The length of the dollhouse is 156 square inches
Use Stokes' theorem for both parts, which equates the surface integral of the curl to the line integral along the surface's boundary.
a. The boundary of the hemisphere is the circle
in the plane
, where the curl is
. Green's theorem applies here, so that

which means the value of the line integral is 3 times the area of the circle, or
.
b. The closed sphere has no boundary, so by Stokes' theorem the integral is 0.
The odds of jimmy winning a free lunch is 0.066.
<h3>What is Probability ?</h3>
Probability is the likeliness of an event to happen.
It is given that
A restaurant will select 1 card from a bowl to win a free lunch,
jimmy puts 10 cards in the bowl.
The bowl has a total of 150 cards in it
The odds of jimmy winning a free lunch is given by
= No. of chances / Total Outcomes
= 10/150
= 1/15
= 0.066
Therefore the odds of jimmy winning a free lunch is 0.066.
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Answer:
70.622 in³
Step-by-step explanation:
Volume of cylinder = 
= (3.14)(2.1^2)(5.1)
= 70.622 in³
Answer:
See explanation
Step-by-step explanation:
The constant of variation is found using the slope formula:

The given relation is
X : -2 , -3, -4, -5
Y : -5, -7.5,-10,-12.5
We can use any two ordered pair to find the constant of variation.
Using (-2,-5) and (-3,-7.5), we have

The constant of variation is 2.5
We need to repeat this for all the options to identify the one with -2.5 as slope.
unfortunately, you did not provide the remaining options.