Wednesday
July 27, 2016

Posts by Reiny

Total # Posts: 35,358

Math
There will be 13 terms, so the middle term is term #7 Term(7) = C(12,6)(2x)^6 (3y)^6 = 924(64x^6)(729y^6) = 43110144 x^6 y^6
March 19, 2016

Stupid Math School Math
let the distance covered by the slower car be x miles then the distance covered by the faster car be 750-x miles time for slower car = x/40 time for faster car = (750-x)/50 aren't those times the same ??? so ... x/40 = (750-x)/50 cross-multiply and solve for x Once you ...
March 19, 2016

math
Eli, if this were a 4 mark question on my test, I would give you 1 mark for the answer. proper method: let Pari's age be x then Finn's age is x-9 x = 2(x-9) x = 2x - 18 -x = -18 x = 18 So Pari is 18, and Finn is 9
March 19, 2016

calc
height ------- h base radius --- h/3 V = (1/3)π r^2 h = (1/3)π (h^2/9)(h) = (π/27) h^3 dV/dt = (π/9) h^2 dh/dt for the given data: 15 = π/9 (100)dh/dt dh/dt = 135/(100π) ft/hr
March 19, 2016

sir damon help on these as well co-ordinate
r = 3, Ø = 150° cos150 = x/3 x = 3(-√3/2) = -3√3/2 sin150 = y/3 y = 3sin150 = 3(1/2) = 3/2 the point is (-3√3/2 , 3/2)
March 19, 2016

Math
y-x = x-8 y = 2x-8 z-y = y-x z = 2y - x = 2(2x-8) - x = 3x - 16 20-z = z-y y = 2z - 20 2x - 8 = 2(3x-16)-20 2x-8 = 6x - 32-20 4x = 44 x = 11 y = 22-8 = 14 z = 33-16 = 17 or, simplest way: 4d = 20-8 d = 3 so the terms are 8, 11, 14, 17, and 20 match the x,y, and z
March 19, 2016

Math
With relatively small numbers like in your problem, we could just "grind out" the answer in the following way: numbers which leave a remainder of 1 when divided by 3: 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 .... numbers which leave a remainder of 2 when ...
March 19, 2016

another correction - math
You would first of all have to expand a(x+2)^2 + b(x+2) + c = a(x^2 + 4x + 4) + bx + 2b + c = ax^2 + 4ax + 4a + bx + 2b + c = ax^2 + (4a+b)x + (4a + 2b + c) now compare: 3x^2 <---> ax^2 ---- a = 3 4a+b)x <---> -x 4a + b = -1 12+b = -1 b = -13 4a+2b+c = -9 12 - 26...
March 19, 2016

another correction - math
area = LW , not 2(L+W) that would be perimeter area = (5 - √12)(4 + 6/√3) = 20 + 30/√3 - 4√12 - 6√4 = 20 + 30/√3 *√3/√3 - 8√3 - 12 = 23 + 10√3 - 8√3 = 8 + 2√3 D^2 = (5-√12)^2 + (4+6/√3)^2 = (5...
March 19, 2016

correction - mathematics-logarithm
or log3 x^2 = -8 2 log3 x = -8 3 x = -4 x = 3^-4 x = 1/81 not 1/27 check with calculator if x = 1/27 3 (1/27)^2 = 23 (1/27) = 2(-3) = -6 ≠ -8 1/81 does check out.
March 19, 2016

Maths
You have conflicting data, as I will explain at the end Make a Venn diagram, with two overlapping circles, label them C and T enter 35 in the intersection. Since the T circle must contain 45, but you have already 35 entered , the part with only tea must be 45-35 or 10 Check ...
March 19, 2016

Math
from 1-20 number of primes is 8 number of perfect squares = 4 with no overlap so prob(primes or perfect squares) = 12/20 = 3/5
March 19, 2016

Geometry
a/4 = b/7 multiply both sides by 4 a = 4b/7 divide both sides by b a/b = 4/7
March 18, 2016

Math
let the number be x (x-1)(x+3) = 32 x^2 + 2x - 3 - 32 = 0 x^2 + 2x - 35 = 0 (x+7)(x-5) = 0 x = -7 or x = 5, but the number was to be positive, so the number is 5 check: 4(8) = 32 looks fine.
March 18, 2016

Maths
interest = 100,000(.10)(4) = .....
March 18, 2016

Word Equations
distance by bus --- x km distance walking -- 35-x km x/5 + (35-x)/60 = 1.5 times 60 12x + 35-x = 90 11x = 55 x = 5 he walked 5 km, and went 30 km by bus check: time walking = 5/5 = 1 hr time on bus = 30/60 = 1/2 hr total is 1.5 hrs
March 18, 2016

Data management check
You ignored that fact that "If all but 2 of the clearance fabrics fitfit a least one of these categories" That tells me that of the 44 bolts there were 2 that did not fit any of the given properties, so we only have 42 so change your equation to: 42 = 28+17+22-12-10-...
March 18, 2016

AP Calculus AB
The concept you are dealing with has to do with distance (s), velocity (v), and acceleration (a) You hopefully learned that ds/dt = velocity and dv/dt = acceleration in #2 v(t) = -2t + 6 then s(t) = -t^2 + 6t + c so s(3) = -9 + 18 + c = 9+c and s(0) = 0+0+c displacement = 9+c...
March 18, 2016

Geometry (check)
deal!
March 18, 2016

trig
Make your sketch, label the base of the building C tan40 = 60/AC AC = 60/tan40 tan 70 = 60/BC BC = 70/tan70 AB = AC - BC you do the button-pushing
March 18, 2016

Math
So you are looking at an arithmetic series : 150 + 200 + 250 + .... ≥ 7000 We need to find the number of terms for this to be true. let the number of terms be n a = 150, d = 50, n = ?, sum(n) = 7000 (n/2)(2a + (n-1)d) = 7000 (n/2)(300 + 50(n-1)) = 7000 n(300 + 50n - 50...
March 18, 2016

Math
Ahh, found my previous answer. I told you what had to be done, you did not follow my instructions. http://www.jiskha.com/display.cgi?id=1458258592
March 18, 2016

Math
I think I answered this for you partially several days ago, but since you don't give yourself a "name", I cannot find the posting. I recall showing you how to get the probabilities of getting the different colours, and then telling you to multiply each of those ...
March 18, 2016

Math
first one --- x second one -- y x+y = -64 ---> y = -x-64 2x = y+1 sub the first into that: 2x = -x-64 + 1 3x = -63 x = -21 y = -(-21) - 64 = -43 the two numbers are -21 and -43 check: yes , their sum is -64 twice the first = -42 one more than the second = -43+1 = -42 All is...
March 18, 2016

Math
I would round off to the nearest whole number, or 667
March 18, 2016

Math
what is 1/6 of 4000 ?
March 18, 2016

Math
correct
March 18, 2016

Math
ahhh, found this in the Related Questions below "In three more years,Miguel's grandfather will be six times as old as Miguel was last year.When Miguel's present age is added to his grandfather's present age, the total is 68.How old is each one now? " ...
March 18, 2016

Math
The wording of your question makes no sense. "In three more years, Miguel's grandfather will be six times as old as Miguel was." --- was when ?? " Last year, when Miguel's present age is added to his grandfather's present age the total is 68."...
March 18, 2016

Math
I did this back here http://www.jiskha.com/display.cgi?id=1458255127 all you had to do is multiply my .68 by 18,000
March 17, 2016

Math
I rotation = 70π cm 25(70π) cm per 10 sec 6(25)(70π) cm per minute 60(6)(25)(70π)/100 m per hour 6300π m/hr 6300π/1000 km/h = appr 19.8 km/h
March 17, 2016

Pre-Calc
carry on ... x^2(x-1) = 48 x^3 - x^2 - 48 = 0 some quick mental gymnastic will show that x = 4 works. (64-16 = 48) so it factors into (x-4)(x^2 +3x+12) = 0 some trivial calculations will show the remaining quadratic has no real roots, so x = 4 the original was 4 by 4 by 4
March 17, 2016

Calculus
Make a sketch. Let the points on the parabola be P(x,y) and Q(x,-y) Area = 2y(3-x) = 2y(3-(1/4)y^2) = 6y - (1/2)y^2 d(Area)/dy = 6 - y = 0 for a max of Area y = 6 the max area is 6(6) - (1/2)(36) = 18 square units check my arithmetic
March 17, 2016

calc
You are correct to the end, but keep it as 2x^3 + x - 3 = 0 try a few numbers, to get "nice" answers, (the thing would factor) , x has to be ±1,±3, ±3/2 sure enough x = 1 works so (x-1) is a factor. Either do long division or use something like ...
March 17, 2016

math
Make a sketch of a right-angled triangle the angle of elevation is 13°, the hypotenuse is 300, you want the horizontal (the adjacent) so clearly, the cosine comes to mind cos13° = x/300 x = 300cos13 = 292.311 , which is B
March 17, 2016

math
Why do you think that ? Wrong guess, btw
March 17, 2016

math
correct
March 17, 2016

math
Now Thomas! What do you think? This one is even easier than the other ones you posted. How about showing us your work?
March 17, 2016

math
and ..... ???
March 17, 2016

math
What part of my answer to your almost identical question about 2 hours ago did you no like ? Could you not make that minuscule adjustment? http://www.jiskha.com/display.cgi?id=1458258526
March 17, 2016

math
prob(yellow, then red) = (2/9)(4/8) = 1/9 follow the same kind of reasoning for your second part
March 17, 2016

math
is the first marble picked returned before the second is picked ? - very important.
March 17, 2016

Trigonometry
x= Arc cos 1/2 <-----> cosx = 1/2 then x = π/3 check: on your calculator, (set at degrees) 2ndF cos .5 = to get 60° which is π/3 radians
March 17, 2016

Trigonometry
LS = 2cosx RS = 2(1 - sin^2 x)/cosx = 2cos^2 x/cosx = 2cosx = LS
March 17, 2016

math
prob(red) = 5/12 prob(blue) = 3/12 etc for the other colours. then multiply each prob by 60 you can check your answer by making sure all the prob's above add up to 1 and the sum in the colour distribution is 60
March 17, 2016

math
prob(red, then green) = (7/20)(5/20) = 35/400 = 7/80
March 17, 2016

Math
let the radius be r ft 2πr = 157 r = 157/(2π) = 24.987.. ft area = πr^2 = 1961.5 ft^2 time = 1961.5/400 = appr 4.9 hours
March 17, 2016

Math
You appear to have a typo You must have meant: $20.25 per hour for overtime. normal weekly wage = 40(3.50) = 140 leaving 661.50-140 or $521.50 for overtime. overtime hours = 521.5/20.25 = 25.75 So he worked 40 + 25.75 or 65.75 hours. strange question: very huge gap between ...
March 17, 2016

Geometry
None of them are if you meant it the way you typed your first equation. If you meant: (e+f)/(a-d) = b/a, then a(e+f) = b(a-d) would be the equivalent
March 17, 2016

Math-Measure's & area
#1 correct #2 if the 3 keeps repeating, then .12333... is a rational number equal to 37/300
March 17, 2016

Math
remaining value after 1 year = .8 or 80% remaining value after 2 years = .8(.85) = .68 or 68%
March 17, 2016

Math
Have you come across this identity and its variations? cos 2A = cos^2 A - sin^2 A = 1 - 2sin^2 A = 2cos^2 A - 1 so .... cos^2 4-sin^2 4 = 1 - sin^2 4 - sin^2 4 = 1 - 2sin^2 4 = cos 8 1 - 2sin^2 3 = cos 6
March 17, 2016

mathematics
Place the circle in such a way that the midpoint of CA becomes the origin, and B lies on the y-axis by Pythagoras BO = 12 cm so we have points A(5,0), B(0,12) and C(-5,0) let the centre be (0,k) and the radius r equation: x^2 + (y-k)^2 = r^2 using (5,0) --> 25 + k^2 = r^2 ...
March 17, 2016

math
number of T/F questions --- x number of multiple choice --- 20-x 3x + 11(20-x) = 100 3x + 220 - 11x = 100 -8x = -120 x = 15 15 T/F questions and 5 multiple choices
March 17, 2016

mathematics
draw lines from the centre to the midpoints of the two chords. You will have two right-angled triangles, one with sides x, 5, 13 the other with sides, y, 12, 13 Use Pythagoras to find x=12, and y=5 so the distance between them is 12+5 or 17 cm
March 17, 2016

Precal/math
(2sin pi/12)(cos pi/12) = 2tan (π/12) by definition
March 17, 2016

statistics
If I recall correctly, sd = √5569 = appr 74.626 so we want between 4088+41 and 4088-41 that is , between 4129 and 4047 Using my favourite webpage for this stuff, http://davidmlane.com/hyperstat/z_table.html and entering the above data, I got a probability of .4173 So for...
March 17, 2016

Precal/Math
LS = (cos^2 B / sin^2 B)/cos^2 B - cos^2 B/sin^2 B = cos^2 B/(sin^2 B cos^2 B) - cos^4 B/(sin^2 B cos^2 B) = cos^2 B(1 - cos^2 B)/(sin^2 B cos^2 B) = cos^2 B sin^2 B/(sin^2 B cos^2 B) = 1 = RS
March 17, 2016

Math
let the tens digit of the original be x so original number was 10x+4 number reversed = 40+x 10x+4 = 40+x + 45 9x = 81 x = 9 the old was 94, the new one is 49 Their sum = 143
March 17, 2016

math
Then the sides of the similar triangles must be 3x, 5x, and 7x 3x+5x+7x=75 15x=75 x=5 the shortest side is 15 or perimeter of original = 15 perimeter of new one = 75 so the sides have been increased by a factor of 5 new triangle is 15, 25, and 35
March 17, 2016

math
110 km/13.5 L = 110(0.621371) miles/(13.5(0.264172)) = appr 19.2 mpg btw, in the metric world, gas consumption is not expressed as km/L, but rather as L/100 km So the above would be 12.27 L/100 km (which is quite poor, I use 8.9 L/100 km on my car)
March 17, 2016

Calculus Related Rates
let that distance be x angle be Ø by the cosine law: x^2 = 25+64-2(5)(8)cosØ x^2 = 89 - 80cosØ 2x dx/dt = 80sinØ dØ/dt dx/dt = 40sinØ dØ/dt / x *** when Ø = π/4 or 45° x^2 = 89-80sin π/4 = 32.431... x = 5....
March 17, 2016

Calculus Related Rates
did you make your sketch ? let the height be h ft let the angle be Ø tanØ = h/70 h = 70tanØ dh/dt = 70sec^2 Ø dØ/dt *** when t = 5 sec, h = 75 ft tanØ = 75/70 = 15/14 sketching a right-angled triangle with that data, shows a hypotenuse...
March 17, 2016

Calculus Related Rates
V = (4/3)πr^3 dV/dt = 4πr^2 dr/dt given: dV/dt = 6, r=3 6 = 4π (9) dr/dt dr/dt = 6/(36π) inches/min = 1/(6π) in/min
March 17, 2016

Algebra
width --- x length ---9x x(9x) = 81 x^2 = 9 x = 3 the pool is 3 ft by 27 ft. (I bet whoever swims in that pool is fantastic at flip-turns )
March 17, 2016

Advance Math
If I recall correctly: cosh(x) = cos(ix) or in your case cos(je) so cos^2 (ej) = (cosh(e))^2 (Haven't done this in over 60 years)
March 17, 2016

math
So perimeter of stamp is 2x + 2y and the perimeter of the envelope is 4x + 4y given: 2x+2y + 8x+8y = 50 10x+10y=50 x+y=5 Hence the perimeter of the stamp = 2x+2y = 2(x+y) =2(5) = 10 cm
March 17, 2016

Math
in 1 hour it gains s seconds in 1 day it gains 24s seconds in d days it gains 24sd seconds in d days it gains 24sd/60 minutes in d days it gains 2sd/5 minutes
March 17, 2016

Math
your answer contains the factor x^16, but it was supposed to be x^8 so you would need (x^2)^4 to be in your expression. term(5) = C(12,4) (x^2)^4 (3)^8 = 495 x^8 (6561) = 3247695 x^8 verification: look for the term containing x^8 in http://www.wolframalpha.com/input/?i=expand...
March 17, 2016

Precal/Math
LS = (1/cos^2 A)(sin^2 A) = tan^2 A RS = (tan^2 A + 1 - 1) = tan^2 A = LS
March 16, 2016

Math/Precal
remember that tan^2 x + 1 = sec^2 x also that cos 2x = 2cos^2 x - 1 RS = (2 - (1 + tan^2 x) )/sec^2 x = (2 - sec^2 x)/sec^2 x = 2/sec^2x - 1 = 2cos^2 x - 1 = cos 2x = LS
March 16, 2016

Geometry
midpoint for (-4,1) and (-2,-3) = (-3,-1) slope through the two given points = -4/2 = -2 so slope of perpendicular = 1/2 equation of right-bisector: y+1 = (1/2)(x+3) 2y + 2= x+3 x- 2y = -1 ** midpoint of (-4,1) and (5,-2) is (1/2 , -1/2) slope of chord = -3/9 = -1/3 so slope ...
March 16, 2016

maths
cos(60° + 45°) = cos60cos45 - sin60sin45 = (1/2)(√2/2) - (√3/2)(√2/2) = ( √2 - √6)/4
March 16, 2016

Math
what is 1.5(8) ? what is 1.5(14) ? What is an em ?
March 16, 2016

maths
Ohh my !!!
March 16, 2016

maths
the statement is false log(1+2+3) ≠ log 1 + log 2 + log 3 we know log(1x2x3)=log 1 + log 2 + log 3 but not the way you wrote it if it were true, then 1x2x3 = 1+2+3 , good luck on that one!
March 16, 2016

algebra
y+9=3/5(x+7) y = (3/5)x + 21/5 - 9 y = (3/5)x - 24/5
March 16, 2016

function:maths
Assuming you mean f(x)=2/(x-1) and g(x)=(2x-2)/(3x+3) then g(x) = 2(x-1)/(3(x+1)) f+g = 2/(x-1) + (2/3)(x-1)/(x+1) = ( 6(x+1) + 2(x-1)(x-1))/(3(x^2 - 1)) = (6x + 6 + 2x^2 - 4x + 2)/(3(x^2 - 1) = (2/3)(x^2 + x + 4)/(x^2 - 1) you do fg, which means you just multiply them domain ...
March 16, 2016

GEOMETRY/ALGEBRA
rate of filling = 40 cm^3/4 min = 10 cm^3/min
March 16, 2016

Maths
Strange wording, since all squares and rectangles are "equiangular". Did you mean , find the side of the square which has the same area as the rectangle? then s^2 = 20(5) = 100 s = 10 cm
March 16, 2016

Data Management
number of ways to choose: 6W,9B 5W,10B Number of ways to arrange 6W,9B = (15!/6!9!) = 5005 number of ways to arrange 5W,10B = 15!/(5!10!) = 3003 total number of ways = 5005+3003 = 8008
March 16, 2016

Math
L's equation is correct 2x=13 x = 6.5 twice the number is 13 What is 9 less than that ?
March 16, 2016

Maths
Tom's amount --- x Bob's amount --- y case 1: tom gives 20 to bob Tom now has x+20 Bob has y-20 x+20 = y-20 x - y = -40 case2: Bob gives tom 22 Bob has y-22 Tom has x + 22 x+22 = 2(y-22) x+22 = 2y - 44 x - 2y = -66 subtract these equations: y = 26 sub back in x - 26...
March 16, 2016

mathematics-simultaneous eqn
from x+y+z=2 (x+y+z)^2= 4 x^2 + y^2 + z^2 + 2xy + 2xz + 2yz = 4 using #2: 14 + 2(xy+xz+yz) = 4 xy+xz+yz= -5 (x+y+z)^3 = 8 x^3 + y^3 + z^3 + 3x^2y + 3x^2z + 3y^2x + 3y^2z + 3z^2x + 3z^2y + 6xyz = 8 20 + 3x^2(y + z) + 3y^2(x + z) + 3z^2(x + y) + 6xyz = 8 starting to get messy ...
March 16, 2016

maths
25x^2+4y^2-50x-16y-59=0 25(x^2 - 50x + ...) + 4(y^2 - 4y + ..) = 59 25(x^2 - 2x + 1) + 4(y^2 - 4y + 4) = 59 + 25 + 16 25(x-1)^2 + 4(y-2)^2 = 100 (x-1)^2 /4 + (y-2)^2 /25 = 1 Now just use all the little formulas you must have to state the properties of this nice ellipse
March 16, 2016

maths help!!!
(1-x)^n = 1 + n(-x) + n(n-1)/2! (-x)^2 + n(n-1)(n-2)/3! (-x)^3 + ... = 1-6x+ax^2+bx^3 so -nx = -6x n = 6 n(n-1)/2! (-x)^2 = ax^2 6(5)/2=a a = 15 n(n-1)(n-2)/3! (-x)^3 = bx^3 6(5)(4)/6 = -b b = -20
March 16, 2016

Math
Shorter version: side costing $20/m --- x side costing $5/m -----y 20(2x) + 5(2y) = 1000 4x+y=100 y=100-4x area = xy = x(100-4x) = 100x - 4x^2 This can be represented by a parabola, whose vertex will yield your answer. the x of the vertex is -100/-8 = 12.5 then y = 100 - 4(12....
March 16, 2016

sequence help!!!!! plz steve,reiny,damon,bob...anyone!!!!
I looked at that yesterday, but I could not find an obvious pattern Found this: 5 = 2^2 + 1^2 13 = 3^2 + 2^2 but then it broke apart on the next one Took differences and got: 5 13 -- 8 32 -- 19 -- 11 69 -- 37 -- 18 -- 7 129 - 60 -- 23 -- 5 -- 2 221 - 92 -- 32 -- 9 -- 4 not ...
March 16, 2016

Math
smaller number --- x larger number ---- (x+10) sum of their squares = (x+10) + x^2 = x^2 + 20x + 100 + x^2 = 2x^2 + 20x + 100 this is a parabola opening upwards so it has a minimum. That minimum happens at the vertex. The x of the vertex is -20/4 = -5 so one number is -5, the ...
March 16, 2016

Geometry Honors
The new perpendicualar must be parallel to CD Let MN be that perpendicular with M on AC and N on AC I agree that AD = 28, so we can set up a ratio: MN/AM = 96/28 = 24/7 MN = 24AM/7 Area of triangle AMN = (1/2)(2304) = 1152 = (1/2)(AM)(MN) (1/2)(AM)(24AM/7) = 1152 AM^2 = 672 am...
March 15, 2016

Algebra
smaller --- x larger ---- x+9 4(x+9) = 10x solve for x
March 15, 2016

Math/Precal
I have no idea what "the coordinates of p(a+b)" is supposed to be. We could find such values as sin(a+b) or tan(a+b). something like sinb = 3/5 has an infinite number of points associated with its end-points. They could be P(4,3) or Q(8,6) or R(40,30) etc Please ...
March 15, 2016

Math/Precal
recall that sin(A+B) = sinAcosB + cosAsinB you have the same angle pair showing up in the two terms in that pattern, so (sin pi/8)(cos pi/24) + (cos pi/8)(sin pi/24) = sin(pi/8 + pi/24) = sin(pi/6) = 1/2 ----> you should know pi/6 =30 degrees and sin(30) = 1/2
March 15, 2016

Maths
Julie --- j her father --- 4j mother ---- 4j+7 more information is needed to find their actual ages
March 15, 2016

Precal
To prove an identity to be true you have to simplify the LS and the RS independently until you have LS = RS The first thing I usually try is to take any angle and sub it into the equation to see if it is valid. Here I took A=20, B=30 LS= cot(50) = .839... RS = cot20cot30-1/(...
March 15, 2016

Geometry
#4 how can you have 2 different scale factors yielding the same figure ?? 9(2/3)--->6 9(2/3)--->6 12(2/3)-->8 So .....? #5 x/(x+4) = 3/5 5x = 3x+12 2x=12 x = 6
March 15, 2016

MATH
Neither arithmetic nor geometric, but there is a nice pattern. We can write it as a recursive formula. term(n) = term(n-1) + n, n>1, term(1) = 2
March 15, 2016

Algebra 1
a^2 + 14a^5 + a^7 - 16 Why is this a problem? Looks like just a nice innocent expression to me.
March 15, 2016

Math
Liv, you are just shuffling the letters around. Surely you can't think that 3P=s, Ps=3 and P=3s are all the same. I gave you the answer
March 15, 2016

Math
just divide both sides by 3 s = P/3
March 15, 2016

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