Answer:
![P(X \geq 2) = 1-P(X](https://tex.z-dn.net/?f=%20P%28X%20%5Cgeq%202%29%20%3D%201-P%28X%3C2%29%20%3D%201-P%28X%20%5Cleq%201%29%20%3D1-%20%5BP%28X%3D0%29%20%2BP%28X%3D1%29%5D)
And we can find the individual probabilities using the probability mass function and we got:
![P(X=0) = (30C0) (0.05)^0 (1-0.05)^{30-0} =0.2146](https://tex.z-dn.net/?f=%20P%28X%3D0%29%20%3D%20%2830C0%29%20%280.05%29%5E0%20%281-0.05%29%5E%7B30-0%7D%20%3D0.2146%20%20)
![P(X=1) = (30C1) (0.05)^1 (1-0.05)^{30-1} = 0.3389](https://tex.z-dn.net/?f=%20P%28X%3D1%29%20%3D%20%2830C1%29%20%280.05%29%5E1%20%281-0.05%29%5E%7B30-1%7D%20%3D%200.3389%20)
And replacing we got:
![P(X \geq 2) = 1-P(X](https://tex.z-dn.net/?f=%20P%28X%20%5Cgeq%202%29%20%3D%201-P%28X%3C2%29%20%3D%201-P%28X%20%5Cleq%201%29%20%3D1-%20%5BP%28X%3D0%29%20%2BP%28X%3D1%29%5D%20%3D%201-%5B0.2146%2B0.3389%5D%20%3D0.4465%20)
Step-by-step explanation:
Previous concepts
The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".
Let X the random variable of interest, on this case we now that:
The probability mass function for the Binomial distribution is given as:
Where (nCx) means combinatory and it's given by this formula:
Solution to the problem
For this case we want this probability:
![P(X \geq 2)](https://tex.z-dn.net/?f=%20P%28X%20%5Cgeq%202%29)
And we can use the complement rule and we got:
![P(X \geq 2) = 1-P(X](https://tex.z-dn.net/?f=%20P%28X%20%5Cgeq%202%29%20%3D%201-P%28X%3C2%29%20%3D%201-P%28X%20%5Cleq%201%29%20%3D1-%20%5BP%28X%3D0%29%20%2BP%28X%3D1%29%5D)
And we can find the individual probabilities using the probability mass function and we got:
![P(X=0) = (30C0) (0.05)^0 (1-0.05)^{30-0} =0.2146](https://tex.z-dn.net/?f=%20P%28X%3D0%29%20%3D%20%2830C0%29%20%280.05%29%5E0%20%281-0.05%29%5E%7B30-0%7D%20%3D0.2146%20%20)
![P(X=1) = (30C1) (0.05)^1 (1-0.05)^{30-1} = 0.3389](https://tex.z-dn.net/?f=%20P%28X%3D1%29%20%3D%20%2830C1%29%20%280.05%29%5E1%20%281-0.05%29%5E%7B30-1%7D%20%3D%200.3389%20)
And replacing we got:
![P(X \geq 2) = 1-P(X](https://tex.z-dn.net/?f=%20P%28X%20%5Cgeq%202%29%20%3D%201-P%28X%3C2%29%20%3D%201-P%28X%20%5Cleq%201%29%20%3D1-%20%5BP%28X%3D0%29%20%2BP%28X%3D1%29%5D%20%3D%201-%5B0.2146%2B0.3389%5D%20%3D0.4465%20)
Answer:
59 degrees
Step-by-step explanation:
98+23=121
180 (total angle in a triangle) - 121 = 59 degrees
brainliest plz
Answer:
Step-by-step explanation:
+ we take t- number of tickets and each ticket cost $7.
So t is too the number of people who buy tickets, then
![0\leq t\leq 200](https://tex.z-dn.net/?f=0%5Cleq%20t%5Cleq%20200)
A) We can calculate the amount of money: M= 7t where ![0\leq t\leq 200](https://tex.z-dn.net/?f=0%5Cleq%20t%5Cleq%20200)
B) The domain for t is
, t is an integer.
C) The range for the amount M:
![0*7\leq M\leq 200*7\\0\leq M\leq 1400](https://tex.z-dn.net/?f=0%2A7%5Cleq%20M%5Cleq%20200%2A7%5C%5C0%5Cleq%20M%5Cleq%201400)
The standard form of the equation of a circle is (x-h)^2 + (y-k)^2 = r^2, where (h,k) is the center of the circle, (x,y) is a point of the circle, and r is the length of the radius of the circle. When the equation of a circle is written, h,k, and r are numbers, while x and y are still variables. (x-2)^2 + (y-k)^2 = 16 is an example of a circle. The problem gives us two of the three things that a circle has, a point (5,9) and the center (-2,3). We need to find the radius in order to write the equation. We substitute -2 for h, 3 for k, 5 for x, and 9 for y to get (5 - (-2))^2 + (9 - 3)^2 = r^2 We simplify: 49 + 36 = r^2, r^2 = 85. We only need to know r^2 because the equation of a circle has r^2. We now have all the information to write the equation of a circle. (x + 2)^2 + (y - 3)^2 = 85.
Each cow eats 12 pounds then 24 will eat 288 pounds so to know how many days it will last we will divide 10656 by 288 which is 37
so it will last for 37 days.