We are to show that if X ⊆ Y then (X ∪ Z) ⊆ (Y ∪ Z) for sets X, Y, Z.
Assume that a is a representative element of X, that is, a ∈ X. By the definition of union, a ∈ X ∪ Z. Now because X ⊆ Y and we assumed a ∈ X, then a ∈ Y by the definition of subset. And because a ∈ Y, then a ∈ Y ∪ Z by definition of union.
We chose our representative element, a, and showed that a ∈ X ∪ Y implies that a ∈ Y ∪ Z and this completes the proof.
Answer:
x = 10
Step-by-step explanation:
l n 20 + l n 5 = 2 l n x
ln (20×5) = ln x²
ln(100) = lnx²
100 = x²
x = +/- 10
Since logs of negative numebrs don't exist, we reject -10
1)
.
2)
.
3) The particle is moving right when the velocity function is positive:
or
.
4) When
the particle is slowing down because the acceleration is close to zero
the particle is speeding up when acceleration is increasing away from zero:
.
5)
.
Answer:
1 1/2
Step-by-step explanation:
The first step is to figure out the lightest and the heaviest bad. The lightest bag is 4 1/4 and the heaviest is 5 3/4. Now to subtract, you can't subtract this as a mixed fraction so turn each fraction into an improper fraction by multiplying the whole number by the denominator then adding the numerator to the product of the whole number multiplied by the denominator (if you didn't know numerator is the top and the denominator is the bottom. To find out 4 1/4 as an improper fraction follow these steps (4*4+1=17) so 4 1/4=17/4. The process is the same for 5 3/4 (5*4+3=23) so 5 3/4= 23/4. Now to subtract, you subtract the numerator but not the denominator. You subtract because the question asks how many more and that means to subtract 23/4-17/4= 6/4. Last step is to turn this back into a mixed fraction do that by dividing the numerator by the denominator, 6 divided by 4 equals 1.5 and turn the decimal into a fraction 1 is a whole number so you don't change that but the 5 behind the decimal needs to be changed so now 1.5= 1 5/10 and last step is simplify 1 1/2. Hope this helped :).
12x50=600 so 60 left
15x50=750 so 60 left
so the administration fee is 60
