Using the binomial distribution, it is found that there is a 0.2617 = 26.17% probability that at least 8 but at most 10 students will complete their assignments before the due date.
For each student, there are only two possible outcomes, either they complete the assignment, or they do not. The probability of a student completing the assignment is independent of any other student, hence the <em>binomial distribution</em> is used to solve this question.
<h3>What is the binomial distribution formula?</h3>
The formula is:
![P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}](https://tex.z-dn.net/?f=P%28X%20%3D%20x%29%20%3D%20C_%7Bn%2Cx%7D.p%5E%7Bx%7D.%281-p%29%5E%7Bn-x%7D)
![C_{n,x} = \frac{n!}{x!(n-x)!}](https://tex.z-dn.net/?f=C_%7Bn%2Cx%7D%20%3D%20%5Cfrac%7Bn%21%7D%7Bx%21%28n-x%29%21%7D)
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:
- The probability of a student successfully completing an assignment before the due date is 0.65, hence p = 0.65.
- Ten students are selected at random, hence n = 10.
The probability is:
![P(X \geq 8) = P(X = 8) + P(X = 9) + P(X = 10)](https://tex.z-dn.net/?f=P%28X%20%5Cgeq%208%29%20%3D%20P%28X%20%3D%208%29%20%2B%20P%28X%20%3D%209%29%20%2B%20P%28X%20%3D%2010%29)
In which:
![P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}](https://tex.z-dn.net/?f=P%28X%20%3D%20x%29%20%3D%20C_%7Bn%2Cx%7D.p%5E%7Bx%7D.%281-p%29%5E%7Bn-x%7D)
![P(X = 8) = C_{10,8}.(0.65)^{8}.(0.35)^{2} = 0.1757](https://tex.z-dn.net/?f=P%28X%20%3D%208%29%20%3D%20C_%7B10%2C8%7D.%280.65%29%5E%7B8%7D.%280.35%29%5E%7B2%7D%20%3D%200.1757)
![P(X = 9) = C_{10,9}.(0.65)^{9}.(0.35)^{1} = 0.0725](https://tex.z-dn.net/?f=P%28X%20%3D%209%29%20%3D%20C_%7B10%2C9%7D.%280.65%29%5E%7B9%7D.%280.35%29%5E%7B1%7D%20%3D%200.0725)
![P(X = 10) = C_{10,10}.(0.65)^{10}.(0.35)^{0} = 0.0135](https://tex.z-dn.net/?f=P%28X%20%3D%2010%29%20%3D%20C_%7B10%2C10%7D.%280.65%29%5E%7B10%7D.%280.35%29%5E%7B0%7D%20%3D%200.0135)
Then:
![P(X \geq 8) = P(X = 8) + P(X = 9) + P(X = 10) = 0.1757 + 0.0725 + 0.0135 = 0.2617](https://tex.z-dn.net/?f=P%28X%20%5Cgeq%208%29%20%3D%20P%28X%20%3D%208%29%20%2B%20P%28X%20%3D%209%29%20%2B%20P%28X%20%3D%2010%29%20%3D%200.1757%20%2B%200.0725%20%2B%200.0135%20%3D%200.2617)
0.2617 = 26.17% probability that at least 8 but at most 10 students will complete their assignments before the due date.
More can be learned about the binomial distribution at brainly.com/question/14424710
The slope intercept form is y=mx+b
in this case y=-x
y=(-1)x + 0
so the slope m=-1 and y-intercept which is b is 0
8x^7y^3 * 3x^3y
Multiply 8 * 3 = 24
Multiply x^7 * x^3 = x^10
Multiply y^3 * y = y^4
Answer: 24x^10y^4
24/6=4
4 belongs to set of integers, even, real, natural numbers.
If a number belongs to the set of rational numbers it must be an integer.
Hello!
This question is about relating vertical angles and their arc lengths.
Vertical angles have equal angle measures, meaning that they will also have the same arc measure.
We know that arc QR and arc UT have equal angle measures because they are formed with vertical angles.
That means since we know the measure of the other two arcs, which will both be 125 since they are formed with vertical angles, we can solve for the two unknown arc lengths.
A circle is 360 degrees, meaning that we can make the following equation,
![360=QR+UT+125+125](https://tex.z-dn.net/?f=360%3DQR%2BUT%2B125%2B125)
![QR+UT+250=360](https://tex.z-dn.net/?f=QR%2BUT%2B250%3D360)
![QR+UT=110](https://tex.z-dn.net/?f=QR%2BUT%3D110)
Since QR = UT
![QR/UT=55](https://tex.z-dn.net/?f=QR%2FUT%3D55)
Now, we can solve for arc URT using all the arc measures we have.
![URT=125+55+125](https://tex.z-dn.net/?f=URT%3D125%2B55%2B125)
![URT=305](https://tex.z-dn.net/?f=URT%3D305)
Hope this helps!