I need help with 10-12
1 answer:
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Answer:
(a)
(b) 10
(c)
(d) 0
(e) 1024
Step-by-step explanation:
(a)
A = {x ∈ Z | 0 < x, x² ≤ 100}
We need to find all the elements of given set.
The given conditions are
... (1)
Taking square root on both sides.
.... (2)
Using (1) and (2) we get
Since x ∈ Z,
(b)
We need to find the value of | {x ∈ Z | 0 < x, x² ≤ 100}| or |A|. It means have to find the number of elements in set A.
| {x ∈ Z | 0 < x, x² ≤ 100}| = 10
(c)
B = {x ∈ Z | x > 10, x² ≤ 100}
We need to find all the elements of given set.
The given conditions are
... (3)
It means
.... (4)
Inequality (3) and (4) have no common solution, so B is null set or empty set.
(d)
We need to find the value of |{x ∈ Z | x > 10, x² ≤ 100}| or |B|. It means have to find the number of elements in set B.
|{x ∈ Z | x > 10, x² ≤ 100}| = 0
(e)
We need to find the value of | P(A) |. P(A) is the power set of set A.
Number of elements of a power set is
where, n is the number of elements of set A.
We know that the number of elements of set is 10. So the value of |P(A)| is
Therefore |P(A)|=1024.
Assuming that there is only 1 bag, there is a set value (we can call that b) for that cost. In addition, there is a set value for what the bag weighs. We can call that m. Therefore, for x pounds, we multiply the amount per pound by the amount of pounds (x) to get m*x+b=cost (y). In a line mx+b=y, m is the rate of change. m can be found by
Using that, with the cost being the y values and the amount of pounds being the x values, we have (20, 25) at one point and (50, 40) at another. For our equation, we have
Dividing both the numerator and denominator by 15 (we know they are both factors of 15 with a little guess and check), we have 1/2 or 0.5 as our answer
Using that, with the cost being the y values and the amount of pounds being the x values, we have (20, 25) at one point and (50, 40) at another. For our equation, we have
Dividing both the numerator and denominator by 15 (we know they are both factors of 15 with a little guess and check), we have 1/2 or 0.5 as our answer