A) Here, sum of two non-adjacent angles: 52 + 25 = 77
Now, ∠3 = 180 - 77 [ sum of all angles in a triangle is 180 ]
so, ∠3 = 103
Now, ∠3 + ∠4 = 180 [ Supplementary angles ]
So, ∠4 = 180 - ∠3
∠4 = 180 - 103 = 77
∠4 = 77 [ which is sum of two non-adjacent angles ]
....Hence proved.
b) m∠4 = 77
[ Solved in previous section ]
Hope this helps!
X=5 , x=3 - just plug in 2 and 3 into x and the lines will make it positive instead of negative
Using the binomial distribution, it is found that the expected values are given by:
a) 120.
b) 150.
<h3>What is the binomial probability distribution?</h3>
It is the probability of <u>exactly x successes on n repeated trials, with p probability</u> of a success on each trial.
The expected value of the binomial distribution is:
E(X) = np
In this problem, for both items, we consider that the number cube is rolled 180 times, hence n = 180.
Item a:
4 of the 6 possible values are greater than 2, hence p = 4/6 = 2/3.
The expected value is given by:
E(X) = 180 x 2/3 = 120.
Item b:
5 of the 6 values are less than 6, hence p = 5/6.
The expected value is given by:
E(X) = 180 x 5/6 = 150.
More can be learned about the binomial distribution at brainly.com/question/24863377
Answer:
Radius of sphere is 3 units.
Step-by-step explanation:
Volume of sphere is given by 
surface area of sphere is given by 
where r is the radius of the sphere.
Given that
The number of cubic units in the volume of a sphere is equal to the number of square units in the surface area of the sphere.
we equate formula of Volume of sphere and surface area of sphere
assuming r as the radius.
thus,
Thus, radius of sphere is 3 units.
Answer:
Step-by-step explanation:
Let us solve
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