If the area of a rectangle is 8x^2+10x-3 and it’s width is 2x+3 what is the perimeter of this rectangle?

The table gives estimates of the world population, in millions, from 1750 to 2000. year population year population 1750 790 1900

Tems11 [23]

The poopulation exponential model is given by

$P(t)=P_0e^{kt}$

Where, P(t) is the population after year t; Po is the initial population, t is the number of years from the starting year; k is the groth constant.

Given that the population in 1750 is 790 and the population in 1800 is 970, we obtain the population exponential equation as follows:

$970=790e^{50k} \\ \\ \Rightarrow e^{50k}=1.228 \\ \\ \Rightarrow 50k=\ln{1.228}=0.2053 \\ \\ \Rightarrow k=0.0041$

Thus, the exponential equation using the 1750 and the 1800 population values is $P(t)=790e^{0.0041t}$

The population of 1900 using the 1750 and the 1800 population values is given by

$P(t)=790e^{0.041\times150} \\ \\ =790e^{0.6158}=790(1.8511) \\ \\ =1,462$

The population of 1950 using the 1750 and the 1800 population values is given by

$P(t)=790e^{0.041\times200} \\ \\ =790e^{0.821}=790(2.2729) \\ \\ =1,796$

From the table, it can be seen that the actual figure is greater than the exponential model values.

7 0

3 years ago

g If a random sample of 18 deliveries was selected instead and the standard deviation of these delivery times was found to be 9.

lana [24]

Answer:

We can use the z score formula given by:

$z= \frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}$

If we use this formula we got:

$z=\frac{21-20}{\frac{9.31}{\sqrt{18}}}= 0.456$

$z=\frac{25-20}{\frac{9.31}{\sqrt{18}}}= 2.279$

And using a calculator, excel or the normal standard table and we have that:

$P(0.456$

Step-by-step explanation:

We assume this previous info: It is known that the amounts of time required for room-service delivery at a certain Marriott Hotel are Normally distributed with the average delivery time of 20 minutes.

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Solution to the problem

Let X the random variable that represent the delivery times of a population, and for this case we know the distribution for X is given by:

$X \sim N(20,9.31)$