Step-by-step explanation:
an object and its shadow create a right-angled triangle.
2 objects and their shadows create 2 similar right-angled triangles.
that means the angles are the same, and the side lengths of one triangle all correlate with the corresponding side lengths of the other triangle via the same factor.
so,
42 × f = 6
f = 6/42 = 1/7
the length of Joel's shadow is then
20 × f = 20 × 1/7 = 2.857142857... ft
Answer:
Step-by-step explanation:
Ill try to break this down, simply:
When we talk about percentages we are talking about how much part of something we have and the percent sign is a just a symbol representing that.
Lets say we have 2 out of 10 apples and we need to convert this to a percentage
First think about how many apples we have in total... and that would be 10, and then how many apples we currently have being 2:
So if we put the part that we have over the whole thing we get:

So now lets turn this into a decimal, when its something over 10 its really easy, all we have to do is move the decimal back one place!
So we have 2 and if we move the decimal back one place we get .2 or 0.2
Now we have our decimal, to convert this into a percentage all we have to do is multiply our decimal by 100
So:
0.2 x 100 = 20%
All you do when you multiply by 100 is move the decimal back over 2 places one place for each zero so:
0.2 --> 2. --> 20.
Which gives us again 20%
Answer:
<em>Assuming person A and person B are part of the 7 people</em>, there are 10 ways the 7 people can line up if A needs to be first or last and B needs to be in the middle.
Step-by-step explanation:
There are 2 places for A (first, last) and 5 places for B (anywhere but first or last). 2 x 5 = 10.
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.
The median is 3 because 1,2,2,3,3,5,6,8
3,3 is directly in the middle so, 3+3=6 divided by 2 numbers=3