Monday
February 8, 2016

# Posts by Reiny

Total # Posts: 32,839

Math
treat the given data as two ordered pairs (0,180000), (10,10000) , where the first element is the time, and the 2nd is the value slope = (10000 - 180000)/(10-0) = -17000 , interpret that as depreciating \$17000 each year equation: V = -17000t + 180000 (0,180000) would be like ...
December 24, 2015

stats
From the several back and forth replies, your post is not very clear. looking at your chart, there are a total of 60 chicken, of which 10 are French hens so prob(selecting 3 French hens from the 60 chicken) = C(10,3)/C(60,3) = 120/34220 = 6/1711 you also make mention of ...
December 23, 2015

physics
h = -4.9t^2 + 100 A. to reach the ground h = 0 0 = -4.9t^2 + 100 4.9t^2 = 100 t^2 = 100/4.9 t = √(100/4.9) = appr 4.5 seconds B. v = -9.8t sub in t = 4.5 C. original equation is h = -4.9t^2 + 12t + 100 set equal to zero again, and solve using the quadratic equation. Take...
December 23, 2015

Math
Paul, if you had looked back, you would have seen that variations of your question have been answered several times I even did it for you both ways, with 300 books and with 3000 books. ignore Oscar's reply, I have shown it to be wrong http://www.jiskha.com/display.cgi?id=...
December 23, 2015

Nicholas
it is generally agreed that the Formula 1 cars of today will go from 0 to 100 km/h in less than 2 seconds. My guess that it will reach 10 m/s within a few metres.
December 23, 2015

Math
ok, y = tanx/x dy/dx = (x(sec^2 x) - tanx (1) )/x^2 which could be split up into sec^2 x/x - tanx/x^2 Did you forget the last term of -tanx/x^2 ? there really is not much point in further simplifying my first line answer of (x sec^2 x - tanx )/x^2
December 23, 2015

Math
y = tanx/x dy/dx = (x sec^2 x - tanx)/x^2 when x = π/4 , which is 45° dy/dx = ( (π/4)(2) - 1)/(π^2/16) =(8π-16)/π^2 so the slope of the normal is π^2/(16-8π) also when x = π/4, y = 1/(π/4)= 4/π equation of normal: y - 4/&#...
December 23, 2015

Math
y = sinx + 3 dy/dx = cosx when x=π, dy/dx = cosπ = -1 so the slope = -1 also when x = π, y = sinπ + 3 = 3 so the point of contact is (π,3) equation of tangent: y-3 = -1(x-π) y = -x + π+3
December 23, 2015

math
triple the first: 9x + 6y = 57 double the 2nd: 4x - 6y = -12 add them: 13x = 45 x = 45/13 sub into first: 3(45/13) + 2y = 19 2y = 19 - 135/13 = 112/13 y = 56/13 I checked the answers, they are correct
December 22, 2015

Math
I don't understand the question the 5 3/5 has no units. Are you saying that it fill with 5 3/5 gallons every 7/5 hrs? At that rate a 50,000 gallon swimming pool would take over 265 days to fill, ooops the swimming season is over. Check your question and repost it
December 22, 2015

Calculus
from 2y-3x=5 , we know that the slope of the tangent must be 3/2 f(x) = a + b√x = a +b(x)^(1/2) f ' (x) = (1/2)b x^(-1/2) or b/2√x so b/2√x = 3/2 2b = 6√x b = 3√x also (1,4) lies on f(x) = a + bx 4 = a + b since b = 3√x = 3√1 = 3 ...
December 22, 2015

Math
Seith = 160 + 8w , where w is the number of weeks Keira = 270 - 3w so we want 160 + 8w = 270 - 3w solve for w, Your solution becomes the explanation
December 22, 2015

MATH HELP
First of all, I would have reduced the equation to x + 2y = 400 , so now you can mentally find the x and y intercepts as (400,0) and (0,200) See how easy it is now to sketch the line ? so you clearly want all the stuff below that line in the first quadrant your answer has to ...
December 22, 2015

Stats
number of Jacks = 4 number of red cards = 26 , of which 2 are Jacks so Jacks or red cards = 26 + 4-2 = 28 prob(Jack or red) = 28/52 = 7/13
December 22, 2015

correction - PrimaryMatheMatics 4A textbook
OOPS, I read that as 300, should have been 3000 easy to fix x+2x+2x+10 = 3000 5x = 2990 x = 598
December 22, 2015

PrimaryMatheMatics 4A textbook
I would start with defining the number of books in the third pile is x then the number of books in the 2nd pile is 2x and the first pile is then 2x+10 (I just translated the English to Math) their sum is 300 x + 2x + 2x+10 = 300 5x = 290 x = 58 Third pile has 58 books (2nd has...
December 22, 2015

Math
the range is from -11 to 27 or 38° so in our trig function we have T = 19sin(.....) + 8 as a start the period is 365 days, so 2π/k = 365 and k = 2π/365 so we have T = 19 sin (2π/365)d + 8 where d is the number of the day in our year (there are charts ...
December 22, 2015

Trignometric Functions
see your post above this one
December 22, 2015

maths, physics,
Please define "heading of 70° Are you pointing clockwise from North?
December 22, 2015

math
Nothing to solve. To "solve" we need an equation, you have given me no equation.
December 22, 2015

math
We don't need the principal nor the time to find the effective annual rate All we are looking for it the annual rate i, which is equivalent to a rate of .0387/12 per month that is, (1+i)^1 = (1+.0387/12)^12 1+i = 1.0393939 i = .03939 or appr 3.939% (note, the decimals only...
December 21, 2015

math
I side with Ms Sue. Doesn't matter what Google said. We solve equations. You did not give us an equation. So "no can do"
December 21, 2015

maths
the smallest 2 digit number is 10, the largest is 99 How many is that ? ---> sum1 multiples of 5 are all those that end in zero or end in 5 e.g. 10, 20 , ... 90 15, 25, 35 ... 95 how many is that --> sum2 prob = sum2/sum1
December 20, 2015

math
2x + 3y = 7 now double the 2nd: 2x - 4y = 8 subtract them: 7y = -1 y = -1/7 sub into the 1st: 2x + 3(-1/7) = 7 2x = 52/7 x = 26/7
December 20, 2015

math
adult tickets sold --- x student tickets sold --- 540-x solve: 10x + 7(540-x) = 4765 or x+y = 540 10x + 7y = 4765
December 20, 2015

Math
number of push-ups for Doug = 8x number of push-ups for Adam = 3x solve: 8x - 3x = 15 take over
December 20, 2015

trigonometry
I will let you play around with http://www.wolframalpha.com/input/?i=y%3D+sin%282%28x%2B1%29%29 remember x is in radians, also notice the extra set of brackets I put in. What happens when we enter it as you typed it ? try y = cos(5(x - 3)) + 2 ignore the fancy math at the ...
December 20, 2015

Danville
According to your data, the height would be given by h =-4.9t^2 + 20t + 5 totally absurd numbers, as you will see when we "solve" this problem we have a downwards parabola and the t of the vertex is -20/-9.8 = appr 2.04 seconds his maximum height is -4.9(2.04)^2 + 20...
December 20, 2015

Maths tangent help me damon or steve help
2x + x dy/dx + y = 0 dy/dx = (-2x - y)/x from the tangent line we can see that the slope is 3 so, (-2x - y)/x = 3 -2x - y = 3x y = -5x sub back into the original equation: x^2 + x(-5x) + 16 = 0 x^2 - 5x^2 = -16 -4x^2 = -16 x^2 = 4 x = ± 2 when x = 2, 4 + 2y + 16 = 0 y...
December 20, 2015

math
picking it up from Damon's first = 4 third = 4+2d 7th = 4+6d but these also form a GP (4+2d)/4 = (4+6d)/(4+2d) 16 + 16d + 4d^2 = 16 + 12d^2 8d^2 -16d = 0 8d(d - 2) = 0 d = 0 , or d = 2 for a=4, and d=2, the sum of the first three AP terms are 4 + 6 + 8 = 18 check: term1 = ...
December 20, 2015

Math
#1, A and D is correct #2 .0112 = 112/10000 = 7/625 they should have reduce the answer of C
December 19, 2015

MATH HELP
I think Oscar meant f(t) = 3(2)^t so f(6) = 3(2^6) = 192 at least that way one of the answers will fit.
December 19, 2015

Maths
to have your expanded cubic start with x^2 you must have cubed a binomial of the form (x + m)^3 if we expand (x+m)^3 we get x^3 + 3x^2 m + 3x m^2 + m^3 compare that with your given x^3 + 3ax^2 + bx + c we can say: 3a = 3 ---> a = 1 3xm^2 = bx ---> b = 3m^2 and c = m^3 so...
December 19, 2015

Maths
I answered this for you when you typed it out correctly, (in its present form, where do the p and q enter the picture ??) http://www.jiskha.com/display.cgi?id=1450523328 What part of my solution did you not like, I even verified my answer.
December 19, 2015

Math
Jocelynn, looking at your answer, I can see that you just multiplied the whole number parts and then the fraction parts of your mixed fractions which is not the way fractions are multiplied Mixed fractions are sort of cute to look at but they serve no purpose, (sort of like ...
December 19, 2015

math
let the weight of the container be x kg let the weight of the water when full be y kg x + y = 2.25 kg x + .2y = .77 subtract them .8y = 1.48 kg y = 1.85 kg then x+1.85 = 2.25 x = .4 kg so x + .4y = .4 + .74 kg = 1.14 kg
December 19, 2015

Maths
Your solution for x = 3 is correct, now all you have to do is sub x = 3 into your 3 terms to get 4, 8, 16 you already knew r = 2 from r = 2(3) - 4 = 2 and a = 4 from a = x+1 = 4
December 19, 2015

Math
let the roots be m and n where n = m^2 we know sum of roots = m+n = p and the product of the roots is mn = q LS = p^3 - q(3p+1) - q^2 = (m+n)^3 - mn(3m+3n+1) - m^2n^2 = m^3 + 3m^2n + 3mn^2 + n^3 - 3m^2 n - 3m n^2 - mn - m^2 n^2 = m^3 + n^3 - mn - m^2n^2 but n = m^2, so ... = m...
December 19, 2015

Maths
we must have squared an expression such as (x^2 + bx + c) let's see what we get: (x^2 + bx + c)^2 = (x^2 + bx + c)(x^2 + bx + c) = x^4 + bx^3 + cx^2 + bx^3 + b^2x^2 + bcx +cx^2 + 2bcx + c^2 = x^4 + 2bx^3 + x^2(c+b^2+c) + 2bcx + c^2 comparing this with x^4+6x^3+13x^2+mx+n...
December 19, 2015

Math
the roots would be (-b +√(b^2 - 4ac)/2a and (-b - √(b^2 -4ac)/2a we are told that the difference between them is 1 so, (-b+√(b^2-4a))/2a - (-b - √(b^2-4ac)/2a = 1 2√(b^2-4ac)/2a = 1 √(b^2 - 4ac) = a square both sides b^2 - 4ac = a^2 b^2 - a^...
December 19, 2015

Math
after you simplify , you get: 6x = 2 x = 2/6 = 1/3 In general, the equation of a line describes the relationship that the x and the y have for each ordered pair on the line. e.g. if we had y = 2x + 1, that would mean that for every x value that you choose, the y will be one ...
December 19, 2015

calc
I will assume you meant s = 1/(t^2 + 1) , (use ^ to show exponentiation) = (t^2 + 1)^-1 v = ds/dt = -1(t^2 + 1)^-2 (2t) = -2t/(t^2 + 1)^2 so at t = 2 v = -4/(5)^2 = -4/25 ft/s the negative tells me the object is slowing down
December 18, 2015

calculus
(1/2)^(t/5730) = .29 (.5)^(t/573) = .29 take logs of both sides and follow rules of logs to get (t/5730)log.5 = log.29 t/5730 = log.29/log.5 t = appr 10,233 years
December 18, 2015

Maths
we would be solving: 50000(1+i)^5 = 100000 (1+i)^4 = 2 take the 4th root 1+i = 1.189207.. i = .18920.. or 18.92 % as the effective rate to 2 decimals
December 18, 2015

Maths trigonomentry
Go with Damon's , he used an easier method (but I thought mine was quite elegant)
December 18, 2015

Maths trigonomentry
let's change 3cosx+4sinx into a single sine curve of the form y = a sin (x+k) we know asin(x+k) = asinxcosk + acosxsink comparing our terms asinxcosk = 4sinx acosk = 4 a = 4/cosk acosxsink = 3cosx a sink = 3 a = 3/sink then 3/sink = 4/cosk 4sink = 3cosk sink/cosk = 3/4 ...
December 18, 2015

math
The sum of the exterior angles of any polygon is 360° the interior sum is 180(n-2), where n is the number of sides so 180(n-2) = 360 n-2 = 2 n = 4 so it is true for any quadrilateral
December 18, 2015

3rd grader
I just memorized them
December 17, 2015

math
prob(white) = 12/20 = 3/5 prob(not white) = 2/5 you want prob that 3 are white or 4 are white or 5 are white = C(12,3) (3/5)^3 (2/5)^9 + C(12,4) (3/5)^4 (2/5)^8 + C(12,5) (3/5)^5 (2/5)^7 I will do the first term, you do the rest = .012457 +....
December 17, 2015

Algerbra
for addition: the sum of 2 odds is even e.g. 3+5 = 8 the sum of 2 evens is even the sum of an even and an odd is odd e.g. 3 + 4 = 7 for multiplication: odd x odd = odd, e.g. 3x5=15 even x even = even , e.g. 6x8 = 48 even x odd = even , 4 x 5 = 20 assuming x is also an integer ...
December 17, 2015

Algerbra
the ^ symbol is used to show exponents (-2x-6)^2 = ( (-2)(x+3) )^2 = (-2^2( (x+3)^2 = 4y btw, where does the f in f y come in? I assumed it meant question f) let me know otherwise Just noticed my assumption was right from the first of the Related Questions below from 2013
December 17, 2015

Math
scalar product or dot product: a∙b = |a| |b|cosØ, where Ø is the angle between then 1(16)cosØ = 90 cosØ= 90/16 = 5.625 , which is not possible, since cos(anything) falls between -1 and +1
December 17, 2015

Math
Recall that perpendicular lines have slopes that are negative reciprocals of each other. so the slope of the given line is 3/5 then the slope of the new line is -5/3 new equation: y = (-5/3)x + b but (-1,3) lies on it, so 3 = (-5/3)(-1) + b b = 3 - 5/3 = 4/3 new line: y = (-5/...
December 17, 2015

math
speed = distance / time = 49/(4/3) = 49(3/4) = 147/4 or 36.75 mph
December 17, 2015

math
If 1/4 inch represents 1 mile, then 1 inch represents 4 miles , and 1 3/4 inches or 7/4 inches will represent (7/4)(4) miles = 7 miles or just use a ratio: (7/4)/(1/4) = x/1 (1/4)x = 7/4 x = 4(7/4) = 7
December 17, 2015

Math
so you need the derivative of this thing. y = 1 + (cscx + cotx)^1/2 dy/dx = (1/2)(cscx + cotx)^(-1/2) ( -cscx cotx - csc^2 x) I was going to simplify this, but then realized that you were missing some information. e.g. what point does the tangent pass through ? I am also ...
December 16, 2015

Math
notice the result is 7.47 x 10^-38 which I would consider close to zero.
December 16, 2015

Math
prob(right ) = 1/5 prob(wrong) = 4/5 let the number that are right be x C(100,80) (1/5)^80 (4/5)^20 I am stymied for a method to evaluate this, my calculator cannot handle it Wolfram says: http://www.wolframalpha.com/input/?i=evaluate+C%28100%2C80%29+%281%2F5%29%5E80+%284%2F5%...
December 16, 2015

Math
You are wrong. Think of it this way: Each of the 12 teams can play against the other 11 teams, that would would be 12x11 = 132 But each of these has a double, e.g team A plays team B is the same game as team B vs team A so we have to divide our 132 by 2 to get 66. Trust me, 66...
December 16, 2015

Math
that would be C(12,2) = 66
December 16, 2015

Pre-calculus
Volume = x(8-2x)(12-2x) , where 0 < x < 4 = 96x -40x^2 + 4x^3 d(volume)/dx = 96 - 80x + 12x^2 = 0 for a max/min of volume 3x^2 - 20x + 24 = 0 use the quadratic formula to solve, reject the x value outside our stated domain above
December 16, 2015

Math
slope = (5/2 + 3)/(-5 + 7/2) = (11/2) / (-3/2) = (11/2)(-2/3) = -22/6 = -11/3 D comes close but is not simplified, it should be
December 16, 2015

algebra 1
3x - y = 1 y = 3x - 1 I assume those values after D: are the x values for x=-3, y = 3(-3) - 1 = -10 ---> point (-3,-10) for x = -1 , y = ..... carry on. Now you have 4 points, so just plot them
December 16, 2015

Algebra 1
change to: y = 2x + 3 pick any x you feel like, but remember you will have to graph the points, e.g. let x = 1, y = 2(1) +3 = (1,5) the charts will differ from student to student, but the graphs must look the same
December 16, 2015

Integers
largest : 4210 smallest: 1024 average = (4210+1024)/2 = ...
December 15, 2015

Algebra 2
2nd number ---- x 1st number = 2x-7 3rd = x + 2x-7 + 1 = 3x - 6 x + 2x-7 + 3x - 6 = 23 carry on
December 15, 2015

Algebra
speed of boat --- x mph speed of current --- y mph 5(x+y) = 20 x+y = 4 8(x-y) = 20 x-y = 2.5 add them: 2x = 6.5 x = 3.25 then y = .75 state the conclusions.
December 15, 2015

Math
clearly you could plug in any x you feel like into the function, so the domain is the set of reals let x = 0, so y = 0, the y-intercept is 0 (the origin) let y = 0 -2x^4 + 3x^2 = 0 x^2(2x^2 - 3) = 0 x = 0 , same as above or 2x^2 = 3 x^2 = 3/2 x = ±√(3/2)
December 15, 2015

Math
now you take the derivative of cosx/sinx using the quotient rule dy/dx = (sinx(-sinx) - (cosx)(sinx))/sin^2 x = -(sin^2 x + cos^2 x)/sin^2 x = -1/sin^2 x = - csc^2 x
December 15, 2015

Kwara State Polytechnic, Ilorin
the three terms as an AP would be a+9d, a+3d, and a if they also form a GP, then (a+3d)/(a+9d) = a/(a+3) a^2 + 6ad + 9d^2 = a^2 + 9ad 9d^2 = 3ad, but a=4 9d^2 = 12d 9d^2 - 12d = 0 3d(3d - 4) = 0 d = 0, or d = 4/3 , we reject d = 0, so our three AP terms are: 4+9(4/3) , 4 + 3(4...
December 15, 2015

Math
In English please. btw, I think I know what you are asking, but please use proper proper mathematical language
December 15, 2015

Math
Each strip should be 48/20 or 2.4 cm The trick would be to cut the paper into those 20 strips without measurement. How could you possible do that?
December 15, 2015

Ggss
just did this , look two posts below this
December 14, 2015

math
odds: 1, 3, 5 perfect squares greater than 1 : 4 so we have 1,3,4,5 and the prob is 4/6 = 2/3 I just realized I did this for you earlier.
December 14, 2015

Mathematics
dy/dx = (cosx(1) - (4+x)(-sinx))/cos^2 x when x = 0 dy/dx = (1(1) - 4(0))/1 = 1 so the slope of the tangent is 1 then the slope of the normal is -1 when x = 0, y = 4/1 = 4 so (y-4) = (-1)(x-0) y = -x + 4
December 14, 2015

math
good grief, this is the 5th time the same question has been asked, and it has been answered. Look at the Related Questions below
December 14, 2015

aacolsn
I had hoped your could continue, so we have 4 cases, prob(odd or perfect square) = 4/6 = 2/3
December 14, 2015

aacolsn
odds: 1,3,5 perfect squares: 1, 4 I count 4 possibilities, so .....
December 14, 2015

Math - not PACT
1. no restrictions, number of committees = C(7,4) = 35 2. 2 men and 2 women, number is C(4,2) x C(3,2) = 6(3) = 18 3. same set-up as #2, you try it 4. at least 2 women ---> 2 women, 2 men + 3women, 1 man = ... let me know what you got
December 14, 2015

maths
done, see your previous post under a different name http://www.jiskha.com/display.cgi?id=1450075351
December 14, 2015

rajput
done, see your previous post under a different name http://www.jiskha.com/display.cgi?id=1450075351
December 14, 2015

math
I will assume you want the radius of a circle that has an area of 154 cm^2. Why not state it properly? area = πr^2 πr^2 = 154 r^2 = 154/π r = √(154/π) = appr 7.00 cm
December 14, 2015

Math
I will assume that the pool is a cylinder. volume = π r^2 h = π(9)(2) = 18π What does the hose have to do with it? Was there supposed to be some rate of flow ?
December 14, 2015

math
make a simple sketch , to see that he completed a rectangle, so he must have traveled 20 km north or, suppose you don't see that right away: label his trips, AB, then BC, then BD from D draw a horizontal to meet AB at E so in right-angled triangle AED, AE^2 + 10^2 = 10^2 ...
December 14, 2015

Math
height-maple = (1/2)t + 4 height - birch = (2/3)t + 2 when they have the same height, (2/3)t + 2 = (1/2)t + 4 times 6, the LCD 4t + 12 = 3t + 24 t = 12 they have the same height 12 years from now subbing t = 12 into either equation yields (1/2)12+4 = 10 ft
December 13, 2015

Mathematics
the bases are both multiples of 2, so this is easy 4^(x-6)=2^(3x) 2^2)^(x-6) = 2^(3x) 2^(2x-12) = 2^3x then 3x = 2x-12 x = -12
December 13, 2015

Beacon house
I will assume that by "divided" you mean split up, and not actual division let one part be x, then the other is 39-x so (2/3)x + (3/4)(39-x) = 28 times 12 , the LCD 8x + 9(39-x) = 336 8x + 351 - 9x = 336 -x = -15 x = 15 so parts are 15 and 24 check: (2/3)(15) = 10 (3...
December 13, 2015

Mathematics
take logs of both sides log 3^(2x+1) = log 12 (2x+1)log3 = log12 2x+1 = log12/log3 2x = log12/log3 - 1 x = (log12/log3 - 1)/2 = .....
December 13, 2015

Advanced algebra
using our definitions, ar = 75 ar^4 = 3/5 divide the 2nd by the 1st: r^3 = 3/375 = 1/125 r = 1/5 back in ar = 75 a(1/5) = 75 a = 375 term7 = ar^6 = 375(1/15625) = 3/125 check my arithmetic
December 13, 2015

Finite Math
correct , small point ..... after 1.5 = e^(.07t) ln 1.5 = .07 lne .07t = ln 1.5 , since lne = 1 t = ln 1.5/.07 = 5.79.... don't put (lne=1) as part of your solution line,
December 13, 2015

math
treat the data as two ordered pairs of the type (s,c) where s is sales and c is commission. so you have (7000,700) and (8000,740) slope = (740-700)/(8000-7000) = 40/1000 = .04 so c = .04s + b , (compare with y = mx+b ) for (7000,700) 700 = .04(7000) + b b = 420 c = .04s + 420 ...
December 13, 2015

correction: math financial services
oops, I misread the question as investing 1000 every month, so amount = 1000(1.0025)^120 = \$1349.35
December 12, 2015

math financial services
I will assume you are familiar with the basic compound interest formulas i = .03/12 = .0025 n = 10(12) = 120 amount = 1000( 1.0025^120 - 1)/.0025 = ....
December 12, 2015

Algebra
slope of given line = 8/3 so slope of perendicular line = -3/8 equation : y-3 = (-3/8)(x+2)
December 12, 2015

Math Help!
first case 1: a = 2b so a^2 + b^2 = 1^2 (2b)^2 + b^2 = 1 5b^2 = 1 b^2 = 1/5 b = 1/√5 one side is 1/√5, the other is 2/√5 you do case 2
December 12, 2015

Algebra
the first has a slope of -2, comparing it to y = mx+b 2nd: I will assume you meant: -5x + 10y = 5 10y = 5x + 5 y = (1/2)x + 1/2 so the slopes are 1/2 and -2, well, now you can be 100% sure they are perpendicular repeat for #2 remember , if the are parallel, the must have the ...
December 12, 2015

algebra
let the tens digit be x then the units digit is x+6 then the number is 10x + (x+6) = 11x + 6 sum of the digits = x + x+6 = 2x+6 11x + 6 = 2(2x+6) + 8 7x = 14 x = 2 the number is 28
December 12, 2015

Math
number of rides --- r 3r + 10 ≤ 50
December 12, 2015

math
i = .18/12 = .015 n = 30 PV = 4500( 1 - 1.015^-30)/.015 = ....
December 12, 2015