A certain field has 3 mice. in five months, you now have 18 mice. if the population grows exponentially, how many mice will be i

Suppose that the number of drivers who travel between a particular origin and destination during a designated time period has a

AnnZ [12381]

Answer:

The likelihood that the number of drivers is at most 18 is 0.381.

Step-by-step explanation:

We are provided with the following details in the question:

The quantity of drivers traveling between a specific origin and destination in a set time frame follows a Poisson distribution characterized by the parameter μ = 20.

The Poisson distribution defines the probability of a certain number of events taking place over a specific period, based on the mean frequency of those events.
The variance for the Poisson distribution matches its mean value of Poisson distribution.

a) P(number of drivers will be at most 18)

Equation:

$P(X =k) = \displaystyle\frac{\mu^k e^{-\mu}}{k!}\\\\ \mu \text{ is the mean of the distribution}$

$P( x \leq 18) =P(x=0) + P(x =1) + P(x = 2) +... + P(x = 18)\\\\= \displaystyle\frac{20^0 e^{-20}}{0!} + \displaystyle\frac{20^1 e^{-20}}{1!} +...+ \displaystyle\frac{20^{18} e^{-20}}{18!}\\\\ = 0.381$

So, 0.381 represents the probability that the number of drivers will be at most 18.

3 0

2 months ago

MATHEMATICS: A boy leaves home at 09:15 hours and arrives at 10:05 hours. If he travels nonstop at an average speed of 6kmh ,wha

PIT_PIT [12445]

5 km. To determine the distance, we apply the speed formula that correlates distance with time: v = d / t. Thus, when rearranging for distance, we get: d = v * t. The speed is noted as 6 km/h, but we need to find the time taken - given he departs at 9:15 and returns at 10:05, the total time is 50 minutes. Converting this duration into hours gives us 50 min * 1 h / 60 min = 0.833 h. Hence, the duration for the journey to school is established as 0.833 hours. Substituting into our equation provides: d = 6 * 0.8333, yielding a distance of 5 km between the school and home.

5 0

2 months ago

Part A: Solve the equation 5(x + 2) = 6x + 3x − 14, and show your work. (5 points)

Leona [12618]

Answer:

x=8

Step-by-step explanation:

5(x+2)=6x+3x-14

This expands to 5x+10=6x+3x-14. using distributive property.

Adding up like terms gives: 10+14=8x-5x.

This simplifies to 24=3x. Here we apply addition and subtraction property.

By dividing both sides by 3, we find: 24/3 = 3x/3. This is the division property in action.

Thus, x equals 8.

> x = 8

5 0

2 months ago

Read 2 more answers

Mookie Betts of the Boston Red Sox had the highest batting average for the 2018 Major League Baseball season. His average was 0.

Leona [12618]

Answer:

Binomial probability, with $n = 5, p = 0.352$

Step-by-step explanation:

Each time Mookie Betts stepped up to bat, there were only two possible results: either he achieved a base hit or he didn't. The odds of hitting during each at-bat remain unaffected by prior attempts. Therefore, the binomial probability distribution applies to tackle this problem.

Binomial probability distribution

The chance of getting exactly x successes over n trials, considering p probability.

His batting average stood at 0.352.

This indicates that $p = 0.352$

Let's assume he bats five times in tonight's matchup against the Yankees.

This means that $n = 5$

a. This showcases what type of probability

Binomial probability, with $n = 5, p = 0.352$

8 0

1 month ago