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scZoUnD [109]
3 years ago
7

Help Are the triangles similar? If so, determine the scale factor of ΔPQR to ΔEFD.

Mathematics
1 answer:
alex41 [277]3 years ago
8 0
The answer is B. 
When you set up a ratio of all the corresponding sides, the ratios all equal 2:1
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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}

8 0
3 years ago
Please help me. What is the y intercept of the graph shown below?
natta225 [31]

Answer:

(0,2)

Step-by-step explanation:

the point where Oy intercepts the graph has x=0 and y= f(0)

so this is (0,2)

7 0
3 years ago
Which city has a higher median?
PIT_PIT [208]

The correct answer is Arcadia

Let me explain why...

The median is the number that's in-between the other 2 numbers so for Millersburg the median around 200ish but the median for Arcadia is is exactly 240.This means that Arcadia is your answer

Hope you have an amazing day <3

-Yo MaMa

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3 years ago
-4 1/2 ÷ (-2 2/3)<br><br> I need it as a mixed number in simplified form.
Leya [2.2K]
(-4 1/2) / (-2 2/3) =.....turn to improper fractions
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-9/2 * -3/8 =
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1 11/16 <==

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Which congruence is used in triangulation?
Sedbober [7]
Side angle side (SAS)
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