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3 years ago

What is the difference between independent and conditional probability? Which one requires the use of the Addition Rule?Explain.

Mathematics

2 answers:

PSYCHO15rus [73]3 years ago

7 0

Answer:

In probability, independent events are those that if one event occurs, it does not change the probability of the other event.

Whereas conditional probability is defined as the probability of one event occurring with some relationship to one or more other events.

The addition rule is used for both the independent and conditional probabilities.

For independent event the probability is shown as :

$P(YorZ)=P(Y)+P(Z)$

For conditional: $P(YorZ)=P(Y)+P(Z)-P(YandZ)$

Scorpion4ik [409]3 years ago

6 0

Independent probability means that the test subjects do not affect one another. One's event occurring does not affect the other.

Conditional probability means that an event happening only happened because another even had already occurred.

The addition rule i believe is a Conditional probability

hope this helps

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Factor completely 5x2 − 40.

Tatiana [17]

,Answer:

I got -30

Step-by-step explanation:

Becuase when I did 5 x 2= 10

and 10 -40 = -30

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3 years ago

the height h(t) of a trianle is increasing at 2.5 cm/min, while it's area A(t) is also increasing at 4.7 cm2/min. at what rate i

nekit [7.7K]

Answer:

The base of the triangle decreases at a rate of 2.262 centimeters per minute.

Step-by-step explanation:

From Geometry we understand that area of triangle is determined by the following expression:

$A = \frac{1}{2}\cdot b\cdot h$ (Eq. 1)

Where:

$A$ - Area of the triangle, measured in square centimeters.

$b$ - Base of the triangle, measured in centimeters.

$h$ - Height of the triangle, measured in centimeters.

By Differential Calculus we deduce an expression for the rate of change of the area in time:

$\frac{dA}{dt} = \frac{1}{2}\cdot \frac{db}{dt}\cdot h + \frac{1}{2}\cdot b \cdot \frac{dh}{dt}$ (Eq. 2)

Where:

$\frac{dA}{dt}$ - Rate of change of area in time, measured in square centimeters per minute.

$\frac{db}{dt}$ - Rate of change of base in time, measured in centimeters per minute.

$\frac{dh}{dt}$ - Rate of change of height in time, measured in centimeters per minute.

Now we clear the rate of change of base in time within (Eq, 2):

$\frac{1}{2}\cdot\frac{db}{dt}\cdot h = \frac{dA}{dt}-\frac{1}{2}\cdot b\cdot \frac{dh}{dt}$

$\frac{db}{dt} = \frac{2}{h}\cdot \frac{dA}{dt} -\frac{b}{h}\cdot \frac{dh}{dt}$ (Eq. 3)

The base of the triangle can be found clearing respective variable within (Eq. 1):

$b = \frac{2\cdot A}{h}$

If we know that $A = 130\,cm^{2}$ , $h = 15\,cm$ , $\frac{dh}{dt} = 2.5\,\frac{cm}{min}$ and $\frac{dA}{dt} = 4.7\,\frac{cm^{2}}{min}$ , the rate of change of the base of the triangle in time is:

$b = \frac{2\cdot (130\,cm^{2})}{15\,cm}$

$b = 17.333\,cm$

$\frac{db}{dt} = \left(\frac{2}{15\,cm}\right)\cdot \left(4.7\,\frac{cm^{2}}{min} \right) -\left(\frac{17.333\,cm}{15\,cm} \right)\cdot \left(2.5\,\frac{cm}{min} \right)$

$\frac{db}{dt} = -2.262\,\frac{cm}{min}$

The base of the triangle decreases at a rate of 2.262 centimeters per minute.

6 0

3 years ago

Problem PageQuestion Working together, two pumps can drain a certain pool in hours. If it takes the older pump hours to drain th

gizmo_the_mogwai [7]

Answer:

10.5 hours.

Step-by-step explanation:

Please consider the complete question.

Working together, two pumps can drain a certain pool in 6 hours. If it takes the older pump 14 hours to drain the pool by itself, how long will it take the newer pump to drain the pool on its own?

Let t represent time taken by newer pump in hours to drain the pool on its own.

So part of pool drained by newer pump in one hour would be $\frac{1}{t}$ .

We have been given that it takes the older pump 14 hours to drain the pool by itself, so part of pool drained by older pump in one hour would be $\frac{1}{14}$ .