Answer:
1/45
Step-by-step explanation:
I assume there are 10 marbles total, 2 of which are yellow.
The probability the first marble is yellow is 2/10.
There's now one less marble, so the probability that the second marble is yellow is 1/9.
The total probability is (2/10) (1/9) = 1/45.
8.9
The equation for the grain size is expressed as the equality:
Nm(M/100)^2 = 2^(n-1)
where
Nm = number of grains per square inch at magnification M.
M = Magnification
n = ASTM grain size number
Let's solve for n, then substitute the known values and calculate.
Nm(M/100)^2 = 2^(n-1)
log(Nm(M/100)^2) = log(2^(n-1))
log(Nm) + 2*log(M/100) = (n-1) * log(2)
(log(Nm) + 2*log(M/100))/log(2) = n-1
(log(Nm) + 2*log(M/100))/log(2) + 1 = n
(log(33) + 2*log(270/100))/log(2) + 1 = n
(1.51851394 + 2*0.431363764)/0.301029996 + 1 = n
(1.51851394 + 0.862727528)/0.301029996 + 1 = n
2.381241468/0.301029996 + 1 = n
7.910312934 + 1 = n
8.910312934 = n
So the ASTM grain size number is 8.9
If you want to calculate the number of grains per square inch, you'd use the
same formula with M equal to 1. So:
Nm(M/100)^2 = 2^(n-1)
Nm(1/100)^2 = 2^(8.9-1)
Nm(1/10000) = 2^7.9
Nm(1/10000) = 238.8564458
Nm = 2388564.458
Or about 2,400,000 grains per square inch.
![\dfrac\partial{\partial y}\left[e^{2y}-y\cos xy\right]=2e^{2y}-\cos xy+xy\sin xy](https://tex.z-dn.net/?f=%5Cdfrac%5Cpartial%7B%5Cpartial%20y%7D%5Cleft%5Be%5E%7B2y%7D-y%5Ccos%20xy%5Cright%5D%3D2e%5E%7B2y%7D-%5Ccos%20xy%2Bxy%5Csin%20xy)
![\dfrac\partial{\partial x}\left[2xe^{2y}-y\cos xy+2y\right]=2e^{2y}+y\sin xy](https://tex.z-dn.net/?f=%5Cdfrac%5Cpartial%7B%5Cpartial%20x%7D%5Cleft%5B2xe%5E%7B2y%7D-y%5Ccos%20xy%2B2y%5Cright%5D%3D2e%5E%7B2y%7D%2By%5Csin%20xy)
The partial derivatives are not equal, so the equation is not exact.
Answer:
1/3
Step-by-step explanation:
simplify
81^(-1/4)
= 1/81^(1/4)
= 1/[3×3×3×3]^(1/4). (factorize 81)
= 1/[3]^(4/4)
= 1/3
Answer:
Step-by-step explanation:
- The sum of a number n and 5 => n + 5
- Thrice the sum of a number n and 5 => 3(n + 5)
- At most means "less than or equal to", the sign of which is "≤"
<u>So, the inequality will be:</u>
3(n + 5) ≤ 100
![\rule[225]{225}{2}](https://tex.z-dn.net/?f=%5Crule%5B225%5D%7B225%7D%7B2%7D)
Hope this helped!
<h3>~AH1807</h3>
