Answer:
The area can be written as

And the value of it is approximately 1.8117
Step-by-step explanation:
x = u/v
y = uv
Lets analyze the lines bordering R replacing x and y by their respective expressions with u and v.
- x*y = u/v * uv = u², therefore, x*y = 1 when u² = 1. Also x*y = 9 if and only if u² = 9
- x=y only if u/v = uv, And that only holds if u = 0 or 1/v = v, and 1/v = v if and only if v² = 1. Similarly y = 4x if and only if 4u/v = uv if and only if v² = 4
Therefore, u² should range between 1 and 9 and v² ranges between 1 and 4. This means that u is between 1 and 3 and v is between 1 and 2 (we are not taking negative values).
Lets compute the partial derivates of x and y over u and v




Therefore, the Jacobian matrix is
and its determinant is u/v - uv * ln(v) = u * (1/v - v ln(v))
In order to compute the integral, we can find primitives for u and (1/v-v ln(v)) (which can be separated in 1/v and -vln(v) ). For u it is u²/2. For 1/v it is ln(v), and for -vln(v) , we can solve it by using integration by parts:

Therefore,

Answer:
It's D, reflects over the x-axis
Step-by-step explanation:
When you have a negative symbol outside the parentheses, all the y values are being multiplied by -1. This means that the points will have the same x, just that the y values will all be the opposite sign.
<u>Answer:</u>
X and Y are stochastically dependent RVs .
<u>Step-by-step explanation:</u>
Let ,
X = sum of the values that come up after throwing n (≥ 1) fare dice.
Y = number of times an odd number come up.
Let, n = 3
then, P(X =6) = p (say) clearly 0 < p < 1
and P (Y = 3) = 
And,
P( X = 6, Y = 3) = 0 ≠ 
Hence, X and Y are stochastically dependent RVs
Fractions are normally parts of a whole thing such that they complement it. In this case, monday= 2/15 of the book was read, Tuesday= 1/3 , wednesday =2/9, Thus for the three days he will have read a fraction of (2/15+1/3+2/9) =31/45. The remainder will be 1- 31/45= 14/45, so on Thursday he read 3/4 × 14/45 = 7/30. On friday he read a fraction of 14/45 - 7/30 = 7/90.
Therefore, a fraction of 7/90 is equivalent to 14 pages. Thus the whole book was 14 × 90/7 =180 pages
= 180 pages