The question is what numbers satisfy A ∩ C.
The symbol ∩ means intersection, .i.e. you need to find the numbers that belong to both sets A and C. Those numbers might belong to the set C or not, because that is not a restriction.
Then lets find the numbers that belong to both sets, A and C.
Set A: perfect squares from A to 100:
1^2 = 1
2^2 = 4
3^2 = 9
4^2 = 16
5^2 = 25
6^2 = 36
7^2 = 49
8^2 = 64
9^2 = 81
10^2 = 100
=> A = {1, 4, 9, 16, 25, 36, 49, 64, 81, 100}
Set C: perfect fourths
1^4 = 1
2^4 = 16
3^4 = 81
C = {1, 16, 81?
As you see, all the perfect fourths are perfect squares, so the intersection of A and C is completed included in A. this is:
A ∩ C = C or A ∩ C = 1, 16, 81
On the other hand, the perfect cubes are:
1^3 = 1
2^3 = 8
3^3 = 27
4^3 = 81
B = {1, 8, 27, 81}
That means that the numbers 1 and 81 belong to the three sets, A, B, and C.
In the drawing you must place the number 16 inside the region that represents the intersection of A and C only, and the numbers 1 and 81 inside the intersection of the three sets A, B and C.
Answer:
- boat: 16 mph
- current: 4 mph
Step-by-step explanation:
speed = distance / time
The rate downriver is (60 mi)/(3 h) = 20 mi/h.
The rate upriver is (60 mi)/(5 h) = 12 mi/h.
The rate of the boat in still water is the average of these:
(20 +12)/2 mi/h = 16 mi/h
The rate of the current is the difference between the boat speed and actual speed:
16 mi/h - 12 mi/h = 4 mi/h
Answer:
Step-by-step explanation:
so u see 8x4 which is 32 and u can see its 90 degress because of the square and also a acute so x is 3 and y is 5
Answer:
Mabel used 12 dimes and 7 quarters to pay for her granola bar.
Step-by-step explanation:
A dime= 10 A quarter= 25
12×10=120
7×25=175
175+120=295
12-7=5
Answer:
fully simplified answer: x^2-2x+8
Step-by-step explanation:
