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Answer: 1. x = (y - 2)² + 8
3. y = 2(x +9)² + 7
<u>Step-by-step explanation:</u>
Notes: Vertex form is: y =a(x - h)² + k or x =a(y - k)² + h
- (h, k) is the vertex
- point of vertex is midpoint of focus and directrix:
- p is the distance from the vertex to the focus
1)
Now let's find the a-value:
Now, plug in a = 1 and (h, k) = (-8, 2) into the equation x =a(y - k)² + h
x = (y - 2)² + 8
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2)
Now let's find the a-value:
Now, plug in a = -1/2 and (h, k) = (1, 10) into the equation x =a(y - k)² + h
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3)
Now let's find the a-value:
Now, plug in a = 2 and (h, k) = (-9, 7) into the equation y =a(x - h)² + k
y = 2(x +9)² + 7
Answer:
p-value = 0.1277
Step-by-step explanation:
p-value is the probability value tell us how likely it is to get a result like this if the Null Hypothesis is true.
Firstly we find the mean and standard deviation of the given data set.
⇒ Mean =
⇒ Mean = 4.368
where, is mean of the distribution.
⇒ Standard Deviation = 0.034
Applying t- test:
Let out hypothesis is:
H₀: μ = 4.35
H₁: μ ≠ 4.35
Now,
Here, μ = Population Mean = 4.35
= Sample Mean = 4.368
σ = Standard Deviation = 0.034
n = 10
Putting all values we get, t = 1.6777 with (10 -1) = 9 degree of freedom.
Then the p-value at 99% level of significance.
⇒ p-value = 0.1277