Answer:
12100
Step-by-step explanation:
If the number B of federally insured banks could be approximated by B ( t ) = − 329.4 t + 13747 from 1985 to 2007 where t = 0 correspond to year 1985
In order to determine the amount of federally insured banks that were there in 1990, we will first calculate the year range from initial time 1985 till 1990
The amount of time during this period is 5years. Substituting t = 5 into the modeled equation will give;
B ( t ) = − 329.4 t + 13747
B(5) = -329.4(5) + 13747
B(5) = -1647+13747
B(5) = 12100
This shows that there will be 12100 federally insured banks are there in the year 1990.
Answer:
Step-by-step explanation:
REcall the following definition of induced operation.
Let * be a binary operation over a set S and H a subset of S. If for every a,b elements in H it happens that a*b is also in H, then the binary operation that is obtained by restricting * to H is called the induced operation.
So, according to this definition, we must show that given two matrices of the specific subset, the product is also in the subset.
For this problem, recall this property of the determinant. Given A,B matrices in Mn(R) then det(AB) = det(A)*det(B).
Case SL2(R):
Let A,B matrices in SL2(R). Then, det(A) and det(B) is different from zero. So
.
So AB is also in SL2(R).
Case GL2(R):
Let A,B matrices in GL2(R). Then, det(A)= det(B)=1 is different from zero. So
.
So AB is also in GL2(R).
With these, we have proved that the matrix multiplication over SL2(R) and GL2(R) is an induced operation from the matrix multiplication over M2(R).
Volume of a cone = (1/3) pi x r^2 x h
Volume of a cylinder = pi x r^2 x h
Volume of the cylinder = pi x 2^2 x 3 = 37.68 cubic inches
Now set the volume for the cone to the volume of the cylinder and solve for the height.
37.68 = (1/3) x pi x r^2 x h
37.68 = (1/3) x pi x 3^2 x h
37.68 = (1/3) x pi x 9 x h
37.68 = 9.42 x h
h = 37.68 / 9.42
h = 4
The height of the cone is 4 cm.
Answer:
Option (i)
Step-by-step explanation:
{2} has only 1 subset i.e. {2} and no other subset. While { } or ∅ has no subset.