Answer:
x+4=20 is a solution to 5(x+4)=100.
Step-by-step explanation:
Following PEMDAS, divide 5 from both sides of the equation 5(x+4)=100, and you have x+4=20 remaining.
This means that both equations have the same solution.
Answer:
The logarithmic function for x = 2y is written as y = log2 x or f(x) = log2 x. The number 2 is still called the base. In general, y = logb x is read, “y equals log to the base b of x,” or more simply, “y equals log base b of x.” As with exponential functions, b > 0 and b ≠ 1
Using the Poisson distribution, there is a 0.8335 = 83.35% probability that 2 or fewer will be stolen.
<h3>What is the Poisson distribution?</h3>
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by:
![P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}](https://tex.z-dn.net/?f=P%28X%20%3D%20x%29%20%3D%20%5Cfrac%7Be%5E%7B-%5Cmu%7D%5Cmu%5E%7Bx%7D%7D%7B%28x%29%21%7D)
The parameters are:
- x is the number of successes
- e = 2.71828 is the Euler number
is the mean in the given interval.
The probability that a rental car will be stolen is 0.0004, hence, for 3500 cars, the mean is:
![\mu = 3500 \times 0.0004 = 1.4](https://tex.z-dn.net/?f=%5Cmu%20%3D%203500%20%5Ctimes%200.0004%20%3D%201.4)
The probability that 2 or fewer cars will be stolen is:
![P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2)](https://tex.z-dn.net/?f=P%28X%20%5Cleq%202%29%20%3D%20P%28X%20%3D%200%29%20%2B%20P%28X%20%3D%201%29%20%2B%20P%28X%20%3D%202%29)
In which:
![P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}](https://tex.z-dn.net/?f=P%28X%20%3D%20x%29%20%3D%20%5Cfrac%7Be%5E%7B-%5Cmu%7D%5Cmu%5E%7Bx%7D%7D%7B%28x%29%21%7D)
![P(X = 0) = \frac{e^{-1.4}1.4^{0}}{(0)!} = 0.2466](https://tex.z-dn.net/?f=P%28X%20%3D%200%29%20%3D%20%5Cfrac%7Be%5E%7B-1.4%7D1.4%5E%7B0%7D%7D%7B%280%29%21%7D%20%3D%200.2466)
![P(X = 1) = \frac{e^{-1.4}1.4^{1}}{(1)!} = 0.3452](https://tex.z-dn.net/?f=P%28X%20%3D%201%29%20%3D%20%5Cfrac%7Be%5E%7B-1.4%7D1.4%5E%7B1%7D%7D%7B%281%29%21%7D%20%3D%200.3452)
![P(X = 2) = \frac{e^{-1.4}1.4^{2}}{(2)!} = 0.2417](https://tex.z-dn.net/?f=P%28X%20%3D%202%29%20%3D%20%5Cfrac%7Be%5E%7B-1.4%7D1.4%5E%7B2%7D%7D%7B%282%29%21%7D%20%3D%200.2417)
Then:
![P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0.2466 + 0.3452 + 0.2417 = 0.8335](https://tex.z-dn.net/?f=P%28X%20%5Cleq%202%29%20%3D%20P%28X%20%3D%200%29%20%2B%20P%28X%20%3D%201%29%20%2B%20P%28X%20%3D%202%29%20%3D%200.2466%20%2B%200.3452%20%2B%200.2417%20%3D%200.8335)
0.8335 = 83.35% probability that 2 or fewer will be stolen.
More can be learned about the Poisson distribution at brainly.com/question/13971530
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Answer:
x = 40°
Step-by-step explanation:
Two sides are the same length, so the angles opposite them are the same size.
The sum of the angles = 180°. One angle is 100°, so the sum of the remaining two angles is 80°.
Since the remaining two angles are congruent, each is 40°.