Joan works on commission for a furniture store. She gets a base pay of $85 a day plus 6 percent of the
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Answer:
Step-by-step explanation:
I understand it! (But I'm a high school math teacher so it might be unfair!) ; )
Anyway you have 2 numbers. You don't know what they are so we will call them x and y. Our first statement says that these numbers multiply to equal 120. So that first equation is
xy = 120
Our second statement says that they add to -22. So that second equation is
x + y = -22
Now we need to find the 2 numbers. We have 2 unknowns, x and y. That means that we have to have 2 equations. No more than 2 no less than 2. Solve the first equation for y. It doesn't matter which equation you pick and which variable you choose to solve for. If you do the work correctly, you will get the correct answers either way. Solving the first equation for y gives you:
Now tht we have a value for y, we can use the substitution property of equality to sub that value into the second equation for y:
Instead of finding a common denominator, we are going to eliminate x in the denominator altogether. Do this by multiplying everything by x to get
Get everything on one side of the equals sign and factor:
Because 12 * 10 = 120 and 12 + 10 = 22, our factors are 12 and 10:
Use factoring by grouping now.
From the first set of parenthesis you can factor out an x, and from the second set you can factor out a 10:
x(x + 12) + 10(x + 12) = 0
Now factor out the common x + 12 to get a factored quadratic:
(x + 12)(x + 10) = 0
By the Zero Product Property, either x + 12 = 0 or x + 10 = 0. Solving both for x gives you x = -12 or x = -10.
If x = -12, then
-12 + y = -22 so
y = -10
If x = -10, then
-10 + y = -22 so
y = -12.
The combinations of x and y are:
If x = -12, y = 10
If x = -10, y = -12
It doesn't matter which one is which. They are not asking you to specifically define x and y. They are asking you to find the numbers, and you did!
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
Answer:
0.6 gallons/can
Step-by-step explanation:
Simply divide the gallons of paint by the number of cans:
= 0.6 gallons/can