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:
The 13th term is 81<em>x</em> + 59.
Step-by-step explanation:
We are given the arithmetic sequence:

And we want to find the 13th term.
Recall that for an arithmetic sequence, each subsequent term only differ by a common difference <em>d</em>. In other words:

Find the common difference by subtracting the first term from the second:

Distribute:

Combine like terms. Hence:

The common difference is (7<em>x</em> + 5).
To find the 13th term, we can write a direct formula. The direct formula for an arithmetic sequence has the form:

Where <em>a</em> is the initial term and <em>d</em> is the common difference.
The initial term is (-3<em>x</em> - 1) and the common difference is (7<em>x</em> + 5). Hence:

To find the 13th term, let <em>n</em> = 13. Hence:

Simplify:

The 13th term is 81<em>x</em> + 59.
Let's consider that number to be 'x'..
So, twice the number (2x) is 12 greater than than the half of the number.
So the equation will be like,
2x=12+x/2
Solving this further,
2x=(24+x)/2
=> 4x=24+x
=>4x-x=24
=>3x=24
=>x=8..
So the number is "8".
Answer:
n= 2/3m=6?
Step-by-step explanation: