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3 years ago

X = a.) 82 b.) 98 c.) 262

Mathematics

1 answer:

Katarina [22]3 years ago

5 0

Answer: Option 'a' is correct.

Step-by-step explanation:

Since we have given that

There is a cyclic quadrilateral .

As we know that Sum of opposite angles of a cyclic quadrilateral is supplementary.

So, it becomes,

$98^\circ+x=180^\circ\\\\x=180^\circ-98^\circ\\\\x=82^\circ$

Hence, the value of x is 82°.

Therefore, Option 'a' is correct.

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At a certain gas station, 40% of the customers use regular gas (A1), 35% use plus gas (A2), and 25% use premium (A3). Of those c

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a.)

P( A₂ ∩ B ) = P(B | A₂) × P(A₂)

P( A₂ ∩ B ) = 0.40 × 0.35

P( A₂ ∩ B ) = 0.14

b.)

P(B) = P( A₁ ∩ B ) + P( A₂ ∩ B ) + P( A₃ ∩ B )

P(B) = 0.08 + 0.14 + 0.125

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c.)

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P(A₁ | B) = P( A₁ ∩ B ) / P(B)

P(A₁ | B) = 0.08 / 0.345

P(A₁ | B) = 0.232

For plus gas:

P(A₂ | B) = P( A₂ ∩ B ) / P(B)

P(A₂ | B) = 0.14 / 0.345

P(A₂ | B) = 0.406

For premium gas:

P(A₃ | B) = P( A₃ ∩ B ) / P(B)

P(A₃ | B) = 0.125 / 0.345

P(A₃ | B) = 0.362

Step-by-step explanation:

We are given the following information

40% of the customers use regular gas (A2)

P(A₁) = 0.40

35% use plus gas (A2)

P(A₂) = 0.35

25% use premium (A3)

P(A₃) = 0.25

Of those customers using regular gas, only 20% fill their tanks (event B).

P(B | A₁) = 0.20

Of those customers using plus, 40% fill their tanks

P(B | A₂) = 0.40

Whereas of those using premium, 50% fill their tanks.

P(B | A₃) = 0.5

a) What is the probability that the next customer will request plus gas and fill their tank?

We are asked to find P(A₂ ∩ B) = ?

Recall that Multiplicative law of probability is given by

P( A₂ ∩ B ) = P(B | A₂) × P(A₂)

P( A₂ ∩ B ) = 0.40 × 0.35

P( A₂ ∩ B ) = 0.14

b) What is the probability that the next customer fills the tank?

We are asked to find P(B) = ?

P(B) = P( A₁ ∩ B ) + P( A₂ ∩ B ) + P( A₃ ∩ B )

P( A₂ ∩ B ) is already calculated, we need to calculate

P( A₁ ∩ B ) and P( A₃ ∩ B )

So,

P( A₁ ∩ B ) = P(B | A₁) × P(A₁)

P( A₁ ∩ B ) = 0.20 × 0.40

P( A₁ ∩ B ) = 0.08

P( A₃ ∩ B ) = P(B | A₃) × P(A₃)

P( A₃ ∩ B ) = 0.50 × 0.25

P( A₃ ∩ B ) = 0.125

Finally,

P(B) = P( A₁ ∩ B ) + P( A₂ ∩ B ) + P( A₃ ∩ B )

P(B) = 0.08 + 0.14 + 0.125

P(B) = 0.345

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For regular gas:

P(A₁ | B) = P( A₁ ∩ B ) / P(B)

P(A₁ | B) = 0.08 / 0.345

P(A₁ | B) = 0.232

For plus gas:

P(A₂ | B) = P( A₂ ∩ B ) / P(B)

P(A₂ | B) = 0.14 / 0.345

P(A₂ | B) = 0.406

For premium gas:

P(A₃ | B) = P( A₃ ∩ B ) / P(B)

P(A₃ | B) = 0.125 / 0.345

P(A₃ | B) = 0.362

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----------------

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