Using the binomial distribution, the probabilities are given as follows:
a) 0.4159 = 41.59%.
b) 0.5610 = 56.10%.
c) 0.8549 = 85.49%.
<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.
For this problem, the values of the parameters are:
n = 3, p = 0.76.
Item a:
The probability is P(X = 2), hence:
![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 = 2) = C_{3,2}.(0.76)^{2}.(0.24)^{1} = 0.4159](https://tex.z-dn.net/?f=P%28X%20%3D%202%29%20%3D%20C_%7B3%2C2%7D.%280.76%29%5E%7B2%7D.%280.24%29%5E%7B1%7D%20%3D%200.4159)
Item b:
The probability is P(X < 3), hence:
P(X < 3) = 1 - P(X = 3)
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 = 3) = C_{3,3}.(0.76)^{3}.(0.24)^{0} = 0.4390](https://tex.z-dn.net/?f=P%28X%20%3D%203%29%20%3D%20C_%7B3%2C3%7D.%280.76%29%5E%7B3%7D.%280.24%29%5E%7B0%7D%20%3D%200.4390)
Then:
P(X < 3) = 1 - P(X = 3) = 1 - 0.4390 = 0.5610 = 56.10%.
Item c:
The probability is:
![P(X \geq 2) = P(X = 2) + P(X = 3) = 0.4159 + 0.4390 = 0.8549](https://tex.z-dn.net/?f=P%28X%20%5Cgeq%202%29%20%3D%20P%28X%20%3D%202%29%20%2B%20P%28X%20%3D%203%29%20%3D%200.4159%20%2B%200.4390%20%3D%200.8549)
More can be learned about the binomial distribution at brainly.com/question/24863377
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Answer:
Part a) The measure of the missing angle is ![90\°](https://tex.z-dn.net/?f=90%5C%C2%B0)
Part b) The triangle of the figure is a right triangle
Part c) The triangle of the figure is a scalene triangle
Step-by-step explanation:
we know that
The sum of the interior angles of a triangle is equal to ![180\°](https://tex.z-dn.net/?f=180%5C%C2%B0)
so
Let
x------> the missing angle
we know that
![x\°+50\°+40\°=180\°](https://tex.z-dn.net/?f=x%5C%C2%B0%2B50%5C%C2%B0%2B40%5C%C2%B0%3D180%5C%C2%B0)
solve for x
![x=180\°-90\°=90\°](https://tex.z-dn.net/?f=x%3D180%5C%C2%B0-90%5C%C2%B0%3D90%5C%C2%B0)
The triangle of the figure is a right triangle --------> by its angles
Because the triangle has an angle measure of ![90\°](https://tex.z-dn.net/?f=90%5C%C2%B0)
The triangle of the figure is a scalene triangle --------> by its sides
Because the three angles and the three sides measures are different
Factor out 18.
The factors for 18 are as listed:
1, 2, 3, 6, 9, 18
Now factor out 30.
The factors for 30 are as listed:
1, 2, 3, 5, 6, 10, 15, 30
Now look at the factors that are both factors for 18 and 30.
So, the common factors are 2, 3, and 6.
Answer:
Step-by-step explanation:
Remark
The way this is worded, it sounds like it is a horizontal distance. However by the marking it looks like they want the hypotenuse. Life can be very confusing sometimes.
The angle of the triangle that you need to know is the one on the right. The line of sight line is parallel to the base of the triangle. So the angle on the right is 8 degrees by the Z theorem.
Solution
Sin(8) = 1817 / x Multiply both sides by x
x*sin(8) = 1817 Divide by sin(8)
x = 1817/sin(8)
sin(8) = 0.1392
x = 1817/0.1392
x = 13055.7
Note
Watch how you do this. I would put it into your calculator as
1817
÷
sin(8)
=
If you use the rounded answer I gave for sin(8), you might get it wrong. This is a big distance and you should just use the exact number you get for sin(8).
They have to be at least 40 abut less than 70, so 40 < (underlined) x < 70.
<span>They have to be at least 60 inches but less than 75 inches tall, so 60 < (underlined) y < 75. </span>
<span>Graph the following lines: </span>
<span>x = 40 </span>
<span>x = 70 (dotted) </span>
<span>y =60 </span>
<span>y= 75 (dotted) </span>
<span>The square the four lines make is the answer. I hoped that help!</span>