Answer: 7/26
Step-by-step explanation:
Number of purple marbles = 6
Number of white marbles = 7
Total number of marbles = 13
The probability of first drawing a white marble will be = 7/13
The probability of drawing a purple marble the second time will be = 6/12 = 1/2
The probability that the first marble is white and the second one is purple will now be:
= 7/13 × 1/2
= 7/26
Note that since there are 13 marbles, when the first purple marble is drawn, there'll be 12 marbles left.
A. f(1)=5 (as defined on the second line, x=1) TRUE because f(1)=5
B. f(5)=5^2=25 (as defined on third line, x>1) FALSE because f(5) ≠ 1
C. f(-2)=2(-2)=-4 (as defined on first line, x<1) FALSE because f(-2) ≠ 4
D. f(2)=2^2=4 (as defined on third line, x>1) TRUE because f(2)=4
First substitute to rewrite the integral as
Now use an Euler substitution, to rewrite it again as
where we take
Partial fractions:
so that
The second integral is trivial,
For the other, I'm compelled to use the residue theorem, though real methods are doable too (e.g. trig substitution). Consider the contour integral
where is a semicircle in the upper half of the complex plane, and its diameter lies on the real axis connecting to . The value of this integral is 2πi times the sum of the residues in the upper half-plane. It's fairly straightforward to convince ourselves that the integral along the circular arc vanishes as , so the contour integral converges to the integral over the entire real line. Note that
since the integrand is even.
Find the poles of .
where .
The two poles we care about are at and . Compute the residues at each one.
By the residue theorem,
We also have
Then the remaining integral is
It follows that
Answer:
16.43
Step-by-step explanation:
gib brainlest or else:0