Tuesday
June 28, 2016

# Posts by Reiny

Total # Posts: 35,087

algebra
x+y=4 or y = 4-x , and xy=6 sub in the first part x(4-x) = 6 4x - x^2 - 6 = 0 x^2 - 4x + 6 = 0 x = (4 ± √-8)/2 = 2 ± √2 If you are dealing with real numbers, there are no numbers to fit your condition. If you allow complex numbers, the two numbers are...
May 4, 2016

Math
May 4, 2016

Math
let the number of chairs over 400 be x now: number of chairs = 400 price per chair = 120 Revenue = 48000 after production increase: number of chairs = 400+x price per chair = 120 - .25x Revenue = R = (400+x)(120-.25x) = 48000 + 20x - .25x^2 which is a downwards opening ...
May 4, 2016

math
log(2+x)-log(x-3)=log2 log( (2+x)/(x-3) ) = log2 "unlog" it (2+x)/(x-3) = 2 2x - 6 = 2+x x = 8 check it with your calculator
May 4, 2016

Math
correct
May 4, 2016

Math
correct, I use http://davidmlane.com/normal.html
May 4, 2016

Math
I used the actual normal distribution and got .9973 http://davidmlane.com/normal.html
May 4, 2016

Math
I used the actual normal distribution and got .9973 http://davidmlane.com/normal.html
May 4, 2016

Math
the largest rectangle would be the square 2W + 2L = 8 W+L=4 for a square each side is 2 cm, and the maximum area is 4 cm^2 There is no such thing as a smallest rectangle. We can make one of the sides very very small, but there would still be an area. e.g. suppose W = .001 then...
May 4, 2016

math
Since it asked for an estimate and and Dπ = C I would approximate 270/3 = 90 so the diameter is about 90, making the radius about 45 Since they wanted an estimated answer, giving answers with those kind of decimals makes no sense. Using 3.14 for π is not estimating.
May 4, 2016

math
Unfinished sentence .... Does your keyboard not have any capital letters? Whatever is missing in your sentence , the probability is 1/9
May 4, 2016

Geometric Sequence
you want: .95^n = .25 take log of both sides nlog.95 = log.25 n = log.25/log.95 = 27.0268.. = appr 27 washings or start with 100% colour after 1 washing ---- 95% left after 2 washings --- .95(.95) left after 3 washings --- .95(.95)^2 left .... after n washings ------ .95(.95)(...
May 4, 2016

Maths
boys --- b girls --- g b+g = 150 (3/4)b = (1/7)g 3b/4 = g/7 4g = 21b g = 21b/4 sub into the first b+g = 150 b + 21b/4 = 150 times 4 4b + 21b = 600 25b=600 b = 24 then g = 21(24/4) = 126 24 boys and 126 girls went to the concert check: is 24+126 = 150 ? , YES is (3/4)(24) = (1/...
May 4, 2016

Algebra
number of adult tickets ---- x number of children tickets -- 2000-x solve: 4x + 2(2000-x) = 6400 solve the value of x into my definitions
May 4, 2016

math
i = .0475/12 = .00395833.. n = 12(10) = 120 PV = 20,000(1.00395833..)^-120 = \$12,449.37
May 4, 2016

math
Formulas are equations that contain an = sign you have an expression, not an equation, so... ???
May 4, 2016

Yes, 3 numbers are divisible by 3 so prob = 3/10
May 3, 2016

mathematics
GP ar^2 = 4a ----> r^2 = 4 r = ±2 ar^5 = 3ar^3 + 32 if r = +2 32a = 24a + 32 8a =32 a = 4 the sequence is 4,8,16,32,64, 128, ... if r = -2 -32a = -24a + 32 -8a = 32 a = -4 the sequence is -4, 8, -16, 32, -64, 128, ...
May 3, 2016

Calculus 3
starting with the 4th term, we have a definite pattern and the general term from that point is 1/(3^n + √(n+1) ) , where n starts with 1 Since you wanted to "write the series", why don't we just add the first 3 terms and begin the serious stuff with term 4 ...
May 3, 2016

MATH
let the number of gigs used be g Runfast: cost = 25 + 10g BA&D: cost = 18+15g let's see for how many g's the plans are the same cost of one = cost of the other 18+15g = 25+10g 5g = 7 g = 7/5 = 1.4 gigs so for 0 gigs over, BA&D would cost \$18 vs \$25 for Runfast, so BA&D...
May 3, 2016

Analytic Geometry
http://www.wolframalpha.com/input/?i=plot+x%5E2-xy%2By%5E2-3%3D0 nice rotated ellipse. This is a good equation for you to use in studying or reviewing the topic of rotation of conics. Obviously I could not possible teach you that on here in one post. When I last taught this ...
May 3, 2016

calculus
Sketch a right angles triangle with a base of 400 m, a height of h m , (the balloon), and an angle of Ø opposite the height. tan Ø = h/400 h = 400 tanØ dh/dt = 400 sec^2 Ø (dØ/dt) given: when Ø = 10° or 10(π/180) radians d&...
May 3, 2016

math 1324
Solve using matrices ??? What can be easier than the following? : amount borrowed at 9.5% ---- x amount borrowed at 8.5% ---- 4x amount borrowed at 7% = 2,000,000 - 5x .095x + .085(4x) + .07(2000000-5x) = 169750 solve for x , and sub back in my definitions
May 3, 2016

Analytic Geometry
factor it y(x+1) = x y = x/(x+1) a rotated hyperbola , with asymptote at x = -1 http://www.wolframalpha.com/input/?i=plot+y+%3D+x%2F(x%2B1)
May 3, 2016

Maths
So it would take 20 man-hours to paint the house, (or "person-hours to be politically correct) No distribute those 20 hours needed among 3 painters, so it would take 20/3 hours = 6 2/3 hours = 6 hours and 40 minutes
May 3, 2016

Nath
work backwards, 2:30 pm ---- 44° noon -------- 41° 7:00 am ----- 29°
May 3, 2016

math
So many questions: are the circles touching each other? are the circles the same size ? are each of the circles touching the length and width of the rectangle? ... etc
May 3, 2016

Math
If you want L/hr, then rate = (4/5) / (1/4) L/h = (4/5)(4/1) L/h = 16/5 L/h Daniel is correct
May 2, 2016

Yup! - Math
-- stands in corner with dunce cap --- looks like I had another "old-timer's " moment.
May 2, 2016

Math
I would have it as 90° < d < 180° think of it as: d is between 90 and 180
May 2, 2016

Pre-calculus
width = 8.5-2x length = 11 - 2x height = x V = x(8.5-2x)(11-2x) domain: 0 < x < 4.25
May 2, 2016

correction - math
use A^3 + B^3 = (A+B)(A^2 - AB + B^2) (memorize it) We call it the sum of cubes, we can also factor the difference of cubes. 8x^3 is a perfect cube and so is 1, so the expression fits the formula 8x^3+ 1 = (2x + 1)(4x^2 - 2x + 1)
May 2, 2016

algebra
first speed --- x mph return speed -- x+16 mph 6/x + 6/(x+16) = 1 times each term by x(x+16) 6(x+16) + 6x = x(x+16) x^2 + 4x - 96 = 0 (x-8)(x+12) = 0 x = 8 or x is a negative her first speed was 8 mph her return speed was 24 mph check: 6/8 + 6/24 = 1 , that's good!
May 2, 2016

Math
smallest angle --- x the other is ------ x+45 third ------ 2x - 5 solve for x: x + x+45 + 2x-5 = 180
May 2, 2016

Trigonometry
easier than it looks: cos^-1(radical3/2), means you want the angle Ø so that cosØ = √3/2 of course you should recognize that as a ratio form our 30-60-90 triangle, and Ø = 30° for tan^-1 (-√11/√5), construct a triangle in quadrant II ...
May 2, 2016

Probability and statistics
prob(choosing child) = 6/12 = 1/2 prob(non-child) = 1- 1/2 = 1/2 prob(exactly one child in choosing two) = C(2,1) (1/2)(1/2) = 1/2 or If C stands for choosing child and N stands for non-child we have these cases: CC -- prob = (1/2)(1/2) = 1/4 CN -- 1/4 NC --1/4 NN -- 1/4 so ...
May 2, 2016

Math
The least perimeter is obtained when you have a square let the side be s s^2 = 32 s = √32 = 4√2 so the least perimeter is 8√2 by Calculus: let the width be x then the length is 32/x P = 2x + 2y = 2x + 64/x P' = 2 - 64/x^2 = 0 for a min of P 2 = 64/x^2 x^2...
May 2, 2016

Math
Well, your homework is poorly stated. Here is an example of what Steve is saying: suppose the width is .1 ft then the length = 39/.1 or 390 ft perimeter = 2(390) + 2(.1) = 780.2 ft check: area = .1(390) = 39 suppose the width is .001 ft then the length is 39/.001 or 39000 ft ...
May 2, 2016

Geometry
3 small ones of 5 in diameter v = 3((4/3)π(2.5)^3) = 125π/2 = 62.5π = appr 196.35 one of diameter 8 v = (4/3)π(4^3) = 256π/3 = appr 268.08 hemisphere of radius 5 = (1/2)(4/3)π(5^3) = 250π/3 = appr 261.8
May 2, 2016

Probability and statistics
we can build our 5 digit number using 5 different numerals all possible numbers = 5! or 120 In all of these, the lead digit, the 10-thousand digit, can be occupied by the "9" 24 times, the "8" 24 times, etc. The value of those 24 9's would be 24(90000...
May 2, 2016

Gr 11 Functions
(1+tanx)^2 ≠ (1-sinx)(1+sinx) RS = 1 - sin^2 x = cos^2 x and cos^2 x is certainly not equal to (1+tanx)^2 try x = 45° (1+tan45)^2 = (1+1)^2 = 4 cos^2 (45°) = (1/√2)^2 = 1/4 no wonder you got nowhere with your work. check the question, or check your typing.
May 2, 2016

Correcion - math
Sarim's solution above makes absolutely no sense consider this one: http://www.jiskha.com/display.cgi?id=1462219074
May 2, 2016

maths
I know that the cost of coffee has gone up, but \$2000 per kg ???? I will assume that you meant \$22.00, (even that is too high) anyway..... let the cost of the mix be \$x per kg 8(20) + 12(22) = x(8+12) 20x = 424 x = \$21.20
May 2, 2016

math
looks for every increase of 1 unit in the x's the corresponding y decreases by 5 so slope = -5 y = -5x + b at x = -2, y = 9 9 = -5(-2) + b b = -1 function rule: y = -5x - 1
May 2, 2016

Math
I have no idea what your line 42pi C=pi*d=pi.pi*42=42pi. is supposed to say or mean. Are you saying the C = 42π ?? in that case the radius would be 21 units and the answer is in exact form now if we use the approximation of 22/7 for π we get C = 42(22/7) = 132 42&#...
May 2, 2016

Algebra
yes, the new vertex will be (4,-1) proof: f(x-2) = (x-2)^2 - 4(x-2) + 3 = x^2 - 4x + 4 - 4x + 8 + 3 = x^2 - 8x + 15 = g(x) vertex of g(x) = -b/(2a) = 8/2 = 4 g(4) = 4^2 - 8(4) + 15 = -1 vertex is (4,-1)
May 2, 2016

calculus
a) let the top right vertex be (x,y) then the area = 2xy A = 2xy = 2x(16-x^2) = 32x - 2x^3 dA/dx = 32 - 6x^2 = 0 for a max of A 6x^2 = 32 3x^2 = 16 x^2 = 16/3 x = 4/√3 , then y = 16 - 16/3 = 32/3 so the rectangle has a base of 2(4/√3) = 8/√3 and a height of ...
May 2, 2016

calculus
sum(1) = 1^3/1^4 = 1 or 4/4 sum(2) = (1 + 8)/16 = 9/16 sum(3) = (1+8+27)/81 = 36/81 = 4/9 or 16/36 sum(4) = (1+8+27+64)/256 = (1+8+27+64)/256 = 100/256 = 25/64 sum(5) = (1+8+27+64+125)/625 = 225/625 = 9/25 = 36/100 I noticed I can change my numerator to (n+1)^2 for sum(n) and ...
May 2, 2016

calculus
recall that tan^2 A +1 = sec^2 A and d(tanA)/dA = sec^2 A so ∫ tan² x/3 dx = ∫ sec^2 (x/3) - 1 dx form 0 to π = [3 tan (x/3) - x] from 0 to π = 3tan π/3 - π -(3tan 0 - 0) = 3 √3 - π
May 2, 2016

maths
volume of cube = (5.5 cm)^3 = 166.375 cm^3 then our cylinder's height would increase by h , such that π(49)h = 166.375 h = 1.081 cm (note that the 9 cm depth of water did not enter the picture)
May 2, 2016

Calculus
let the water level have a radius of r ft let the height of the water be h ft by ratio: r/h = 5/12 12r = 5h ---> r = 5h/12 V = (1/3)π r^2 h = (1/3)π(25h^2/144)(h) = (25/432)π h^3 dV/dt = (25/144)π h^2 dh/dt plug in our given stuff 1 = (25/144)π(64) ...
May 2, 2016

Calculus
dy/dt = 2ax dx/dt + dx/dt dy/dt = dx/dt(2ax + 1) but dy/dt = dx/dt , so 1 = 2ax + 1 2ax = 0 x = 0 then y = b at the point (0,b)
May 2, 2016

Calculus
did you make your sketch ?? let the length of the man's shadow be x ft let the distance he is from the lightpost be y by ratios: 6/x = 15(x+y) 6x + 6y = 15x 6y = 9x 2y = 3x 2dy/dt = 3dx/dt but dy/dt = 3 so 6 = 3 dx/dt dx/dt = 2 His shadow is lengthening at 2 ft/s but he is...
May 2, 2016

Math
your def: a*b= a+b-ab = first + last - product of first times last (a*b)*c = (a+b-ab)*c = a+b-ab + c - ac - bc + abc = a+b+c - ac - ab - bc + abc a*(b*c) = a*(b+c - bc) = a+b+c-bc - ab - ac + abc = a+b+c - ac - ab - bc + abc = (a*b)*c so the operation is associative -5*8 = -5+...
May 2, 2016

calculus too hard help
let's try this: let y = x^x lny = xlnx y'/y = x(1/x) + lnx dy/dx = y(1 + lnx) = x^x + x^x(lnx) let u = x^x^x , the x's are staggered ln u = x ln(x^x) u'/u = x(x^x + x^x(lnx))/x^x) + ln(x^x) argghhhh!! I was looking for a pattern. What am I not seeing ????
May 2, 2016

calculus too hard help
second last line should have been 532 = 5^9 = 1953125
May 2, 2016

calculus too hard help
y=x^x^x^x... take ln of both sides ln y = ln(x^x^x^x... ) ln y = x ln(x^x^x^x... ) lny = x ln(y) 1 = x well, that got me nowhere. are the x's staggered upwards or on the same level? e.g 532 = 5^8 = 390625 but (5^3)^2 = 5^6 ≠ 5^8
May 2, 2016

maths
r = 50 volume of full tank = (4/3)π(50)^3 = ... so half of that is .....
May 2, 2016

Math
with no restrictions, number of 4 digit permutations are 10x10x10x10 = 10,000 as you stated but , if we exclude the 9, we have only 9 numerals to play with number of 4 digit phone number endings = 9x9x9x9 = 6561 (now, a nicer question would have been: of those 4 digit endings...
May 2, 2016

Maths
sin(2Ø + π/3) = 1/2 we know sin (π/6) = 1/2 , (sin 30° = 1/2) so 2Ø + π/3 = π/6 OR 2Ø + π/3 = 5π/6 (sin30° = 1/2 and sin150° = 1/2) case1: 2Ø + π/3 = π/6 2Ø = π/6 - π/3 = -π/6...
May 2, 2016

Math
do you want something like this ? RR --> (4/12)(3/11) = 1/11 RG --> (4/12)(8/11) = 8/33 GR --> (8/12)(4/11) = 8/33 GG --> (8/12)(7/11) = 14/33 note that 1/11 + 8/33 + 8/33 + 14/33 = 1
May 2, 2016

Math
We have similar triangles Juan is 6' 1" = 73 inches so we can say: 73 inches/5 m = x inches/12 m notice we have the same units in each ratio, so 73/5 = x/12 5x = 12(73) x = 175.2 inches x = 14.6 ft = 14 ft and 7.2 inches
May 2, 2016

MATH
1 m^2 = 1.1959905 yards^2 so 76000 m^2 = 90895.278 yards^2 cost = 80(90895.278) = \$7,271,622.24 (In reality, the cost would be found in terms of Euros/m^2. )
May 2, 2016

Math
A marathon is 42.195 km = 42,195 m time = 42195/1.8 = 23441.666.. seconds = 6.5116 hrs or 6 hours and 31 minutes or 1.8 m/s = 64800 m/h = 6.48 km/h rate = 42.195/6.48 hours = 6.5116 hrs as above or 1.8 m/s = 180 cm/s = 70.866.. inches/s = 5.90551... ft/s ,(stored in calculator...
May 2, 2016

maths
"u" is not an English word, however "you" is one. let the number of bikes be b let the number of tricycles be t 2b + 3t = 19 integer solutions (b,t) are (8,1) , (5,3) , (2,5) for 2b + 3t = 23 integer solutions are: (10,1) , (7,3) , (4, 5) , (1, 7)
May 2, 2016

Math
depends on the rate of exchange. The current rate is \$1 CND = \$.80 US so \$76025 CND = \$60820 US So which is the better offer ?
May 2, 2016

math
Since positions of the board are stated, we are dealing with a permutation, so the number of boards = 30(29)(28)(27) = ....
May 2, 2016

Math
Are your two models supposed to be in a ratio equal to the ratio of the height of the two buildings? The buildings do not have the same shape, so we can't make a ratio comparison between their volumes. The wording of the first two Related Questions below deal with the ...
May 2, 2016

Maths (Need Help)
given line: 8y = 2x+ 3 y = (2/8)x + 3/8 y = (1/4)x + 3/8 The slope of the given line is 1/4 a) find the slope of AB and show it is equal to -4 b) midpoint of AB = ( (3+2)/2 , (-1+3)/2 ) or ( 5/2 , 1) --- show that ( 5/2 , 1) satisfies the given equation by subbing it in to see...
May 2, 2016

Finance
if left alone: amount = 500(1.055)^8 = .... if \$150 is take out, amount = 350(1.055)^8 - ... take the difference between the two answers
May 2, 2016

Math
Instead of taking 10% off, think of what would be left after you do that 100% - 10% = 90% <-----> 1 - .10 = .90 e.g. suppose your car costs R122 000, take 10% which is R12 200 off R122 000 - R 12 200 = R 109 800 - now take 90% or .9 of 122 000, that would also be 109 800...
May 2, 2016

Exponential Modeling
Having done a few of these kind of problems for you, it is time for you to tell me what you got for this one
May 1, 2016

Exponential Modeling
what is 100(1.32)^10 ??
May 1, 2016

Exponential Modeling
if the rate of increase is linear, then rate = (1.25 - .10)/(2012-1972) = 1.15/40 = .02875 or appr 3 cents a year
May 1, 2016

Exponential Modeling
huhh??? value at end of year 1 = 25000(.65) = 16250 value at end of year 2 = 16250(.65) = 10562.50 value at end of year 3 = 10562.50(.65) = 6865.63 or in 1 step value = 25000(.65)^3 = 6865.63 So much for you little trick, it is blatantly wrong.
May 1, 2016

Algebra 1
It is not exponential the way you typed it. If you meant y = 15,000(1.07)^x , which is what I suspect ... A is certainly not the one B is out since that would be linear C. 2 = 1.07)^x log2 = xlog1.07 x = log2/log1.07 = 10.24 so that is a correct choice so far D 3 = 1.07^x x = ...
May 1, 2016

math
Assuming they play all 5 games, to get 5 points in 5 matches, it could be DDDDD --- arranged in 1 way WDDDL --- arranged in 5!/3! or 20 ways WWDLL--- arranged in 5!/(2!2!) or 30 ways Prob(win) = 1/3 prob(draw) = 1/6 prob(loss) = 1/2 prob(DDDDD) = (1/6)^5 = 1/7776 prob(WDDDL...
May 1, 2016

algebra tricky q
Just translate to Math number of breads --- b milk ---------------- 2b cereal ------------- b+1 meat -------------- b+1 now for the cost: 70(2b) + 60b + 50(b+1) + 150(x+1) = 1000 140b + 60b + 50b + 50 + 150b + 150 = 1000 400b = 800 b = 2 2 loaves of bread 4 cartons of milk 3 ...
May 1, 2016

math
First let arrange the 10 boys. This can be done in 10! ways Now there are 9 places in this arrangement where we can place a girl, but we only have 6 girls. So we have to choose 6 of those 9 places to insert the single girls. There are C(9,6) or 84 ways of doing so But we can ...
May 1, 2016

Trigonometry
2nd part I will make a similar substitution let x/2 = y, then we have prove: tany + coty = 2cscy LS = siny/cosy + cosy/siny = (sin^2 y + cos^2 y)/sinycosy but (2sinycosy = siny) = 1/((1/2)siny) = 2cscy = 2csc(x/2) = RS
May 1, 2016

Trigonometry
let x/2 = Ø , then your equation becomes sinØ - cosØ = ±√(1 - sin 2Ø) we know that if LS = RS , then (LS)^2 = (RS)^2 LS = sinØ - cosØ (LS)^2 = (sinØ - cosØ)^2 = sin^2 Ø - 2sinØcosØ + cos^...
May 1, 2016

diameter
No They are chargint \$40 per <b<square yard, so we are dealing with area, not circumference Area = πr^2 = π(48)^2 = 2304π feet ^2 = 256π yards^2 cost = \$40(256π) = \$32,169.91 or appr \$32,170 Your answer of only \$105.90 should have sounded totally...
May 1, 2016

calculus
or using discs V π∫ y^2 dx from x= 0 to 4 = π∫x dx from x = 0 to 4 = π[ (1/2)x^2] from 0 to 4 = π(16/2 - 0) = 8π
May 1, 2016

Calculus
May I suggest two excellent videos from the Khan Academy The first develops the standard method of finding the area https://www.khanacademy.org/math/integral-calculus/solid_revolution_topic/area-polar-graphs/v/formula-area-polar-graph And the second just about matches your ...
May 1, 2016

Calculus
So at 2:00 pm the first ship would be 5 nautical miles directly south of the second ship. Let the time passes since 2:00 pm be t hours So the two ships form a right-angled triangle, with a horizontal side of 10t nmiles and a vertical of (5+5t) nmiles Let the distance between ...
May 1, 2016

math
Effectively, you have all the numbers form 100 to 999 , (can't start with 0 or else we have a 2 digit number) There would be 999-100 + 1 = 900 of them or using the standard permutation method choices for 1 digit = 9 choices for 2nd digit = 10 choices for 3rd digit = 10 ...
May 1, 2016

Exponential Modeling
what is 100(1.24)^5 ?
April 30, 2016

Calculus
My sketch shows the following: M is the man's position 16 m off shore A is the point on the shore perpendicular to M B is the point where he wants to go, AB = 30 Let P be the optimum point between A and B, let AP = x, then PB = 30-x distance in water = MP MP = (x^2 + 256...
April 30, 2016

Math
In your sketch , draw a perpendicular from the vertex to the base. You now have 2 identical right-angled triangles. let the base for each be x units (your whole base would then be 2x) by simple trig, cos 67.5° = x/10 x = 10cos67.5 = 3.8268.. , Use your calculator for this ...
April 30, 2016

MATH
a = 11 d = 3 term(n) = a + (n-1)d 83 = 11 + (n-1)(3) 72 = 3n - 3 3n = 75 n = 25 83 is the 25th term check: term(25) = a + 24d = 11 + 24(3) = 83
April 30, 2016

Math
did you make your sketch? On mine I labeled the top of the pole as P and it bottom as Q. I marked the bird on the tree as A Draw a horizontal from A to meet PQ at R let PR = x, then PQ = 10.65+x In triangle ARQ tan60° = 10.65/AR AR = 10.65/tan60 Triangle ARP is right-...
April 30, 2016

algebra
Volume = (4/3)π (1.9)^3 = 28.7309... SA = 4π (1.9)^2 = 45.36459... ratio of V : SA = 28.7309.../45.36459... = .63333... in general , ratio of volume/SA = (4/3)πr^3/(4πr^2) = (1/3) r using our values above ratio vol. / SA = (4/3)π(1.9)^3 / (4π (1.9...
April 30, 2016

Algebra
This question makes absolutely no sense to me. You say that you already have a pool . Are you going to change it?? How deep is the pool to be? Will people be able to stand with their heads above water? Is the pool circular? That way you would have the largest surface area, but...
April 30, 2016

Math
factors of 40 : 2,4,5,8,10,20 but only 5, 8, 10 fall within our domain So numbers which are even OR a factor of 40 are: 5,6,8,10,12,14 --> 6 of them prob(of your event) = 6/10 = 3/5
April 30, 2016

Math
1.8 m = 180 cm length = 18900/180 cm = .. make sure you express above in metres.
April 30, 2016

geometry
sketch a cross-section, and complete the right-angled triangle let the radius be r r^2 = 10^2 + 15^2 r = √325 depth of water = 10 + √325 = ...
April 30, 2016

math
final value = \$60(.8)(.9)(1.55) = \$66.96
April 30, 2016

math
original fraction : x/y new fraction : (.5x)/(.75y) = (2/3) (x/y) so the new fraction is 2/3 of the old one, thus it was decreased by 1/3
April 30, 2016

math
According to your wording: - you wanted the percentage increase , so my answer is correct 3.5/.432 = 8.102 so the new price is 810% of the old one, but the increase is 710% e.g. suppose the cost of a coat went from \$100 to \$120 so it increased by 120%, but the percentage ...
April 30, 2016

math
number of dozen in the bucket = 450/12 = 37.5 so cost price per dozen = 16.20/37.5 = .432 So they bought them at \$ 0.432 per dozen and sold them at \$3.50 per dozen percentage increase = 3.5/.432 - 1 = 7.102 or 710%
April 30, 2016