Using the binomial distribution, it is found that there is a 0.857 = 85.7% probability that at least 2 of the rolls come up as a 3 or a 4.
For each die, there are only two possible outcomes, either a 3 or a 4 is rolled, or it is not. The result of a roll is independent of any other roll, hence, the <em>binomial distribution</em> is used to solve this question.
Binomial probability distribution
The parameters are:
- x is the number of successes.
- n is the number of trials.
- p is the probability of a success on a single trial.
In this problem:
- There are 9 rolls, hence
.
- Of the six sides, 2 are 3 or 4, hence

The desired probability is:

In which:

Then



Then:


0.857 = 85.7% probability that at least 2 of the rolls come up as a 3 or a 4.
For more on the binomial distribution, you can check brainly.com/question/24863377
The area of a rectangle is Base x height whereas the area of a triangle is Base x height divided by 2
(a+b)(a-b)=a^2 - b^2
so
<span>(4x-7)(4x+7) = 16x^2 - 49
answer
</span>16x^2 - 49
Answer:

Step-by-step explanation:
You have the following quadratic equation given in the problem:

You must make the equation equal to zero, as following:

Add like terms:

Now, to factor the equation, you must find two numbers whose sum is -2 and whose product is -15. Therefore, you have:
