Wednesday

November 25, 2015
Total # Posts: 31,838

**math**

they will form a straight line, passing through the origin. let the radius of the first one be r then the first point is (2r, 2πr) slope of line passing through (0,0) and (2r, 2πr) = (2πr)/(2r) = π
*November 12, 2015*

**Algebra 2**

(243 m^10 n^35) / m^5
*November 12, 2015*

**Algebra**

easy way to graph a straight line is to use the intercepts for the first one: let x=0, y = 3, (should be able to do this in your head) let y = 0, x = 6 so you have two points, (0,3) and (6,0) plot the points and join with a straight line Do the same with the 2nd equation it ...
*November 12, 2015*

**Precalculus**

1. it becomes an arithmetic series so you want: 5 + 10 + 15 + ... = 680 , a = 5 , d = 5 , n = ? we dont know how many terms, let n be the number of terms (n/2)(2a + (n-1)d ) ≥ 680 (n/2)(10 + 5(n-1) ≥ 680 n(5n + 5) ≥ 1360 5n^2 + 5n - 1360 ≥ 0 n^2 + n - ...
*November 12, 2015*

**algebra pls help**

−ax + 3b > 5 -ax > 5 - 3b ax < 3b - 5 x < (3b-5)/a or x < (5-3b)/-a to fit the last choice
*November 12, 2015*

**Math**

correct
*November 12, 2015*

**Math**

(85+84+90+95+88 + x)/6 > 88 I will let you solve it
*November 12, 2015*

**Maths**

We don't "complete the square" for a cubic let's look at the graph of y = x^3 - 2x^2 - 16 to see if it worth doing http://www.wolframalpha.com/input/?i=plot+y+%3D+x%5E3-2x%5E2-16 looks like there is only one real root. Have you learned a method to solve a ...
*November 12, 2015*

**Maths**

Rephrasing the question: Find the intersection points of the line y = 2x-3 with the curve y = (x+2)(x-4) , a parabola (x+2)(x-4) = 2x- 3 x^2 - 2x - 8 = 2x - 3 x^2-4x-5 = 0 (x-5)(x+1) = 0 x = 5 or x = -1 if x=5 , y = 2(5)-3 = 7 if x=-1, y = 2(-1)-3 = -6 the line crosses the ...
*November 12, 2015*

**Maths**

let's do it by completing the square 10x-x^2-27 = -x^2 + 10x - 27 = -(x^2 - 10x ..... ) - 27 = -(x^2 - 10x + 25 - 25) - 27 = -( (x-5)^2 - 25) - 27 = -(x-5)^2 + 25 - 27 = -(x-5)^2 - 2 -----> the form you wanted argument: (x-5)^2 is always positive so -(x-5)^2 is always ...
*November 12, 2015*

**Maths**

(x-1)(x^2+x+1) = x^3 + x^2 + x - x^2 - x - 1 = x^3 - 1 so (x-1)(x^2+x+1)=2x^2-17 x^3 - 1 = 2x^2 - 17 x^3 - 2x^2 + 16 = 0 error in the constant you also lost the fact that it was an equation your instructions should have been: "Rewrite in form of ax^3+bx^2+cx+d = 0 " ...
*November 12, 2015*

**Math**

agree, but why did you pick that?
*November 12, 2015*

**algebra**

amount used from the Rs 40 --- x amount used from the Rs 90 --- 630-x 40x + 90(630-x) = 70(630) 40x + 56700 - 90x = 44100 -50x= -12600 x = 252 state conclusions.
*November 12, 2015*

**Math**

since the length of the strip you want matches the length of the available cloth, 45 inches, all we care about is the width. What is 36 ÷ 3 3/8 ?
*November 12, 2015*

**Math**

Your running distances are in an arithmetic sequence with a = 12 , d = 7/10 or .7 you want a + (n-1)d = 26 12 + .7(n-1) = 26 .7n - .7 = 14 .7n = 14.7 n = 21 So it will take 20 MORE weeks to reach 26 miles
*November 12, 2015*

**precalc**

you must memorize the 3 main rules of logs 1. log (AB) = log A + log B 2. log (A/B) = logA - logB 3 log (A^n) = nlogA for any base of the log as long as the base is the same throughout the equation e.g. #22 7log 2^16 + log (2^(1/16)) , I assumed a typo here = 7(16)log 2 + (1/...
*November 12, 2015*

**Math 141**

prob(W from boxA) = 3/7 now we transfer a ball case1, ball transferred is W now we have 7white in B prob(W from boxB) = 7/12 prob as stated = (3/7)(7/12) = 1/4 case 2, ball transferred is B now we still have 6 W in B prob(W from B) = 3/7 x 6/12 = 3/14 prob(of our event) = 1/4...
*November 12, 2015*

**math**

y = 2x^2 - 3 inverse: x = 2y^2 - 3 2y^2 = x+3 y^2 = (x+3)/2 y = ± √( (x+3)/2 ) btw, the inverse is not a function
*November 11, 2015*

**math**

no, 0 is not considered an odd number 20 = 2*2*5 5 is the odd factor, 2 is the even factor
*November 11, 2015*

**math**

the only multiple of 10 between 15 and 28 is 20.
*November 11, 2015*

**Math 141**

prob(non-defective, second machine) = (.92)(.15) = .138
*November 11, 2015*

**precalc(LOGS) CONFUSED!**

2 logx = loga - 4logb logx= loga - log b^4 logx = log (a/b^4) x = 1/b^4 3. lnt = (3/2)ln a - ln p ln t = ln ((√a)^3) - ln p ln t = ln( (√a)^3 /p) t = √a)^3 /p 4. you do this one the same way of course you will have to know the rules of logs
*November 11, 2015*

**Math**

How many times has this same set of questions been posted now, I keep seeing it btw, all answers are finally correct
*November 11, 2015*

**Precalc**

a) correct b) log(5/7) = log 5 - log 7 you have both of these, just do the subtraction c) log 1.5 = log (3/2) = log3 - log 2 you have both of these d) log (3/14) = log(3/( (2)(7) ) = log 3 - log2 - log 7 again, you have those 3 values log 12 = log(4 x 3) = log 4 + log3 = log 2...
*November 11, 2015*

**Geometry**

Why did you not look at my solution ? http://www.jiskha.com/display.cgi?id=1447283907
*November 11, 2015*

**mATH**

Heather, your answer does not work 10 more than 7 times 59 = 423 9 fewer than 5 times his age reversed = 5(95) - 9 = 466 let the tens digit of his age be x let the units digit of his age be y his age is 10x+y 10 more than 7 times his age = 7(10x+y) + 10 9 fewer than 5 times ...
*November 11, 2015*

**Math**

I constructed the triangle so that DE || BC AB = 5+3.5 = 8.5 DE: DE/5 = 5.1/8.5 DE = 25.5/8.5 = ... AC: x/6 = 3.5/5 x = 6(3.5)/5 = ... AC = 6 + x EC: just found that AC: also done
*November 11, 2015*

**Algebra**

just solve the two equations... p^2 + 16q = 1200 ---> p^2 = 1200 - 16q 300 - p^2 + 6q = 0 ---> p^2 = 300 + 6q 300 + 6q = 1200-16q 22q = 900 q = 900/22 = 450/11 = appr 40.9 then p^2 = 300 + 6(450/11) = 4650/11 = appr 422.7
*November 11, 2015*

**Geometry**

Method 1: use the slope of the 3 lines to find the angles the lines make with the x-axis. Then subtract the angles to determine the angle between the lines method 2: use the formula tanØ = |(m1-m2)/(1+m1m2)| where Ø is the angle between lines with slope m1 and m2...
*November 11, 2015*

**ALGEBRA**

function1 is a parabola with a vertex of (-1,-3) so its minimum is -3 since function2 shows a minimum value of 0 the first statement is true min value of -3 at the point (-1,-3).
*November 11, 2015*

**Algebra**

after cutting out squares with sides n by n we would have the following: n=1 , dimensions: 18 by 26 by 1 , not given n=2, dimensions: 16 by 26 by 2 , given incorrectly n=3, dimensions: 14 by 24 by 3 , not given , but V = n=4, dimensions: 12 by 22 by 4 , V = 1056 n=5, ...
*November 11, 2015*

**Math**

#2, h^2 = 12^2 + 9^2 = 225 h = √225 = 15 , so B #3 C, 3^3 = 27 , none of the others are cubes #4 √9 - 7 = 3-7 = -4 , which is an integer, so D #5 C , √(36/49) = 6/7 #6 He needs √11 which is appr 3.3 , so your choice of a piece of 3 feet would not even ...
*November 11, 2015*

**Math**

1. irrational means not rational So if a number is not rational, then it is irrational B
*November 11, 2015*

**Math**

number of adult tickets --- x number of children tickets -- 99-x 4x + 2.5(99-x) = 300 solve for x
*November 11, 2015*

**math**

F = 1.8°C + 32 F - 32 = 1.8C C = (F-32)/1.8 or C = (5/9)(F - 32)
*November 11, 2015*

**math**

temp six hours ago ---- x 2x - 6 = 20 go for it
*November 11, 2015*

**math**

practise to translate from English to Math let her original amount be x "she added $26 to the amount originally in the account " ---> 26+x "and doubled the sum" ----> 2(26+x) "she would get the new amount" ---> 2(x+26) = 264 your turn
*November 11, 2015*

**math**

The number is not 36, it is 63 "my tens digit is twice my ones digit" : so, if the ones digit is x then the tens digit is 2x x+2x=9 3x=9 x=3 so the number is 63
*November 11, 2015*

**correction - Math**

prob(4reds) = (9/23)(8/22)(7/21)(6/20) = 18/1265 or prob(4reds) = C(9,4) / C(23,4) = 126/8855 = 18/1265 = appr .014 prob(2 out of 4 are red) = C(9,2) * C(14,2)/C(23,4) = 36*91/8855 = 468/1265 = appr .37
*November 11, 2015*

**Calculus 1**

Well, I simply offered another approach. I would have expected you to change the 40 to 23.
*November 11, 2015*

**Calculus 1**

Steve, I had my definitions reversed, but http://www.jiskha.com/display.cgi?id=1384823309 Only superficially checked the arithmetic on both
*November 11, 2015*

**correction - math**

so you would have 3/7 of your money left (3/7)x = 15 3x= 105 x = 35 so you spent 4/7 of that which $20 check: you started with $35 spent 4/7 of that which is $20, leaving you with $15, as stated
*November 10, 2015*

**correction - Math**

I did the first 2 parts here: http://www.jiskha.com/display.cgi?id=1447035932 #3. prob(none of the 4 are red) = C(14,4)/C(23,4) = 1001/8855 = 13/115
*November 10, 2015*

**Compound interest**

The title of your post says "compound interest" but then you use "simple interest". i = .0525/12 = .004375 n = 36 cost of stereo = 200 + 70(1 - 1.004375^-36)/.004375 = 200 + 2326.87 = 2526.87 you had that, ok, good b) paid: = 36*70+200 = 2720 Do they accept...
*November 10, 2015*

**Math**

how did you possible get 60? from above: 2(3x) + 3x = 144 9x = 144 x = 16 as defined each boy gets 3x = 3(16) = 48 (each girl gets 18) check: 2boys + 3 girls = 2(48) + 3(16) = 144 , as needed
*November 10, 2015*

**Math**

amount for girl -- x amount for boy -- 3x 2(3x) + 2x = 144 8x = 144 take over
*November 10, 2015*

**Math**

translation into math: (3/4)x - (3/5)x = 9 the LCD is 20, so multiply each term by 20 20(3/4)x - 20(3/5)x = 20(9) 15x - 12x = 180 3x = 180 x = 60 , after dividing both sides by 3 so the number is 60 check: (3/4) of 60 = 45 (3/5) of 60 = 36 their difference is 9 My answer is ...
*November 10, 2015*

**Algebra**

clock question: yes
*November 10, 2015*

**maths**

i = .08/12 = .006666... n = 3(12) = 36 let the monthly payment be p p(1 - 1.00666...^-36)/.006666.. = 5000 p = 156.68 Is the second part a new question? Not sure how this "arrangement" fee works in. Do the payments change? Clearly the interest rate is not 8%, or else...
*November 10, 2015*

**Algebra 2**

#2 g(x-1) = 2(x-1)^2 - 2(x-1) - 5 = 2x^2 - 4x + 2 - 2x + 2 - 5 = 2x^2 - 6x - 3 #3 g(3x+2) = -2(3x+2)^2 - 3(3x+2) + 5 = -18x^2 -24x -8 - 9x - 6 + 5 = -18x^2 - 33x - 1
*November 10, 2015*

**Math (algebra)**

looks like a simple typo to me +15 should be +35 surely you could have figured this out yourself
*November 10, 2015*

**math**

your rate contains a typo in the acceleration rate if you have 30 m/s^2 you got yourself some nasty superturbo-charged bus If you have 30 m/min^2, you have yourself a slow chicken bus anyway.... a = 30 v = 30t + c assume it starts from zero, 0 = 30(0) + c , ----> c = 0 v = ...
*November 10, 2015*

**Area and Perimeter Shepes**

2l + 2w = 32 l + w = 16 , but w = 5 (or l=5, if you prefer) l+5 = 16 l = 11 area = lw = 11(5) = 55 cm^2
*November 10, 2015*

**pioneer math**

Is there a question somewhere ?
*November 10, 2015*

**Somanay high school**

Make a rough sketch of the two vectors of 6N and 10N, completing a parallelogram so that the major diagonal is 12N So looking at the triangle with sides 10,6, and 12 we can find the obtuse angle Ø by 12^2 = 6^2 + 10^2 - 2(6)(12)cosØ 144 cosØ = -8 cos&...
*November 10, 2015*

**Mathematics**

let's work backwards, by looking at the number after it was reversed. Since the sum of the digits is 5 it could only be 14, 41, 23, or 32 but that result is caused by having added a 9 so the original number could only be: 9 , not a two digit number, so NO 32 14 23 So the ...
*November 10, 2015*

**math**

x+y = 3.8 ---> y = 3.8-x xy=3.6 plug first into 2nd x(3.8-x) = 3.6 3.8x - x^2 - 3.6 = 0 times -10 10x^2 - 38x + 36 = 0 5x^2 - 19x + 18 = 0 (x-2)(5x - 9) = 0 x = 2 or x = 9/5 or 1.8 if x=2 , y = 3.8-2 = 1.8 if x = 1.8, y = 3.8-1.8 = 2 (symmetric answers) the two numbers are ...
*November 9, 2015*

**maths**

more info needed
*November 9, 2015*

**Calculus**

btw, I also did your other very long question. Did you look at it ?
*November 9, 2015*

**Calculus**

exactly. I left it up to you to finish the problem. Oh well .... f(9) = 9^3 - 12(9)^2 - 27(9) + 7 = -479 etc for f(-1) = 21
*November 9, 2015*

**Calculus**

dy/dx = 3x^2 - 24x - 27 = 0 for a max/min divide by 3 x^2 - 8x - 9 = 0 it factors nicely ... (x-9)(x+1) = 0 x = 9 or x = -1 f(9) = ..... f(-1) = .... take over. this confirms our work http://www.wolframalpha.com/input/?i=plot+f%28x%29+%3D+x%5E3+%E2%88%92+12x%5E2+%E2%88%92+27x...
*November 9, 2015*

**Calculus-antiderivative**

f'Ø) = -cosx + sinx + C you differentiated instead of integrated. Had you checked your answer by taking the derivative you would have seen your error since f'(0) = 3 3 = -cos0 + sin0 + c 3 = -1 + 0 + c ----> c = 4 so f'(x) = -cosx + sinx + 4 f(x) = -sinx...
*November 9, 2015*

**Precalculus**

if tanx = √15 or √15/1 , and x is in quad I make a sketch of a right-angled triangle with opposite = √15 adjacent = 1 r^2 = (√15)^2 + 1^2 = 16 r = 4 then sinx = √15/4 and cosx = 1/4 if x is in quad I, then certainly x/2 is in quad I and everybody ...
*November 9, 2015*

**Calculus**

f'(Ø) = -12sinØ + 6cos2Ø = 0 for max/min I will use x instead of Ø , easier to type 12sinx = 6cos 2x 2sinx = cos 2x but cos 2x = 1 - 2sin^2 x 2sinx = 1 - 2sin^2 x 2sin^2 x + 2sinx - 1 = 0 sinx = (-2 ± √12)/4 = (-1 ± √3...
*November 9, 2015*

**math**

Ok, 18 consecutive posts without any work shown or any indication where your difficulties lie. A classical case of "homework dumping" Have you not noticed that nobody is replying to your posts ?
*November 9, 2015*

**math**

Ok, four consecutive posts without any work shown or any indication where your difficulties lie. A classical case of "homework dumping"
*November 9, 2015*

**math**

(x/100)P = Y xP = 100Y P = 100Y/x
*November 9, 2015*

**math**

Volume at r = 4 = (4/3)π 4^3 = 256π/3 = appr 268.08... that increased by 40% ----> 256π/3 * 1.4 = 256π/3(14/10) = 3584π/30 = appr 375.32 then 3584π/30 = (4/3)π r^3 (3584/30)(3/4) = r^3 r^3 = 89.6 r = appr 4.47 ft
*November 9, 2015*

**Trig**

You know that the sine is positive in quads I and II, which is your given domain if sinØ = 1/4 Ø = 14.5° or Ø = 180 - 14.5 = 165.5°
*November 9, 2015*

**pythagorean triple**

test each one: I will do the 3rd, is 10^2 + 14^2 = 17^2 ? 100 + 196 = 289 296 = 289, obviously not, so it is NOT a Pythagorean triple repeat for the others psst, there is only one
*November 9, 2015*

**algebra**

now --- 32000 at end of year 1 = 32000(1.05) = .... at end of year 2 = 32000(1.05)^2 = 35280 .... at end of year 5 = 32000(1.05)^5 = ... I will let you do the button pushing, I did one of them so you know your answers are correct
*November 9, 2015*

**ALGEBRA**

day1 = term1 = 16 day2 = term2 = 24 , an increase of 8 day3 = term3 = 32 , an increase of 8 looks like an arithmetic sequence where a = 16, d = 8 so on day 12 we have term12 = a + 11d = 16+11(8) = 104 somebody better call Jack
*November 9, 2015*

**Geometry**

clearly the angles are equal and immediately we can say that they are similar. I used to insist that my students write the triangles in such a way that the vertices correspond in order. so triangle RST is similar to triangle FED notice that way angle S = angle E , etc since RS...
*November 9, 2015*

**math, a.p. calc**

I will assume you meant if g ' (x) = x^2 - 16/(x - 2) or else why would you have x ≠ 2 g(x) = (1/3)x^3 - 16ln(x-2) + c but (3,4) lies on it, so 4 = (1/3)(27) - 16ln1 + c 4 = 9 - 0 + c c = -5 so g(x) = (1/3)x^3 - 16ln(x-2) - 5 when x = 3 g ' (x) = 9 - 16/1 = -7 ...
*November 9, 2015*

**Math**

#1 If you make a sketch and assume the two points form the hypotenuse, then it should be easy to see the third point could be (3,-5) or (-4,2) #2 give yourself an actual circle with a radius e.g. r = 10 Draw in different lines and test each case Make sure your consider the ...
*November 9, 2015*

**Mathematics of INVESTMENT**

rate of first account --- r , the rate in decimals rate on 2nd account --- r+.02 interest on 1st account = 2000r interest on 2nd account = 8000(r + .02) 8000(r + .02) - 2000r = 459 8000r + 160 - 2000r = 459 6000r = 299 r = 299/6000 = .0498333 = appr 4.98% the lower rate is 4....
*November 9, 2015*

**math**

adult tickets --- a children tickets --- 404-a 5.5a + 3.5(404-a) = 1708 solve for a
*November 9, 2015*

**@ Jake - math**

Jake, don't just state an answer, which is wrong anyway amount of the 20% stuff --- x amount of the 50% stuff --- 9-x .2x + .5(9-x) = .3(9) times 10 2x + 5(9-x) = 27 2x + 45 - 5x = 27 -3x = -18 x = 6 So he needs 6 L of the 20% solution, and 3 L of the 50% solution
*November 9, 2015*

**prealgebra**

one roll = .9π 37 rolls = 37(.9)π = 104.6 m
*November 8, 2015*

**math**

#1 , you found the cost of a program each concert ticket costs $14, program costs $4 #2, ?? can't see any diagram #3 is correct #4, can't see a diagram #5. .09x - .06x = 36 .03x = 36 x = 36/.03 = 1200
*November 8, 2015*

**Math**

f(x+h) = 2(x+h)^2 + 4(x+h) = 2x^2 + 4xh + 2h^2 + 4x + 4h f ' (x) = lim (2x^2 + 4xh + 2h^2 + 4x + 4h - 2x^2 - 4x)/h , as h ---> 0 = lim (4xh + 2h^2 + 4h)/h = lim h(4x + 2h + 4)/h = lim 4x + 2h + 4 , as h --> 0 = 4x + 4
*November 8, 2015*

**math**

mark both on a number line to see that n > 2
*November 8, 2015*

**Math**

slope of first = 4/3 slope of 2nd = 8/6 = 4/3 notice that x1/x2 = y1/y2 ≠ c1/c2 so they are two parallel lines
*November 8, 2015*

**math**

prob(all 5 are red) = (5/19)(4/18)(3/17)(2/16)(1/15) = 1/11628 or , if you know how to calculate combinations = C(5,5)/C(19,5) = 1/11628 from here we can do prob(no red) = 1 - 1/11628 = 11627/11628 prob(exactly 2 are red) = C(5,2)xC(14,3)/C(19,5) = 10(364)/11628 = 91/2907
*November 8, 2015*

**math**

done, look back
*November 8, 2015*

**Math**

notice you have 2 groupings of 'difference of squares', I would do those first 10(x-2)(x+2)(x-3i)(x+3i) = 10(x^2 - 4)(x^2 + 9) now just slug it out ... = 10(x^4 + 9x^2 - 4x^2 - 36) = 10x^4 + 50x^2 - 360 let's use Wolfram to check: http://www.wolframalpha.com/input...
*November 8, 2015*

**math**

we must assume that each CD's name begins with a different letter number of ways to arrange 9 of 19 items = P(19,9) = 19x18x17x16x15x14x13x12x11 = 3.3522... x 10^10 so only one of these is in the correct order prob(correct order) = 1/3.3522 x 10^10 = appr 2.98 x 10^-11
*November 8, 2015*

**math**

number of possible arrangements = 11!/(2!2!2!) , 2 A's, 2 T's, 2 M's = 4989600 number with E first = 1x10!/(2!2!2!) = 453600 prob E first = 453600/4989600 = 4536/49896 = 1/11 with M first number of arrangements = 2x10!/(2!2!2!) = 907200 prob with M first = 907200/...
*November 8, 2015*

**math**

prob of ring = 16/58 prob(2 rings in 2 draws) = (16/58)(15/57) = 40/551 or C(16,2)/(C(58,2)) = 120/1653 = 40/551
*November 8, 2015*

**math**

your first part is (1/2)(1/2)(1/2)(1/2) = (1/2)^4 = 1/16 2nd part: possible outcomes: BGGG GBGG GGBG GGGB , so 4 in all each one has a prob of 1/16 so 4/16 or 1/4
*November 8, 2015*

**math**

What part of my earlier solution did you not like ? http://www.jiskha.com/display.cgi?id=1447016603
*November 8, 2015*

**math**

wouldn't the two hemispheres make up a whole sphere? I I would get V = (4/3)π x^3 + 140π x^2 , where x is the radius
*November 8, 2015*

**math**

easy to do in metric 450 km/h = 450000 m/3600 seconds = 450000/3600 m/s = 125 m/s Now if we could only agree to make time measurement metric ....
*November 8, 2015*

**Pre-Calculus**

Just noticed that this problem has been posted several times before. Here is the same problem with just a variation in the angles, done by Steve about a year ago http://www.jiskha.com/display.cgi?id=1416619227 I am sure you can make the necessary changes.
*November 8, 2015*

**Pre-Calculus**

Since of course you can't post the picture, this is too messy to figure out without a diagram. e.g. are A and B at the same elevation? That would be critical. I also don't know where to place your 42° and 81° angles
*November 8, 2015*

**math**

amount = 250 (1/2)^(t/3) , where t is hours b) pop = 34560(1.03)^n , where n is in years you try the third one
*November 8, 2015*

**math**

You stated the domain, it asked for the range range: y < 3 OR y > 3 , y ∈ R or range is {y| y ∈ R, y ≠3 } I will let you change that to interval notation, not really familiar with that notation. We did not have that in the "olden days" when I ...
*November 8, 2015*

**Math**

I don't like your notation. how about this ? (x,y) ----> (x+1 , y+3) then ((-2,-5) ---> (-2+1 , -5+3) = (-1, -2) your answer is correct, just clean up that notation a bit. Is that how you were taught to write it ?
*November 8, 2015*

**math**

so each of the 14 places can be filled in 26+26+10 or 62 ways so number of possible passwords of 14 characters = 62^14 , assuming that the same character can be repeated. so prob of guessing correctly = 1/62^14 = 8.063 x 10^-26 in scientific notation
*November 8, 2015*

**Math**

rate of cold tap = 1/x , where x is in seconds rate of hot tap = 1/(x+100) combined rate = 1/x + 1/(x+100) = (x+100 + x)/(x(x+100)) = (2x+100)/(x(x+100)) time at combined rate = 1/(2x+100)/(x(x+100)) = x(x+100)/(2x+100) but we know this is 360 seconds x(x+100)/(2x+100) = 360 ...
*November 8, 2015*