Monday
August 31, 2015

Posts by Reiny


Total # Posts: 30,693

math
cost to make the cakes = 200(2.7)= 540 To make a profit of 66% she needs 1.66(540) = 896.40 But she discards 10% of her cakes, so only sells 180 Selling price = 896.4/180 = $ 4.98 check: profit = 4.98(180) - 540 = 356.40 rate of profit = 356.4/540 = .66 or 66%
February 16, 2015

Algebra
-3x^2 - 18x + 15 since 3x^2 + 18x - 15 = 0 does not have any rational roots since b^2 - 4ac is not a perfect square, it does not factor over the rationals
February 15, 2015

math
area of a rhomus = (1/2)(product of its diagonals) let the other diagonal be a (1/2)(15a) = 60 15a= 120 a = 8 So let's find the hypotenuse of one of the right-angled triangles formed by the intersection of its diagonals base = 4, height = 7.5 if h is the hypotenuse, h^2 = ...
February 15, 2015

Calculus
You would now sub those two values into the original equation. The larger answer is your maximum the smaller value is your minimum
February 15, 2015

Algebra 1
I agree. Unless the coeffiecients are relatively small, I usually don't waste too much time trying to factor it. If the x^2 term has a coefficient of 1, and the x term is even I ALWAYS complete the square, it is much faster than the formula. Otherwise, I do a quick ...
February 15, 2015

Math
3^12 /(3x3^6) = 3^12 / 3^7 = 3^5 = 243
February 15, 2015

calc
You must have an idea what the tangent function looks like. As Ø approaches 90° or π/2 from the left, tanØ becomes infinitely large positively. as Ø approaches 90° from the right, it is infinitely negative now look at (x^7 - x^9), as x -->...
February 15, 2015

algebra
expand first , then collect like terms x - 9x + 10 + 11 = 12 - 6x + 1 -8x + 6x = 13 - 21 -2x = -8 x = 4
February 15, 2015

Math
number of quarters --- x number of dimes --- 21-x 25x + 10(21-x) = 345 25x + 210 - 10x = 345 15x = 135 x = 9 He has 9 quarters and 12 dimes check: 9(25) + 12(10) = 345 , check!!
February 15, 2015

math
1.41/100 = 1/x 1.41x = 100 x = 100/1.41 = $70.92 ( your textbook must be from the Clinton era. During the Bush years, it was reversed, the Canadian dollar was worth more. Now under Obama we are slipping again and the US dollar is rising, 1 US = appr 1.18 CND . As you can tell ...
February 15, 2015

math
since you end up with 12 = 4 , which is false, there is no solution
February 15, 2015

maths(urgent answer pls)
Still messing around with #2 #3, ∑ k(k+2)(k+4) , where k = 1 to n if you expand this you will get a cubic , so you will have to have ∑ k^3 for k=1 to n equal to (1/4)n^2(n+1)^2 ( I had to look that one up) for the square and first degree terms use the ones I gave ...
February 15, 2015

maths(urgent answer pls)
I answered the first part in your previous post
February 15, 2015

mathematics
prob(red, black, red) = (3/10)(7/9)(2/8) = 7/120
February 15, 2015

MATHS(sum of series)
yes it will Sum(1) = (4(2)(3) - 12(2) + 6)/6 = 1 sum(2) = (8(3)(5) - 24(3) + 12)/6 = 10 sum(3) = 12(4)(7) - 36(4) + 18)/6 = 35 etc. It works! I am sure!
February 15, 2015

MATHS(sum of series)
I will do the first one We were lucky to have the general term, in most cases you have to find that first Secondly you have to know some basic summation formulas ∑ k ,where k = 1 to n is n(n+1)/2 ∑ k^2 , where k = 1 to n is n(n+1)(2n+1)/6 ∑ c , where k = 1 to...
February 15, 2015

calculus
I will assume you meant: lim (2x + 1 - cosx)/(3x) then ... = lim ( (2x)/(3x) + 1/(3x) - (1/3)(cosx/x) ) as x --> 0 = lim ( 2/3 + 0 - (1/3)(0) ) = 2/3
February 15, 2015

mathematics
let the first 3 terms be a , ar , and ar^2 ar = a + 4 ar - a = 4 a(r-1) = 4 a = 4/(r-1) ar^2 = ar + 9 ar^2 - ar = 9 a = (9/(r^2 - r) so 9/(r^2-r) = 4/(r-1) 4r^2 - 4r = 9r - 9 4r^2 - 13r + 9 = 0 (4r - 9)(r - 1) = 0 r = 9/4 or r = 1 if r = 9/4, a = 4/(9/4 - 1) = 16/5 the first 3...
February 15, 2015

math
.6/1 = 384/x x = 384/.6 = 640 the gas occupies 640 cm^3 in the can volume of can = πr^2 h π(3.2^2)h = 640 h = 640/(10.24π) = 19.89 cm
February 15, 2015

math
let's pick one particular suit, say the hearts to get the above in that order: prob = (1/52)(1/(51)(1/50)(1/49)(1/48) = 1/311875200 but there are 4 such suits prob(of your event) = 4/311875200 = 1/77968800
February 14, 2015

Pythagoras
Hope you made a sketch. In mine I can use the cosine law let the distance from the starting point be x x^2 = 520^2 + 387^2 - 2(520)(387)cos45° = 135572.6627 x = √.... = 368.2 km
February 14, 2015

Algerba
dimes ---- x quarters ---- x+10 nickels ---- 2(x+10) = 2x+20 10x + 25(x+10) + 5(2x+20) = 575 10x + 25x + 250 + 10x + 100 = 575 45x = 225 x = 5 So he has 5 dimes, 15 quarters and 30 nickels check: 5 dimes = 50 cents 15 quarters = 375 cents 30 nickels = 150 cents total = 575 ...
February 14, 2015

Calculus
I took out the highest common factor
February 14, 2015

Calculus
no, you have to use the product rule f(x) = (7^x)(x^7) f ' (x) = (7^x)(7x^6) + (x^7)(ln7)(7^x) = (7^x)(x^6) (7 + x ln7)
February 14, 2015

Calculus
Why are you using days when t was defined in years so t = 1/2 f ' (1/2) = -9 e^(-3(1/2)) = -9 e^(-1.5) = appr -2.008
February 14, 2015

Finance
let the quarterly rate be i then (1+i)^4 = (1+.07/12)^12 take 4th root of both sides 1+i = 1.0058333..^4 1+i = 1.023538 i = .023538 or 2.3538% per quarter times 4, gives us 9.4153% per annum compounded quarterly.
February 14, 2015

Finance
Don't know what EAR is, but I will assume your rate is 11% per annum compounded semi-annually i = .11/2 = .055 PV = 1000(1 - 1.055^-10)/.055 = 7537.63
February 14, 2015

Finance
assuming payments at the end of the day. 100(1 - 1.0006^-n)/.0006 = 27500 1 - 1.0006^-n = .165 1.006^-n = .835 log both sides and use log rules -n(log 1.0006) = log .835 -n = -300.6 300 full daily payments of $100 plus a partial payment on the 301st day.
February 14, 2015

Math
When they "meet" the difference in their travel time is 20 minutes or 1/3 of an hour let the distance from from Tigersville be x x/85 - (154-x)/60 = 1/3 times 1020 , the LCM of 85, 60 and 3 12x - 17(154-x) = 340 12x - 2618 + 17x = 340 29x = 2958 x = 102 time for ...
February 14, 2015

Finance
good question. must find the monthly payment. i = .0675/12 = .005625 (I stored that in my calculator) n = 12x30 = 360 let the payment be p p(1 - 1.005625)^-360)/.005625 = 249000 p = 1615.01 first month interest = .005625(on full amount) = 1400.63 so split-up of first payment: ...
February 14, 2015

Finance
You did not state how each of the rates are compounded, that is critical
February 14, 2015

Math
using de Moivre's Theorem: let z^4 = -46 + 9i changing -46 + 9i to rectangular form r = √46^2+9^2 =√2197 tanØ = 9/-46 Ø = 168.9298° z^4 = √2197(cos168.9298° + i sin 168.9298°) z = ..... so there will be 4 roots, z = √2197^(...
February 14, 2015

Calculus
simplify it ... f(x) = √(sinxcosx) = √( (1/2)(sin(2x) ) = 1/√2 (sin(2x))^(1/2) f ' (x) = (1/√2)(1/2)(sin(2x))^(-1/2)(2cos(2x)) = (1/√2) (cos 2x)/(sin 2x) = 1/√2 cot (2x) or , the way it stands f(x) = (sinxcosx)^(1/2) f ' (x) = (1/2)(...
February 13, 2015

Calculus
1) in that case why not just write the exponent as -5x ? y = 5 e^(-5x) y' = -25 e^(-5x) 3. but your answer resembles the other interpretation, for which I gave you a solution. I stand by that answer.
February 13, 2015

Calculus
1) if you have a function f(x) , what is that 9z doing there in the exponent? 2) yes 3.) is that a stair-case exponent or is it f(x) = (e^x)^-1 ? = e^-x ? on the other hand, Wolfram read your equation as y = e^(1/x) http://www.wolframalpha.com/input/?i=plot+y+%3D+e%5Ex%5E-1 in...
February 13, 2015

Calculus help and please check answer for a)
a) correct b) since you want the rate at a time of t, your derivative is your answer c) you would sub t = 3 into the derivative, the rate of change, that you found in b)
February 13, 2015

math calculus
then go with Steve's suggestion and plot the two curves y = 2^x and y=(1/2)^x to see the result http://www.wolframalpha.com/input/?i=plot+y+%3D+2%5Ex+%2C+y+%3D+%281%2F2%29%5Ex
February 13, 2015

math calculus
the difference between the function 2^x and (1/2)^x = |2^x - (1/2)^x| = | 2^x - 2^-x |
February 13, 2015

algebra
8 + (1/3)(6-p) or to be more specific 8 + (1/3)|6-p|
February 13, 2015

Calculus
So they will need as much in the account to annually generate 10,000 in interest x e^.08 - x = 10000 x(e^.08 - 1) = 10000 x = 10000/(e^.08 - 1) = $120,066.66 Since G is supposed to in thousands G ≥ 120.06666 check: amount of the 120066.66 after 1 year of continuous ...
February 13, 2015

calculus- min value of function
f(x) = sinxcosx = (1/2) sin (2x) by a common identity At this point I have my answer. y = (1/2)sin(2x) has an amplitude of 1/2 that is , its maximum is 1/2 and its minimum is -1/2
February 13, 2015

Algebra 2
.......... D ..R ...T You 60 x+10 60/(x+10) Marley 50 x 50/x 50/x - 60/(x+10) = 2 times x(x+10) 50(x+10 - 60x = 2x(x+10) 50x + 500 - 60x = 2x^2 + 20x 2x^2 + 30x - 500 = 0 x^2 + 15x - 250 = 0 (x+25)(x-10) = 0 x = 10 or x = -25, the latter being silly Marley went 10 mph on a ...
February 13, 2015

pre- calculus
treat the "mother and father" as one entity. So we are arranging 5 around the table which is 5! but we can rotate each particular arrangement 5 times around the table without changing any order, since there is no specified position around the table (e.g. everybody ...
February 13, 2015

GS not AS - maths
in a GS 3rd term = ar^2 = 12 6th term = ar^5 = 96 divide them r^3 = 96/12 = 8 r = 2 then in ar^2 = 12 4a = 12 a = 3 so you have 3 + 6 + 12 + ... +(the last value before 2000) so term(n) = ar^(n-1) < 2000 3(2^(n-1) ) = .. if n = 9, 3(2^8) = 768 n = 10 , 3(2^9) = 1536 n = 11...
February 13, 2015

math
the new equation will differ from the old equation only in the constant so new: x+2y = c , but (5,-2) is on it, so 5-4 = c = 1 x + 2y = 1
February 12, 2015

math
Assume Aaron had x dollars he gave 3/7 x away, so he has 4x/7 left. he gives 1/4 of what he has left to his sister, so he has (3/4)(4x/7) left (3/4)(4x/7) = 120 12x/28 = 120 x = 120(28/12) = $ 280
February 12, 2015

linear algebra
and we both called the variables a, b, and c What's that old saying, something about great minds, lol
February 12, 2015

linear algebra
I will use a, b, and c, instead of c1, c2 and c3 a(3,3,-1) + b(1,2,-3) + c(-11,-13,9) = (0,0,0) 3a + 2b - 11c = 0 3a + 2b - 13c = 0 -a - 3b + 9c = 0 subtract 2nd from 1st 2c = 0 c = 0 sub into 2nd and 3rd 3a + 2b = 0 -a - 3b = 0 triple the 3rd: -3a - 9b = 0 3a + 2b = 0 -7b = 0...
February 12, 2015

math
The only tricky part in this question is to ignore data which is irrelevant, like the 6 ft girl's initial mirror placement. The only fact we care about is that we have two similar right-angled triangles, formed by the second student and the mirror, and the tree and the ...
February 12, 2015

math
current price of ticket = $2.00 number of sales = 600 let the number of 50 cent increases be n price per ticket = 2 +.5n number of sales = 600-30n income = (2+.5n)(600-30n) = 1200 - 60n + 300n - 15n^2 = 1200 + 240n - 15n^2 not sure if you know Calculus, so I will not use that ...
February 12, 2015

Calculus
did you mean something like y = √( (x^2 + 5x)/(5x) ) original form derivative: dy/dx= (1/2)((x^2+5)/(5x))^(-1/2) ( 5x(2x) - (x^2+5)(5))/(25x^2) etc , but still has to be simplified using logs first: take ln of both sides: ln y = ln((x^+5)/(5x))^(1/2) = (1/2)(ln (x^2+5...
February 12, 2015

math
ahh, I see you corrected it 1st: length -- 3x width ---2x area = 6x^2 2nd : lenth : width = 3y : 2y area = 6y^2 but length of larger : length of smaller = 7:5 3y : 3x = 7 : 5 y/x = 7/5 y = 7x/5 so area of 2nd = 6(7x/5) = 294x^2/25 larger area / smaller area = (294x^2/25) / 6x^...
February 11, 2015

Find the domain of the function
remember we can't divide by zero so anything goes for the x, except 0 Write that up in the format that you have learned.
February 11, 2015

math
first: length -- 3x width --- 2x area = 6x^2 2nd: ??? "The ratio of the length of the larger is 7:5" don't know what that means
February 11, 2015

Math
a) you would simply choose 3 of the 11 = C(11,3) = 165 b) 3 men of 5, 4 women of 6 = C(5,3) x C(6,4) = 10x15 = 150
February 11, 2015

Math (Interest)
yes, it would be 18.6387 since the time is so short, it is no surprise that the two answers are the same
February 11, 2015

Math (Interest)
don't make it look so complicated i = .025/12 = .00208333.. (I use my calculator's memory to store such numbers, don't round them off yet) amount = 18.6(1.00208333...)^1 , for 1 month = 18.6(1.00208333.. = $ 18.64 Wow, we gained 4 cents interest !
February 11, 2015

Algebra
let x^(1/4) = k then we have k^2 - 7k + 12 = 0 (k-3)(k-4) = 0 k = 3 or k = 4 x^(1/4) = 3 or x^(1/4) = 4 x = 81 or x = 256
February 11, 2015

perpendicular vectors
Nice !
February 11, 2015

linear algebra
I will read that as [(a -b) -3] = [7 (a+b)] then a-b=7 a+b=-3 add them 2a = 4 a = 2 and then 2+b=-3 b = -5
February 11, 2015

MATH
100^2 ÷ 10^-5 = 10^4/10^-5 = 10^9 , which is 1 billion times as large
February 11, 2015

math
width -- x length -- 2x+1 x+x + 2x+1 + 2x+1 = 29 6x+2=29 take over Just realized I used x instead of w, no big deal.
February 11, 2015

Algebra 1
width --- x length --- 2x+4 (17)(x)(2x+4) = 2720 x(2x+4) = 160 2x^2 + 4x - 160=0 x^2 + 2x - 80 = 0 (x+10)(x-8) = 0 x = -10 , which would make no sense or x = 8 The box is 8 inches wide check: w=8 l= 20 h=17 V = 8x20x17=2720 All looks good
February 11, 2015

Algebra
I suggest googling "factoring trinomials" or "factoring quadratic trinomials" Also there are many good youtubes and Khanacademy has many clips to show you how.
February 11, 2015

Algebra
if you mean factored form, then = (2x+1)(3x+2)
February 11, 2015

Algebra 1
there is no solution in the set of real numbers, but there are two complex number solutions. see: http://www.jiskha.com/display.cgi?id=1362104847
February 11, 2015

Algebra 1
there are two solutions x^2 + 6x + 5 = 0 (x+1)(x+5) = 0 x = -1 , you had that one or x = -5
February 11, 2015

Algebra 1
take 1/2 of the middle term coefficient and square that number (1/2)(11 = 11/2 squared gives us 121/4 so x^2 + 11x + 121/4 = (x+11/2)^2 so n = 121/4 or 30.25 if you want a decimal
February 11, 2015

algebra
let her initial speed be x mph time for first trip = 320/x new speed = x+10 mph time for second part of trip = 500/(x+10) so.. 500/(x+10) - 320/x = 2 times x(x+10) 500x - 320(x+10) = 2x(x+10) 500x - 320x - 3200 = 2x^2 + 20x 2x^2 - 160x + 3200 = 0 x^2 - 80x + 1600 = 0 (x-40^2...
February 11, 2015

math
.342 = 342/1000 so its reciprocal is 1000/342 = 500/171
February 11, 2015

Math - Answer Check
all your answers are correct
February 11, 2015

Algebra
suppose something costs $x and you increase it by 5% doing it your ways: increase = .05x end result = x + .05x = x(1 + .05) = 1.05x so you get the result after anything is increased by 5% , just multiply by 1.05 or to get the result after anything is increased by 16% , just ...
February 11, 2015

maths
The LCM of 2, 3, 5, 7, and 12 is 420 So they will all fire together again 420 minutes, or 7 hours from now
February 11, 2015

math
Ok, I made a sketch and concluded that the angle at X is 150° Is there another question?
February 11, 2015

Andrew , Meg, Sarah - math
We are not going to do your assignment/homework for you. What have you learned from my previous answers so far?
February 11, 2015

math
same stuff (any reason why you switched names ?)
February 11, 2015

math
use the concepts I used in my previous answer to your similar question.
February 11, 2015

math
how about y = 3x^2/( (x-3)(x-6) )
February 11, 2015

math
Did you mean y = (3x+6)/(x-7) ?? Vertical asymptotes: What happens when the denominator is zero? For what value of x does this happen ? horizontal : Which terms fall by the wayside as x→∞ ? what remains of y = (3x ...)/(x ....) ?
February 11, 2015

math
by the "just look at it" theorem lim x→∞ sqrt(x^2+9) = x , so there is no limit e.g. let x = 1,000,000 ,using my calculator I got 1,000,000
February 11, 2015

math
I am sure you meant: lim (2- e^x)/(2+9e^x) divide each by e^x = Lim (2/e^x - 1)/(2/e^x + 9) now as x→∞ , e^x ---> 0 and we approach the value (0-1)/(0+9) = -1/9
February 11, 2015

math
area of original = 40(20) =800 cm^2 after cutoff, new size is 32 by 12 area of that = 32(12) = 384 cm^2 area of strip cut out = 800-384 = 416 cm^2
February 11, 2015

maths(Probability)
There are 36 ways for the 2 dice to fall (make yourself a 6by6 matrix) a) there is only one way to get a sum of 2 ---> 1,1 prob (a sum of 2) = 1/36 b) a sum of 7: 1 6, 2 5, 3 4, 4 3, 5 2, 6 1, so 6 ways prob(a sum of 7) = 6/36 = 1/6 c) a prime: the primes are 2, 3, 5, 7, or...
February 11, 2015

math
actually it should be -2 notice that x ---> negative infinity, so the x^3 is negative
February 11, 2015

Calc
There is no "formal" way to do this. One method is Newton's Method if you know Calculus Another way is to have a good calculator, and finetune your values of x e.g. let x = 1 LS = e^1 = 2.71828.. Rs = 4 let x = 2 LS = e^2 = 738 RS = 6 , ahh, I went too high let x...
February 11, 2015

Algebra 1
teams left after 1 week = 64 = 128(1/2) teams left after 2 weeks = 32 = 128(1/2)^2 .. teams left after 6 weeks = 128(1/2)6 = 2
February 11, 2015

math101
I will assume compound interest: 6900(1.12)^n = 9384 (1.12)^n = .1.36 take log of both sides, and use log rules nlog1.12 = log1.36 n = log1.36/log1.12 = 2.7 it would take 2 years and appr. 8.5 months check: balance after 1 year = 6900(1.12) = 7740.32 balance after 2 years = ...
February 11, 2015

Math
Did you make your sketch? area of larger square = (2s)^2 = 4s^2 For the side of the smaller square: x^2 = s^2 + s^2 x = √2s area of smaller is (√2s)^2 = 2s^2 so the ratio of their areas = 4s^2 : 2s^2 = 2 : 1
February 10, 2015

algebra
number of quarters --- x number of dimes ---- 2x number of nickels ---- 2x+47 25x + (10)(2x) + 5(2x+47) = 400 solve for x, then sub into my definitions
February 10, 2015

algebra
let the amount of pure acid added be x ml x + .45(600) = .5(x+600 x + 270 = .5x + 300 .5x = 30 x = 60
February 10, 2015

Math
no, it said that she flew at 800 mph for one hour, so she used up 1 hour of flying time To average 1000 mph in flying 1000 miles would take exactly one hour, which she has already spent flying. So she must do the remaining 200 miles in zero time. That is why it is not possible.
February 10, 2015

Math
She must fly faster than the speed of light, that is, it can't be done. I want your explanation of why I said that.
February 10, 2015

math - exponent laws
You must be referring to the post from yesterday where you had -( -11/-17)^-10 ÷ (9/5)^(1/10) http://www.jiskha.com/display.cgi?id=1423540960yes , you could have done that. I treated the (-11/-17)^-10 as 1/(11/17)^10 which was 77.725... You want to do (17/11)^10 which ...
February 10, 2015

Algebra 1
outer area = (10x+89)(7x+7)= 70x^2 + 693x + 623 skylight area = (x+5)(3x+3)= 3x^2 + 18x + 15 remaining area = 70x^2+693x+623 - (3x^2+18x+15) = 67x^2 + 675x + 608
February 10, 2015

Algebra 2
first of all notice that each term divides by 2, so (6x^2+4x-16)/(2x-2) = (3x^2 + 2x-8)/(x-1) hard to show the actual long division on here but you should get 3x+5 with a remainder of -3
February 10, 2015

Algebra 2
factor it, you are looking at the difference of squares x^4 - 81 = 0 (x^2 + 9)(x^ - 9) = 0 , and again (x^2 + 9)(x+3)(x-3)= 0 x= -3 or x = +3 or x^2 = -9 ---> x = ± 3i If you have not studied complex numbers, then just go with the x = ± 3
February 10, 2015

math
if that is supposed to say u^2 - 14u + 49 , then can you think of two numbers which multiply to get 49 and have a sum of -14 ? -7 and -7 come to mind = (u - 7)(u - 7) or (u-7)^2
February 10, 2015

Math
volume is proportional to the cube of their corresponding sides V/280 = 2.5^3/1^3 V = 280(15.625) = 4375 cm^3
February 10, 2015

Algebra
area of first = x^2 area of 2nd = (x+5)^2 x^2 + x^2 + 10x + 25 = 193 2x^2 + 10x - 168 = 0 x^2 + 5x - 84 = 0 (x - 7)(x + 12) = 0 x = 7 or x = -12 , which would be a silly square the first square is 7 by 7 the second is 12 by 12 check: 49 + 144 = 193 , yeahhh!
February 10, 2015

math
The following OA , OB etc are vectors OA + AB = OB AB = OB - OA AB = OB + AO = (4,1,-3) + (-3,2,-1) = (1,3,-4) |AB| = √(1^2 + 3^2 + (-4)^2) = √26 = appr 5.10
February 10, 2015

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