Samuel, Tasha, and Ben are each growing plants. They want to know whose 1pc
1 answer:
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For an airplane we need to create a function. The airplane flies in straight line so this means that we will have linear function. The airplane starts left of the rainbow. So let's take the following function:
y=x+8
"<span>Create a table of at least four values for the function that includes two points of intersection between the airplane and the rainbow."
To find the intersection points we need to solve system of two equations:
</span>
Solution are two points:
(-1,35) and (0,36)
Now we can create a table
x -1 0 1 2
f(x) 35 36 37 38
<span>
"</span><span>What is the domain and range of the rainbow? Explain what the domain and range represent. Do all of the values make sense in this situation? Why or why not?"
The domain represents all possible values that x can have. The range represents all possible values that y can have.
In this example not all values make sense. Rainbow goes above ground and touches it.
Limitations exist if we have fraction, root, logarithm, trigonometric function... We do not have any of these so there are no limitations, so x can have any value.
Domain: -6</span>≤x≤6 because x can not have smaller values than those at ground touch.
The formula for parabola is:
Depending on sign of
the maximum or minimum value of y is equal to b. All other smaller or greater values are possible.
Range: 0≤y≤36 because y can not have smaller values than those at ground touch.
"<span>What are the x- and y-intercepts of the rainbow? Explain what each intercept represents."
x- and y- intercepts represent points at which function touches x- and y- axis.
To find y- intercept we insert x=0 into equation:
y=0+36
y=36
To find x- intercept we insert y=0
0=-</span>+36
"<span>Is the linear function you created with your table positive or negative? Explain."
Function is positive if it lies above x-axis. Function is negative if it lies below x-axis.
Positive on interval: x </span>∈ <-6,∞>
Negative on interval: x ∈ <-∞,-6>
Not defined: x= -6
"What are the solutions or solution to the system of equations created?Explain what it or they represent."
We already found these solutions:
Solution are two points:
(-1,35) and (0,36)
These solutions represent points of intersection of linear function and parabola.
"Explain, using complete sentences, the steps for graphing the function."
Step 1) we need to find domain and range
Step 2) we need to find x- and y- intercepts
Step 3) if the function is exponential we find minima and maxima
Step 4) we find at least three values for the function
y=x+8
"<span>Create a table of at least four values for the function that includes two points of intersection between the airplane and the rainbow."
To find the intersection points we need to solve system of two equations:
</span>
Solution are two points:
(-1,35) and (0,36)
Now we can create a table
x -1 0 1 2
f(x) 35 36 37 38
<span>
"</span><span>What is the domain and range of the rainbow? Explain what the domain and range represent. Do all of the values make sense in this situation? Why or why not?"
The domain represents all possible values that x can have. The range represents all possible values that y can have.
In this example not all values make sense. Rainbow goes above ground and touches it.
Limitations exist if we have fraction, root, logarithm, trigonometric function... We do not have any of these so there are no limitations, so x can have any value.
Domain: -6</span>≤x≤6 because x can not have smaller values than those at ground touch.
The formula for parabola is:
Depending on sign of
Range: 0≤y≤36 because y can not have smaller values than those at ground touch.
"<span>What are the x- and y-intercepts of the rainbow? Explain what each intercept represents."
x- and y- intercepts represent points at which function touches x- and y- axis.
To find y- intercept we insert x=0 into equation:
y=0+36
y=36
To find x- intercept we insert y=0
0=-</span>
"<span>Is the linear function you created with your table positive or negative? Explain."
Function is positive if it lies above x-axis. Function is negative if it lies below x-axis.
Positive on interval: x </span>∈ <-6,∞>
Negative on interval: x ∈ <-∞,-6>
Not defined: x= -6
"What are the solutions or solution to the system of equations created?Explain what it or they represent."
We already found these solutions:
Solution are two points:
(-1,35) and (0,36)
These solutions represent points of intersection of linear function and parabola.
"Explain, using complete sentences, the steps for graphing the function."
Step 1) we need to find domain and range
Step 2) we need to find x- and y- intercepts
Step 3) if the function is exponential we find minima and maxima
Step 4) we find at least three values for the function
Answer:
Obese people
Lean People
Step-by-step explanation:
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".
The empirical rule, also referred to as the three-sigma rule or 68-95-99.7 rule, is a statistical rule which states that for a normal distribution, "almost all data falls within three standard deviations (denoted by σ) of the mean (denoted by µ). Broken down, the empirical rule shows that 68% falls within the first standard deviation (µ ± σ), 95% within the first two standard deviations (µ ± 2σ), and 99.7% within the first three standard deviations (µ ± 3σ)".
Solution to the problem
Obese people
Let X the random variable that represent the minutes of a population (obese people), and for this case we know the distribution for X is given by:
Where and
On this case we know that 95% of the data values are within two deviation from the mean using the 68-95-99.7 rule so then we can find the limits liek this:
Lean People
Let X the random variable that represent the minutes of a population (lean people), and for this case we know the distribution for X is given by:
Where and
On this case we know that 95% of the data values are within two deviation from the mean using the 68-95-99.7 rule so then we can find the limits liek this:
The interval for the lean people is significantly higher than the interval for the obese people.