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3 years ago

Find the exact surface area of the following. The exact surface area is

Mathematics

1 answer:

Nataliya [291]3 years ago

7 0

Answer:

Surface area: 4323pi

Fill the box with the value "4323", as there is a "pi" after the box.

Step-by-step explanation:

We need to find the surface area of the cone (without the base) and the surface area of the semi sphere (without the base).

The surface area of the cone, without the base, is:

S1 = pi * r * s

Where s is the slant height.

To find s, we can use the Pythagoras' theorem with the radius and the height:

s^2 = h^2 + r^2

s^2 = 56^2 + 33^2 = 4225

s = 65

So the surface area is:

S1 = pi * 33 * 65 = 2145pi

Now, to find the surface area of the semi sphere, we just need to find half of the surface area of a sphere:

S2 = (1/2) * 4 * pi * r^2

S2 = 2 * pi * 33^2 = 2178pi

Finally to find the total surface area we just need to sum both surface areas:

S = S1 + S2 = 2145pi + 2178pi = 4323pi.

As after the box to answer there is a pi, we just need to fill the box with the value "4323"

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Answer:

33√2 in ≈ 46.7 inches

Step-by-step explanation:

The diagonal of a square is √2 times the side length, so for side length s we have ...

s√2 = 66 in

s = (66 in)/√2

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3 years ago

This triangle is a multiple of one of the triples listed here. What is the hypotenuse?

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Answer:

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Step-by-step explanation:

you use Pythagorean-theorem which means A^2+B^2 =C^2

It does not matter the order of A and B because it is adding. But C is the hypotenuse.

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48*48=2,304

then you add

196+2,304=C^2

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2 years ago

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Paul works for a company that deals in paints and dyes. He is paid a fixed monthly salary plus 15 percent commission on monthly

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3 years ago

There are 4 green marbles and 2 red marbles in the jar. You just randomly draw one by one without replacement and stop when you

zalisa [80]

Answer:

Then the probability distribution is:

P(0) = 1/3

P(1) = 4/15

P(2) = 1/5

P(3) = 2/15

P(4) = 1/15

The expected value for X is:

EV = 1.33...

Step-by-step explanation:

We have a total of 6 marbles in the jar.

The probability of getting a red marble in the first try (X = 0) is equal to the quotient between the number of red marbles and the total number of marbles, this is:

P(0) = 2/6 = 1/3

The probability of drawing one green marble (X = 1)

is:

First, you draw a green marble with a probability of 4/6

Then you draw the red one, but now there are 5 marbles in the jar (2 red ones and 3 green ones), then the probability is 2/5

The joint probability is:

P(1) = (4/6)*(2/5) = (2/3)*(2/5) = 4/15

The probability of drawing two green marbles (X = 2)

Again, first we draw a green marble with a probability of 4/6

Now we draw again a green marble, now there are 3 green marbles and 5 total marbles in the jar, so this time the probability is 3/5

Now we draw the red marble (there are 2 red marbles and 4 total marbles in the jar), with a probability of 2/4

The joint probability is:

P(2) = (4/6)*(3/5)*(2/4) = (2/6)*(3/5) = 1/5

The probability of drawing 3 green marbles (X = 3)

At this point you may already understand the pattern:

First, we draw a green marble with a probability 4/6

second, we draw a green marble with a probability 3/5

third, we draw a green marble with a probability 2/4

finally, we draw a red marble with a probability 2/3

The joint probability is:

P(3) = (4/6)*(3/5)*(2/4)*(2/3) = (2/6)*(3/5)*(2/3) = (1/5)*(2/3) = (2/15)

Finally, the probability of drawing four green marbles (X = 4) is given by:

First, we draw a green marble with a probability 4/6

second, we draw a green marble with a probability 3/5

third, we draw a green marble with a probability 2/4

fourth, we draw a green marble with a probability 1/3

Finally, we draw a red marble with a probability 2/2 = 1

The joint probability is:

P(4) = (4/6)*(3/5)*(2/4)*(1/3)*1 = (1/5)*(1/3) = 1/15

Then the probability distribution is:

P(0) = 1/3

P(1) = 4/15

P(2) = 1/5

P(3) = 2/15

P(4) = 1/15

The expected value will be:

EV = 0*P(0) + 1*P(1) + 2*P(2) + 3*P(3) + 4*P(4)

EV = 1*(4/15) + 2*( 1/5) + 3*( 2/15) + 4*(1/15 ) = 1.33

So we can expect to draw 1.33 green marbles in this experiment.

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3 years ago