Saturday
September 20, 2014

Posts by Reiny


Total # Posts: 27,130

Albegra
I would first of all divide both sides by 20 to get the numbers a bit smaller 121/(570+r) = 107(570-r) now cross-multiply 60990 + 107r = 68970 - 121r 228r = 7980 r = 7980/228 = 35 or, look at it this way: the LCD is (570+r)(570-r) so in effect I just multiplied both sides of ...
March 8, 2014

applied algebra
what is 800(1.0275)^14 ?
March 8, 2014

math
3x^2 - 24x + 45 =0 first divide by 3 to simply x^2 - 8x + 15 = 0 (x-3)(x-5) = 0 x = 3 or x = 5 check: http://www.wolframalpha.com/input/?i=plot+y+%3D+3x%5E2+-+24x+%2B+45
March 8, 2014

math
To have more than 30 cents, the right pocket must have the quarter and the dime. possible cases, order does not matter: L --- left pocket, R -- right pocket L -- R QP ND QN PD QD PN PN QD PD QN ND QP -----> so we have 6 cases prob = 1/6
March 8, 2014

Math
y = 2(x^2 - 2x +1 -1) - 6 = 2( (x-1)^2 - 1) - 6 = 2(x-1)^2 - 2 - 8 = 2(x-1)^2 - 10 the vertex is ........
March 8, 2014

Math
y=x^2 - 4x-21 = (x^2 - 4x + 4 - 4) - 21 = ( (x-2)^2 - 4) - 21 = (x-2)^2 - 4 - 21 = (x-2)^2 - 25 take over
March 8, 2014

MATH
I agree with Damon that your gravitational constant is off. Since you are using metric , your equation should be h = -4.905t^2 + 16t + 9 let's ballpark it to h = -5t^2 + 16 + 9 a) ..... b) sub in t = 1 , h = -5+16+9 = 20 m c) for t of the vertex ... t =-b/(2a) = -16/-10 = ...
March 8, 2014

Statistics
I thought I had given you the answer. finding the z-score results in a mean of 0 and a standard deviation of 1 so in the link I gave you .... http://davidmlane.com/hyperstat/z_table.html enter 0 for the mean 1 for the sd click on "below" and enter -.75 click on "...
March 8, 2014

further maths
calculate the area of a circle with 23 m - area of circle with 20 m. = (23^2)π - (20^2)π = .....
March 8, 2014

Statistics
Fun to play around with this excellent site http://davidmlane.com/hyperstat/z_table.html
March 8, 2014

Statitics
prob(lost) = 5/1000 = 1/200 prob(not lost) = 199/200 prob( 2 of 22 are lost) = C(22,2) (1/200)^2 (199/200)^20 = .005224.. Question for you. would this be the same as "....a group of people who have 11 pieces of luggage. What is the probability that 1 of these are lost? &...
March 8, 2014

Statistics
Use David's excellent "normal distribution" calculator http://davidmlane.com/hyperstat/z_table.html click on "area from a value" enter the data, click on "between" and enter 8 and 11 to get .4467 You can enter the data directly, no need to ...
March 8, 2014

maths
There are 2 ways to get a sum of 11 in a throw of 2 dice --- 6,5 or 5,6 prob of sum of 11 = 2/36 = 1/18
March 7, 2014

Algebra
Hint for the factors: Can you think of 2 numbers, one positive and the other negative, which when multiplied give you -30 and when added give you +7 ?
March 7, 2014

Algebra 1 Answer Check (Reiny)
you are welcome
March 7, 2014

Algebra 1 Answer Check (Reiny)
all 3 are correct.
March 7, 2014

Calc :(((((
first cross-multiply y + y x^2 = x dy/dx + y(2x) + 2x dy/dx = 1 dy/dx(1 + 2x) = 1 - 2xy dy/dx = (1-2xy)/(1+2x) at (4, 1/4) dy/dx = (1 - 2(4)(1/4))/(1 + 2(4)) = -1/9 equation of tangent: y = (-1/9)x + b at (4,1/4) 1/4 = (-1/9)(4) + b b = 5/9 equation is y = (-1/9)x + 5/9 slope...
March 7, 2014

Calculus Help
dy/dx = 2ax + bx when x = 1, 2a + b = 6 when x = -1 -2a +b = -14 add them 2b = -8 b= -4, then a = 5 to find c, sub in (2,17) into the original: 17 = 4a + 2b + c 17 = 20 -8 + c c = 5 y = 5x^2 - 4x + 5 check: for (2,17) 17 = 20 - 8 + 5 ---> true dy/dx = 10x - 4 at x = 1, dy/...
March 7, 2014

Algebra word problem
x^2 + 6x - 27 = (x+9)(x-3) So possible sides are x+9 and x-3 however, that would not be the only possibility. e.g. suppose one side is x-2 then the other side is (x^2 + 6x - 27)/(x-2) or ( x+8 - 11/(x-2) ) or with actual values suppose the area is 27 and one side is 3 then we ...
March 7, 2014

Probability
let N be a normal coin, and let DH be a double - headed coin let DT be double-tailed H -- heads, T --- tails for N, prob(H) = 1/2, prob(T) = 1/2 for DH, prob(H down) = 1, prob(Tdown) = 0 for DT, prob(H down) = 0, prob(Tdown) = 1 so you could draw N or DH or DT prob(heads down...
March 7, 2014

Algebra
area of lot = (6x)(10x) = 60x^2 area of field = x(4x) = 4x^2 area left for bleachers = 60x^2 - 4x^2 = 56x^2
March 7, 2014

maths
we know tht sin (-Ø) = -sinØ so if sinA = 3/5 sin(-A) = -3/5 check: from the given, A = 143.13.. sin(-143.13..) = -.6
March 7, 2014

Trig
In my sketch I see a non-rightangled triangle with angles 42° , 110° and 28° with the side opposite the 42° as the guy wire by the sine law: x/sin42 = 25/sin28 x = 25sin42/sin28 = .....
March 7, 2014

Calculus Please help!
f(-3) = 54 + 18 + 9 + 2 = 83 f(-1) = -2 + 2 + 3 + 2 = 5 slope = (5-83)/(-1+3) = -39 f ' (x) = -6x^2 + 4x - 3 then -6x^2 + 4x - 3 = -39 6x^2 - 4x -36 = 0 3x^2 - 2x - 18 = 0 x = (2 ± √220)/6 = appr 2.8054 or appr -2.1388
March 7, 2014

Calculus...URGENT..show steps please
The "solving" becomes a bit easier if you change the original equation to (x-y)^2 - 6x + 2y + 17 = 0 sub in : y = x - 3 (x - (x-3))^2 - 6x + 2(x-3) + 17 = 0 9 - 6x + 2x - 6 + 17 = 0 -4x = -20 x = 5 then y = 2 the horizontal asymptote touches at (5,2) I will do the ...
March 7, 2014

math
change in volume of tank = (5000)(4400)(21) cm^3 = 462,000,000 cm^3 = 462,000 L 15 km/hr = 1,500,000 cm/hr Volume moved = 1,500,000(49π) cm^3/hr time to fill 462,000,000 = 462,000,000/1,500,000 hrs = 308 hrs check my arithmetic
March 7, 2014

Algebra Question
Of course not! expand each of your factored expression. Notice that the middle terms are not the same
March 7, 2014

Math
part left = 1 - 3/8 - 1/3 = 24/24 - 9/24 - 8/24 = 7/24
March 7, 2014

Trig
absurd angles, check your typing. did you mean 70° instead of 700 ?
March 6, 2014

Math(check answer)
odds and probability are not quite the same odds in favour of some event = prob of that event : prob of NOT that event so ... prob of picking a green = 9/20 prob of not picking green = 11/20 odds in favour of picking a green = 9/20 : 11/20 = 9 : 11 which is D
March 5, 2014

MATH
radius after 24 hrs = 500(24) = 12000 m or 12 km area after 24 hrs = π(12)^2 = 144π square km radius after 48 hrs = 500(48) = 24000 m - 24 km area after 48 hrs = π(24^2) = 576 km^2 growth of spill between 24 hrs and 48 hrs = 432 km^2
March 5, 2014

Math
What is C(16,3) ?
March 5, 2014

Math
distance covered by faster driver --- x km distance covered by slower driver --- 320-x km The must have driven the same abount of time, so x/95 = (320 - x)/65 65x = 30400 - 95x 160x = 30400 x = 190 time = 190/95 = 2 hrs check: time of faster driver = 190/95 = 2 time of slower ...
March 5, 2014

Math
same old
March 5, 2014

Math
Are you reading my other replies to your questions with the same concept?
March 5, 2014

Math
A prime has no factors other than 1 and itself 5x^2 + x - 2 does not factor, so ....
March 5, 2014

Math
Using distance = rate x time 105t = 45(t+4) 105t = 45t + 180 60t = 180 t = 3 distance covered by each = 105(3) = 45(7) = 315 miles
March 5, 2014

Math
Very similar to the other I just answered for you. Difference in this one: the item is not replaced Prob = (6/20)(2/19) = 12/380 = 3/95
March 5, 2014

Math
oops , you wanted 3 decimals, 5.791 or 1.209
March 5, 2014

Math
use the formula x = (7 ± √21)/2 ---- > this is exact or appr, 5.79 or appr 1.21
March 5, 2014

Algebra
look at it as 2 ordered pairs (1/2 , 480) and (3/4 , 720) and find the linear equation slope = (720-480)/(3/4 - 1/2) = 240/(1/4) = 960 S = 960g + b , (using y = mx + b ) for (1/2, 480) 480 = 960(1/2) + b 480 = 480 + b b = 0 S = 960G (tells me 1 gallon covers 960 square feet)
March 5, 2014

Math
P(red, then blue) = (9/41(10/41) = 90/1681
March 5, 2014

Math
starting number --- x Anita's method 2x + x = 3x Amit: (x+x)(2) = 4x 4x - 3x = 9 x = 9 My algebra becomes the explanation. check: Anita ---> 2(9) + 9 = 27 Amit ---> (9+9)(2) = 36 difference = 36-27 = 9 all is good!
March 5, 2014

Correction - Math(Check answer)
Both are wrong Odds and probability are not the same thing you have found the prob(picking a vowel) Odds in favour of picking a vowel = prob of picking a vowel : prob of NOT picking a vowel = 3/7 : 4/7 = 3 : 4 the second question simply reverses the odds should be 4 : 3
March 5, 2014

Algebra
variance is defined as the square root of the standard deviation since variance is 4, sd = 16 go to http://davidmlane.com/hyperstat/z_table.html enter , 195 for the mean and 16 for sd click on below, and enter 190.2 to get .3821
March 5, 2014

Alg help
I had that too, hit the 4 instead of the 2, sorry.
March 5, 2014

Alg help
What is √(12^2 + 4^2 + 9^2) ?? I get √441 , which is not any of your choices.
March 5, 2014

math
what about it ?
March 4, 2014

algebra
amount invested at 5% --- x amount invested at 8% --- y x+y = 5000 (5/100)x + (8/100)y = 331 times 100 5x + 8y = 33100 first equation times 5 5x + 5y = 25000 subtract them: 3y = 8100 y = 2700 take over....
March 4, 2014

algebra
x+y = 30 x-y = 2 add them 2x = 32 x = 16 then, mentally, y = 14 check: 16+14 = 30 16-14 = 2 , yeahhh!
March 4, 2014

Differential Equations
".. by making many small deposits throughout the year. " I don't know what you mean by that. - how often are they made ? - are the payments the same ?
March 4, 2014

Algebra
volume = length x width x height = (2x+3)(x+2)(x-3) or, if it needs to be expanded .... = (2x+3)(x^2 - x - 6) = 2x^3 - 2x^2 - 12x + 3x^2 -3x - 18 = 2x^3 + x^2 - 15x -18
March 4, 2014

Math
600 g + 1 kg = 600 g + 1000 g = 1600 g = 1.6 kg
March 4, 2014

algebra (solve for y)
treat it like a quadratic equation ... let e^y = x then your equation becomes 0 = 2x^2 - x x(2x - 1) = 0 x = 0 or x = 1/2 then e^y = 0 -----> no solution or e^y = 1/2 take ln of both sides and use the rules of logs y lne = ln1 - ln2 y (1) = 0 - ln 2 y = -ln2 or e^y( 2e^y - ...
March 4, 2014

math
I will define x in a different way, the way you suggest introduces unnecessary complicated fractions. The the radius of the circle be r, let each side of the square be x 4x + 2πr = 24 2x + πr = 12 x = 6 - (π/2)r let A be the total area A = πr^2 + (6 - (&#...
March 4, 2014

math
y = cosx tanx = cosx (sinx/cosx) y = sinx
March 4, 2014

Geometry
no, it is b SSA often results in 2 different triangles with the same properties, thus no congruency.
March 4, 2014

math
square: a quadrilateral with 4 equal sides, all angles 90° rhombus: a quadrilateral with 4 equal sides. A square is a rhombus, but a rhombus is not necessarily a square. http://www.mathsisfun.com/quadrilaterals.html
March 4, 2014

Algebra - Domain
I see a few problems here. 1. In the usual terminology, the word "function" implies the relationship between two variables, usually x and y, where the value of y depends on x. You have an equation that contains only one variable y (the "solution" to your ...
March 4, 2014

Algebra
correct
March 4, 2014

math
By sheer coincidence this same question was posted on March3 , three years ago http://www.jiskha.com/display.cgi?id=1299163469
March 3, 2014

Algebra
ascending powers of b ----> the terms containing b with exponents from smallest to largest, so -7dm + 25 b^5 - 6 d b^6 + 3 b^10 your answer makes no sense, there were 4 terms, so you still have to have 4 terms.
March 2, 2014

Algebra
descending means from highest to lowest. just look at the exponents of p
March 2, 2014

Math
speed = distance /time speed ≥ 420/8 ≥ 52.5 mph
March 2, 2014

Geometry
Did you not read our objection to your problem. Why would you repost exactly the same way ? http://www.jiskha.com/display.cgi?id=1393701722 Steve gave you a solution according to one interpretation.
March 2, 2014

geometric progresions
sum of first 8 terms = a(r^8 - 1)/(r-1) sum of first 4 terms = a(r^4 - 1)/(r-1 ( a(r^8 - 1)/(r-1) ) / ( a(r^4 - 1)/(r-1) ) = 97/81 (r^8 - 1) / (r^4 - 1) = 97 / 81 81r^8 - 81 = 97r^4 - 97 81^8 - 97r^4 + 16 = 0 let r^4 = x 81x^2 - 97x+16 = 0 x = (97 ± √4225)/162 = (...
March 2, 2014

algebra
Will there be some kind of question ?
March 1, 2014

math(algebra)
Or you could say that each costs $1.99 with the first 4 costing a dollar more so .. y =1.99x + 4 that would be the simplest equation, Too bad they don't have it
March 1, 2014

Algebra 1--Please, help me!
show that slope AB = slope DC and slope AD = slope BC I will do the first pair, you do the second slope AB = (5-5)/6+2) = 0/8 = 0 slope DC = (-3+3)/(-4-4) = 0/-8 = 0 so AB || DC test if AD || BC if so, then by definition, it is a parallogram.
March 1, 2014

Geometry
Strange wording. How high is the lighthouse above the sea level ?
March 1, 2014

Algebra 1--Step-by-Step
3 and 4 are correct #2 14q^2 - 21q + 6 - 4q = 7q(2q - 3) + 2(3-2q) = 7q(2q-3) - 2(2q-3) = (2q-3)(7q-2)
March 1, 2014

Algebra 1--Step-by-Step
look at my answer ... (r-3)(2r-4) = (r-3)(2)(r-2) = 2(r-3)(r-2)
March 1, 2014

Algebra 1--Step-by-Step
Surely you could see that 2 was an additional common factor contained in my (2r-4) factor.
March 1, 2014

Algebra 1--Step-by-Step
1. 2r(r - 3) + 4(3 - r) , ahhh, did you notice that the brackets are opposite? , so .. = 2r(r-3) - 4(r - 3) = (r-3)(2r-4) Use the same "trick" on the others if you have to.
March 1, 2014

algebra
sub the first into the 2nd ... 3x - 18y = 4 3(6y+2) - 18y = 4 18y + 6 - 18y = 4 6 = 4 , which of course is nonsese, so .. there is no solution (You have two parallel lines)
March 1, 2014

algebra
number of people---- x cost = 20x + 35 20x + 35 ≤ 350 20 x ≤ 315 x ≤ 315/20 ≤ 15.75 So he can invite 15 people maximum test: if he invites 15 cost = 20(15) + 35 = 335 , within his budget if he invites 16 cost = 20(16) + 35 = 355 , above budget.
March 1, 2014

algebra
Does the fence run on 4 sides or on 3 sides ?
March 1, 2014

Math
|2x-7|=11 2x-7 = 11 OR -2x+7 = 11 2x = 18 OR -2x = 4 x = 9 OR x = -2 so the sum of the solutions is 9-2 = 7
March 1, 2014

Algebra
I = k(1/R), where I current, R is resistance and k is a constant given: I = 5, R = 20 5 = k(1/20) k = 100 I = 100(1/R) so when R = 25 I = 100(1/25) = 4
March 1, 2014

Trigonometry
from last night at 10:06 pm RS = (1-sinØ)/(1+ sinØ) = (1-sinØ)/(1+ sinØ) * (1-sinØ)/(1- sinØ) = (1 - 2sinØ + sin^2 Ø)/(1 - sin^2 Ø) = (1 - 2sinØ + sin^2 Ø)/cos^2 Ø = 1/cos^2 Ø - 2sin&...
March 1, 2014

Trigonometry
ok I usually start with the more complicated looking side and try to change it to the more simplified LS = cosØ/(sinØ - 1) + cosØ(sinØ + 1) , note it didn't matter to change the order of that last denominator common denominator of (sinØ-1...
March 1, 2014

Trigonometry
I see no equal signs What are we verifying ?
March 1, 2014

MATH
5√8 - 3√18 + √3 in general to change √k to a mixed radical, look for factors of k which are perfect squares e.g. 18 = (3)(6) or 2(9) the choice of (3)(6) does not do us any good, since neither factor is a perfect square so your problem can be written as...
March 1, 2014

MATH
4√2 + 6√4 = 4√2 + 6(2) = 4√2 + 12
March 1, 2014

Probability
let S be the event of being dealt a spade, x the event of a non-spade One such 5 spade hand could be SSSSSXXXXXXXX The prob of that is (13/52*12/51*11/50*10/49*9/48)(39/47*38/46*37/45*36/44*35/43*34/33*33/32*32/31) a quicker way would be to say prob(exactly 5 spades) = ( C(13,...
February 28, 2014

Trig
That's a better job of typing it. I did the first of these in your previous post.. the 2nd: LS = (1-sinØ)/(1+ sinØ) = (1-sinØ)/(1+ sinØ) * (1-sinØ)/(1- sinØ) = (1 - 2sinØ + sin^2 Ø)/(1 - sin^2 Ø) = (1 - 2sin&...
February 28, 2014

Math
how about just treating it like 2 ordered pairs (1991, 4.25) and (1997, 5.15) ? rate of change = (5.15-4.25)/(1997-1991) = .15
February 28, 2014

Trig
Don't try to build up fractional equations using your method, the spacing will not work out instead do something like this: 1/(tanØ - secØ) + 1/(tanØ + secØ) = -2tanØ LS = (tanØ + secØ + tanØ - secØ)/(tan2 &...
February 28, 2014

Pre-Calculus
we know x =rcosØ and y = rsinØ -3rcosØ + (1/2)rsinØ = 2 -6rcosØ + rsinØ = 2 r(sinØ - 6cosØ) = 2 or r = 2/(sinØ - 6cosØ) looks good: http://www.wolframalpha.com/input/?i=polar+r+%3D+2%2F%28sinx+-+6cosx%29
February 28, 2014

Calculus Please help!
dy/dx = 3(x^2 + 6)^2 dy = 3(x^2 + 6)^2 dx when x = 2 and dx = .05 dy = ...... just plug in the above values.
February 28, 2014

Probability
#1 is correct, in effect what you are doing is C(60,60) (.99^60 (.01)^0 = .547 #2, you want to have 59 correct and one wrong = C(60,59) (.99)^59 (.01)^1 = 60(.55268..)(.01) = .33161 #3 , same way, 58 correct, 2 wrong prob = C(60,58) (.99)^58 (.01)^2 = .09881 #4 , at least 2 ...
February 28, 2014

Probability
at least 4 means 4 or 5 or 6 or ... or 20 are colourblind so exclude cases of none, 1 , 2, and 3 colourblind = .05 not colourblind = .95 None: C(20,0) (.05)^0 (.95)^20 = .358486 one: C(20,1) (.05) (.95)^19 = .37735.. two: C(20,2) (.05)^2 (.95)^18 = .1886768 three: C(20,3)(.05...
February 28, 2014

Math:Probability
1. could be 1 in math or 1 in history or 1 in Spanish that is (math)(no history)(no Spanish) + .... prob = .9(.4)(.25) + .6(.1)(.25) + .25(.1)(.4) = .115 Exclude the case of no homework in any which is (.1)(.4)(.25) = .01 prob(homework in at least 1 class) 1 - .01 = .99
February 28, 2014

Math (Statistics)
Perfect data, one standard of devation below and above. so appr 68% or prob of .68 confirmed by David's webpage http://davidmlane.com/hyperstat/z_table.html fill in the data to see and get .6827
February 28, 2014

Calculus Please help!
Let the radius be r, so the diameter is 2r then the height is 2r V = (1/3)π r^2 h = (1/3) π r^2 (2r) = (2/3)π r^3 dV/dt = 2π r^2 dr/dt when h = 24 2r = 24 r = 12 and dV/dt = 30 30 = 2π (144) dr/dt dr/dt = 30/(288π) = 5/(48π) ft/min or appr ....
February 28, 2014

Calculus Please help!
darn them brackets 23t^2 vs (23t)^2
February 28, 2014

Calculus Please help!
let the time be t hours past noon. I see a right-angled triangle , with sides 23t and 50 + 18t, with D as the distance between them D^2 = (23t)^2 + (50+18t)^2 D^2 = 529t^2 + 2500 + 1800t + 324t^2 = 853t^2 + 1800t + 2500 2D dD/dt = 1706t + 1800 dD/t = (853t + 900)/D , #1 at 3:...
February 28, 2014

Algebra 2 Help!
No, since the disc I negative, you will have 2 complex roots
February 28, 2014

Algebra 2 Help!
f(x) = 5x^2 - 10x + 3 , notice how we use exponents in this format = 5(x^2 - 2x + 1 - 1) + 3 = 5 ( (x-1)^2 - 1) + 3 = 5(x-1)^2 - 5 - 3 = 5(x-1)^2 - 8 6= 4x - 5x^2 5x^2 - 4x + 6 = 0 b^2 - 4ac = 16 - 4(5)(6) = -104 What do you think ?
February 28, 2014

Algebra 2 Help!
[sqrt3 + 2i][sqrt3 - 2i] = 3 - 2i√3 + 2i√3 - 4i^2 = 3 - 4(-1) = 7 (y - 4)^2 = -18 y - 4 = ± √18 y = 4 ± 3√-2 = 4± 3√2 i
February 28, 2014

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