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2 years ago

P(A) = 7/20 P(B) = 7/20 P(A or B) = 49/80, P(A and B)= ?

Mathematics

1 answer:

OverLord2011 [107]2 years ago

8 0

Answer:

P(A and B) = 7/80

Step-by-step explanation:

The given values of the probabilities of the different events are;

P(A) = 7/20

P(B) = 7/20

P(A or B) = 49/80

P(A and B) = Required

We have by probability theory for any event;

P(A or B) = P(A) + P(B) - P(A and B)

Therefore;

P(A and B) = P(A) + P(B) - P(A or B)

Plugging in the values gives;

P(A and B) = 7/20 + 7/20 - 49/80 = 7/80

∴ P(A and B) = 7/80

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2 years ago

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Artemon [7]

Answer:

a) 8

b) 2 1/4 hours

c) 4 7/8 hours

d) 4 1/8 hours

Step-by-step explanation:

a) LCD to be used to solve this problem is calculated as the Lowest common denominator of the above mixed fractions.

We have 1 1/2 hours and 1 1/8 hours

The lowest common denominator is the denominator calculated by

Multiplying the two denominators together and dividing by the common factor of the two denominators

Hence , we have

2 × 8 = 16

The common factor of 2 and 8 = 2

LCD = 16/2 = 8

b) How long did Matt drive?

We are told that Matt drove twice as long as John

John drove for 1 1/8 hours

Hence, the number of hours that Matt drove for =2 × 1 1/8

= 2 × 9/8 = 9/4 hours = 2 1/4 hours

c) How long the Sam, John and Matt drive ?

We are told in the question that

Sam drove for 1 1/2 hours

John drove for 1 1/8 hours

Matt drove for 2 1/4 hours

We would sum up the number of hours that each of them drove.

1 1/2 + 1 1/8 + 2 1/4

The Lowest common multiple of denominators is 8

= (1 + 1 + 2)( 4 + 1 +2/8)

= 4(7/8)

= 4 7/8 hours

d) How many hours is left for Bob to drive

We are told that the entire journey = 9 hours

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The number of hours Bob will drive for is calculated as

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2 years ago

A town is planning a playground. It wants to fence in a rectangular space using an existing wall. What is the greatest area it c

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Answer:

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Step-by-step explanation:

We are given that the playground is fenced on three sides of the playground and the four side has an existing wall.

Let the length of the rectangle be 'X' feet and width be 'Y' feet.

As the fencing is done using 100 feet of fence. We get the relation between the sides and the fence as, X + 2Y = 100.

As, X + 2Y = 100 → X = 100 - 2Y

Now, the area of the rectangle = XY = X × ( 100 - 2Y ).

i.e Area of the rectangle = $-2Y^{2} +100Y$ .

The general form of a quadratic equation is $y=ax^{2}+bx+c$ .

The maximum value of a quadratic equation is given by $x=\frac{-b}{2a}$ .

Therefore, the greatest value of $-2Y^{2} +100Y$ is at Y = $\frac{-100}{2 \times -2}$ = $\frac{-100}{-4}$ = 25.

Thus, Y = 25 and X = 100 - 2Y → X = 100 - 2 × 25 → X = 50.

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3 years ago

I need help on the Math question?

mrs_skeptik [129]

Answer:

The answer is D.

Step-by-step explanation:

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3x*2= 6x

5*3x=15x

5*2=10

6x+15x=21x

9x^2+21x+10

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3 years ago

P(A) = 7/20 P(B) = 7/20 P(A or B) = 49/80, P(A and B)= ?​

P(A) = 7/20 P(B) = 7/20 P(A or B) = 49/80, P(A and B)= ?