Answer:
Mean = 113.72
The estimator of 113.72 is point estimate used for the conceptual population of all first-graders in this school
Step-by-step explanation:
Data provided in the question:
Data:
82 96 99 102 103 103 106 107 108 108 108 108 109 110 110 111 113 113 113 113 115 115 118 118 119 121 122 122 127 132 136 140 146
Number of data = 33
In the hint it is also given that the sum of the data value i.e ∑x = 3753
Now,
Point estimate of mean is given as;
Mean = 
or
⇒ Mean = 
or
⇒ Mean = 113.72
Hence,
The estimator of 113.72 is point estimate used for the conceptual population of all first-graders in this school
Answer:
The figure is attached and the total distance is 1031 feet.
Step-by-step explanation:
The graph is indicated in the attached figure.
For calculation of distance consider following
Point Flagpole is (0,0)
Point Clue1 is (0,5)
Point Clue2 is (6,0)
Point Clue3 is (0,-5)
So the distance is calculated as follows
![d_{T}=[d_{FP\ to\ Clue1}+d_{Clue1\ to\ Clue2}+d_{Clue2\ to\ Clue3}]*distance\ per\ unit\\d_{T}=[\sqrt{(Clue1_x-FP_x)^2+(Clue1_y-FP_y)^2}+\sqrt{(Clue2_x-Clue1_x)^2+(Clue2_y-Clue1_y)^2}+\sqrt{(Clue3_x-Clue2_x)^2+(Clue3_y-Clue2_y)^2}]**distance\ per\ unit\\](https://tex.z-dn.net/?f=d_%7BT%7D%3D%5Bd_%7BFP%5C%20to%5C%20Clue1%7D%2Bd_%7BClue1%5C%20to%5C%20Clue2%7D%2Bd_%7BClue2%5C%20to%5C%20Clue3%7D%5D%2Adistance%5C%20per%5C%20unit%5C%5Cd_%7BT%7D%3D%5B%5Csqrt%7B%28Clue1_x-FP_x%29%5E2%2B%28Clue1_y-FP_y%29%5E2%7D%2B%5Csqrt%7B%28Clue2_x-Clue1_x%29%5E2%2B%28Clue2_y-Clue1_y%29%5E2%7D%2B%5Csqrt%7B%28Clue3_x-Clue2_x%29%5E2%2B%28Clue3_y-Clue2_y%29%5E2%7D%5D%2A%2Adistance%5C%20per%5C%20unit%5C%5C)
Substituting the values
![d_{T}=[\sqrt{(0-0)^2+(5-0)^2}+\sqrt{(6-0)^2+(0-5)^2}+\sqrt{(0-6)^2+(-5-0)^2}]*50 \text{ feet}\\d_{T}=[\sqrt{(0)^2+(5)^2}+\sqrt{(6)^2+(-5)^2}+\sqrt{(-6)^2+(-5)^2}]*50 \text{ feet}\\d_{T}=[\sqrt{0+25}+\sqrt{36+25}+\sqrt{36+25}]*50 \text{ feet}\\d_{T}=[\sqrt{25}+\sqrt{61}+\sqrt{61}]*50 \text{ feet}\\d_{T}=[5+7.81+7.81]*50 \text{ feet}\\d_{T}=[20.62]*50 \text{ feet}\\d_{T}=1031 \text{ feet}\\](https://tex.z-dn.net/?f=d_%7BT%7D%3D%5B%5Csqrt%7B%280-0%29%5E2%2B%285-0%29%5E2%7D%2B%5Csqrt%7B%286-0%29%5E2%2B%280-5%29%5E2%7D%2B%5Csqrt%7B%280-6%29%5E2%2B%28-5-0%29%5E2%7D%5D%2A50%20%5Ctext%7B%20feet%7D%5C%5Cd_%7BT%7D%3D%5B%5Csqrt%7B%280%29%5E2%2B%285%29%5E2%7D%2B%5Csqrt%7B%286%29%5E2%2B%28-5%29%5E2%7D%2B%5Csqrt%7B%28-6%29%5E2%2B%28-5%29%5E2%7D%5D%2A50%20%5Ctext%7B%20feet%7D%5C%5Cd_%7BT%7D%3D%5B%5Csqrt%7B0%2B25%7D%2B%5Csqrt%7B36%2B25%7D%2B%5Csqrt%7B36%2B25%7D%5D%2A50%20%5Ctext%7B%20feet%7D%5C%5Cd_%7BT%7D%3D%5B%5Csqrt%7B25%7D%2B%5Csqrt%7B61%7D%2B%5Csqrt%7B61%7D%5D%2A50%20%5Ctext%7B%20feet%7D%5C%5Cd_%7BT%7D%3D%5B5%2B7.81%2B7.81%5D%2A50%20%5Ctext%7B%20feet%7D%5C%5Cd_%7BT%7D%3D%5B20.62%5D%2A50%20%5Ctext%7B%20feet%7D%5C%5Cd_%7BT%7D%3D1031%20%5Ctext%7B%20feet%7D%5C%5C)
So the total distance travelled is 1031 feet.
1 is 4 and 4 and 4 is 11 and 5 is 15
u - v = <5, 2> - <2, - 3> = <5 - 2, 2 + 3> = <3, 5>
given a vector <u, v> then the magnitude is √ (u² + v² ) and it's angle of direction is
θ = 
(
)
thus the magnitude of <3, 5> = √(3² + 5²) = √34 ≈ 5.83 ( to 2 dec. places )
Θ = (
) = 59.04° ( to 2 dec. places )
