Answer:
123.5
Step-by-step explanation:
Answer:
The length of the resulting segment is 500.
Step-by-step explanation:
Vectorially speaking, the dilation is defined by following operation:
(1)
Where:
- Center of dilation.
- Original point.
- Scale factor.
- Dilated point.
First, we proceed to determine the coordinates of the dilated segment:
(
,
,
,
)
![P'(x,y) = O(x,y) + k\cdot [P(x,y)-O(x,y)]](https://tex.z-dn.net/?f=P%27%28x%2Cy%29%20%3D%20O%28x%2Cy%29%20%2B%20k%5Ccdot%20%5BP%28x%2Cy%29-O%28x%2Cy%29%5D)
![P(x,y) = (0,0) +5\cdot [(10,40)-(0,0)]](https://tex.z-dn.net/?f=P%28x%2Cy%29%20%3D%20%280%2C0%29%20%2B5%5Ccdot%20%5B%2810%2C40%29-%280%2C0%29%5D)

![Q'(x,y) = O(x,y) + k\cdot [Q(x,y)-O(x,y)]](https://tex.z-dn.net/?f=Q%27%28x%2Cy%29%20%3D%20O%28x%2Cy%29%20%2B%20k%5Ccdot%20%5BQ%28x%2Cy%29-O%28x%2Cy%29%5D)
![Q' (x,y) = (0,0) +5\cdot [(70,120)-(0,0)]](https://tex.z-dn.net/?f=Q%27%20%28x%2Cy%29%20%3D%20%280%2C0%29%20%2B5%5Ccdot%20%5B%2870%2C120%29-%280%2C0%29%5D)

Then, the length of the resulting segment is determined by following Pythagorean identity:


The length of the resulting segment is 500.
Answer:
1/2
-1/2
Step-by-step explanation:
we know that
If a dilation produce a contraction that means that the absolute value of the scaling factor is less than 1
If a dilation produce an enlargement that means that the absolute value of the scaling factor is greater than 1
<u><em>Verify each case</em></u>
case 1) 2

----> is a enlargement
case 2) 1/2

----> is a contraction
case 3) -2

----> is a enlargement
case 4) -1/2

----> is a contraction
Answer:
Therefore, the area of the ellipse is:
Area = 78.5 inches
Step-by-step explanation:
The formula to find the area of the ellipse is

The major axis of an ellipse = 25 inches
The minor axis of an ellipse = 4 inches
- The value of a = major axis/2 = 25/2 = 12.5 inches
- The value of b = minor axis/2 = 4/2 = 2 inches
Thus
The area of the ellipse:
Area = 


inches ∵ 
Therefore, the area of the ellipse is:
Area = 78.5 inches
Answer:
(a) Null Hypothesis (H₀) = Mean of x₁ > Mean of x₂
Alternative Hypothesis (H₁) = Mean of x₁ ≠ Mean of x₂
(b) We will use here t-test for two sample means which is given by,
[/tex]
Putting all values we get, t = 17.5 with 20 degree of freedom
At α = 0.05
p-value = 95% Confidence Interval for the Difference ( 6.6068 , 8.3932 )