Suppose the fish population in a local lake increases at a rate proportional to the population each moment. there were 1000 fish 5 years ago and 2000 fish 4 years ago. How many fish are there right now?

6000

Step-by-step explanation:

If the fish population in a local lake increases at a rate proportional to the population each moment, this can be expressed as;

P = k/t (the scenario is an inverse proportionality because as the time is reducing, the population is increasing by the same factor)

If there are 1000 fish 5 years ago and there are 2000 fish 4 years ago

Yearly percentage increase will be;

2000-1000/1000 × 100%

1000/1000×100%

= 100%

This means that the population increases by 100% on a yearly basis (by a factor of 1000)

The population 3 years ago will be population

P = 2000+1000

P = 3000

The population 2 years ago will be population

P = 3000+1000

P = 4000

The population 1 year ago will be population

P = 4000+1000

P = 5000

The population now will be population

P = 5000+1000

P = 6000 populations

There is enough statistical evidence to suggest that there is no difference between the mean number of households picking either service

Step-by-step explanation:

The parameters of the music streaming service are;

The average number of households using Apple Music, = 1.73 million

The standard deviation, σ₁² = 0.46 million

The average number of households using Spotify, = 2.17 million

The standard deviation, σ₂² = 0.33 million

The significance level = 0.01

Hypothesis testing with different population standard deviation

H₀: ≠

H₁:   =

p-value for the test statistic = 2 × P(Z <-2.6923) = 2 × 0.00357 = 0.00714

Therefore, the p-value is less than the significance level, and it is therefore unlikely that the result will be observed under the null hypothesis

We therefore reject the null hypothesis and there is enough statistical evidence to suggest that there is no difference between the mean number of households picking either service