the number of elements in the union of the A sets is:5(30)−rAwhere r is the number of repeats.Likewise the number of elements in the B sets is:3n−rB
Each element in the union (in S) is repeated 10 times in A, which means if x was the real number of elements in A (not counting repeats) then 9 out of those 10 should be thrown away, or 9x. Likewise on the B side, 8x of those elements should be thrown away. so now we have:150−9x=3n−8x⟺150−x=3n⟺50−x3=n
Now, to figure out what x is, we need to use the fact that the union of a group of sets contains every member of each set. if every element in S is repeated 10 times, that means every element in the union of the A's is repeated 10 times. This means that:150 /10=15is the number of elements in the the A's without repeats counted (same for the Bs as well).So now we have:50−15 /3=n⟺n=45
Given:
A figure of a triangular prism.
Height of triangular base =
yd
Base of triangular base = 4 yd
Height of prism = 4 yd.
To find:
The volume of the triangular prism.
Solution:
Volume of a triangular prism is:
...(i)
Where, B is the area of triangular base and h is the height of the prism.
Area of triangular base is:




Putting
and h=4 in (i), we get




The volume of the triangular prism is 77.3 cubic yards. Therefore, the correct option is 2.
i think the answer is c :)
Answer:

Step-by-step explanation:
we know that
The surface area of the figure is equal to the lateral face of the triangular pyramid plus the lateral face of the rectangular prism plus the area of the base of the rectangular prism
step 1
Find the lateral face of the triangular prism
The lateral area is equal to the area of its four lateral triangular faces

step 2
Find the lateral area of the rectangular prism
The lateral area is equal to the perimeter of the base multiplied by the height

step 3
Find the area of the base of the rectangular prism

step 4
Find the surface area

Answer:
r = - 13 / 15 inches/week
Step-by-step explanation:
The numerator is 13
and the denominator is 15, then we have
r = - 13 / 15 inches/week
r < 0 since the water level of the lake fell