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nignag [31]
3 years ago
11

Help plz all my points

Mathematics
1 answer:
dimaraw [331]3 years ago
4 0

9514 1404 393

Answer:

  A: ∠W'Z'Y' = 60°; angles aren't changed by rotation

  B: W'(-3, 6), X'(9, 6), Y'(8, 1), Z'(-4, 1)

Step-by-step explanation:

<u>Part A</u>:

Angle WZY is the supplement of the given angle ZWX, so is ...

  ∠WZY = 180° -120° = 60°

Rotation about the origin (or anywhere else) does not change angles. The new parallelogram will have ...

  ∠W'Z'Y' = 60°

__

<u>Part B</u>:

The transformation right 2 and up 3 can be described by ...

  (x, y) ⇒ (x +2, y +3)

Then the translated vertices are ...

  W(-5, 3) ⇒ W'(-3, 6)

  X(7, 3) ⇒ X'(9, 6)

  Y(6, -2) ⇒ Y'(8, 1)

  Z(-6, -2) ⇒ Z'(-4, 1)

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By definition of conditional probability,

P(X_1=4\text{ or }X_2=4\mid X_1+X_2=7)=\dfrac{P((X_1=4\text{ or }X_2=4)\text{ and }X_1+X_2=7)}{P(X_1+X_2=7)}

=\dfrac{P((X_1=4\text{ and }X_1+X_2=7)\text{ or }(X_2=4\text{ and }X_1+X_2=7))}{P(X_1+X_2=7)}

Assuming a standard 6-sided fair die,

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Both outcomes are mutually exclusive with probability \frac1{36} each, hence total probability \frac2{36}=\frac1{18}.

Of the 36 possible outcomes, there are 6 ways to sum the integers 1-6 to get 7:

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and so a sum of 7 occurs \frac6{36}=\frac16 of the time.

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