Answer:
At a certain pizza parlor,36 % of the customers order a pizza containing onions,35 % of the customers order a pizza containing sausage, and 66% order a pizza containing onions or sausage (or both). Find the probability that a customer chosen at random will order a pizza containing both onions and sausage.
Step-by-step explanation:
Hello!
You have the following possible pizza orders:
Onion ⇒ P(on)= 0.36
Sausage ⇒ P(sa)= 0.35
Onions and Sausages ⇒ P(on∪sa)= 0.66
The events "onion" and "sausage" are not mutually exclusive, since you can order a pizza with both toppings.
If two events are not mutually exclusive, you know that:
P(A∪B)= P(A)+P(B)-P(A∩B)
Using the given information you can use that property to calculate the probability of a customer ordering a pizza with onions and sausage:
P(on∪sa)= P(on)+P(sa)-P(on∩sa)
P(on∪sa)+P(on∩sa)= P(on)+P(sa)
P(on∩sa)= P(on)+P(sa)-P(on∪sa)
P(on∩sa)= 0.36+0.35-0.66= 0.05
I hope it helps!
Answer:
x - y + z = 8
2x +3y -z= -2
3x - 2y -9z = 9
Step-by-step explanation:
[1 - 1 1 8]
[2 3 -1 -2]
[3 -2 -9 9]
9514 1404 393
Answer:
C. (9, 18)
Step-by-step explanation:
Given R(3, 5), a dilation by a factor of 3 will multiply each coordinate to give ...
(9, 15)
Then the translation up by 3 will give you the image coordinates ...
(x, y) ⇒ (x, y+3)
(9, 15) ⇒ (9, 15 +3) = (9, 18)
The coordinates of R' are (9, 18), matching choice C.
_____
<em>Comment on multiple choice answers</em>
As it often does, here it works to "guess" the answer that has the coordinates that are most-repeated. An x-coordinate of 9 is part of 3 answer choices; a y-coordinate of 18 is the only repeated value in the answer choices. If you were to guess, an appropriate guess would be (9, 18). That happens to be correct in this case.
Answer:
(6, -2)
Step-by-step explanation:
To get to x=1 from x=-2, you must add 3 to the x-coordinate. Only one answer choice has an x-coordinate that is 3 more than that of the given point:
3 + 3 = 6
The image point is (6, -2).
_____
<em>Check</em>
To get from a y-coordinate of 5 to an image point y-coordinate of 1, you must subtract 4. If you subtract 4 from the y-coordinate of (3, 2), you get 2-4 = -2, the y-coordinate in the chosen answer above.
Answer:
The measure of anle MNP is
Explanation:
The image attached shows the figure corresponding to this question.
The <em>angle MNP</em>, wich is also the angle LNP, is formed by the intersection of a secant and a tanget to a circle.
Then, you can use the theorem:
- the angle formed by a secant and a tangent to a circle that intersect outside the circle is half the difference of the major arc minus the minor arc.
The major arc formed is identified with the letter x and the minor arc is identified witht he letter y. Thus, the measure of the angle MNP is half the differenc x - y:
