The correlation coefficient of the data given in the table, using a calculator, is of 0.35
<h3>How to find the correlation coefficient of a data-set using a calculator?</h3>
To find the coefficient, we need to insert the points (x,y) in the calculator.
In this problem, we have that:
- The values of x are: 90, 95, 80, 84, 75, 80.
- The values of y are: 80, 90, 90, 95, 75, 85.
Using a calculator, the coefficient is of 0.35.
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Answer:
The GDP gap is 9 % when there is 4.5 % unemployment.
Step-by-step explanation:
The statement shows a reverse relationship, where an increase in unemployment is following by decrease in potential GDP and can be translated into the following rate:
The GDP gap at a given increase in unemployment can be estimated by the following expression:
Where:
- GDP gap-unemployment increase rate, dimensionless.
- Increase in unemployment rate, measured in percentage.
- GDP gap, measured in percentage.
If and 
, the GDP gap is:
The GDP gap is 9 % when there is 4.5 % unemployment.
The surface area of the cone is: A. 184π units².
<h3>What is the Surface Area of a Cone?</h3>
Surface area of a cone = πr(l + r), where r is the radius and l is the slant height.
Given the following:
- Slant height (l) = 15 units
- Radius = (r) = 8 units
Surface area of a cone = π8(15 + 8)
Surface area of a cone = 184π units²
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We have the <span> Trigonometric Identities : </span>secx = 1/cosx; (sinx)^2 + (cosx)^2 = 1;
Then, 1 / (1-secx) = 1 / ( 1 - 1/cosx) = 1 / [(cosx - 1)/cosx] = cosx /
(cosx - 1 ) ;
Similar, 1 / (1+secx) = cosx / (1 + cosx) ;
cosx / (cosx - 1) + cosx / (1 + cosx) = [cosx(1 + cosx) + cosx (cosx - 1)] / [ (cosx - 1)(cox + 1)] =[cosx( 1 + cosx + cosx - 1 )] / [ (cosx - 1)(cox + 1)] = 2(cosx)^2 / [(cosx)^2 - (sinx)^2] = <span> 2(cosx)^2 / (-1) = - 2(cosx)^2;
</span>
Tan of an angle = perpendicular / base
<span>Here, perpendicular is the side of the triangle opposite the angle. </span>
<span>And base is the arm of the angle other the hypotenuse. </span>
<span>If the side of the triangle to be found (marked as ? in the figure) is x, then </span>
<span>perpendicular = 20 feet </span>
<span>base = x </span>
<span>so, tan 30 = 20/x </span>
<span>so, x = 20/(tan 30 degrees) = 34.64 feet </span>
<span>= 35 feet to the nearest foot</span>
