9 hundred thousands
8 ten thousands
7 thousands
1 hundreds
6 tens
4 ones
.3 tenths
.00 hundredths
.002 thousandths
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Answer: 15120
Step-by-step explanation:
10×12×7×2×9=15120
The area of the ellipse 
is given by
To use Green's theorem, which says
(
denotes the boundary of ), we want to find 
and 
such that
and then we would simply compute the line integral. As the hint suggests, we can pick
The line integral is then
We parameterize the boundary by
with 
. Then the integral is
###
Notice that 
kind of resembles the equation for a circle with radius 4, 
. We can change coordinates to what you might call "pseudo-polar":
which gives
as needed. Then with , we compute the area via Green's theorem using the same setup as before:
Answer:
Step-by-step explanation:
For the random variable 
we define the possible values for this variable on this case ![[1,2,3,4,5]](https://tex.z-dn.net/?f=%20%5B1%2C2%2C3%2C4%2C5%5D)
. We know that we have 2 defective transistors so then we have 5C2 (where C means combinatory) ways to select or permute the transistors in order to detect the first defective:
We want the first detective transistor on the ath place, so then the first a-1 places are non defective transistors, so then we can define the probability for the random variable 
like this:
For the distribution of 
we need to take in count that we are finding a conditional distribution. given 
, for this case we see that ![N_2 \in [1,2,...,5-a]](https://tex.z-dn.net/?f=%20N_2%20%5Cin%20%5B1%2C2%2C...%2C5-a%5D)
, so then exist 
ways to reorder the remaining transistors. And if we want b additional steps to obtain a second defective transistor we have the following probability defined:
And if we want to find the joint probability we just need to do this:
And if we multiply the probabilities founded we got:
