Wednesday
June 29, 2016

Posts by Reiny

Total # Posts: 35,103

math
The letters: AA RR NN G EE M T Number of arrangements = 11!(2!2!2!2!) = 2,494,800
April 11, 2016

math
let the number of students be 19x let the number of teachers be x 19x + x = 500 20x = 500 x = 25 There are 19(25) or 475 students and 25 teachers check: total = 25+475 = 500 ratio = 475 : 25 = 19:1
April 11, 2016

calculus
h = -16t^2 + 79t + 4 we need the vertex of this downwards parabola the t of the vertex = -b/2a = -79/-32 = 79/32 sec for that time height = -16(79/32)^2 + (79/32)(79) + 4 = 197.796.. = 197.80 correct to 2 decimals check my arithmetic
April 11, 2016

Math HELP PLEASE QUICK!
3.54x10^7 m /(3x10^8 m/s) = .118 seconds
April 11, 2016

Calculus
I will assume that you had y'' = 2(x-12)/x^4 f(x) will be concave up when y" > 0 and concave down when y" < 0 we don't have to worry about x^4, it will always be positive, except when x = 0 , which is a restriction on f(x) anyway. I don't see ...
April 11, 2016

Calculus
f(x) = ax^3 + cx^2 + d f'(x) = 3ax^2 + 2cx + 0 f'(-4) = 9 48a - 8c = 9 ** the point (-4,9) is on f(x) -64a + 16c + 6 = 9 *** 2 times ** ---> 96a - 16c = 18 *** ---------> -64a + 16c = 3 add them: 32a = 21 a = 21/32 in 48a - 8c = 9 48(21/32) - 8c = 9 -8c = -45/2 c...
April 11, 2016

mathematics-root of cubic eqn
let f(x) = x^3 + 2x^2 + 3x - 4 by trial: attempt x = ±1 , ±2, ±4 f(1) = 1+2+3-4 ≠ 0 f(-1) = -1+2-3-4 ≠ 0 f(2) = 8+8+6-4 ≠ 0 f(-2) = -8 + 8 - 6 - 4 ≠ 0 f(4) ≠ 0 f(-4) = -64 + 32 - 12 - 4 ≠ 0 There are no nice rational ...
April 11, 2016

Math
The 300 would be correct if he gave no discount So his final selling price has to be P300 let the marked price be x so .6x = 300 x = 300/.6 = 500 check: the marked price is 500 giving a discount of 40%, which is 200 means that he sells at 300 profit = 300-200 = 100 percentage ...
April 11, 2016

Math
distance of 1st bounce --- 8 distance of 2nd bounce --- 2(4) = 8 distance of 3rd bounce --- 2(2) = 4 distance of 4th bounce --- 2(1) = 2 distance of 5th bounce --- 2(1/2) = 1 distance of 6th bounce --- 2(1/4) = 1/2 distance of 7th bounce --- 2(1/8) = 1/4 distance of 8th bounce...
April 11, 2016

@ Anonymous
If you are going to give a detailed solution, then you should not gloss over the critical part of your solution: SO Equation 1 X + (6/X) = 5 X=2 or else you might just as well state the obvious solution at the beginning.
April 11, 2016

math
2 and 3 just sort of popped into my mind.
April 11, 2016

Math
Your distance of 450.69 miles is correct However, the angle of 17.43 is the angle within the triangle. You must add the original direction of 27 degrees to get S 44.3 E
April 11, 2016

Math
After you make your sketch, and after you enter your angles, you should realize that the plane makes a 90 degree turn. So you just have a right-angled triangle. Use Pythagoras to find the distance. Let the angle opposite the 135 side be θ then tanθ = 135/430 θ...
April 11, 2016

Math: Trigonometry
ahhh, missed the part where we want the sum of the first 3 π/12 + 5π/12 + 7π/12 = 13π/12
April 10, 2016

Math: Trigonometry
4cos^2(2x-pi) = 3 cos^2 (2x - pi) = 3/4 cos (2x-pi) = ± √3/2 I know that cos 30° = √3/2 so 2x - pi = pi/6 2x = pi + pi/6 x = 7pi/12 ---->105° since we had cos(2x-pi) = ± √3/2 2x - pi could have been in any of the 4 quadrants 2x - pi...
April 10, 2016

Geometry
simplest way: Heron's Formula A = √(s(s-a)(s-b)(s-c)), where s = (1/2)the perimeter. s = (1/2)(15 + 15 + 8) = 19 s-a = 19-15 = 4 s-b = 19-15 = 4 s-c = 19-8 - 11 area = √(19(4)(4)(11) = √3344 = appr 57.83 2nd way: works in this case because it is isosceles...
April 10, 2016

math
First let's choose the books top shelf = C(6,4) = 15 middle shelf = C(3,2) = 3 bottom shelf = C(6,3) = 20 so he can read 15x3x20 or 900 different combinations of 9 books Now for each of the choices of 9 books, he can read them in 9! ways. so the number of ways he can read ...
April 10, 2016

math
ahh, behold the beauty of the metric system 130 mm = 13 cm
April 10, 2016

Math
Don't know what you mean by "I had to make prisms out of construction paper of the same size". Did you mean the same volume? , the same height? What stays the same?
April 10, 2016

Trig
you need to sketch right-angled triangles to get the missing sides given: sinx = -1/4, y = -1, r = 4 x^2 + y^2 = r^2 x^2 + 1 = 16 x = -√15 in III So sinx = -1/4 , cosx = -√15/4 , tanx = 1/√15 given: cosy = -4/5, x = -4, r = 5 then y = -3 siny = -3/5, cosy = -...
April 10, 2016

algebra
So this flagpole is almost 4 miles high? WOW And the cables are attached almost 2 miles from the base of this massive flagpole?? Check your typing, I bet you dropped a decimal point or something.
April 10, 2016

Math
Other than the fact that you can't bushwhack on the Appalachian Trail, we have a clear cut case of using the cosine law: let the distance back be x miles x^2 = 8^2 + 10^2 - 2(8)(10)cos113° = 273.40... x = 16.534.. (don't round off your calculator answer) now by the...
April 10, 2016

Math
#1, correct #2, to be horizontal, they must have the same y to be vertical, they must have the same x So, do you wish to change your answer?
April 10, 2016

Math
assuming that numbers and letters can be repeated ... number of cases = 26x10x10x10x26 =
April 10, 2016

Trigonometry
for each one, use the CAST rule to find where else a certain trig ratio is positive or negative for #1, you have found the angles in quadrant I, but the tangent is also positive in III, (the T of CAST) So è = 30 degrees in I ---> pi/6 or è = 210 in III ------ ...
April 10, 2016

interest
no time given for the first part. 2nd part: 500(1.04)^n = 1000 1.04^n = 2 take log of both sides n log 1.04 = log 2 n = log2/log1.04 = 17.67 years or n = 17.7 years correct to one decimal
April 10, 2016

Geometry
confusing question. Where does A come from. your 4 points R,S,T,U do not form a parallogram What are Rec1 etc ?
April 10, 2016

math
I know that Sixteen tons will get you another day older and deeper in debt
April 10, 2016

Math
Just did this less than an hour ago http://www.jiskha.com/display.cgi?id=1460275337
April 10, 2016

Maths
volume = pi r^2 h plug in your numbers, your r = .8
April 10, 2016

Math
a) for 25 therms cost = $.6686(25)) = $16.72 b) cost = 16.72 + (45-25)(.8587 = $33.89 c) cost = (x-25)(.8587) + 16.72 , for x > 25 or = .6686x , for 0 < x ≤ 25
April 10, 2016

math
morning of day 1 -- 3 ft evening of day 1 -- 1 ft ,(3-2) morning of day 2 -- 4 ft evening of day 2 -- 2 ... morning of day 27 -- 29 ft evening of day 27 -- 27 ft morning of day 28 -- 30 ft He has reached the top, no sliding back He will reach the top on Feb 28th
April 10, 2016

maths
a+11d - (a + 2d) = 36 9d = 36 d = 4 term(16) = a+15d = 64 a + 60 = 64 a = 4 so a = 4, d = 4
April 10, 2016

Math
between √13 and what ? And zero? since √13 = appr 3.6 that would be {1,2,3} correct your typing otherwise.
April 10, 2016

Calculus (30min before deadline help pls )
Make a sketch. Let the length of the girl's shadow be x let her distance from the lamp be y so you have 2 similar triangles: 5/x = 16/(x+y) 5x + 5y = 16x 5y = 11x 5 dy/dx = 11 dx/dx dy/dx = 11/5 so her shadow is increasing at 11/5 ft/sec or2.2 ft/sec but it is moving at 11...
April 9, 2016

Calculus
Make a sideview sketch let the radius of the cone be r cm let the distance from the base of the cone to the centre of the circle be h So the height of the cone is h+10 cm draw a radius from the centre to the base of the cone, it will be a right triangle r^2 + h^2 = 100 r^2 = ...
April 9, 2016

Algebra
time = distance/rate let her rate on the first trip be x mph 6/x + 6/3x = 2 each term by 3x 18 + 6 = 6x x = 4 she went out at 4 mph, and came back at 12 mph (12 mph for 6 miles in a kayak???, Wow!!)
April 9, 2016

Math
prob(defective) = 4/12 = 1/3 prob(not defective) = 2/3 a) prob(both defective) = C(2,2) (1/3)^2 = 1/9 b) one defective: = C(2,1)(1/3)(2/3) = 2(2/9) = 4/9 c) at most 1 is defective ----> rule out both defective, which we did in a) so Pro(of at most 1 defective) = 1 - 1/9 = 8...
April 9, 2016

Math
Do you know what a scale factor is? e.g. there are 12 inches in a foot so if we have a patio which is 10 ft by 14 ft, I could make a drawing where 1 inch repesents 1 foot. My scale factor is 12 so I would draw my patio as 10 inches by 14 inches In our case the scale factor is ...
April 9, 2016

Calculus
let the width be x and the length y , were the brick wall is along the length. the xy = 102 y = 102/x Cost = 50(2x) + 50y + 60y = 100x + 110y = 100x + 110(102/x) = 100x + 11220/x d(cost)/dx = 100 - 11220/x^2 = 0 for a min of cost 11220/x^2 = 100 100x^2 = 11220 x^2 = 11220/100 ...
April 9, 2016

Probability
prob(success) = 3/4 prob(fail) = 1/4 prob(2 of 11 to fail) = C(11,2)(1/4)^2 (3/4)^9 = .258 check my arithmetic
April 9, 2016

Mathematics
write it up this way: 9-5[8-3]*2+6 = 9 - 5[5]*2 + 6 = 9 - 50 + 6 = -35 I have no idea what happened in your "second" step
April 9, 2016

math
time for first car --- t hours time for 2nd car ------ t+2 hrs distance covered by first car = 55t miles distance covered by 2nd car = 40(t+2) 50t - 40(t+2) = 10 50t - 40t - 80 = 10 10t = 90 t = 9 the first car went for 9 hrs, and the second went 11 hrs. check: distance ...
April 9, 2016

algebra
I have no idea what this means. Are you solving some equation? What is the original equation?
April 9, 2016

LOGARITHM
totally unreasonable answer some number squared has to be 7 so a quick mental check would be (2(17) - 1)^2 = 33^2 = 1089 , certainly not 7 this is a standard quadratic, which is in a nice form (2x-1)^2 = 7 2x-1 = ± √7 2x = 1 ± √7 x = (1 ± &#...
April 9, 2016

Logarithm
I answered this further up the listing
April 9, 2016

Logarithm
Ln2+Lnx=1 ln(2x) = 1 by definition of ln e^1 = 2x x = e/2
April 9, 2016

Math: Parametric Equations
does this help? https://www.wolframalpha.com/input/?i=plot+x+%3D++cos(4t),+y+%3D+sin(6t)
April 9, 2016

MAth
let n be the number of half-years i = .072/2 = .036 73,000(1.036)^n = 100,000 1.036^n = 1.36986... log both sides and use log rules n log 1.036 = log 1.36986.. n = 8.898.. half-years = appr 4.45 years
April 9, 2016

algebra
number of whites --- x number of yellows --- 18-x 995x + 1250(18-x) = 22245 (I changed the $'s to cents) solve for x, has to come out as a whole number
April 9, 2016

Canadian finances
I have placed *** behind my choices. If you see no *** or no comment, I agree with your answer. which of the following services do banks not provide? a. lines of credit b. health insurance *** c. currency exchange d. none of above (THIS ONE) which institutions does not offer ...
April 9, 2016

Math
x(x+5) = 350 x^2 + 5x - 350 = 0 too bad it doesn't factor. By the formula x = (-5 + √1425)/2 = appr 16.37 ft take over remember perimeter = 2width + 2length
April 9, 2016

math
i = .038/365 n= 365(4) = 1460 principal = 3500 amount = 3500( 1 + .038/365)^1460 = 4074.53 So interest earned = 4074/53-3500 = 574.53 which is choice a)
April 9, 2016

Geometry
width ---- x length ---- 2x+5 x(2x+5) = 1375 2x^2 + 5x - 1375 = 0 solve the quadratic hint: it factors, but it may be just as fast to use the formula
April 9, 2016

Precalculus
How about this way: Since AC supports a 45 degree angle at the circle, AC must support a 90 degree angle at the centre. let the radius be r r^2 + r^2 = 8^2 2r^2 = 64 r^2 = 32 Area = pi r^2 = 32 pi or appr 100.53 Notice just as Damon pointed out, we don't even need to know ...
April 9, 2016

karki
let the AP be a, a+d, a+2d so 3a + 3d = 45 a+d = 15 ---> d = 15-a and a(a+d)(a+2d)=300 a(a^2 + 3ad + 2d^2) = 300 a(a^2 + 3a(15-a) + 2(15-a)^2) = 300 a(a^2 + 45a - 3a^2 + 450 - 60a + 2a^2) = 300 a(- 15a + 450) = 300 -15a^2 + 450a - 300 = 0 a^2 - 30a + 20 = 0 a = (30 ±...
April 9, 2016

Trigonometrt
sin ( 810- theta) I am sure you meant: sin(180 - θ) which is sinθ cot(θ - 360) .... recall that tan(-x) = -tanx and tan(360-x) = -tanx and of course the cot behaves just like the tan cot(θ-360) = -cot(360-θ) = -(-cotθ) = cotθ cos(-180 - θ...
April 9, 2016

Probability (Math)
You are correct
April 9, 2016

math
Since Mathematics is a precise language, it requires precise and correct English to express a problem to be solved. Please re-type your problem using correct and proper English so that it makes sense to me. "Texting" English doesn't cut it.
April 9, 2016

gemoetry
I don't see any diagram but by a simple trig ratio, we have cos 75.5 = 20/L L = 20/cos75.5 = appr 79.9 ft Wow, a ladder to go up about 8 stories high???
April 9, 2016

Math
If x = 2√2 and x = -2√2 then two of the factors are (x - 2√2) and (x + 2√2) or (x^2 - 8) must be a factor of your polynomial. Do a long algebraic division to get x^4+4x^3-4x^2-32x-32 = (x^2 - 8)(x^2 - 4x + 4) we can get more roots from x^2 - 4x + 4 = 0...
April 9, 2016

math
Just replace the units with their equivalents. 24 miles / 1 hour = 24*1760 yards / 60 minutes = (42240/60) yards/min = 704 yards/min I agree with your answer
April 9, 2016

MATH
I agree with your equation and I get $4011.25. Beyond that, I can't help you since I don't know what you mean by "syntax" error.
April 9, 2016

I NEED HELP!!!
arrange it in more standard form 2x^2 + 6x - 5 = 0 use the formula: x = (-6 ± √76)/4 = (-6 ± 2√19)/4 = (-3 ± √19)/2
April 9, 2016

Algebra
you are basically looking for the vertex of this downwards opening parabola the t of the vertex is -b/2a = -64/-32 = 2 seconds it will take 2 seconds to reach the maximum height when t = 2 h = -16(4) + 64(2) + 9 = 73 ft
April 8, 2016

Algebra
the real parts of the left side must match the real parts of the right side, and the imaginary parts .... your steps are correct, so x = -4, y = 1
April 8, 2016

Algebra
A(t) = 3- 2t^2 + 4^t A(2) - A(1) = 3 - 2(4) + 4(4) - (3 - 2(1) + 4(1)) = 3 - 8 + 16 - 3 + 2 - 4 = 6 you are correct
April 8, 2016

Math
let y = (3x - 7)/(x + 1) for the inverse , exchange the x and y's x = (3y-7)/(y+1) now solve this for y ... xy + x = 3y - 7 xy - 3y = -x - 7 y(x-3) = -x - 7 y = (-x - 7)/(x - 3) = (x+7)/(3-x) f^-1 (x) = (x+7)/(3-x) check: f(1) = (3-7)/(2 = -2 f^-1 (-2) = (-2+7)/(3-(-2)) = ...
April 8, 2016

MATH
Your formula is a creative variation of the real one amount = 60000( (1 + .07/2)^50 - 1)/(.07/2) = 60000( 1.035^50 - 1)/.035 =
April 8, 2016

Math
8% per annum compounded semi-annually ---> 4% every half year so i = .04 number of half-years in 18 years = 36 amount = 20,000( 1.04^36), as Bob had = $82,078.65
April 8, 2016

math
number of small trucks --- x number of vans ----- 2x number of large trucks = 280 - 3x 30,000x + 25,000(2x) + 40,000(280-3x) = 8,000,000 divide by 5000 6x + 10x + 8(280-x) = 1600 carry on
April 8, 2016

Algebra 1-HELP!
(6^3/8)^2/5 = 6^((3/8)(2/5)) = 6^(3/20)
April 8, 2016

math
original fraction : x/y new fraction = .9x/(.5y) = 9x/5y (9x/5y) / (x/y) = 9x/5y * y/x = 9/5 = 1.8 so it increased by 80% e.g suppose we had 100/200 or 1/2 new fraction = 90/100 or 9/10 new ratio = (9/10) / (1/2) = 9/5
April 8, 2016

math
increases expressed as a single increase = 1.2(1.15) = 1.38 it increased by 38%
April 8, 2016

math
correct
April 8, 2016

math
Distance walking --- x distance by cab ---- 31-x time walking = x/4 time by cab = (31-x)/50 Your "formula", we call it an equation x/4 + (31-x)/50 = 2 solve for x, plug x into 31-x
April 8, 2016

geometry
The radius of the whole circle = 2πr = 10π Now, what fraction of that circumference is a 45 degree sector?
April 8, 2016

Math w/business apps
solve for x x(1 + .06/12)^12 = 20000
April 8, 2016

Algebra 1-HELP!
Did you first look for the HCF ? I see: 8(4a^2 + 12a^2 + 9) hint#2: Did you notice the perfect squares at front and end of the trinomial?
April 8, 2016

Algebra 1
hint: if there are x cans and you have 800 cans and bottles, wouldn't the number of bottles be 800-x ?
April 8, 2016

algebra
As Bob noted you don't have an equation. you probably have the expression (x - 1/x)/(1 + 1/x) and are asked to simplify it. Hint: how about multiplying the fraction by x/x
April 8, 2016

math
Why would "guess" for math problems Surely you could have tried to work them out #6 is trivial #8-12 deal with the rules of multiplying and dividing powers When multiplying powers with the same base, keep the base and add the exponents e.g. x^4 * x^8 = x^12 When ...
April 8, 2016

math {sequences}please help
#3 is geometric with a common ratio of 1/3 your other answers are correct
April 8, 2016

GEOMETRIC SEQUENCES
No Think of how you would obtain the next term you could take .18 of the previous term and subtract or just take .82 of it so the sequence is: 20000 , 20000(.82), 20000(.82)^2 , .... so r = .82 I am sure you can now answer the question
April 8, 2016

math
No interest ? Give it to me and after 35 years, my estate will pay you back 1000(12)(35) or $ 420,000
April 8, 2016

math
let the tens digit be x then the unit digit is 3x so the number is 10x + 3x = 13x the number reversed is 10(3x) + x = 31x 31x + 13x = 88 44x = 88 x = 2 3x = 6 The original number was 26 check: is 26 + 62 = 88 ? YES my answer is correct
April 8, 2016

linear equation in one variables
let unit digit be x then tens digit is 9-x the number is : 10(9-x) + x = 90 - 9x the number reversed is 10x + 9-x = 9x + 9 9x+9 - (90-9x) = 27 18x - 81 = 27 18x = 108 x = 6 unit digit is 6 tens digit is 3 The number is 36
April 8, 2016

elementary quantitative methos
This is just finding the P of a PV. Same formula, same story.
April 8, 2016

elementary quantitative methos
beginning of 2nd year ---> end of first year. I will assume the 12th payment has been made outstanding balance = 230000(1.01625)^12 - 3817.23( 1.01625^12 - 1)/.01625 = ....
April 8, 2016

elementary quantitative methos
subtract 100,000 from 240,000, that is your PV i = .195/12 = n = 240 P = ? straight formula application ( I got 3817.23 )
April 8, 2016

elementary quantitative methos
Use the PV formula I showed you in your previous post
April 8, 2016

elementary quantitative methos
i = .085/4 = .02125 n = 20 amount = A = 30000 payment = P = ? You must memorize the formulas A = P( (1+i)^n - 1)/i and PV = P (1 - (1+i)^-n )/i, where PV is the present value just sub in all your data and solve for the missing variable. 30000 = P( 1.02125^20 - 1).02125 30000...
April 8, 2016

Math
number of stickers ---- x number of ballons --- 6x bubbles ----- (1/3)(6x) = 2x x + 6x + 2x = 135 solve for x
April 7, 2016

Math
I assume you mean by just guessing. he must get 8 right, or 9 right or 10 right = C(10,8)(1/2)^8 (1/2)^2 + C(10,9)(1/2)^9(1/2) + C(10,10) (1/2)^10 = (1/2)^10 ( 45 + 9 + 1) = 55(1/2)^10 = 55/1024 not good, better study
April 7, 2016

Math
let the side of square ABCD be x then area = x^2 area of square EFGH = 2x^2 side of square EFGH = √2 x EF = √2 x AC^2 = x^2 + x^2 = 2x^2 AC = √2 x AB/AC = x/√2x = 1/√2 AB/EF = x/√2x = 1/√2 thus AB/AC = AB/EF
April 7, 2016

Math
original price ----- x dollars .85(1.08)x = 688.50 solve for x
April 7, 2016

Math
In a refection over the x-axis, the x coordinate would stay the same, but the y would turn into its opposite that is, (x,y) ---> (x, -y) A(2,-5) ---> A'(2,5) find the choice that matches this
April 7, 2016

pre ap math
If it is lauched from a height of 48 ft, then the equation should be h = -16t^2+32t+48 I will assume a typo you want h = 0 (at ground level h=0) 0 = -16t^2+32t+48 t^2-2t-3 = 0 It factors, (t-3)(t+1) = 0 t = 3 or t = -1, rejecting the negative time it took 3 seconds
April 7, 2016

linear equations in one variable
Let the number of ₹5 coins be x then the number of ₹2 = 3x and the number of ₹1 = 160 - x - 3x = 160 - 4x Now for the value: 5x + 2(3x) + 1(160 - 4x) = 300 5x + 6x + 160 - 4x = 300 7x = 140 x = 20 You have 20 ₹5 coins 60 of the ₹2 coins and 80 of ...
April 7, 2016

math probability
The prob that you get a 7 when rolling two dice = 1/6 so when two friends roll , (the same result as you rolling twice) prob(2 7's ) = (1/6)(1/6) = 1/36
April 7, 2016

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