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
Given:
is subtracted from 3.
To find:
The result of the given statement in the standard form of the polynomial.
Solution:
We need to find the result when
is subtracted from 3.
So, the resulted polynomial can be written as:
![P(x)=3-(3x+7)^2](https://tex.z-dn.net/?f=P%28x%29%3D3-%283x%2B7%29%5E2)
On simplification, we get
![[\because (a+b)^2=a^2+2ab+b^2]](https://tex.z-dn.net/?f=%5B%5Cbecause%20%28a%2Bb%29%5E2%3Da%5E2%2B2ab%2Bb%5E2%5D)
Therefore, the resulted polynomial in standard form is
.
The constant is -12. I think of constant as the "lonely little number".... Hope this helped =)