Friday

April 18, 2014

April 18, 2014

Total # Posts: 26,007

**Math**

from the 2nd: x = 5y+7 plut into the first: x + 2y = -7 5y+7 + 2y = -7 7y = -14 y = -2 back in x = 5y+7 = 5(-2)+7 = -3 x = -3 , y = -2

**Math**

I understand bi-monthly to mean every other month, or 6 times a year. The main problem here is that the payment period does not coincide with the interest period, so my normal formula does not work so we will convert the 6% compounded bi-monthly to one of i compounded semi-mon...

**precal**

|y-8.0|<=1.5 y-8 ≤ 1.5 and -y+8 ≤ 1.5 y ≤ 9.5 and -y ≤ -6.5 y ≤ 9.5 and y ≥ 6.5 which can be written as 6.5 ≤ y ≤ 9.5 (or in words, y is between 6.5 and 9.5 inclusive

**Math**

each individual question has a prob of 1/2 of being correct so you want (1/2)(1/2) .... (1/2) --- (8 times) = (1/2)^8 = 1/256

**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...

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