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Ira Lisetskai [31]
3 years ago
11

The function g(n)=n²-6n+16 represents a parabola.

Mathematics
1 answer:
goblinko [34]3 years ago
4 0

Part A: (n^2-6n)+16

[(n^2-6n+9)-9]+16

(n-3)^2+7

Part B: From the above result,

Vertex (3,7) this is the minimum point of the graph since the coefficient of a is positive

Part C: The axis of symmetry is basically the x coordinate of the vertex, so the axis of symmetry is x=3

Hope this helps!

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Answer:

a) 0.5588

b) 0.9984

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 24

Standard Deviation, σ = 6.4

We are given that the distribution of score is a bell shaped distribution that is a normal distribution.

Formula:

z_{score} = \displaystyle\frac{x-\mu}{\sigma}        

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P(20 \leq x \leq 30) = P(\displaystyle\frac{20 - 24}{6.4} \leq z \leq \displaystyle\frac{30-24}{6.4}) = P(-0.62 \leq z \leq 0.94)\\\\= P(z \leq 0.94) - P(z < -0.62)\\= 0.8264 - 0.2676 = 0.5588 = 55.88\%

P(20 \leq x \leq 30) = 55.88\%

b) Sampling distribution

Sample size, n = 22

The sample will follow a normal distribution with mean 24 and standard deviation,

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P(20 \leq x \leq 30) =99.84\%

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