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3 years ago

Which of the following formulas is used to calculate the probability of independent events A and B?

Mathematics

2 answers:

maksim [4K]3 years ago

8 0

P (A and B) = P(A) * P(B)...answer is D

Jlenok [28]3 years ago

4 0

<h2>Answer:</h2>

The formula that is used to calculate the probability of independent events A and B are:

D. P(A and B)=P(A)·P(B)

<h2>Step-by-step explanation:</h2>

Independent events--

Two events A and B are said to be independent if the happening of one event do not affect the happening of the other event.

For example-- The probability of getting two heads on rolling a die two times.

Hence, the formula that calculate the probability of independent events A and B is given by:

$P(A\bigcap B)=P(A)\cdot P(B)$

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Answer:

The no. of traditional type birdhouses are 4 and the no. of lavish type birdhouses are 3.

Step-by-step explanation:

Let x be the no. of traditional type birdhouses

The more traditional type takes 4 pieces of wood and 2 hours to build.

One house requires wood = 4

x houses requires wood = 4x

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x houses requires time = 2x

Let y be the no. of lavish type birdhouses

The more lavish type takes 10 pieces of wood and 7 hours to build.

One house requires wood = 10

y houses requires wood = 10y

One house requires time = 7 hours

y houses requires time = 7y

Now we are given that he has a total of 46 pieces of wood and 29 hours to work,

So, equations becomes : $4x+10y = 46\\2x+7y=29$

Plot these equations on graph

$4x+10y = 46$ ---Blue line

$2x+7y=29$ ---Green line

Refer the attached figure

The intersection point provides the solution

Intersection point : (4,3)

So, x = 4 and y = 3

Hence the no. of traditional type birdhouses are 4 and the no. of lavish type birdhouses are 3.

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2 years ago

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2 years ago

In a randomized controlled trial in Kenya, insecticide treated bednets were tested as a way to reduce malaria. Among 343 infants

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Answer:

Step-by-step explanation:

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(one tailed test)

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3 years ago

Part a at what speed v should an archerfish spit the water to shoot down an insect floating on the water surface located at a di

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3.01 m/s
This is a simple projectile calculation. What we want is a vertical velocity such that the time the droplet spends going up and going back down to the surface exactly matches the time the droplet takes to travel horizontally 0.800 meters. The time the droplet spends in the air will is:
V*sqrt(3)/2 ; Vertical velocity.
(V*sqrt(3)/2)/9.8 ; Time until droplet reaches maximum height
(V*sqrt(3))/9.8 ; Double that time for droplet to fall back to the surface.

The droplet's horizontal velocity will be:
V/2.

So the total distance the droplet travels will be:
d = (V*sqrt(3))/9.8 * V/2
d = V^2*sqrt(3)/19.6

Let's substitute the desired distance and solve for V
d = V^2*sqrt(3)/19.6
0.8 = V^2*sqrt(3)/19.6
15.68 = V^2*sqrt(3)
15.68/sqrt(3) = V^2
15.68/1.732050808 = V^2
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So after rounding to 3 significant figures, the archerfish needs to spit the water at a velocity of 3.01 m/s
Let's verify that answer.
Vertical velocity: 3.01 * sin(60) = 3.01 * 0.866025404 = 2.606736465
Time of flight = 2.606736465 * 2 / 9.8 = 0.531987034 seconds.
Horizontal velocity: 3.01 * cos(60) = 3.01 * 0.5 =

8 0

3 years ago