Saturday
December 3, 2016

Posts by Reiny

Total # Posts: 36,897

maths
OK, even though have always been told that we can't add apples and oranges, ..... let the amount of apples be x lbs amount of oranges ----- (52 - x) lbs 5.25x + 3.8(52-x) = 4.25(52) 5.25x + 197.6 - 3.8x = 221 1.45x = 23.4 x = 16.1 lbs of apples and 35.9 lbs of oranges appr...
November 22, 2016

math
cost = 7.2(12) = 86.4 18 eggs = 1.5 dozen so you sold 10.5 dozen at 7.5 return = 10.5(7.5) = 78.75 loss = 86.4 - 78.75 = 7.65
November 22, 2016

Maths
Four times as much, or 32 kg Can you show me why that is so?
November 22, 2016

maths
volume of ball = (4/3)?(4.5)^3 So that is the change in volume in the cylinder once removed ?(6^2) h = (4/3)?(9/2)^3 36h = (4/3)(729/8) = 243/2 h = 243/72 = 27/8 the water will fall 27/8 cm or 3.375 cm check my arithmetic.
November 22, 2016

Algebra 1
The boat will be .15 miles from Ellen coming and going away. So 1 - 70t = .15 OR -1 + 70t = .15 t = .01214... hrs or t = .01642.. hrs t = .01214(3600) sec or t = .01642(3600) sec t = 43.7 sec OR t = 59.1 sec
November 22, 2016

check - Math
ok, the cat's were adopted, that means the count was reduced by 120, not increased. I read the question incorrectly number of cats after adoption = 2x - 120 make the simple change in the equation and solve
November 22, 2016

Math
number of cats ---- 2x number of dogs ----3x after adoption: number of cats = 2x + 120 (2x+120) : 3x = 3 : 7 (2x+120)/(3x) = 3/7 14x + 840 = 9x 5x = -840 x is a negative, which is not possible. notice 2:3 = .66.. and 3:7 = .42 , which is < 2/3 How can the ratio of cats : ...
November 22, 2016

maths
Area of a triangle = (1/2)(ab)sinØ where a and b are sides with Ø as the angle between them. Your data is perfectly suited for that formula
November 22, 2016

found my error - Go with Steve - maths need help
The second equation had addition, I read it as another subtraction.
November 22, 2016

maths need help
Log (a+3) (base 9) - log b(base 9)= c + (1/2) log9 (a+3) - log9 b = c+1/2 log9 ((a+3)/b) = c+1/2 ---> 9^(c+1/2) = (a+3)/b 3^(2c+1) = (a+3)/b ** log (a-3) (base 3) + log b (base 3)=c - 1 log3 (a-3)+ log3 b = c-1 log3 ( (a-3)/b )= c-1 --> 3^(c-1) = (a-3)/b *** divide ** by...
November 22, 2016

Math
let the roots of ax^2+bx+c=0 be m and n then m:n = r:1 m/n =r/1 m = rn sum of roots = m+n = rn + n = n(r+1) = -b/a ** product of roots = mn = n^2 r = c/a *** divide ** by *** (r+1)/nr = (-b/a) / (c/a) = -b/c rc + c = -bnr rc + bnr = -c r(c + bn) = -c r = -c/(c+bn) For acr^2+(...
November 21, 2016

math
A standard rotation is 2?. So whatever angle you have either adding or subracting multiples of 2? will yield a coterminal angle. e.g 8?/3 -----> think 480° 8?/2 - 2? = 2?/3 -----> think 120° 8?/3 + 2? = 14?/3 -----> think 840° 8?/3 - 4? = -4?/3 -----> ...
November 21, 2016

calculus
c(x)=3x^3 - 12x^2 +9000x c ' (x) = 9x^2 - 24x + 9000 = 0 for a max/min of c(x) 9x^2 - 24x + 9000 = 0 This equation has no real solution. c(0) = 0, for all values of x > 0, c(x) increases so our minimum cost is when we don't produce anything, (that actually makes ...
November 21, 2016

Math
If you are referring to your previous post, look at my reply to it.
November 21, 2016

Math
For any number to be divisible by 6, it must be divisible by both 2 and 3 To be divisible by 2, the unit digit must be even or zero, so that eliminates A - 5. To be divisible by 3, the sum of the digits must be a multiple of 3 (divisible by 3) Since we have a sum of 8 for the ...
November 21, 2016

Algegra
So let's just change Ax + By = C to the form y = mx + b Ax + By = C By = -Ax + C divide each term by B y = (-A/B)x + C/B So compare that to y = mx + b m = -A/B so I have just developed a quick way to find the slope of any equation in general form e.g. 7x + 9y = 17 has slpe...
November 21, 2016

Math
so with her new test, there will be 6 tests (sum of what you have so far + x)/6 = 69 solve for x
November 21, 2016

maths
original fraction --- x/y first new fraction: (x+1)/(y+1) = 2/3 3x + 3 = 2y + 2 3x - 2y = -1 ** second new fraction: (x-2)/(y-2) = 3/5 5x - 10 = 3y - 6 5x - 3y = 4 *** solve the two equations ** and ***
November 21, 2016

mathematical methods for economics
Did you try Venn diagrams? Start filling in from the intersection of all three circles. Put 50 in that intersection, then work your way outwards from there.
November 21, 2016

Math, Surds
let the length of each side be s s^2 = 60 s = ?60 = ?4*?15 = 2?15 each side is 2?15 m perimeter = 8?15 m
November 21, 2016

Mathss
If you have a right-angled triangle, the area is (1/2) base x height You have the base and height, clearly 65 will not be used since it is the hypotenuse. So go for it. For the second, if you have two sides and the contained angle, then the area is (1/2)(a)(b)sinØ, ...
November 21, 2016

maths
The first two triangles are clearly right-angled. Is the third one ? is 65^2 = 33^2 + 56^2 ??, YES So make sketches of each one. for a) I labeled by triangle ABC, where a = 30 angle A = 90, and angle B = 30° sin35° = 30/b bsin35 = 30 b = 30/sin35 = appr 52.30 tan35 = ...
November 21, 2016

MATHS
All of the trig ratios shown are based on "standard" angles. We used to have math kits that contained a compass, a protractor and two triangles. One had angles 45-45-90°, the other had 30-60-90° The ratio of sides of the 30-60-90 were 1 : ?3 : 2 and for the ...
November 21, 2016

Math probability
prob(big winner) = 1/C(68,5) = 1 / 10,424,128 = appr .000,000,1
November 20, 2016

algebra
first number ---- x second number --- x+9 third number ----- 82 - x - x - 9 = 72 -2x all three numbers are expressed in terms of one variable: x , x+9, and 72-2x
November 20, 2016

algebra 1
just subtract them: 10y = -10 y = -1 plug that into the first: -4x + 7(-1) = -3 -4x = -3+7 = 4 x = -1 x = -1, and y = -1
November 20, 2016

Math
There are no "points in the table below"
November 20, 2016

Math
y+x =10 y - x = 20 add them: 2y = 30 y = 15 15+x = 10 x = -5 x = -5, y = 15
November 20, 2016

Life Science Math
acceleration --- a then v = at + c at the start, t = 0, and v=0 0 = 0 + c ---> c = 0 so v = at when t = 3 sec = 3/3600 hrs or 1/1200, v = 60 60 = a(1/1200) a = 72000 ------> v = 72000t if s is the distance travelled , s = 36000t^2 + k when t = 0 , s = 0, so k = 0 s = ...
November 20, 2016

f math
I will assume that by t ta you mean Ø so sin(90 - 5Ø) = cos(180 - Ø) but sin(90 - 5Ø) = cos Ø just like sin(90 - 30) = cos30 so we have cos(5Ø) = cos(180-Ø) take arccos of both sides 5Ø = 180-Ø 6Ø = 180 &...
November 20, 2016

f math
What is "t ta" ?? Where does "d" enter the picture?
November 20, 2016

Math
agree with C I did not answer the question that was asked My 4 slices would represent 1/2 of an 8 slice pizza.
November 20, 2016

Math
If each pizza is cut into 8 slices, then in the 7 pizzas there are 56 slices So each of the 14 student would get 56/14 or 4 slices. You did not post any "answer choices", so I hope 4 is in there.
November 20, 2016

Math
let one number be x let the other be x+7 x + x+7 = 63 solve for x, and all that is unknown shall be revealed.
November 20, 2016

Math
Done the way you typed it: |1-15x/5| < 3 1 - 15x/5 < 3 AND -1 + 15x/5 < 3 -3x < 2 AND 3x < 4 x > -2/3 AND x < 4/3 What you probably meant: | (1-15x)/5 | < 3 (1 - 15x)/5 < 3 AND (-1 + 15x)/5 < 3 1 - 15x < 15 AND -1 + 15x < 15 -15x < 14 AND...
November 20, 2016

Math Quadratic Equations . URGENT!!!!
look back when you posted this earlier
November 20, 2016

Trig
Did you make a sketch? I followed your labels and let the base of the building be B in triangle DAB, tan30 = DB/30 DB = 30tan30° = ... in triangle CAB, tan 60 = CB/30 CB = 30tan60 = ... CD = CB - DB = ....
November 20, 2016

Math
correct, ***80 is the only one divisible by 4
November 20, 2016

Math
A number is divisible by 4 if its last two digits are divisible by 4, or the last two digits are zeros. I see only one such case
November 20, 2016

Math, Quadratic equations
this was answered when you were Rachel.
November 20, 2016

Math, Quadratic equaitons
your data does not match the equation , so I don't know which is the correct one I will go with the equation: h = -4t^2 + 8.1t + 3 , (according to your data it would be 8.2t) when h = 6 6 = -4t^2 + 8.1t + 3 4t^2 - 8.1t + 3 = 0 using the formula: t = (8.1 ± ?17.61)/8...
November 20, 2016

College Math
You are partly on the right track. The C(13,7) is the number of to choose 7 of the 13 marbles. you want the case of 3 reds plus 4 non-reds prob(your stated event) = C(3,3)*C(10,4)/C(13,7) = 1*210/1716 = 35/286
November 20, 2016

f math
1 - cos^2 x = 0 , for 0 ? x ? 270° cos^2 x = 1 cos x = ± 1 now look at the cosine curve. Where is the y equal to either +1 or -1 within your domain ?
November 20, 2016

Calculus
y = ln(sint) dy/dt = (1/sint)(cost) = cost/sint for x= cos^2 t = (cost)^2 dx/dt = 2cost(-sint) (dy/dt) / (dx/dt) = (cost/sint) / (-2sintcost) dy/dx = -1/(2 sin^2 t) = (-1/2)(sint)^-2 d(dy/dx) / dx = (-2)(-1/2)(sint)^-3 (cost) = cost / sin^3 t sub in t = ?/4 d(dy/dx) / dx = (?2...
November 20, 2016

Maths
remember that sinx = cos(90-x) - property of complementary angles, "co-sine" vs sine Your statement is only true if (cos40-sin30)/(sin60-cos50) =tan50 , but not the way you typed it. cos40 = sin50 and sin60 = cos30 so LS = (sin50 - sin30)/(cos30 - cos50) remember ...
November 20, 2016

Math
let the obtuse angle be A and its opposite diagonal be x. By the cosine law: x^2 = 45^2+28^2-2(48)(28)cosA similarly... y^2 = 45^2+28^2-2(48)(28)cosB but A+B = 180 B=180-A and cosØ = -cos(180-Ø) by the CAST rule e.g. cos 60 = - cos120 then cos B = -cosA x^2+y^2...
November 19, 2016

math
original fraction: x/y case1 (x+5)/(y+5) = 1/2 2x + 10 = y+5 2x - y = -5 ** case2 (x-1)/(y-1) = 1/5 5x - 5 = y - 1 5x - y = 4 *** subtract ** from *** 3x = 9 x = 3, then from ** 6 - y = -5 , y = 11 the original fraction was 3/11 check: (3+5)/(11+5) = 8/16 = 1/2, check! (3-1)/(...
November 19, 2016

Math Quadratic Functions
A squaring of the input value is involved. A rather vague question.
November 19, 2016

math
just like in 5/6 - 3/7 you will need a common denominator. In my example, it would be 42? How did I get 42 ? Next step 35/42 - 18/42 ---> how did I get those fractions = 17/42 Now to your problem 5/(x-2) - 4(x-3) LCD = (x-2)(x-3) ---> same step as above e.g = 5(x-3)/((x-...
November 19, 2016

Calculus
I will assume you are saying $1 per square foot let the base be x ft by x ft, let the height be y area of top and 4 sides = x^2 + 4xy cost of top and 4 sides = 1(x^2 + 4x) = x^2 + 4xy area of base = x^2 cost for the base = 2x^2 total cost = 3x^2 + 4xy = 114 y = (114 - 3x^2)/4x...
November 19, 2016

Math (Calculus) (mean value theorem emergency)
your secant equation is correct checking the other parts: f '(x) = 2x - 1 ---> you had that setting that equal to 1, since the slope of our secant is 1 2x-1 = 1 2x = 2 x = 1 so all you have to do is sub that back into the original f(1) = 1 - 1 - 12 = -12 So the point ...
November 19, 2016

algebra
yes
November 19, 2016

algebra
no Why do you think it is C or are you just guessing?
November 19, 2016

algebra
no , B does not have the necessary brackets
November 19, 2016

algebra
if the point is (a,b) and the slope is m then the equation is y - b = m(x - a) now which one of the given answers follows that pattern?
November 19, 2016

Math help pls. !!
(2x-3)(5x+2)=0 This is only possible if one or more of the given factors equal zero. But we don't know which one, so 2x-3 = 0 OR 5x+2=0 2x = 3 OR 5x = -2 x = 3/2 or x = -2/5
November 19, 2016

Math
(1/2)x^2 - 2x = 6 times 2 x^2 - 4x = 12 x^2 - 4x - 12 = 0 it factors: (x - 6)(x + 2) = 0 now follow the steps I showed you here http://www.jiskha.com/display.cgi?id=1479598571
November 19, 2016

math
number of digits = 3x2x1 = 6 , we could actually list them 137 173 317 371 713 731 Here is a list of primes: http://primos.mat.br/indexen.html you will find that all are prime except 371, 713 and 731 731 =17 x 43 713 = 23 x 31 371 = 7 x 53
November 19, 2016

math algebra
I did this when you were rita http://www.jiskha.com/display.cgi?id=1479589996
November 19, 2016

FUNCTIONS HELPPPPP????
After seeing how you responded to Steve when he helped you with this question .... http://www.jiskha.com/display.cgi?id=1479505703
November 19, 2016

Math
Volume of cylinder = ?(r^2)(h) plug in your values.
November 19, 2016

math algebra
rate of gandola in still water --- x mph speed of current ---- y mph time to go 2.8 miles with the current = 2.8/(x+y) time to go 2 miles against the current = 2/(x-y) they are the same! 2.8/(x+y) = 2/(x-y) 2.8x - 2.8y = 2x+2y .8x = 4.8y 8x = 48y x = 6y or y = (1/6)x All we ...
November 19, 2016

math algebra
Gray's rate = 1/15 Anna' rate = 1/20 Job done by Gray = 6(1/15) = 2/5 leaving 3/5 of the job left to be done by Anna time for Anna to complete = (3/5) / (1/20) = 12 It will take her 12 days to finish the roof
November 19, 2016

Math
6 1/7 - 1 5/21 = 43/7 - 26/21 = 129/7 - 26/21 = 103/21
November 19, 2016

math algebra
assuming that you meant: f(x) = (x+1)/(x^2-9) and g(x) = x/(x-3) The domain for both f(x) and g(x) are all values of x except those that make the denominator zero domain of f(x): all x's except x = ±3 domain of g(x): all x/s except x = 3 (f+g)(x) = (x+1)/(x^2 - 9...
November 19, 2016

math - business
Steve is probably off line now, so I will answer. For any quadratic function of the form y = ax^2 + bx + c the x of the vertex is -b/(2a), once you have the x you just sub that back into the equation to get the y of the vertex. In your case: P = -.005x^2 + 4x - 200 a = -.005 b...
November 19, 2016

GEOMETRY
You have similar triangles. Since XA = AY AY : XY = 1 : 2 triangle XYZ is similar to triangle AYB XZ/XY = AB/AY 8.4/2 = AB/1 AB = 8.4/2 = 4.2
November 19, 2016

Algebra
3n^2+5n-100=? If this is a quadratic equation, the your ? is 0 If you are dealing with the corresponding quadratic function you would normally find it as y = 3n^2 + 5n - 100 , where y is the dependent variable, and n is the independent variable What about it ?
November 19, 2016

Pre-calculus
Watch those brackets, you must have meant: (sin(x+y)+sin(x-y))/(cos(x+y)+cos(x-y))=tanx LS = (sinxcosy + cosxsiny + sinxcosy - sinxcosy)/(cosxcosy - sinxsiny + cosxcosy + sinxsiny) = 2sinxcosy/(2cosxcosy) = (sinx/cosx)(cosy/cosy) = tanx = RS
November 19, 2016

Pre-calculus
I checked with my calculator and actually found the angles. It works !!!
November 19, 2016

Pre-calculus
If siny = -2/?13 , and coty ?0, then y is in quad III so cosy = -3/?13 then sin 2y = 2sinycosy = 2(-2/?13)(-3/?13) = 12/13 cos 2y = cos^2 y - sin^2 y = 9/13 - 4/13 = 5/13 so sin 2y = 12/13 and cos 2y = 5/13 if sin 2x = 7/25 remember cos^2 (2x) = 1 - sin^2 (2x) = 1 - 49/625 = ...
November 19, 2016

Probability Help
at least one boy ----> exclude the case of all 5 girls, which is (1/2)^5 = 1/32 prob(at least one boy in 5) = 1 - 1/32 = 31/32
November 19, 2016

Math
A:B:C = 5:5:7 or 5x : 5x : 7x Cindy ate 30 Skittles less than Ann and Ben together -----> 7x = 5x + 5x - 30 -3x = -30 x = 10 5x = 50 7x = 70 They ate 50+50+70 = 170 of them
November 18, 2016

Calculus
g(x) = sinxcosx g ' (x) = sinx(-sinx) + cosxcosx = cos^2 x - sin^2 x = cos 2x at x = ?/3 g '(x) = cos (2?/3) = -.5 equation: y - ?3/4 = (-1/2)(x - ?/3) So I agree with your answer. for a max/min of g(x) , g '(x) = 0 cos 2x = 0 2x = ?/2 or 2x = 3?/2 x = ?/4 or x = 3...
November 18, 2016

Calculus
with the information given, you should be able to form the equation h = -16t^2 + 68t + 6 dh/dt = -32t + 68 = 0 for a max of h 32t = 68 t = 2.125 evaluate h when t = 2.125
November 18, 2016

argghh - Calc
forgot to change the units from km/h to m/s go with Damon's answers
November 18, 2016

Calc
if we have acceleration of a, then v = at + c case1: when t=0, v=25 25 = 0+c ---> v = at + 25 so when t = 13, v = 90 90 = 13a + 25 a = 65/13 = 5 m/s^2 -----> v = 5t + 25 distance = (5/2)t^2 + 25t + k when t=0 , distance = 0 , so k = 0 distance = (5/2)t^2 + 25t when t = ...
November 18, 2016

Math
I agree with all of them
November 18, 2016

Math
amount taken out as loan = 25 - .2(25) = 20 or just take .8(25) = 20 amount owing after 8 years = 20(1.025)^8 = 24.368 gh cedis
November 18, 2016

Math
1 7/10 = 17/10 "as many" suggests multiplication e.g. bill eats 3 times as many donuts as Bob if Bob eats 4 donuts, then Bill would eat 3*4 or 12 donuts so Elizabeth has (17/10) as many as Rosalie. let Rosalie's number of plants be x then: (17/10)x = 51 ----> ...
November 18, 2016

Math
time for first trip = d/x time for return = d/y total time = (d/x + d/y) = (dy + dx)/(xy) = d(x+y)/(xy) total distance = 2d average speed = 2d/( d(x+y)/(xy) ) = 2xy/(x+y) = 50 xy/(x+y) = 25 xy = 25x + 25y 25y - xy = 25x y(25 - x) = -25x y = 25x/(x-25) e.g. let x = 50, then y...
November 18, 2016

math
horizontal path = 15(2.5) = 37.5 units^2 vertical path = 9(2.5) = 22.5 units^2 total = 60 units^2 BUT, we counted the intersection of the paths twice, so we have to subtract 2.5(2.5) or 6.25 units^2 leaving us with 63.75 units^2
November 18, 2016

Geometry
So what is (3/2)(4.8) ? Just add up your 4 sides, remember they come in equal pairs.
November 18, 2016

Order MATH!
I suggest you change them all to decimals, and then it is easy to see.
November 18, 2016

Pre-calculus
correction for #1, should say: (1+cosx)/(1-cosx) = (secx + 1)/(secx - 1) RS = (1/cosx + 1)/(1/cosx - 1) = (1/cosx + 1)/(1/cosx - 1) * cosx/cox = (1+ cosx)/(1 - cosx) = LS Well, that was easy. #2, hint: change everything to sines and cosines expand and simplify the LS #3, use ...
November 18, 2016

Maths
So in 60 minutes he can type 3200 words. How many words can he type in 1 minute? Then how many in 15 minutes ?
November 18, 2016

additional maths (maths)
so you just want the max of d(t) find the derivative, set it equal to zero, and solve that for t Once you have the value of t which gives you the maximum, plug it back into d(t) to actually find that distance. Very straight-forward.
November 18, 2016

Maths
The missing angle ? = 45° by the sine law: a/sin35 = 40/sin100 a = 40sin35/sin100 = appr 23.3 c/sin45 = 40/sin100 c = 40sin45/sin100 = appr 28.7 area = (1/2)(ab)sin45 = appr 329.5 units^2
November 18, 2016

maths
so he gave away 60%, leaving him with 40% .4x = 9600 solve for x
November 18, 2016

Math (Differentials)
our f(x) = x^(1/3) , and f ' (x) = (1/3)x^(-2/3) = 1/(3(x)^(2/3) ) I will go with your x = 27 , dx = -2 f(x + dx) is appr = f(x) + f ' (x) (dx) f(25) = f(27) + (1/3)(27)^(-2/3) = 3 + (1/27)(-2) = 3 - .0741 = 2.926 you simply added the part at the end instead of ...
November 18, 2016

algebra 2
Your calculations are correct (sum of roots = 2+3i + 2-3i = 4 product of roots = (2+3i)(2-3i) = 4-(-9) = 13 ) It said to write the quadratic equation, which is x^2 - 4x + 13 = 0 you had y = x^2 - 4x + 13 , which is the quadratic function.
November 17, 2016

Math
I will place the parabola as opening to the right, with its vertex at (0,0) so the equation is y^2 = 4px, where (p,0) is the focus but (6,16) lies on it 16^2 = 4p(6) p = 256/24 = 32/3 So it should be placed at (32/3 , 0)
November 17, 2016

Geometry
original area = base x height = bh new area = .7b x 1.2h = .84bh so there is a 16% decrease in the area
November 17, 2016

Calculus: Centers of Mass
A quick calculation shows that the line intersects the parabola at (2,2) in the first quadrant lots of work ahead of us: first you must find the area of the region, it has to be done in two parts: from x=0 to x=2 under the curve, then from x=2 to x=4 under the straight line ...
November 17, 2016

correction - Difficult Math
I misread "Thirty of the cards from his cousin are National League players" as one third of the cards from his cousin are NL players
November 17, 2016

Difficult Math
total collection ---- x from dad --- x/4 from uncle --- x/5 ---> (.2)x = (2/10)x = x/5 from brother --- x/2 leaving : x -x/4 - x/5 - x/2 = x/20 so from cousin = x/20 so (1/3)(x/20) = 30 x = 1800 Steve has 1800 cards check: from dad = 1800/4 = 450 from uncle = .2(1800) = 360...
November 17, 2016

Math
999,999,999,999 = appr 1,000,000,000,000 = 10^12 ( you would be off by $1 on 1 Trillion dollars) 100,000,000,000,000 = 10^14 so 100,000,000,000,000 times 999,999,999,999 = 10^12 * 10^14 = 10^26 that would be 100 septillion.
November 17, 2016

Math
In arithmetic "of" means multiplication, so 1/10 of 2(10)+4(1)+6(1/10)+7(1/100)+8(1/1000) = (1/10)(20) + 4 + .6 + .07 + .008 = 2+4+.6+.07+.008 = 6.678 http://www.wolframalpha.com/input/?i=evaluate+1%2F10+*+2(10)%2B4(1)%2B6(1%2F10)%2B7(1%2F100)%2B8(1%2F1000) if you ...
November 17, 2016

Algebra
Help with what? You have given us two different circles. What do you want to do? They do intersect. Here is a picture of your problem http://www.wolframalpha.com/input/?i=plot+x%5E2%2By%5E2%2B6y%2B5%3D0+,+x%5E2%2By%5E2-2x-8%3D0
November 17, 2016

Maths
no XYYYY , where X is the vowel, Y can be anything else number of ways = (2)(4!) = 48 e.g. E(BGIN) - one of the 24 ways to arrange BGIN I(GBEN) - one of the 24 ways to arrange GBEN
November 17, 2016

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