the perimeter of a rectangle is 48 in. if the length is twice the width, what is the length of the rectangle?
1 answer:
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We can start by writing all that we know about the problem. Let us write down how many scones each boy has:
Note that k is the increase, we know it's a constant. This is not a system of equations, please keep that in mind. We will use rest of the information given to build the system. We have two variables x (the number of cookies the first boy bought) and k( the increase), that means we need to have two equations to solve this problem.
We know that total amount of scones is 60, so we can use that information to build our first equation. We sum all of the scones and we get 60.
We know that Robbie and Cameron combined have 3/7 of <span>Louis, Tom and Charlie combined. We can use this information to build our second equation.
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Now this piece of information alows us to solve the first equation that we made and this will solve our problem. We simply plug in x=4k into 5x+10k=60.
Now we can plug this information into the same equation 5x+10k=60 and get x.
And that's it. Now we can write out how many cookies each boy has bought.
If you add them all up you get 60.
Note that k is the increase, we know it's a constant. This is not a system of equations, please keep that in mind. We will use rest of the information given to build the system. We have two variables x (the number of cookies the first boy bought) and k( the increase), that means we need to have two equations to solve this problem.
We know that total amount of scones is 60, so we can use that information to build our first equation. We sum all of the scones and we get 60.
We know that Robbie and Cameron combined have 3/7 of <span>Louis, Tom and Charlie combined. We can use this information to build our second equation.
</span>
Now this piece of information alows us to solve the first equation that we made and this will solve our problem. We simply plug in x=4k into 5x+10k=60.
Now we can plug this information into the same equation 5x+10k=60 and get x.
And that's it. Now we can write out how many cookies each boy has bought.
If you add them all up you get 60.
Answer:
Step-by-step explanation:
Hello!
1)
The variable of interest is
X: level of toxin ergovaline on the grass after being treated with Moose saliva.
>The parameter of interest is the population mean of the level of ergovaline on grass after being treated with Moose saliva: μ
The best point estimate for the population mean is the sample mean:
>X[bar]=0.183 Sample average level of ergovaline on the grass after being treated with Moose saliva.
Assuming that the sample comes from a normal population.
>There is no information about the sample size takes to study the effects of the Moose saliva in the grass. Let's say that they worked with a sample of n=20
Using the Student-t you can calculate the CI as:
X[bar] ± *
Where
0.183 ± 2.093 * (0.016/√20)
[0.175;0.190]
Using a 95% confidence level you'd expect that the interval [0.175;0.190] will contain the true average of ergovaline level of grass after being treated with Moose saliva.
2)
The information of a study that shows how much does the consumption of canned soup increase urinary BPA concentration is:
Consumption of canned soup for over 5 days increases the urinary BPA more than 1000%
75 individuals consumed soup for five days (either canned or fresh)
The study reports that a 95% confidence interval for the difference in means (canned minus fresh) is 19.6 to 25.5 μg/L.
>This experiment is a randomized comparative experiment.
Out of the 75 participants, some randomly eat canned soup and some randomly eaten fresh soup conforming to two separate and independent groups that were later compared.
>The parameter of interest is the difference between the population mean of urinary BPA concentration of people who ate canned soup for more than 5 days and the population mean of urinary BPA concentration of people that ate fresh soup for more than 5 days.
>Using a 95% confidence level you'd expect that the interval 19.6 to 25.5 μg/L would contain the value of the difference between the population mean of urinary BPA concentration of people who ate canned soup for more than 5 days and the population mean of urinary BPA concentration of people that ate fresh soup for more than 5 days.
> If the sample had been larger, then you'd expect a narrower CI, the relationship between the amplitude of the CI and sample size is indirect. Meaning that the larger the sample, the more accurate the estimation per CI is.
3)
> The parameter of interest is Average Long-Term Weight Gain Overeating for just four weeks can increase fat mass and weight over two years later of people with an average age of 26 years old.
> The only way of finding the true value of the parameter is if you were to use the information of the whole population of interest, this is making all swedes with an average age of 26 increase calorie intake by 70% (mostly by eating fast food) and limit their daily activity to a maximum of 5000 steps per day and then measure their weight gain over two years. since this es virtually impossible to do, due to expenses and size of the population, is that the estimation with a small but representative sample is conducted.
>
n= 18
X[bar]= 6.8 lbs
S= 1.2
X[bar] ± * (S/√n)
6.8 ± 2.101 * (1.2/√18)
[6.206;7.394]
With a 95% confidence level, you'd expect that the interval [6.206;7.394] will contain the true value of the Average Long-Term Weight Gain Overeating for just four weeks can increase fat mass and weight over two years later of people with an average age of 26 years old.
>
The margin of error of the interval is
* (S/√n)= 2.101 * (1.2/√18)= 0.59
With a 95% it is expected that the true value of the Average Long-Term Weight Gain Overeating for just four weeks can increase fat mass and weight over two years later of people with an average age of 26 years old. will be 0.59lbs away from the sample mean.
I hope it helps