Answer: The probability that a randomly selected adult doesn’t regularly consume at least one of these two products is 30%
Be:
A: Adults regularly consume coffee
B: Adults regularly consume carbonated soda
C: Adults doesn't regularly consume at leas one of these two products.
55% of all adults regularly consume coffee→P(A)=55%=55/100→P(A)=0.55
45% regularly consume carbonated soda→P(B)=45%=45/100→P(B)=0.45
70% regularly consume at least one of these two products→P(A U B)=70%=70/100→P(A U B)=0.70
a) What is the probability that a randomly selected adult regularly consumes both coffee and soda?
P(A ∩ B)=?
P(A U B)=P(A) + P(B) - P(A ∩ B)
Replacing P(A U B)=0.70; P(A)=0.55; and P(B)=0.45 in the equation above:
0.70=0.55 + 0.45 - P(A ∩ B)→
0.70=1.00 - P(A ∩ B)
Solving for P(A ∩ B): Subtracting 1.00 both sides of the equation:
0.70-1.00=1.00 - P(A ∩ B) -1.00→
-0.30 = - P(A ∩ B)
Multiplying both sides of the equation by (-1):
(-1)(-0.30) = (-1)[ - P(A ∩ B)]→
0.30 = P(A ∩ B)→
P(A ∩ B) =0.30→
P(A ∩ B) = (0.30)*100%→
P(A ∩ B) = 30%
Answer: The probability that a randomly selected adult regularly consumes both coffee and soda is 70%
b. What is the probability that a randomly selected adult doesn’t regularly consume at least one of these two products?
P(C)=?
P(A U B) + P(C)=1
Replacing P(A U B)= 0.70 in the equation above:
0.70+P(C)=1
Solving for P(C). Subtracting 0.70 both sides of the equation:
0.70+P(C)-0.70=1-0.70→
P(C)=0.30→
P(C)=(0.30)*100%→
P(C)=30%
Answer: The probability that a randomly selected adult doesn’t regularly consume at least one of these two products is 30%
<span>If you want to know the domain of a function through its graph, I simply have to "scan" the graph of the function from left to right along the X axis and see the ranges of values of the x for which it exists a value on the Y axis. In this graph it is observed that for any value of X there will be a value of Y, so that the domain of the graph function is all the real values of X</span><span>
the domain of the graphed function is</span><span>
{x | x is a real number}</span>
Answer: The bill was $150 without tip and 172.50 with tip
Step-by-step explanation:
Answer:
Circumcenter - (1.5, -0.5)
Orthocenter - (0, -2)
Centroid - (1.3, 0.7)
hope this helps :)