Wednesday
April 23, 2014

Posts by Reiny


Total # Posts: 26,103

Math
red from 1st ---> 8/18 = 4/9 red from 2nd ---> 10/13 prob(2res) = (4/9)(10/13) = 40/117

Math
Are we to assume that the other 9 customers did receive a star, thus are winners? If so, then the prob of winning = 9/156 = 3/52

Math
what is 10( 1.015^540 - 1)/.015 ? (don't be surprised if you get over 2 Million dollars)

Algebra 1
what you need is the vertex. for any parabola of the form y = ax^2 + bx + c the x of the vertex is -b/(2a) once you have the x of the vertex, plug into the original to get y y will be your maximum, and it happens at the x value. (make sure you get a max height of 156.25 ft )

Algebra 2
e^3x>e^x-1 you probably meant: e^(3x) > e^(x-1), (huge difference from what you typed) ln both sides ln (e^(3x)) > ln e^(x-1) 3x > x-1 2x > -1 x > -1/2 PROOF: http://www.wolframalpha.com/input/?i=plot+y+%3D+e%5E%283x%29+%2C+y+%3D+e%5E%28x-1%29+from+-1+to+0 -6...

Math (Probability)
to make a sum of 5 , the two dice would be : 1-4 , 2-3, 3-2, or 4-1 so 4 ways prob (sum of 5) = 4/36 = 1/9

Math
If what you want is the effective annual rate, all we need is the 6% per annum compounded monthly let the annual rate be i then 1+i = (1 + .06/12)^12 1+i = 1.005^12 = 1.0616778.. i = .0616778 the effective annual rate correct to 3 decimals is 6.168 % check: amount of 12300 at ...

Algebra
your LCD is 6x , so multiply each term by that 20 + 8x = 3(7+x) 20+8x = 21+3x 5x = 1 x = 1/5

Math
let the tens digit be x, let the unit digit be y the number is 10x+y (10x+y)/(x+y) = 2 + 2/(x+y) times (x+y) 10x+y = 2x+2y + 2 8x - y = 2 ----> y = 8x-2 (10x+y)(x+y) = 112 10x^2 + 11xy + y^2 = 112 sub in y = 8x-2 10x^2 + 11(8x-2) + (8x-2)^2 = 112 10x^2 + 88x - 22 + 64x^2 - ...

Algebra
anticipated cost/doz --- x anticipated number of dozen bought = 210/x actual cost/doz = x+3 number of dozen he bought = 210/(x+3) 210/x - 210/(x+3) = 1/2 multiply each term by 2x(x+3) 420(x+3) - 420x = x^2 + 3x x^2 + 3x - 1260 = 0 x = appr 34.03 or some negative value 210/34 =...

Math
A terminal position of ((-15/13),(12/13)) puts you in quadrant II and using similar triangles we could have the same angle for a terminal position at (-5,4) so r = √(25+16) = √41 x = -5, y = +4 , r = √41 sin è = 4/√41 ----> csc è = W...

math
prob(Ruben winning) = 16/24 = 2/3 prob(Ruben NOT winning) = 1/3 so prob(Manuel winngin) = 1/3 prob(Man not winning) = 2/3 odds in favour of Manuel winning = (1/3) : (2/3) = 1 : 2

math homework
Just add them up.

Algebra
What you meant was ... For what value of b is the expression undefined? when b = -4, the denominator is zero, and you would be dividing by zero. Division by zero is undefined, so b ≠ -4

statistics
what is .8^3 = ?

Algebra
I will assume you meant: 1/(2x) + 1/x = -12 times 2x 1 + 2 = -24x x = 3/-24 = -1/8 if you meant it the way it was typed: 1/2 x + 1/x = -12 times 2x x^2 + 2 = -24x x^2 + 24x + 2 = 0 x = (-24 ± √568)/2 = -12 ± √142

Calculus
let be base be x ft by x ft let the height be y ft (x^2)(y) = 3 y = 3/x^2 Cost = 3(x^2) + 2(4xy) = 3x^2 + 8x(3/x^2) = 3x^2 + 24/x d(cost)/dx = 6x - 24/x^2 = 0 for a min of cost 6x = 24/x^2 x^3 = 4 x = cuberoot(4) = appr 1.6 ft the base should be appr 1.6 ft by 1.6 ft (the heig...

Math
Forgot to mention that we could also have placed out third point on the left side of the y-axis, e.g. (-4,8) would work

Math
let's consider (0,1) and (0,6) to be the base, the the base is 5 units. let the height be h giving us a nice isosceles triangle (1/2)(5)h = 10 5h = 20 h = 4 so a possible third point is (4, 3.5) As a matter of fact, we could now take any point along the vertical line x = 4...

Math emergency I have 10 minutes to submit it.
did you not notice that the derivative of the denominator is sitting in the numerator ? and if y = ln(u) then dy/du = u'/u, exactly our pattern integral of e^x/(7+e^x) from 0 to 2 = [ ln (7 + e^x) ] from 0 to 2 = ln(7 + e^2) - ln(7 + e^0) = ln (7+e^2) - ln(7+1) = ln ( (7+e...

Algebra
3/(4x-36)- 5/(2x-4) - 2x/(x^2-11x+18) = 3/(4(x-9) ) - 5(2(x-2)) - 2x/( (x-9)(x-2)) so the LCD = 4(x-9)(x-2) = ( 3(x-2) - 5(2)(x-9) - 2x(4) )/(4(x-9)(x-2)) = (3x-6 - 10x + 90 - 8x)/(4(x-9)(x-2)) = (84 - 15x)/(4(x-9)(x-2))

Math
The standard 3by3 magic square is 8 1 6 3 5 7 4 9 2 --> notice ever row, column and diagonal adds up to 15 for a total of 45. Any 9 numbers in an arithmetic sequence can be arranged in the above order and you would have a magic square with the properties you want. change al...

Algebra 2
term1= 3(1) - 3 = 0 term2 = 3(2) - 3 = 3 term3( = 3(3) - 3 = 6 .... looks like an arithmetic sequence , with a=0 and d = 3 sum(1) = (10/2)(2(0) + 9(3)) = 5(27) = 135

@ Sandra - Algebra
Looks like Connexus is new to this site, looks like he just added his question to yours. about yours ..... (x^2 – 1) / (x^2 – x – 2) – (x-1) / (x-2) = (x+1)(x-1)/( (x-2)(x+1) - (x-1)/(x-2) = (x-1)/(x-2) - (x-1)/(x-2) = 0 , x ≠ -1

Rectangular coordinates to polar coordinates
remember that while rectangular coordinates define one and only point, the position of a point using polar coordinates is not unique. In general any point (r, Ø) can also be represented by (-r, π+Ø) e.g. (using degrees) look at the point defined by (6, 150&d...

mathematics
Did you notice that 1.4 = 7/5 ? log5 1.4 = log5 (7/5) = log5 7 - log5 5 = 1.209 - 1 = .209 A property of logs that comes in handy here is loga b = 1/logb a b) log7 75 = log7 (3*5^2) =log7 3 + 2log7 5 = (log5 3) / (log5 7) + 2/log5 7) = .683/1.209 + 2/1.209 = 2.683/1.209 = 2683...

math
log4(2x+4) - 3 =log4 3 log4(2x+4) - 3log44 = log4 3 log4(2x+4) - log4 4^3 = log43 log4[(2x+4)/64] = log43 (2x+4)/64 = 3 2x+4 = 192 2x=188 x = 94

calculus help please
let each side of the square be x m let each side of the equilateral triangle be 2x (that way, the height is √3y, from the ratio of the 30-60-90° triangle) a) for a max area, you are right, all should be used for the square b) 4x + 6y = 14 2x + 3y = 7 x = (7-3y)/4 OR ...

Algebra
For what value of b would you be dividing by zero ?

MAth
cos 31° = PQ/20

Math
the way you typed it, the entire bracket is divided by 2. 5(2x - 10)/2 + 14 = 19 5(x - 5) + 14 = 19 5x - 25 = 19-14 5x = 5 + 25 5x = 30 x = 6

Trig
ARggghhhh!!!!

Trig
we need cos 225° and sin225° 225 = 180+45 , it is in quadrant III and has the same numerical trig values as 45°, but in III both the sine and cosine are negative sin 225 = - sin 45° = -1/√2 cos 225 = - cos 45° = -1/√2 so 7(cos255degrees + isin25...

MATH
sin 10.5° = PR/120 PR = 120 sin 10.5° = ....

Math
P(x) = 1.3x-.01x^2-30 = -.01x^2 + 1.3x - 30 in more standard notation you will need the vertex. The x of the vertex is -b/(2a) = -1.3/(-.02) = 65 then P(65) = -.01(65)^2 + 1.3(65) - 30 = 12.25 when x = 65

geometry
surface area of box = 2(2.5)(7) + 2(2.5)(12) + 2(7)(12) = 263 inches^2 surface area of cylinder = 2πr^2 +2πrh = 2π(3^2) + 2π(3)(7.5) = 18π + 45π = 63π or appr 197.9 inches^2 so what do you think?

Math
I recommend getting rid of brackets first to get nice straightforward terms, then simplify, and then "move" terms from side to side. -5 - x = 2x - 4x - 6 -5 - x = -2x - 6 2x - x = -6 + 5 x = -1 (your -x on the right side should have been +x )

mathematics for management
I will assume they are the same x recall that loga b = log b/log a so logxy = logy/logx and logyx = logx/logy so your equation can be written as: logy/logx + logx/logy = 5/2 let logx/logy = a then we have 1/a + a = 5/2 times 2a 2 + 2a^2 = 5a 2a^2 - 5a + 2 = 0 (a - 2)(2a - 1) =...

mathematics for management
I saw this one pass by me before. Are you distinguishing between "x" and "X"? If so, you have 4 variables with only 2 equations.

math
first bounce --- 3 ft 2nd bounce = 2(1/4)(3) = 6(1/4) 3rd bounce = 2(1/4)(3)(1/4) = (6)(1/4)^2 4th bounce = ... = (6)(1/4)^3 .... so we have 3 + 6(1/4) + 6(1/4)^2 + 6(1/4)^3 + ... to infinity = 3 + 6(1/4) (1 + 1/4 + (1/4)^2 + ...) from the 2nd term on, we have a geometric seri...

Math
short leg --- x longer leg --- 2x-1 x^2 + (2x-1)^2 = 17^2 x^2 + 4x^2 - 4x + 1 = 289 5x^2 - 4x - 288 = 0 (x-8)(5x + 36) = 0 x = 8 or x is an inadmissable negative number short leg = 8 ft long leg = 15 ft area = (1/2)(8)(15) = 60 ft^2

Algebra 1 Explanation (Anyone, please!)
If you know very little about the topic, a good way would be to simply make a table of values for x and y pick reasonable small values for x and evaluate to get the y e.g. x y 0 -3 1 -4 2 -3 ------> 2^2 - 2(2) - 3 = 4-4-3 = -3 3 0 4 5 ----> 4^2-2(4)-3 = 16-8-3 = 5 5 12 -...

Algebra
first rate ---- x mph return rate --- x+11 sum of times = 22.5 550/x + 550/(x+11) = 22.5 times x(x+11) 550x + 6050 + 550x = 22.5x(x+11) 1100x + 6050 = 22.5x^2 + 247.5x 22.5x^2 - 852.5x - 6050 = 0 using the formula x = 44 or a negative he went at 44 mph going there, and 55 mph ...

statistics
same webpage ... click on "between" and enter -3 and 3 to get .9973 choose you matching answer.

statistics
Use either your tables available to your or use http://davidmlane.com/hyperstat/z_table.html to get .9772 or .98 from your choices

MATHS - AREA
2L + 2W = perimeter 2(80) + 2w = 410 2W = 410 - 160 2W = 250 W = 125 area = LW = 80(125) = 10,000 m^2

Stats
RANDOM can be arranged in 6! or 720 ways. prob of getting it in that form = 1/720

Math
plug your data into this ... http://davidmlane.com/hyperstat/z_table.html click on "above" and enter 6 to get .3694 (that's very high SD )

mathematics for management
logv[ 2x/(x+2b) [ = 1 2x/(x+2b) = b^1 2x =bx + 2b^2 2x - bx = 2b^2 x(2 - b) = 2b^2 x = 2b^2/(2 - b)

math
3 important rules of logs 1. log (AB) = log A + log B 2. log(A/B) = log A - log B 3. log A^n = nlogA so 2log15 + log(5-x) - log 4x = 2 log 15^2 + log(5-x) - log 4x = 2 log (225(5-x)/(4x) ) = 2 225(5-x)/(4x) = 10^2 = 100 400x = 1125 - 225x 625x = 1125 x = 1125/625 = 9/5 or 1.8

college Algebra
let each of the two end fences be x ft long let the side parallel to the river be y ft long so we have: cost = 12y + 8(2x) = 12y + 16x but 12y + 16x = 3600 3y + 4x = 90 y = (90-4x)/3 area = xy = x(90-4x)/3 = 30x - (4/3)x^2 d(area)/dx = 30 - (8/3)x = 0 for a max of area (8/3)x ...

Precalculus
1. a) and b) are correct c) the normal is perpendicular to the tangent So if the slope of the tangent at (3,9) is 6 then the slope of the normal is -1/6 y = (-1/6)x + b, plug in the point (3,9) 9 = (-1/6)(3) + b b = 19/2 y = (-1/6)x + 19/2 or y = (-1/6)x + 9.5 2. a) good! g) i...

Math
did this yesterday http://www.jiskha.com/display.cgi?id=1397441682

Math
profit = 6n - 2n - 400 - 100 = 4n + 600 , where n is the number of people 4n - 500 = 400 4n = 900 n = 225 need 225 people to make $400

Math
Did this for Lynda back in December http://www.jiskha.com/display.cgi?id=1386034705

Trigonometric Function
6 rotations take 1 minutes 1 rotation takes 1/6 minutes 2π/k = 1/6 k = 12π let's start using only amplitude and frequency to get height = 10 sin ( 12πt) We want to move the curve up 12 units height = 10 sin (12πt) + 12 so now we have to have a horizonta...

Math
This little YouTube fits your problem quite nicely http://www.youtube.com/watch?v=62Lj-g5owgo

statistics
z-score for chemistry = (82-75)/6.25 = 1.12 z-score for physics = (63-59)/3.57 = 1.12044 I would consider the difference insignificant, so the two scores would be equivalent.

math
Jerry-height = 50 + (1/24)m Adam-height = 47 + (1/8)m they have the same height when ... 50 + m/24 = 47 + m/8 3 = m/8 - m/24 m/12 = 3 m = 36 or, from 50 + m/24 = 47 + m/8 multiply each term by 24 to get rid of fractions 1200 + m = 1128 = 3m 72 = 2m m = 36

Math
let the speed of the river current be x mph speed going upstream = 9 -x mph speed going downstream = 9 + x mph 10/(9-x) = 20/(9+x) 90 + 10x = 180 - 20x 30x = 90 x = 3 the speed of the river is 3 mph

math
The side parallel to the highway be x ft let each of the other two sides by y 2x + y = 640 y = 640 - 2x area = xy = x(640-2x) = -2x^2 + 640x I assume you know how to find the vertex of this downwards parabola, and that vertex is (160 , 51200) if x = 160 y = 640 - 2(160) = 320 ...

math
z is defined in two ways ? what's with the 1 2 ?

Math help asap
I interpreted your question this way: e^(x/2.9099) =ln (7.8x10^10) take ln of both sides , so we taking ln (ln(...)) on the right side x/2.9099 = ln (ln (7.8 x 10^10) ) x/2.9099 = 3.22207 x = 9.3759...

HELP! 5th grade math
There is more than one way to do this What Alison gave you is one of those. I would use the two containers measuring only Litres to hold the whole numbers e.g. 4 L + 4 L that leaves .53 L or 530 ml now you can split the 530 into any two parts using the two containers that meas...

Calculus Help Please Urgent!!!
lim -> 0 (cot(x)-(1/x)) , x---> 0 = sec^2 x + 1/x^2 by L'Hospital's Rule but that is just as bad try experimentally ... using a Calculator let x = .0001 I get -.0000333 let x = .000001 my calculator says 0 http://www.wolframalpha.com/input/?i=limit+cot%28x%29+-+1...

Math
did you notice that the derivative of the denominator is 9 e^(9x) which just happens to be sitting in the numerator as a multiple thereof. Which is the ln derivative pattern. So without any great fanfare..... ∫(e^(9x))/(2 + e^(9x)) dx = (1/9) ln (2 + e^(9x) + c

Math
How about giving this one a try ?

math
Are you saying f(x) = 17/(x^2 + 4x - 12) ? (I will assume that) = 17/((x+6)(x-2) ) remember we can't divide by zero, which happens if x = 2 or x = -6 We can use any other value of x so domain: = { x ∈ R | x ≠ -6,2 }

oops - Math
didn't see the "monthly" part rate = .05/12 = .0041666... amount = 125000(1.00416666...)^6 = $128,157.73

Math
125,000 invested for 6 months = 125000(1.025 = $128,125 So what do you think?

Math
Wilder: amount = 85000(1.05)^2 = $93,712.50 after 1st year Cheapskate: amount = 85000(1.0081666..)^12 = $93,714.53 after 1st year b) you try it, (you only have to change the exponents)

Math
Tom: Paym(1.08)^3 = 15000 Paym = 15000/1.08^3 = $11,907.48 Lana: monthly rate = .07875/12 = .0065625 Paym(1.0065625)^36 = 15000 Paym = 15000/1.0065625^36 = $11,852.89 etc

Math
a) ridiculous question ! , makes no sense the "arithmetic" would be 8200(1.0988) = .... b) weekly rate = .0988/52 = .0019 number of weeks in 18 years = 936 amount = 8200(1.0019)^936 = $48,465.24

Calculus
let the length of the side using bricks be x ft let the other two sides each be y ft given: xy = 900 --> y = 900/x cost = 5(x + 2y) + 10x = 15x + 10y = 15x + 10(900/x) d(cost)/dx = 15 - 9000/x^2 = 0 for min of cost 15 = 9000/x^2 15x^2 = 9000 x^2 = 600 x = √600 = 10...

Algebra
amount invested at 11% --- x amount invested at 8% ---- 6300-x solve for x ..... .11x + .08(6300-x) = 597

Math
∫5(1+1/u + 1/u^2) du from 5 to 7 = 5[u + ln u -1/u] from 5 yo 7 = 5( 7 + ln7 - 1/7 - (5 + ln5 - 1/5) = 5(2 + ln7 - ln5 -1/7 + 1/5) = 10 +2/7 + 5ln 7 - 5ln5 = appr 11.97

Math 10
sure, all you have to do is to find the vertex of this "downwards" parabola. I will assume that you do not know Calculus , so (easiest way): the x of the vertex for y = ax^2 + bx + c is -b/(2a) so for your equation, the t of the vertex is -10/-10 = 1 sub into the equ...

Algebra
amount of 20% juice used ...... x L amount of 5% juice used ....... 15 - x L .20x + .05(15-x) = .16(15) times 100 to get rid of those decimals 20x + 5(15-x) = 16(15) 20x + 75 - 5x = 240 15x = 165 x = 11 Answer as needed.

Math
All four choices fit the description. As to your "most specific term", it probably refers to its main property. Since a parallelogram is most often defined in terms of its parallel sides, that would be choice.

math
I am used to expressing complex numbers in the form a + bi, instead of your a + bj if z = 1 + 2i r = √(1^2+2^2) = √5 and if Ø is our angle, tan Ø = 2/1 , Ø is in I of your complex plane Ø = appr 1.107 radians then z = √5(cos 1.107 ...

maths
let the tens digit be x let the unit digit be y x+y = 12 x-y = 4 add them 2x = 16 x = 8 y = 4 the number is 84 Since the choices were quite limited, (x = 5,6,7,8,or9 ) it would have been just as fast to "guess" at the solution

math
Kelly's original number of bonus point --- x Julia's original number of bonus points -- x-150 let the number used by both be y each. now Kelly has x - y Julia has x-150 - y for Kelly: (x-y)/x = 3/4 4x - 4y = 3x x - 4y = 0 or x = 4y for Julia: (x-150-y)/(x-150) = 1/2 2x...

math
the surface area of similar solids is proportional to the square of their corresponding sides Area / 90 = 10^2/5^2 = 100/25 = 4 Area = 90(4) = 360 inches^2

math
downpayment = 629.95(.25) = $157.49 amount to be financed = 472.46 The rest of the question sounds like something from the last century. A very silly way of doing the financing and it misleads the uninformed. I will assume they will now take 472.46 , add on $60 to get $532.46 ...

maths
Kg is used to measure mass, not volume Please fix your question, since a suitable unit for the circumference would be cm (centimetre)

Pre-Calculus
10000(1.03)^n = 11000 , where n is half=years 1.03^n = 1.1 n log 1.03 = log 1.1 n = log 1.1/log 1.03 = 3.224 half years it will take 1.612 years or about 1 1/2 years

Algebra
Surely you meant: F(t)= 30000/(1+20e^-1.5t ) a) let t = - F(0) = 30000/(1+20) = appr 1429 b) when t = 4 F(4) = 30000/(1 + 20e^-6) = 28,583 check my "button-pushing" on the calculator

Algebra
done, see below, please don't switch names

algebra
you are solving 6 e^12.77x = 20 e^12.77x = 10/3 ln both sides and use rules of logs 12.77x lne = ln(10/3) , recall that ln e = 1 x = ln(10/3) /12.77 = appr .094

Algebra
log2 x + log2 (x-7) = 3 log2( x/(x-7) ) = 3 x/(x-7) = 2^3 = 8 8x - 56 = x 7x = 56 x = 8

Algebra
ln( x+2)/(4x+3) ) = ln (/x) (x+2)/(4x+3) = 1/x x^2 + 2x = 4x+3 x^2 - 2x - 3 = 0 (x-3)(x+1) = 0 x = 3 or x = -1 but if x = -1 , ln(4x+3) is undefined, so x = 3

algebra
ln ( (x+3)/(x-5) ) = ln 7 (x+3)/(x-5) = 7 7x - 35 = x+3 6x = 38 x = 38/6 = 19/3

Algebra Word Problem
let the number of men be x original share of debt = 100/x men actually paying back = x-5 new share = 100/(x-5) 100/(x-5) - 100/x = 1 100x - 100x + 500 = x(x-5) x^2 - 5x - 500 = 0 (x - 25)(x+20) = 0 x = 25 or x = a negative, which is not admissible So there were 25 men, of whic...

Algebra
let speed of steamer in still water be x mph let the speed of the current be y mph 108/(x-y) - 108/(x+y) = 3 108x + 108y - 108x + 108y = 3(x^2 - y^2) 216y = 3(x^2 - y^2) 72y = x^2 - y^2 ---- #1 let speed of "boat" be x-6 108/(x-6 - y) - 108/(x-6 + y) = 9 108x - 648 +...

Algebra - functions
Here is a "picture" of your graph It should help you to answer your questions. http://www.wolframalpha.com/input/?i=plot+y%3D+5%2F%28x-1%29%5E2+

Algebra
Your first version is correct, the "others" are wrong To interpret along the second version it would have been (-16)^(1/4) , but there were no brackets just like in -2x^2 , it is only the x that is squared, not the -2 There is a major difference between -2x^2 and (-2...

Statistics
Using this webpage you don't even have to find the z-scores (you may if you wish) just enter the mean, the SD, click on "below" and enter 2 in that field and "recalculate" to get .2743 http://davidmlane.com/hyperstat/z_table.html perfect substitute for ...

math
|2n^2 - 7| < 1 We could go into a formal solution with all the AND and OR operators, but clearly n must be a small integer, so lets just try some values of n n = 0 ---> |-7| < 1 , no n = ± 1 --> |2-7| < 1 , no n = ± 2 ---> |8-7| < 1 , no n = ...

finance
PV = 163291.18 (1 - 1.075)^-20)/.075 = $ 1,664,670.52

algebra
follow this method, yours is even easier than the one in the link http://www.jiskha.com/display.cgi?id=1397241650

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