Answer:
14
Step-by-step explanation:
Given the indicinal expression 64^5/6 + 27^2/3 - 81^3/4
According to indices;
![a^{m/n} = (\sqrt[n]{a}) ^m](https://tex.z-dn.net/?f=a%5E%7Bm%2Fn%7D%20%3D%20%28%5Csqrt%5Bn%5D%7Ba%7D%29%20%5Em)
Applying this to the question
![64^{5/6} \\= (\sqrt[6]{64}) ^5\\= 2^5= 32](https://tex.z-dn.net/?f=64%5E%7B5%2F6%7D%20%5C%5C%3D%20%28%5Csqrt%5B6%5D%7B64%7D%29%20%5E5%5C%5C%3D%202%5E5%3D%2032)
Similarly
![27^{2/3}\\= (\sqrt[3]{27}) ^2\\= 3^2\\= 9\\](https://tex.z-dn.net/?f=27%5E%7B2%2F3%7D%5C%5C%3D%20%28%5Csqrt%5B3%5D%7B27%7D%29%20%5E2%5C%5C%3D%203%5E2%5C%5C%3D%209%5C%5C)
Also;
![81^{3/4}\\= (\sqrt[4]{81}) ^3\\= 3^3\\= 27](https://tex.z-dn.net/?f=81%5E%7B3%2F4%7D%5C%5C%3D%20%28%5Csqrt%5B4%5D%7B81%7D%29%20%5E3%5C%5C%3D%203%5E3%5C%5C%3D%2027)
Substitute inti the original equation
64^5/6 + 27^2/3 - 81^3/4
= 32 + 9- 27
= 41 - 27
= 14
Hence the required answer is 14
Answer:
Therefore the probability of getting both blue marbles is
.
Step-by-step explanation:
Probability : The ratio of favorable outcomes to the total outcomes.
Given that a bag contains 7 marbles which are red in color, 2 marbles which are blue in color and 3 marbles which are green in color.
Total number of marbles = (7+2+3) = 12
The probability of getting a blue on first drawn is



Now the number of blue marbles = (2-1)= 1 [ since 1 blue marbles is drawn]
Total number of marbles = (12-1) =11
The probability of getting a blue marble on second drawn is


Therefore the probability of getting both blue marbles is


8x-2(4)=48 Then, 8x-8=48 Then, 8x=56 Then X=7
The value of x in the equation is 7.
Answer:
x+y=68
x-y=15
Step-by-step explanation:
A "sum" means that we will be using addition, while a "difference" indicates subtraction. Anytime we have two unknown numbers we generally use "x" and "y".
Answer:
A. 60 feet B. 7200 ft²
Step-by-step explanation:
A. Find the length of the corral along the river that will give the maximum area
To find the length of the corral that will give the maximum area, we differentiate A with respect to x and equate it to zero.
So, dA(x)/dx = d[x(240 - 2x)]/dx
= (240 - 2x)dx/dx + xd(240 -2x)/dx
= 240 - 2x -2x
= 240 - 4x
So, dA(x)/dx = 0
240 - 4x = 0
4x = 240
x = 240/4
x = 60 feet
B. Find the maximum area of the corral
The maximum area at x = 60 feet is
A(x)=x(240−2x)
A(60)=60(240−2(60))
A(60) = 60(240 - 120)
A(60) = 60(120)
A(60) = 7200 ft²