Tuesday
May 3, 2016

Posts by Reiny

Total # Posts: 34,470

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

Calculus
.638 = 1(1/2)^(t/5730) log .638 = (t/5730)log .5 t/5730 = log .638/log .5 = .64837... t = appr 3715 years
March 27, 2016

maths
If y = x/2 - 7/2 and it passes through C and E which are the x and y intercepts respectively, the for C, let y = 0 0 = x/2 - 7/2 x/2 = 7/2 x = 7, so C is (7,0) Why all that extra stuff about parabolas etc ?
March 27, 2016

math
Yesterday, I gave you this solution, but for some reason you didn't like it: See Related Question #1 below. "Let the amount of old stuff drained be x gallons so you have 4-x gallons left of 25% solution .25(4-x) + x = .5(4) 1 - .25x + x = 2 .75x = 1 (3/4)x = 1 x = 4/3...
March 27, 2016

math
so have a diamond, which means there are 51 cards left, of which 13 are still spades Prob(spade) = 13/51
March 26, 2016

precal
Always proofread your post before sending it, to make sure it makes sense.
March 26, 2016

Calculus
You probably expected this to come out as S = c/x^2 + k/(d-x)^2 = c x^-2 + k(d-x)^-2 dS/dx = -2cx^-3 - 2k(d-x)^-3 = 0 for a min c/x^3 = k/(d-x)^3 but k = 9c c/x^3 = 9c/(d-x)^3 1/x^3 = 9/(d-x)^3 (d-x)^3 = 9x^3 d-x = (9^(1/3))x d = x( 9^(1/3) - 1) x = d/(9^(1/3) - 1)
March 26, 2016

Algebra
400/s + 160/s + 240/(s-20) = 11 ok, hint: multiply each term by s(s-20) to get a quadratic. Hint: it comes out to be a nice whole number
March 26, 2016

Algebra
I did this for you here http://www.jiskha.com/display.cgi?id=1458920959 hoping you would be able to find the equation yourself then Steve finished it for you here: http://www.jiskha.com/display.cgi?id=1458939085
March 26, 2016

math
tan(t)=1/tan (t) tan^2 t = 1 tan t = ± 1 t = π/4, 3π/4, 5π/4, and 7π/4 2sin(t)cos(t) + sin(t) -2cos(t)-1= 0 by grouping: sint(2cost + 1) - (2cost + 1) = 0 (2cost+1)(sint-1) = 0 cost = -1/2 or sint = 1 I will let you finish that one 2cos3x = 1 cos3x...
March 26, 2016

calculus2
amount = a (1/2)^(t/74) where t is in years so when t = 10 amount = a(.5)^(10/74) = .91058.. a so appr 91% will be left
March 26, 2016

Algebra 1
corresponding function: y = x^2 - 9 which is a parabola opening upwards, centre at (0,-9) and x-intercepts of ±3 I assume you know how to graph a curve like this. solution : x = ±3
March 26, 2016

contempory math
I noticed the Fibonacci Number property, that is, adding the last two numbers produces the next number. note: 3+4=7 4+7=11 11+7=18 etc
March 26, 2016

math
Let the amount of old stuff drained by x gallons so you have 4-x gallons left of 25% solution .25(4-x) + x = .5(4) 1 - .25x + x = 2 .75x = 1 (3/4)x = 1 x = 4/3 so drain 4/3 gallon of the current solution, then top it up with pure antifreeze
March 26, 2016

math
easiest algorithm for area of any polygon: list the points in a column going counterclockwise, repeat the first point listed: area = (1/2)(downproducts - upproducts) 8 11 2 3 8 3 11 7 8 11 area = (1/2)(24+6+56+121 - (22+24+33+56)) = 36
March 26, 2016

math
could be AB or BA , but the order in which they are sold shouldn't matter, so prob(AB) = (1/9)(1/3) = 1/27
March 26, 2016

math
Prob(defect) = .2 prob(not defective = .8 prob(exactly 2 of 10 are defective_ = C(10,2) (.2)^2 (.8)^8 = .... 2. Use the "back-door" approach if 2 or more are defective, then we can't have: none defective or only 1 defective. = 1 - C(10,0) (.2)^0 (.8)^10 - C(10,1...
March 26, 2016

maths
what is 55-40 ? what is 15/40 ?
March 26, 2016

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