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Free_Kalibri [48]
3 years ago
6

A rectangle has a perimeter of 28 units, an area of 48 square units, and sides that are either horizontal or vertical. If one ve

rtex is the point (−5, −7) and the origin is in the interior of the rectangle, find the vertex of the rectangle that is opposite (−5, −7).

Mathematics
1 answer:
crimeas [40]3 years ago
3 0

Answer:

Opposite coordinate of (−5, −7) = (1,1)

Step-by-step explanation:

Let the sides of rectangle be a and b

Perimeter = 2 ( a+b ) = 28

                       a + b = 14

Area = ab = 48

The sides with sum 14 and product 48 is 8 and 6.

a = 8 and b = 6

Since origin is inside the circle, the side with 8 unit is parallel to y axis and side with 6 unit is parallel to x axis

        Opposite coordinate of (−5, −7) = (−5+6, −7+8) =(1,1)

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Please help I will be very grateful for this
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On a water ride at the amusement park, a rotating valve sprays water for 15 ft in all directions. What its the area of the circu
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<span>Now plug it in. </span>

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An insurance company examines its pool of auto insurance customers and gathers the following information: (i) All customers insu
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The question is incomplete! Complete question along with answer and step by step explanation is provided below.

Question:

An insurance company examines its pool of auto insurance customers and gathers the following information: (i) All customers insure at least one car. (ii) 70% of the customers insure more than one car. (iii) 20% of the customers insure a sports car. (iv) Of those customers who insure more than one car, 15% insure a sports car. Calculate the probability that a randomly selected customer insures exactly one car, and that car is not a sports car?

Answer:

P( X' ∩ Y' ) = 0.205

Step-by-step explanation:

Let X is the event that the customer insures more than one car.

Let X' is the event that the customer insures exactly one car.

Let Y is the event that customer insures a sport car.

Let Y' is the event that customer insures not a sport car.

From the given information we have

70% of customers insure more than one car.

P(X) = 0.70

20% of customers insure a sports car.

P(Y) = 0.20

Of those customers who insure more than one car, 15% insure a sports car.

P(Y | X) = 0.15

We want to find out the probability that a randomly selected customer insures exactly one car, and that car is not a sports car.

P( X' ∩ Y' ) = ?

Which can be found by

P( X' ∩ Y' ) = 1 - P( X ∪ Y )

From the rules of probability we know that,

P( X ∪ Y ) = P(X) + P(Y) - P( X ∩ Y )    (Additive Law)

First, we have to find out P( X ∩ Y )

From the rules of probability we know that,

P( X ∩ Y ) = P(Y | X) × P(X)       (Multiplicative law)

P( X ∩ Y ) = 0.15 × 0.70

P( X ∩ Y ) = 0.105

So,

P( X ∪ Y ) = P(X) + P(Y) - P( X ∩ Y )

P( X ∪ Y ) = 0.70 + 0.20 - 0.105

P( X ∪ Y ) = 0.795

Finally,

P( X' ∩ Y' ) = 1 - P( X ∪ Y )

P( X' ∩ Y' ) = 1 - 0.795

P( X' ∩ Y' ) = 0.205

Therefore, there is 0.205 probability that a randomly selected customer insures exactly one car, and that car is not a sports car.

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