Answer:
a. independent event P(AuB)=P(A)+P(B)
b. mutually exclusive event P(AuB) = P(A) + P(B) - P(AnB)
c. independent event P(A and B) = P(A).P(B)
d. complement P(A') = 1 - P(A)
Step-by-step explanation:
a. For two events A and B the union of the two sets is simply all the elements present in both set. This can be expressed as
P(AuB)=P(A)+P(B)
b. Two events are said to be mutually exclusive if they cannot occur at the same time. i.e no same element must be present in both events at a time. This can be expressed as
P(AuB) = P(A) + P(B) - P(AnB)
c. event A and event B are said to be independent if the incidence of event A does not affect the probability of the event B.
This can be expressed as
P(A and B) = P(A).P(B)
d. complement of an event are simply all the occurrence not in he set but in the universal set.
the complement of set A can be expressed as
P(A') = 1 - P(A)
Answer:
12.
The cereal tastes like wheat
<h2>
Hello!</h2>
The answer is:
The correct option is:
B) ![5^{12}\div5^{4}=5^{8}](https://tex.z-dn.net/?f=5%5E%7B12%7D%5Cdiv5%5E%7B4%7D%3D5%5E%7B8%7D)
<h2>
Why?</h2>
To solve the problem, we need to remember the quotient of power property, it's defined by the following relation:
![\frac{a^{m} }{a^{n} }=a^{m-n}](https://tex.z-dn.net/?f=%5Cfrac%7Ba%5E%7Bm%7D%20%7D%7Ba%5E%7Bn%7D%20%7D%3Da%5E%7Bm-n%7D)
If we have a quotienf of powers that have the same base, we need to keep the same base and subtract the exponent of the denominator power to the exponent of the numerator power.
So, we are given the expression:
![5^{12}\div5^{4}](https://tex.z-dn.net/?f=5%5E%7B12%7D%5Cdiv5%5E%7B4%7D)
Which is equal to write:
![\frac{5^{12} }{5^{4}}](https://tex.z-dn.net/?f=%5Cfrac%7B5%5E%7B12%7D%20%7D%7B5%5E%7B4%7D%7D)
Then, calculating we have:
![\frac{5^{12} }{5^{4}}=5^{12-4}=5^{8}](https://tex.z-dn.net/?f=%5Cfrac%7B5%5E%7B12%7D%20%7D%7B5%5E%7B4%7D%7D%3D5%5E%7B12-4%7D%3D5%5E%7B8%7D)
Hence, the answer is:
B) ![\frac{5^{12} }{5^{4}}=5^{8}](https://tex.z-dn.net/?f=%5Cfrac%7B5%5E%7B12%7D%20%7D%7B5%5E%7B4%7D%7D%3D5%5E%7B8%7D)
or
![5^{12}\div5^{4}=5^{8}](https://tex.z-dn.net/?f=5%5E%7B12%7D%5Cdiv5%5E%7B4%7D%3D5%5E%7B8%7D)
Have a nice day!
Answer:
20
Step-by-step explanation:
→ First find the value of x and y
x + y = 5
x - y = 4
→ Add the equations to cancel out the y's
2x = 9
→ Divide both sides by 2 to find the value of x
x = 4.5
→ Substitute x = 4.5 back into x - y = 4 to find the value of y
4.5 - y = 4
→ Minus 4.5 from both sides to isolate -y
-y = -0.5
→ Multiply everything by -1
y = 0.5
→ Substitute x = 4.5 and y = 0.5 into x² - y²
4.5² - 0.5² = 20.25 - 0.25 = 20