Sets l, m, and n are shown. which of the sets represents l ∪ (m ∩ n) (the union of l with the intersection of sets m and n)? l = {0, 20, 40, 80, 100} m = {5, 10, 15, 20, 25} n = {10, 20, 30, 40, 50} a) {0, 5, 10, 15, 20, 25, 30, 40, 50, 80, 100} b) {0, 10, 20, 40, 80, 100} c) {20, 40} d) {20}

B) L ∪ (M ∩ N)={0,10,20,40,80,100}

Step-by-step explanation:

The given sets are;

L = {0, 20, 40, 80, 100}

M = {5, 10, 15, 20, 25}

and

N = {10, 20, 30, 40, 50}

(M ∩ N) are elements in set M and set N

(M ∩ N) ={10,20}

The elements in L ∪ (M ∩ N)  are elements in L or M ∩ N or both

L ∪ (M ∩ N)={0,10,20,40,80,100}

The correct choice is B.

B

Step-by-step explanation:

L ∪ (M ∩ N)  means take "common" between M and N and take "sum of that and L".

Let's find (M ∩ N) (common between M and N):

We know

M = {5, 10, 15, 20, 25} , and

N = {10, 20, 30, 40, 50}

Thus, the common elements are 10 & 20, thus (M ∩ N) = {10,20}

Now we have:

L = {0, 20, 40, 80, 100}

(M ∩ N) = {10,20}

So sum of L and (M ∩ N)  are all the unique elements of both the sets. They are 0, 10, 20, 40, 80, 100, or Option B

answer: expected value of x = 1.0

step-by-step explanation:

p(x=0) = 0.25

p(x=1) = 0.50

p(x=2) = 0.25

expected value for x = 0×0.25 + 1×0.5 + 2×0.25 = 1.0

the answer is b: 18

step-by-step explanation:

use the pythagorean theorem to .

a^2+b^2=c^2

plug 18 for "r"

the 2 legs are 18 and 24

18^2+24^2=c^2

324+576=c^2

900=c^2

c=30

30-12=18

18 is the radius

: )