Step-by-step explanation:
Regression analysis is used to infer about the relationship between two or more variables.
The line of best fit is a straight line representing the regression equation on a scatter plot. The may pass through either some point or all points or none of the points.
<u>Method 1:</u>
Using regression analysis the line of best fit is:
Here <em>α </em>= intercept, <em>β</em> = slope and <em>e</em> = error.
The formula to compute the intercept is:
Here<em> </em> and are mean of the <em>y</em> and <em>x</em> values respectively.
The formula to compute the slope is:
And the formula to compute the error is:
<u>Method 2:</u>
The regression line can be determined using the descriptive statistics mean, standard deviation and correlation.
The equation of the line of best fit is:
Here <em>r</em> = correlation coefficient =
and are standard deviation of <em>x</em> and <em>y</em> respectively.
- The area of the circle is:
A=πr²
A is the area of the circle.
π=3.14
r is the radius of the circle.
- To calculate the area of <span> the sector indicated in the problem, you must apply the following formula:
As=(</span>θ/2π)πr²
As is the area of the sector.
θ is the central angle (θ=2π/9)
π=3.14
r is the radius.
- First, you must find the radius:
r=Diameter/2
r=20.6 mm/2
r=10.3 mm
- Now, you can substitute the values into the formula As=(θ/2π)πr². Then, you have:
As=(θ/2π)πr²
As=(2π/9/2π)(π)(10.3)²
As=(π/9π)(π)(10.3)²
As=(3.14/9x3.14)(3.14)(10.3)²
- Finally, the area of the sector is:
As= 37.01 mm²
Answer:
x - 3
Step-by-step explanation:
let's call the unknown number x to express its value that's three less than actual number we say x - 3
Answer:
Therefore the population will be maximum when x=30 inches.
Step-by-step explanation:
Given that, the mosquito population is a function of rainfall and can be approximated by the formula
where x is the number of inches of rainfall.
Differentiating with respect to x
Again differentiating with respect to x
Now we set N'(x)=0
Since at x=30, N''(x)<0, So at x=30, N(x) has maximum value.
Therefore the population will be maximum when x=30 inches.