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3 years ago

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A triangle in the coordinate plane has the following vertices: P(-4,-3), 1(-2,-2), G(-2,-4). What are the new coordinates if the

triangle is translated 3 units right and 4 units up?

1 answer:

Aloiza [94]3 years ago

7 0

Answer:

P’(-1, 1), I’ (1, 2), G’(1,0)

Step-by-step explanation:

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M_6 is (2x – 5)º and m_8 is (x + 5)º.

HACTEHA [7]

m_6 + m_8 = 180º because they form a straight line.

So, (2x-5) + (x+5) = 180

3x = 180

x = 60

So, m_115º (2•60 - 5 = 115)

Also, because the two lines are parallel m_6 = m_3 by alternate interior angles.

So, m_3 = 115º

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A commuter must pass through 5 traffic lights on her way to work and will have to stop at each one that is red. She estimates th

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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:

$\mu=E(X)=\sum x.P(X=x)$

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

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

The formula of E (X²) is:

$E(X^{2})=\sum x^{2}.P(X=x)$

(a)

Compute the expected value of <em>X</em> as follows:

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

Thus, the mean or expected value of <em>X </em>is 2.2.

(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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