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.
Answer:
A
Step-by-step explanation:
Answer:(x^5−4) and (x^10+4x^5+16)
Answer:
A recent report estimated that 25% of all college students in the United States have a sexually transmitted disease (STD). The director of the campus health center believes that the proportion of students with STDs is higher at their campus.
According to the American Heart Association guidelines, the daily maximum amount of sugar a teenager should have is 4 teaspoons. The parents of a local high school have expressed concerns that the average daily sugar intake of their students is higher than these guidelines and have been pressuring school officials to limit unhealthy snack and beverage choices offered in the cafeteria and student store.
Step-by-step explanation:
The first two researches involve the single sample compared to mean of population.
The 3rd and 4th research involves comparing samples of men and women that is two individual groups.
