Answer:
C. √2 - 1
Step-by-step explanation:
If we draw a square from the center of the large circle to the center of one of the small circles, we can see that the sides of the square are equal to the radius of the small circle (see attached diagram)
Let r = the radius of the small circle
Using Pythagoras' Theorem 
(where a and b are the legs, and c is the hypotenuse, of a right triangle)
to find the diagonal of the square:
So the diagonal of the square = 
We are told that the radius of the large circle is 1:
⇒ Diagonal of square + r = 1
Using the quadratic formula to calculate r:
As distance is positive, 
only
You can first distribute the number into the parenthesis: 3n + 2 - 8n. Now, combine the like terms (n): -5n + 2. It can either be -5n + 2 or 2 - 5n.
Answer:
to get the probability you add the number of figure all together
divide the number of spheres with the total
ie
2 ÷ 10
you get 1÷ 5
you get the answer as 0.2
E and F are two events and that P(E)=0.3 and P(F|E)=0.5. Thus, P(E and F)=0.15
Bayes' theorem is transforming preceding probabilities into succeeding probabilities. It is based on the principle of conditional probability. Conditional probability is the possibility that an event will occur because it is dependent on another event.
P(F|E)=P(E and F)÷P(E)
It is given that P(E)=0.3,P(F|E)=0.5
Using Bayes' formula,
P(F|E)=P(E and F)÷P(E)
Rearranging the formula,
⇒P(E and F)=P(F|E)×P(E)
Substituting the given values in the formula, we get
⇒P(E and F)=0.5×0.3
⇒P(E and F)=0.15
∴The correct answer is 0.15.
If, E and F are two events and that P(E)=0.3 and P(F|E)=0.5. Thus, P(E and F)=0.15.
Learn more about Bayes' theorem on
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