This is the way I interpreted your question:
Solve for x: (3 log(2))/log(x) + log(18)/log(x) = 2
Bring (3 log(2))/log(x) + log(18)/log(x) together using the common denominator log(x):
(3 log(2) + log(18))/log(x) = 2
Take the reciprocal of both sides: log(x)/(3 log(2) + log(18)) = 1/2
Multiply both sides by 3 log(2) + log(18):
log(x) = 1/2 (3 log(2) + log(18)) Evaluate the RHS
Log(x) = 1.0791812460 Raise the RHS to the power of 10
x = 10^1.0791812460
x = 12
3 logx 2 + logx 18 = 2 change to log10
3 log 2/log x + log 18/logx = 2
3 log 2 + log 18 = 2 log x
3/2 log 2 + 1/2 log 18 = log x
1.07918 = log x
Logically, you should use the 20% off coupon first. This is because if you use it first, you will cut off the highest price with it. You will cut off $8, but if you use it second, you will only cut off $7.
You should use the store coupon first and the manufacturer's coupon second for the maximum discount. If you use this way, the box will cost $27
You can start by giving one mansion to each child ahead of time. Now you have to distribute 6 mansions among three children. You use stars and bars and get 9 choose 3, which is 84 possibilities. Now you have to subtract the number of possibilities in which the two or three children have the same houses.
Everyone gets 3 houses: 1 possibility.
Two people get 1 house: 3 possibilities. This is because A and B get them, B and C get them, or A and C get them.
Two people get 2 houses: 3 possibilities.
Two people get 4 houses: 3 possibilities.
84-3-3-3-1 = 74.
The Answer is 74 possibilities.
Hope I helped. :)
You can multiply Danielle's amount by 4, so she has 12 TG's and 20 STGLO Fist for 224.08 dollars. Then, you can multiply Ellen's fish so she has 12 TG's and 9 STGLO Fish for 125.19 dollars. Then, you subtract them and the TG fish cancel out and you have 11 STGLO Fish for 98.89 dollars. Then you find that one STGLO Fish is 8.99 dollars by dividing it by 11. After that, u plug that into Ellen's equation by substituting the STGLO Fish with 8.99 each STGLO Fish there is. This makes the equation 4 TG + $26.97 = $41.73. Subtract 26.97 from both sides and you get 4TG = $14.76. Divide both sides by 4 and u get 3.69 a Turquoise Guppy. The answer is 3.69 a Turquoise Guppy. Hope I helped. :)
Given:
4 t + 3s = 41.73 and
3 t + 5 s = 56.02 we want to find t , turquoise guppy price, so eliminate 's'
multiply second equaion by - 3/5 to get
-9/5 t - 3s = - 33.612 and add to the first equation to get
11/5 t = 8.118
t = $ 3.69 each
f(x) = .05 x
g(x) = .075(x+2500)
f+g = .05x + .075 (x+2500)
.05x + .075x + 187.50
= .125 x + 187.50
f+g (18500) would represent the interest from an acccount with 18500 and from an account with 21000 in it ( BOTH accounts)
= .125 (18500) + 187.5
2312.50 + 187.50 = $ 2500
f(x) = 3x^2 - 4x
f(k-x) = 3 (k-x)^2 - 4(k-x)
3 (k^2-2kx+x^2) - 4k +4x and this equals 3x^2 - 4x
3 k^2 - 6kx + 3 x^2 - 4k + 4x = 3x^2 - 4x simplify
3 k^2 - 6kx - 4k + 8x = 0
(3k -4)( k -2x) = 0
so k = 4/3 or k = 2x though I do not think this is a 'constant'
How many pizzas ?
(25 kids x 2/4 slice/kid ) / 8 slices/pie = 25 x 2/4 / 8 = 12.5 / 8 = 1.5625 pies
Does each kid really get only 2/4 = 1/2 slice of pizza? or does each get 2/4 of a whole pizza ?
What is the slope of the line 2y = -3x + 6?
By definition, wnen expressed as y = mx + b the slope is represented by m.
Divide both sides by 2 to obtain y = –(3/2)x + 3
The slope is –(3/2)
5 c + 3 p = 41 c = corn p = program and
3 c + 2 p = 26 multiply this equation by - 1.5 to get
-4.5 c -3p = -39 and add to the first eq to get
.5 c = 2
c = $ 4
then use this value of ' c' , substitute into one of the equations to find 'p' the program cost
What is the slope of the line 2y = -3x + 6? divide both sides of the eqaution by '2' to get
y = -3/2 x + 3 this is the line equation in form y = mx +b where 'm' = slope = -3/2
f= flamingoes 2f = legs f = heads
l = lions 4l = lions l = heads
2f + 4l = 96
f + l = 35 since we are looking for lions, let's eliminate the 'f's Multiply this equation by -2
-2f -2l = -70 and add this to the first equation to get
2l = 26 so l = 13 lions
ax + (a + 1)y = a + 2
We are given that (4, -8) is a solution to this equation.
That means if we substitute 4 in for x and -8 in for y , we will make a true equation.
So the following equation must be true:
a(4) + (a + 1)(-8) = a + 2
We can distribute -8 to the terms in parenthesees and simplify the left side of the equation.
4a - 8a - 8 = a + 2
Add 8 to both sides of the equation.
4a - 8a = a + 2 + 8
Subtract a from both sides of the equation.
4a - 8a - a = 2 + 8
Combine like terms.
-5a = 10
Divide both sides of the equation by -5
a = -2
Check: https://www.desmos.com/calculator/cq30o2b4j7
We have this equation :
y = mx + b where b is the y intercept and ( x, y) is a point on the graph....so we have
-3 = (1/2)(2) + b
-3 = 1 + b subtract 1 from both sides
-4 = b
If the diameter of the fountain is 10 ft.....then its radius = 5 ft
Then the total diameter of the outer boundary of the walking path is
2 ( radius of fountain + 8 ft + 6 ft ) =
2 ( 5 ft + 8 ft + 6 ft) =
2 ( 19 ft) =
38 ft
Let the number of small boxes = S
So....the number of large boxes = 3S
So
S ( 50) + 3S ( 400) = 2500 simplify
50S + 1200S = 2500
1250S = 2500 divide though by 10
125S = 250 divide both sides by 125
S = 2 = small boxes
3S = large boxes = 3(2) = 6
WolframAlpha gives
a b
-14 4
-8 6
-6 12
-4 -6
-2 0
4 2
This is analogous to the number of identitifable "words" we can make from the letters RRRWWWWWW where the "R's" occur together
The "R's" can occur together in 7 ways :
1-2-3
2-3-4
3-4-5
4-5-6
5-6-7
6-7-8
7-8-9
And the number of identifiable draws is 7!
______ = 35
3! * 4!
So....the probability is 7 / 35 = 1/5
Suppose f(x) is a function that has this property: For all real numbers a and b such that a
listfor(n,8,23,(4*n^3+6*n^2+4*n+1))
(2465, 3439, 4641, 6095, 7825, 9855, 12209, 14911, 17985, 21455, 25345, 29679, 34481, 39775, 45585, 51935)=327,680
Possible combos =
8 * 3 * 4 =
96
Put your latex in a latex box and see if it works properly.
It is obviously not readable like this.
If ten parachutists jump at one time, what is the ratio of the probability that eight land on the north half and two on the south half to the probability that five land on each half?
\(10C2*0.5^{10} : 10C5*0.5^{10}\\ 10C2 : 10C5\\ 45:252\\ 5:28 \)
+9477 
