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:

Step-by-step explanation:
You need 2 things in order to solve this equation:  a trig identity sheet and a unit circle.
You will find when you look on your trig identity sheet that 

so we will make that replacement, getting everything in terms of sin:

Now we will get everything on one side of the equals sign, set it equal to 0, and solve it:

We can factor out the sin(theta), since it's common in both terms:

Because of the Zero Product Property, either
 or
 or

Look at the unit circle and find which values of theta have a sin ratio of 0 in the interval from 0 to 2pi.  They are:

The next equation needs to first be solved for sin(theta):
 so
 so
 and
 and

Go back to your unit circle and find the values of theta where the sin is -1/2 in the interval.  They are:

 
        
             
        
        
        
Answer:
A
Step-by-step explanation:
please please please mark as brainliest