the 105° is also the hypotenuse of a right-angled triangle ...
April 27, 2014

Geometry
Ms Sue solved the "same" question. Just change the numbers http://www.jiskha.com/display.cgi?id=1398287442
April 27, 2014

MATHS
x/2 + 2y/3 = -1 ---> 3x + 4y = -6 x - y/3= 3 --------> 3x - y = 9 elimination: subtract them: 5y = -15 y = -3 sub into the 2nd 3x - (-3) = 9 3x = 6 x = 2 x = 2, y = -3 by substitution: from the 2nd: y = 3x-9 into the 1st: 3x + 4(3x-9) = -6 3x + 12x - 36=-6 15x = 30 x = 2...
April 27, 2014

math
to me this says: x = 4sin^3 t y = 7cos^3 t dx/dt= 12(sin^2 t)(cost) = 12cost(sint)^2 dy/dt= 21(cos^2 t)(-sint) or -21sint(cost)^2 both dx/dt and dy/dt must be zero for dx/dt =0 , dy/dt=0 12cost(sint)^2 = 0 , -21sint(cost)^2 = 0 in other words, wherever the sine or cosines are ...
April 27, 2014

Pre algebra
1 km/h = (1/60) km/minute (how many minutes are there in 1 hour? ) You don't post an actual speed (typo?). so suppose you have 80 km/h = (80/60) km/min = (4/3) km/min replace my speed with whatever speed you have, then simplify ??/60 to lowest term fractions.
April 26, 2014

Jim and Mia : - Math (6)
Jim, they do intersect at one point only, thus creating an open region on the left. By squaring you are introducing a part of the graph which was originally undefined. y = √x is defined only for x ≥ 0 Mia: Both Steve and I gave answers to this earlier http://www....
April 26, 2014

math (4)
graph of your function http://www.wolframalpha.com/input/?i=y%3D++-xe%5E%28-x%5E2%29++from+0+to+1 notice the region will be below the x-axis, so height = 0 - (-xe^(-x^2)) = xe^(-x^2) area = integral (xe^(-x^2)) dx from 0 to 1 = (-1/2) e^(-x^2) from 0 to 1 = (-1/2) e^-1 - (-1/2...
April 26, 2014

math (2)
Here is what your curve looks like from x = -1 to +1 http://www.wolframalpha.com/input/?i=y%3D+2x%2F%28x%5E2%2B4%29+from+-1+to+1 So where is the shaded region? Are you finding the area between the curve and the x-axis? (That is the usual case for this question, but let me know...
April 26, 2014

Trig
Or use the old sum of roots and product of roots property sum of roots = 5+i√2 + 5-i√2 = 10 product of roots = (5+i√2)(5-i√2) =25-2i^2 = 25+2 = 27 x^2 - (sum)x + product = 0 x^2 - 10x + 27 = 0
April 26, 2014

Calculus
draw a sketch of the situation, at a time of t hours after 9:00 am let A1 be the position of Aida let I1 be the position of Ian Join A1 and I1, to get a right-angled triangle let D be the distance between them D^2 = (6t)^2 + (20-8t)^2 = 36t^2 + 400 - 320t + 64t^2 = 100t^2 - ...
April 26, 2014

Deepa
let the number of 50 cents increases be n NOW: number of riders = 10000 cost per ride = 20 after increase number of riders = 10000- 200n cost per ride = 20+ .5n Revenue = (10000-200)(20 + .5n) expand this and you will have a quadratic representing a parabola that opens ...
April 26, 2014

For fizz - math
I answered this for you already http://www.jiskha.com/display.cgi?id=1398482333 I counted about 8 problems dealing with series of discounts, plus numerous questions that have been answered dealing with compound interest. I don't see a single reply by you or even a response...
April 26, 2014

math (trade and cash discount)
let the list price be x .85(.92)x = 239.29 x = 239.29/(.85(.95)) = ....
April 26, 2014

math
One step calculation price = 1780(.7)(.9)(.95) = 1065.33 Discount = 1780-1065.33 = $714.67 or first discount = .3(1780) = 534 leaving 1246 2nd discount = .1(1246) = 124.60 leaving 1121.4 3rd discount = .05(1121.4 = 56.07 leaving 1065.33 Discount = 1780 - 1065.33 = 714.67 as ...
April 26, 2014

MATH
tried: ±1, ±2, ±3 success at x = -3 by synthetic division 21x^3+67x^2-36=(x+3)(21x^2+ 4x - 12) = (x+3)(3x-2)(7x+6) so what do you think?
April 26, 2014

good catch- maths
Good catch Steve, the smallest 3-digit number divisible by 7 is 105 So count one more, 128 of them
April 26, 2014

maths
smallest 3 digit number divisible by 7 is 112 largest 3 digit number divisible by 7 is 994 look at the arithmetic sequence 112, 119, .... 987 , 994 how many terms are there? a=112, d = 7 term(n ) = a+(n-1)d 994= 112 + (n-1)(7) 882 = 7n - 7 889 = 7n n = 127 2. really!? (I will ...
April 26, 2014

maths
I will assume you meant, "How many red marbles should be added" let the reds to be added be x so we have 10+x reds total = 40+x (10+x)/(40+x) = (3/5) 50 + 5x = 120 +3x 2x = 70 x = 35 #5 reds should be added check: reds = 45 total = 75 percentage of reds = 45/75 = .6 ...
April 26, 2014

Maths
a) flipping 2 counters, Cam's outcomes: 11 , 12 , 21, and 22 , two ways to get a 3 ---> prob(3) = 2/4 = 1/2 flipping a die, outcomes 1,2,3,4,5,6 , one way to get a 3 --> prob(3) = 1/6 prob(both get a 3) = (1/2)(1/6) = 1/12 CA DE ---- Cam's loss ---> Dean's...
April 26, 2014

math
amount left of 1 unit after the series of 3 discounts = (.8)(.9)(.96) = .6912 amount left of 1 after a single discount of 32% = .68 which is the better discount?
April 25, 2014

Math
Just like 3(2x+5) = 6x + 15 just like 3(7+2) = 21 + 6 so is √5(2+√5) = 2√5 + √25 = 2√5 + 5 you could also check by evaluating it with your calculator.
April 25, 2014

Math
√5/(2-√5) ?? what about it? If you are rationalizing it, then = √5/(2-√5) * (2+√5)/(2+√5) = (2√5 + 5)/(4-5) = -2√5 - 5
April 25, 2014

Calculus
" 50 m away from you" -measured along the string, or measured along the ground? There is not enough information , there are 3 rates involved, but you only give one. Are we ignoring the fact that the string cannot form a straight line ? Is the kite always 40 m high?
April 25, 2014

Algebra 1
sure, if it exists For a "vertical " parabola there will always be a y-intercept For a sideways parabola, there may not be one.
April 25, 2014

math (9)
picture: http://www.wolframalpha.com/input/?i=plot+y%3D+-x%5E2%2B2x%2B4+%2C+y+%3D-x%2B4 looks like they intersect at (0,4) and((3,1) (the points satisfy both equations) area = ∫( -x^2 + 2x + 4 - (-x+4)) dx from 0 to 3 = ∫( -x^2 + 3x ) dx from 0 to 3 = [ -x^3/3 + 3x...
April 25, 2014

math (2)
we see no shaded region.
April 25, 2014

Math (6)
Since x ≥ 0 for y = √x the graph shows that we cannot have a closed region. see ... http://www.wolframalpha.com/input/?i=plot+y%3D+√%28x%29+%2C+y%3D+x-2
April 25, 2014

math
must exclude no heads and 1 head prob(no heads) = (1/2)^6 = 1/64 prob(1 head) = C(6,1) (1/2)^1 (1/2)^5 = 6/64 prob (more than 1 head) = 1 - 1/64 - 6/64 = 57/64
April 25, 2014

Calculus Please Help4
You appear to have found their intersection correct as (3,3) and (19,-5) USING VERTICAL SLICES: y^2 = x+6 so y = ± √(x+6) = ± (x+6)^(1/2) so for the part from -6 to 3 height = (x+6)^ - ( -(x+6)^(1/2) = 2(x+6)^(1/2) integral of that is (4/3)(x+6)^(3/2) area ...
April 25, 2014

Calculus Please Help3
intersection points: y = 5 with 2y = 3√x ---> (100/9 , 5) y = 5 with 2x+2y = 5 ---> (-2.5, 5) 2y = 3√x with 2x + 2y = 5 ---> 1 , 3/2) So I see it as area = ∫(5 - (5-2x)/2) dx from -2.5 to 1 + ∫((5-(3/2)(x^.5) )dx from 1 to 100/9 = 6.125 + 14....
April 25, 2014

Algebra
Suppose the question had said: when a number is divided by 4 the quotient is 6 with a remainder of 1 we would write: number = 6(4) + 1 = 25 so f(x) = (x^3 + x^2 - 4)(x+3) + 8 = x^4 + 3x^3 + x^3 + 3x^2 - 4x - 12 + 8 = x^4 + 4x^3 + 3x^2 - 4x - 4
April 24, 2014

Calculus Help Please Urgent!!!
height = -1.6t^2 + 32t + 3 b) need the vertex of that parabola t of vertex = -b/(2a) = -32/-32 = 1 second height = -16(1) + 32(1) + 3 = 19 m c) hits the moon ground when h = 0 -16t^2 + 32t + 3 = 0 t = (-32 ± √1216)/-32 = -.089 or 2.09 seconds so , "in the air...
April 24, 2014

Math
prob(H win) = 1/3 , prob(A win) = 2/3 prob(H loss) = 2/3 , prob(A loss) = 1/3 a) not good on trees in this forum, hard to show b) Prob (HH) = (1/3)(1/3) = 1/9 Prob(AA) = (2/3)(2/3) = 4/9 c) to go 3 games, could be AHA or HAH prob of that = (2/3)(1/3)(2/3) + (1/3)(2/3)(1/3) = 4...
April 24, 2014

mathematics
1. What is 1 - 1/13 ? 2. ....... 3. to get a 2 ---> 11 to get a 5 ---> 14, 41, 23, 32 or 4 ways so to get a 2 or 5 ----> 5 possible outcomes prob(2 or 5) = 5/36 so in 1000 tosses we expect (5/36)(1000) or appr 139 times
April 24, 2014

typo correction -Math
my first equation should have been cosØ = 49/50 = .98
April 24, 2014

Math
Make a situation diagram where you have a triangle with the vertical angle as Ø, the hypotenuse 50 cm (the pendulum) and a vertical leg of 49 cm so we would get cosØ - 49/50 = .98 then Ø = .20033.. (I stored that in my calculator to keep accuracy) so we ...
April 24, 2014

finances
P(1.04^35 - 1)/.04 = 1000000 P = $ 13,577.32
April 24, 2014

Algebra
I did a synthetic division (or you can do a long algebraic division) to get a remainder of (c+1188) So for the division to be exact, x+1188 = 0 c = - 1188 http://www.wolframalpha.com/input/?i=%28x%5E4+-+3x%5E2+-1188%29%2F%28+x%2B6%29 look at "quotient and remainder" ...
April 24, 2014

Math
a) the only even prime is the number 2 so prob = 1/6 b) primes less than 5 are : 2 and 3 so prob = 2/6 = 1/3 c) if not a 6, then it must be: 1, 2, 3, 4, or 5 how many of those are prime? d) which of 1 or 2 is prime ? e) how many even's < 4 are prime? etc.
April 24, 2014

Algebra
(√5a^-2)/(√10a^-1) = (√5 a)/(√10 a^2) = 1/(√2 a)
April 24, 2014

Math
volume of whole apple = (4/3)π(6^3) = 288π cm^3 volume of inner part of apple with radius 5 cm = (4/3)π(5^3) = 500π/3 cm^3 part of apple within 1 cm of outside = 288π - 500π/3 = 364π/3 prob(being in outer part of apple) = (364π/3) / (288...
April 24, 2014

Math
expected income = .2(0) + .3(-1000) .25(-10000) + .25(20000) = 2200
April 24, 2014

Math
Let the line joining (1,-4) and (6,-4) be the base of your triangle. This is a horizontal line, and it should be easy to see that its length is 5 let the height be h (1/2)(5)h = 20 5h = 40 h = 4 so any point on the x-axis (or 4 units above your base) would be such a third ...
April 24, 2014

math
So they must enter in the order G B B B G number of ways = 2 * 3*2*1 * 1 = 12
April 24, 2014

Math
could be 1. YY --->(5/29)(4/28) = 20/812 2. GG ---> (7/29)(6/28) = 42/812 ... 5. BB ---> 4/29)(3/28) = 12/812) Add them up (20 + 42 + .. + 12)812 = ....
April 24, 2014

Math
so prob that 5 of the 10 smoke = C(10,5)(.4^5)(.6^5) = appr .2 40% of college students smoke ??? Are those stats from the 50's ?
April 24, 2014

Math
number of slices per pizza = 360/40 =9 so for 2 pizzas we have 18 pieces and at 1 slice per person, we would have 18 people. (cutting a pizza into 9 pieces ??? Good luck Are you going to lay a protractor on the pizza and measure 40° ?)
April 24, 2014

Math - Answer Check
What is (2/3) of (2 1/10) ? = (2/3)(21/10) = 7/5 units of distance or 1.4 units or 1 2/5 units
April 24, 2014

Math
First one is easy. The cow can cover 3/4 of a circle with radius 40 (the missing quarter is the barn) area = (3/4)(π(40^2) = 1200π yds^2 2nd one: let's tie the cow up at the top left corner. with a rope of 75 yds, the cow can cover (3/4)(π(75^2) or 4218.75&#...
April 24, 2014

math
Since cost usually varies with the area and the area is proportional to the square of the corresponding sides, the area would be 4 times as large, thus the cost would be 4($1.5) or $6.00 ( ratio of sides = 2:1 so ratio of areas = 2^2 : 1^2 = 4 : 1 ratio of costs = 4 : 1 )
April 24, 2014

Math
√(3f^3) = √3 * √(f^2) * √f = √3*f*√f = f√3√f = f√(3f)
April 24, 2014

Math
Taking it just the way you typed it ... = √3/( (√f)^-3) = √( 3/f^-3) = √(3f^3) = f√(3f)
April 24, 2014

math
? ? ? What does that mean?
April 24, 2014

math
I would make time (t) my horizontal axis marking it up to 5 hours. Make your vertical axis the calorie axis , marking it as 100 , 200, ... up to 1000 calories. plot the ordered pairs (1,300) , (2, 600) , (3, 900) and (4,1200) you should get a straight line Notice (0,0) should ...
April 24, 2014

Calculus
mmmhh v = ∫(5t/4)(t^2 + 1)^2 dt = (5t/4)(((1/3)(1/(2t)) (t^2 + 1)^3 + c = (5/24)(t^2 + 1)^3 + c differentiate to get ((5/4)(t)(t^2 + 1)^2
April 24, 2014

Calculus
right now: price of rent = 900 number of units rented = 50 Let the number of $25 increases be n (e.g. If n= 2 , new rent is 900+2(25) = 950 if n = 5 , the new rent 900 + 5(25) = 1025 so the new rent = 900 + 25n number rented = 50-n maintenance cost = 75(50-n) Profit = P = (900...
April 24, 2014

Calculus
Make a sketch ... Place the first vehicle A at the origin P, showing the position of the first vehicle draw a short line east of P and label it A2 Place the second vehicle B at a distance of 5 above P showing the initial position of the second vehicle draw line downwards from ...
April 24, 2014

math
Steve did this for you http://www.jiskha.com/display.cgi?id=1398006054 All that was required of you want a bit of "counting" .
April 24, 2014

Math Help
You have been helped repeatedly by several tutors for these same type of questions. I think it is time that you try them yourself and show where your difficulties lie with these. e.g In every one, wasn't the first step to find the LCD ? We then multiplied each term by that...
April 24, 2014

trig
16cos(x)-3sec(x)=0 16cos(x) = 3sec(x) 16cosx = 3/cosx cos^2 x = 3/16 cosx = ± √3/4 x = 1.123 or x = π - 1.123 = 2.0186 or x = P + 1.123 = 4.266 or x = 2π - 1.123 = 5.160
April 23, 2014

algebra
you LCD is 12 so .... 6x/12 + 4y/12 - 3z/12 = (6x + 4y - 3z)/12
April 23, 2014

math
given function: y = x+1 Two step process inverse function: (interchange x and y variables) 1. x = y+1 2. solve new equation for y y = x-1 so f^-1 (x) = x-1 Use the above two step method for finding any inverse if it exists.
April 23, 2014

Math Help? Check my answers.
#1 Aren't the terms decreasing by 8 ? So after 6 , you would have -2, -10, -18 #2 aren't the terms increasing by 3 each time ??? So how can you possibly get 14 as the next number after 12 ??? #3 I am puzzled by your choices you started with -1, 9, 19, 29, adding 10 ...
April 23, 2014

math
Draw a "side view" of the cut sphere. draw a line from centre of the circular cut to the centre of the sphere. You will have a right-angled triangle with base 10 (half the diameter of the circle) and a hypotenuse of 15. let the third side be h h^2 + 10^2 = 15^2 h...
April 23, 2014

Math
Your given example illustrates a case where there is a definite number of ways for things to happen, thus it is a theoretical probability situation, you had that one. But you said: You draw five cards from a standard deck of 52 cards. P(heart) = 4/5 (fraction) Did you mean ...
April 23, 2014

ALGEBRA
For any centre (a,b) and radius r, the equation of the circle is (x-a)^2 + (y-b)^2 = r^2 look at your second equation, (x+6)^2 + (y-4)^2 = 16 or 4^2 doesn't it fit that pattern perfectly ? for a centre of (-6,4) and radius of 4 Now you can sketch it. Do the same for the ...
April 23, 2014

math
think of money $.700 = 70 cents $.007 = .7 cents which would you rather have ? or .700 contains 7 tenths .007 contains zero tenths, none, nada, nichts, nil. ...
April 23, 2014

math
No, the area of similar shapes is proportional to the square of the corresponding sides So 2:1 ----> 2^2 : 1^2 = 4 : 1 The area would be 4 times as large, or quadrupled. Proof: area of original = 5*3 = 15 new sides are 10 and 6 new area = 10*6 = 60 and 60 = 4 times 15
April 23, 2014

triangle measurements
Are you sure that there was no angle given, or perhaps the area was given? With only 2 pieces of information, we can't go further.
April 22, 2014

triangle measurements
Trying very hard to visualize a triangle that has a "top length" and a "lower length". You appear to give the length of 2 sides, which is not enough information to find anything else.
April 22, 2014

angle measurements HELP ME PLZ QUICKLY!!!
Yes, it is right-angled triangle. I thought you had answered A) and used "a" as your answer. Since you don't use any capitals in your sentence, and use "no" instead of "know" etc, it was easy to mis-interpret your answer. Your statement : I ...
April 22, 2014

angle measurements HELP ME PLZ QUICKLY!!!
yes, you are wrong I don't know how much more of a hint I could have given you. 1. I ruled out your choice with a reason for doing so 2. I gave you a very blatant hint !
April 22, 2014

angle measurements HELP ME PLZ QUICKLY!!!
An acute angle is an angle less than 90° your triangle has a 90° angle, often called a "right angle" Do you wish to rethink your choice? Aghast at : I no what this triangle would look like thought u should no!
April 22, 2014

Math
monthly rate = .0575/12 = .004791666.. n = 12(12) = 180 P ( 1 - 1.00479166..^-180)/.00479166.. = 250000 I get P = $ 2076.03
April 22, 2014

math
using the formula x = (-2 ± √(4 - 4(3)(2) )/6 = (-2 ± √ -20)/6 = (-2 ± 2√5 i )/6 = (-1 ± √5 i )/3
April 22, 2014

bearings
for intersection , use substitution in the 2nd equation 2x + 3y - 21 = 0 2x + 3(4x-7) = 21 2x + 12x - 21 = 21 14x = 42 x = 3 y = 4(3) -7 = 5 so we have the line going through (3,5) and (-2,8) slope of line = (8-5)/(-2-3) = -3/5 using (3,5) y-5 = (-3/5)(x-3) times 5 5y - 25 = -...
April 22, 2014

Pre-Cal
what about it? here is a picture of it http://www.wolframalpha.com/input/?i=y%3D%281%2F2%29cos%284%28t-6%29%29%2B6
April 22, 2014

math
Wow, 17% interest from a savings account ? anyway .... P( 1 - 1.17^-20)/.17 = 250000 .. P = $57, 309.99 this might seem unreasonably high, but remember the interest rate is unreasonable, As a matter of fact his fund will earn .17(250,000) or $42,500 in interest the first year...
April 22, 2014

Math
This time you want future amount i = .065/52 = .00125 P( 1.00125^312 - 1)/.00125 = 15000 ... P = 39.34 weekly payment is $39.34
April 22, 2014

Math
see same question in first of "Related Questions" below
April 22, 2014

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