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notsponge [240]
2 years ago
7

Two of the angles in a triangle measure 154° and 20°. What is the measure of the third angle?

Mathematics
1 answer:
Phoenix [80]2 years ago
7 0

Answer:

6°

Step-by-step explanation:

The angles in a triangle always add up to 180°. Let’s call the third angle x. That means that:

154 + 20 + x = 180 ->

174 + x = 180 ->

x = 180 - 174 ->

x = 6°

Hope that help! :)

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Calculate the slope from 2 points.

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Substitute b, -1, into the equation from step 2.

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A manufacturer knows that on average 20% of the electric toasters produced require repairs within 1 year after they are sold. Wh
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Answer:

(a) The value of <em>x</em> is 5.

(b) The value of <em>y</em> is 15.

Step-by-step explanation:

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And the let the random variable <em>Y</em> represent the number of electric toasters produced that does not require repairs within 1 year.

The probability of the random variables are:

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The event that a randomly selected electric toaster requires repair is independent of the other electric toasters.

A random sample of <em>n</em> = 20 toasters are selected.

The random variable <em>X</em> and <em>Y</em> thus, follows binomial distribution.

The probability mass function of <em>X</em> and <em>Y</em> are:

P(X=x)={20\choose x}(0.20)^{x}(1-0.20)^{20-x}

P(Y=y)={20\choose y}(0.20)^{20-y}(1-0.20)^{y}

(a)

Compute the value of <em>x</em> such that P (X ≥ x) < 0.50:

P (X \geq x) < 0.50\\\\1-P(X\leq x-1)

Use the Binomial table for <em>n</em> = 20 and <em>p</em> = 0.20.

0.411=\sum\limits^{3}_{x=0}[b(x,20,0.20)]

The least value of <em>x</em> that satisfies the inequality P (X ≥ x) < 0.50 is:

<em>x</em> - 1 = 4

<em>x</em> = 5

Thus, the value of <em>x</em> is 5.

(b)

Compute the value of <em>y</em> such that P (Y ≥ y) > 0.80:

P (Y \geq y) >0.80\\\\P(Y\leq 20-y)>0.80\\\\P(Y\leq 20-y)>0.80\\\\\sum\limits^{20-y}_{y=0}[{20\choose y}(0.20)^{20-y}(1-0.20)^{y}]>0.80

Use the Binomial table for <em>n</em> = 20 and <em>p</em> = 0.20.

0.630=\sum\limits^{4}_{y=0}[b(y,20,0.20)]

The least value of <em>y</em> that satisfies the inequality P (Y ≥ y) > 0.80 is:

20 <em>- y</em> = 5

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Thus, the value of <em>y</em> is 15.

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