MATHEMATICS
HIGH SCHOOL

Answer:

Answer:

P(B|A)=0.25 , P(A|B) =0.5

Step-by-step explanation:

The question provides the following data:

P(A)= 0.8

P(B)= 0.4

P(A∩B) = 0.2

Since the question does not mention which of the conditional probabilities need to be found out, I will show the working to calculate both of them.

To calculate the probability that event B will occur given that A has already occurred (P(B|A) is read as the probability of event B given A) can be calculated as:

P(B|A) = P(A∩B)/P(A)

= (0.2) / (0.8)

P(B|A)=0.25

To calculate the probability that event A will occur given that B has already occurred (P(A|B) is read as the probability of event A given B) can be calculated as:

P(A|B) = P(A∩B)/P(B)

= (0.2)/(0.4)

P(A|B) =0.5

MIDDLE SCHOOL

The sum of my digits is 11 when rounded to the nearest hundred i am 500 rounding to the nearest ten makes me 530 what number am I?

The mystery number is 533. Rounds to 500. Rounds to 530 and 5+3+3=11

MIDDLE SCHOOL

Which eqation is equivalent to 3x + 4y = 15 A) y=15-3x

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4

B) y=3x-15

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4

C) y=15-3x

D) y=3x-15

Answer:

Step-by-step explanation:

Here we are given an equation in x and y and we are required to solve it for y

we have

subtracting 3x from each sides we get

now we divide both sides by 4 we get

Hence A) is our right answer.

COLLEGE

A paper cup has the shape of a cone with height 10 cm and radius 3 cm (at the top. if water is poured into the cup at a rate of 2cm3/s, how fast is the water level rising when the water is 5 cm deep?

Using implicit differentiation, it is found that the water level is rising at a rate of 0.0764 centimetres per second.

The volume of a cone of radius r and height h is given by:

Applying implicit differentiation, the rate of change is given by:

In this problem:

- The radius is constant, thus .
- Height of 5 cm and radius of 3 cm, thus .
- Water poured at a rate of 2 cm³/s, thus

Then

The water level is rising at a rate of 0.0764 centimetres per second.

A similar problem is given at brainly.com/question/13461339

Let

h: height of the water

r: radius of the circular top of the water

V: the volume of water in the cup.

We have:

r/h = 3/10

So,

r = (3/10)*h

the volume of a cone is:

V = (1/3)*π*r^2*h

Rewriting:

V (t) = (1/3)*π*((3/10)*h(t))^2*h(t)

V (t) =(3π/100)*h(t)^3

Using implicit differentiation:

V'(t) = (9π/100)*h(t)^2*h'(t)

Clearing h'(t)

h'(t)=V'(t)/((9π/100)*h(t)^2)

the rate of change of volume is V'(t) = 2 cm3/s when h(t) = 5 cm.

substituting:

h'(t) = 8/(9π) cm/s

Answer:

the water level is rising at a rate of:

h'(t) = 8/(9π) cm/s

h: height of the water

r: radius of the circular top of the water

V: the volume of water in the cup.

We have:

r/h = 3/10

So,

r = (3/10)*h

the volume of a cone is:

V = (1/3)*π*r^2*h

Rewriting:

V (t) = (1/3)*π*((3/10)*h(t))^2*h(t)

V (t) =(3π/100)*h(t)^3

Using implicit differentiation:

V'(t) = (9π/100)*h(t)^2*h'(t)

Clearing h'(t)

h'(t)=V'(t)/((9π/100)*h(t)^2)

the rate of change of volume is V'(t) = 2 cm3/s when h(t) = 5 cm.

substituting:

h'(t) = 8/(9π) cm/s

Answer:

the water level is rising at a rate of:

h'(t) = 8/(9π) cm/s

HIGH SCHOOL

The two perpendicular number lines that are used for graphing are called

The x-axis (horizontal) and the y-axis (vertical).

X axis and y axis I think