The numbers of beans in some cocoa pods
1 answer:
Answer:
a) <em>Mean number of beans = 33.4 per coco pad</em>
<em>b) Standard deviation of the beans = 5.2 per coco pad</em>
Step-by-step explanation:
<u><em>Step(i)</em></u>:-
a)
Given data 30, 28, 30, 35, 40, 25, 32, 36, 38 and 40.
mean of beans
x⁻ = ∑x/n
<em>Mean number of beans per coco pad = 33.4</em>
<em>step(ii):-</em>
<em>b) </em>
<u><em>standard deviation</em></u>
<em>∑(xi - x⁻)² = (30-33.4)²+ (28-33.4)²+(30-33.4)²+(35-33.4)²+(40-33.4)²+(25-33.4)²+(32-33.4)²+(36-33.4)²+ (38-33.4)²+(40-33.4)²</em>
<em>On calculation , we get</em>
<em> ∑(xi - x⁻)² = 242.4</em>
<em>standard deviation </em>
<em> = </em><em></em>
<em>Standard deviation of the beans (σ) = 5.2 per coco pad</em>
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To solve the problem we must know about the equation of a circle and complex numbers.
<h2>Equation of circle</h2>Radius² = (Distance between the center and any point on the circle)²
Radius =
Complex Number, z = (x +iy)
Another point that will lay on the same circle is (12 + 10i).
<h2>Explanation</h2>Given to us
- center = (4 – 5i)
- point on the circle = (19 – 13i)
Solution
We know that equation for a circle can be written as,
<h3>Radius of the Circle </h3>Radius of the Circle
= √(Distance between the center and any point on the circle)²
Radius of the Circle = √[4-19]²+[-5 -(-13)]²
= √[-15]²+[8]²
= √225 + 64
= √225 + 64
= √289
= 17
Now compare the distance between the center of the circle and the points.
<h3>Comparison</h3>A.) –11 –3i
Distance between the center and point on the circle
= √[4-(-11)]² + [-5 - (-3)]²
= √[15]² + [-2]²
= √225 + 4
= √229
B.) –4. 5+3. 5i
Distance between the center and point on the circle
= √[4-(-4.5)]² + [-5 - (3.5)]²
= √[9.5]² + [-8.5]²
= √90.25+ 72.25
= √162.5
C.) 12 + 10i
Distance between the center and point on the circle
= √[4-(12)]² + [-5 - (10)]²
= √[-8]² + [-15]²
= √64+ 225
= √289
= 17
D.) 21 + 12i.
Distance between the center and point on the circle
= √[4-(21)]² + [-5 - (12)]²
= √[17]² + [-17i]²
= √289+ 289
= √578
Hence, another point that will lay on the same circle is (12 + 10i).
Learn more about Equation of Circle:
solve for "K", to see what "K" is, or the "constant of variation",
once you found K, plug it back in y=Kx, and that's the equation