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dalvyx [7]
3 years ago
7

Given the g(x)=f(x)+k ,identify a k that transforms f into g

Mathematics
1 answer:
Fiesta28 [93]3 years ago
4 0

Answer:

k = 7

Step-by-step explanation:

Given

g(x) = f(x) + k

Required

The value of k

From the attached graph, line f(x) is shifted up 7 times to match g(x).

This implies that:

g(x) = f(x) + 7

Compare: g(x) = f(x) + k and g(x) = f(x) + 7

k = 7

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Answer:

(a) The mean or expected value of <em>X </em>is 2.2.

(b) The standard deviation of <em>X</em> is 1.3.

Step-by-step explanation:

Let <em>X</em> = number of times the traffic light is red when a commuter passes through the traffic lights.

The probability distribution of <em>X</em> id provided.

The formula to compute the mean or expected value of <em>X </em>is:

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The formula to compute the standard deviation of <em>X </em>is:

\sigma=\sqrt{E(X^{2})-(E(X))^{2}}

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E(X)=\sum x.P(X=x)\\=(0\times0.06)+(1\times0.25)+(2\times0.35)+(3\times0.15)+(4\times0.13)+(5\times0.06)\\=2.22\\\approx2.2

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(b)

Compute the value of E (X²) as follows:

E(X^{2})=\sum x^{2}.P(X=x)\\=(0^{2}\times0.06)+(1^{2}\times0.25)+(2^{2}\times0.35)+(3^{2}\times0.15)+(4^{2}\times0.13)+(5^{2}\times0.06)\\=6.58

Compute the standard deviation of <em>X</em> as follows:

\sigma=\sqrt{E(X^{2})-(E(X))^{2}}\\=\sqrt{6.58-(2.22)^{2}}\\=\sqrt{1.6516}\\=1.285\\\approx1.3

Thus, the standard deviation of <em>X</em> is 1.3.

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