Listed below are the weights in pounds of 11 players randomly selected from the roster of the Seattle Sea-hawks when they won Su
per Bowl XLVIII (the same players from the preceding exercise). Are the measures of variation likely to be typical of all NFL players? 1. 1892. 2543. 2354. 2255. 1906. 3057. 1958. 2029. 19010. 25211. 305
1 answer:
Answer:
No. These measures show a thinner team of NFL players according to the mean, variance, standard deviation, and quartiles.
Step-by-step explanation:
1) The measures of variation, namely The Range, Variance, Quartiles, Interquartiles, Sum of Squares, etc. shows us how the data are dispersed.
The Range Δ is calculated:
Maximum value - Minimum value for weight
Mean:
Variance:
The Standard Deviation of the sample
2) Since there is no preceding exercise, the comparison was made to a recent study in which a NFL player average weight is about 245 pounds (average),
Since 25% of this list are player whose weight is 192.5 lbs and 50% (2nd Quartile) =225 lbs , finally only at the 3rd Quartile we have players above the regular NFL average with 253. This, added with the other data, allow us to say that this list is not a typical of all NFL players.
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Answer:
See Below.
Step-by-step explanation:
In the given figure, AP = BP = PC.
And we want to prove that ∠ABC is a right angle.
Since AP = BP and BP = PC, we can create two isosceles triangles: ΔAPB and ΔCPB.
By the definition of isosceles triangles, in ΔAPB, ∠PAB and ∠PBA are equivalent. Let the measure of each of them be <em>x°</em>.
Likewise, in ΔCPB, ∠PCB and ∠PBC are equivalent.
And since AP = BP = PC, each of the angles∠PCB and ∠PBC will also be equivalent to <em>x°.</em>
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And since the sum of the interior angles of a triangle total 180°, we acquire:
Since they are all equivalent:
Hence:
∠ABC is the sum of ∠PBA and ∠PBC, each of which measures 45°. Hence:
The cone equation gives
which means that the intersection of the cone and sphere occurs at
i.e. along the vertical cylinder of radius
when 
.
We can parameterize the spherical cap in spherical coordinates by
where
and 
, which follows from the fact that the radius of the sphere is 3 and the height at which the sphere and cone intersect is . So the angle between the vertical line through the origin and any line through the origin normal to the sphere along the cone's surface is
Now the surface area of the cap is given by the surface integral,
which means that the intersection of the cone and sphere occurs at
i.e. along the vertical cylinder of radius
We can parameterize the spherical cap in spherical coordinates by
where
Now the surface area of the cap is given by the surface integral,