Answer:
5/8
Explanation: 8/8 - 3/8 = 5/8
Hey, okay so each quadrant of the plane is 90 degrees. Added all up together, if a circle was drawn with its center being the origin, it would be 360 degrees. 180 degrees is half of 360, and two times 90. So 180 would take up two quadrants.
Now, since the problem states the object was rotated ABOUT THE ORIGIN, you have to account for the position of the entire object within its quadrant, rather than just a single point of the object. So, the original object has points at (-1, -2), (-4, -4), and (-3, -7). Now, the way I usually do a problem like this is that I find the point closest to the origin (in this case, (-1, -2)), and I draw a little imaginary line from that point to the origin. Then, I flip that little line according to what the problem tells me to (in this case, 180 degrees). So my little imaginary line is now from the origin to the point (1, 2) instead of the point (-1, -2). Then I do the same for all the other points.
I hope this helps!!!
Using the binomial distribution, there is a 0.2094 = 20.94% probability that exactly 5 of them stayed on their job for less than one-year.
<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, there is a fixed number of independent trials, each with only two possible outcomes, hence the <em>binomial distribution </em>is used. The values of the parameters are:
n = 15, p = 0.36.
The probability is P(X = 5), 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 = 5) = C_{15,5}.(0.36)^{5}.(0.64)^{10} = 0.2094](https://tex.z-dn.net/?f=P%28X%20%3D%205%29%20%3D%20C_%7B15%2C5%7D.%280.36%29%5E%7B5%7D.%280.64%29%5E%7B10%7D%20%3D%200.2094)
0.2094 = 20.94% probability that exactly 5 of them stayed on their job for less than one-year.
More can be learned about the binomial distribution at brainly.com/question/24863377
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In this scenario, the parameter is the sample proportion, which is of 0.7.
<h3>What is the parameter?</h3>
- When a hypothesis is tested, the parameter is the information obtained from the sample, mean or proportion.
- In this case, it is the <em>sample proportion</em>, which is the <u>number of desired outcomes divided by the number of total outcomes</u>.
She goes to the correct object in 70 of those 100 trials, hence:
![p = \frac{70}{100} = 0.7](https://tex.z-dn.net/?f=p%20%3D%20%5Cfrac%7B70%7D%7B100%7D%20%3D%200.7)
The parameter is the sample proportion, which is of 0.7.
You can learn more about sample proportion at brainly.com/question/25868626