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3 years ago

9

Determine the missing angle

1 answer:

Assoli18 [71]3 years ago

4 0

Answer:

106°

Step-by-step explanation:

These angles are alternate interior, therefore they are equal to each other.

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What is the equation of the line that passes through the points given in the table

Zepler [3.9K]

Answer:

B: y = -2x + 5

Step-by-step explanation:

-2 - 1 = -3

9 - 3 = 6

$\frac{6}{-3}$ = -2

gradient = -2

3 = 1 x -2 + c

3 = -2 + c

5 = c

y intercept = 5

equation = y = -2x + 5

so the answer is option b

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3 years ago

I need help with this ^

Nady [450]

<h3>Answer is 20 </h3>

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3 years ago

There are three power plants [X, Y, Z] that at any given time each one either generates electricity or idles. Event A is that pl

insens350 [35]

We're told that

$P(A\cap B)=0.15$

$P(A\cup B)^C=0.06\implies P(A\cup B)=0.94$

$P(B\mid A)=P(B^C\mid A)=0.5$

where the last fact is due to the law of total probability:

$P(A)=P(A\cap B)+P(A\cap B^C)$

$\implies P(A)=P(B\mid A)P(A)+P(B^C\mid A)P(A)$

$\implies 1=P(B\mid A)+P(B^C\mid A)$

so that $B\mid A$ and $B^C\mid A$ are complementary.

By definition of conditional probability, we have

$P(B\mid A)=P(B^C\mid A)$

$\implies\dfrac{P(A\cap B)}{P(A)}=\dfrac{P(A\cap B^C)}{P(A)}$

$\implies P(A\cap B)=P(A\cap B^C)$

We make use of the addition rule and complementary probabilities to rewrite this as

$P(A\cap B)=P(A\cap B^C)$

$\implies P(A)+P(B)-P(A\cup B)=P(A)+P(B^C)-P(A\cup B^C)$

$\implies P(B)-[1-P(A\cup B)^C]=[1-P(B)]-P(A\cup B^C)$

$\implies2P(B)=2-[P(A\cup B)^C+P(A\cup B^C)]$

$\implies2P(B)=[1-P(A\cup B)^C]+[1-P(A\cup B^C)]$

$\implies2P(B)=P(A\cup B)+P(A\cup B^C)^C$

$\implies2P(B)=P(A\cup B)+P(A^C\cap B)\quad(*)$

By the law of total probability,

$P(B)=P(A\cap B)+P(A^C\cap B)$

$\implies P(A^C\cap B)=P(B)-P(A\cap B)$

and substituting this into $(*)$ gives

$2P(B)=P(A\cup B)+[P(B)-P(A\cap B)]$

$\implies P(B)=P(A\cup B)-P(A\cap B)$

$\implies P(B)=0.94-0.15=\boxed{0.79}$

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3 years ago

Describe how to use Scientific Notation to write a very large number. Give an example, written in both Standard Form and Scienti

mel-nik [20]

A short way of writing really large numbers or really small numbers
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3 years ago

Daniel earns $760 each month he pays 15% of his earning in tax.

Gwar [14]

15 percent of 760 is 114
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3 years ago