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oee [108]
3 years ago
6

A jar contains 6 blue, 4 red, and 2 green marbles. What is the probability that three blue marbles are drawn with out replacemen

t?
Mathematics
1 answer:
ch4aika [34]3 years ago
6 0

Answer:  The required probability is 9.09%.

Step-by-step explanation:  Given that a jar contains 6 blue, 4 red, and 2 green marbles.

We are to find the probability that three blue marbles are drawn with out replacement.

Total number of marbles = 6 + 4 + 2 = 12.

After drawing one blue marble, we are left with total 11 marbles. And after drawing the second blue marble, we are left with total 10 marbles.

Therefore, the probability of drawing three blue marbles without replacement is given by

p\\\\\\=\dfrac{^6C_1}{^{12}C_1}\times\dfrac{5C_1}{^{11}C_1}\times\dfrac{^4C_1}{^{10}C_1}\\\\\\=\dfrac{6}{12}\times\dfrac{5}{11}\times\dfrac{4}{10}\\\\\\=\dfrac{1}{11}\\\\\\=\dfrac{1}{11}\times100\%\\\\=9.09\%.

Thus, the required probability is 9.09%.

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A space telescope on a mountaintop is housed inside of a cylindrical building with a hemispheric dome. If the circumference of t
Vlad1618 [11]

Answer:

 185553.7\text{ feet}^3

Step-by-step explanation:

GIVEN: A space telescope on a mountaintop is housed inside of a cylindrical building with a hemispheric dome. If the circumference of the dome is 84\text{ feet}, and the total height of the building up to the top of the dome is 91\text{ feet}.

TO FIND: what is the approximate total volume of the building.

SOLUTION:

let the height of the mountaintop be h\text{ feet}

As the dome hemispherical.

circumference of a hemisphere =\frac{1}{2}\times2\pi\times radius

                                                    =\pi\times radius

                                                    \frac{22}{7}\times radius=84

                                                    radius=26.75\text{ feet}

total height of the building up to the top of the dome =\text{radius of hemisphere}+\text{height of mountaintop}

=26.75+h=91

h=64.25\text{ feet}

Volume of building =\text{volume of cylindrical mountaintop}+\text{volume of dome}

                                =\pi(radius)^2h+\frac{2}{3}\pi(radius)^3

as radius of mountain top is same as dome

putting values

                                =3.14(26.75)^264.75+\frac{2}{3}3.14(26.75)^3      

                               =145484.6+40069.1

                               185553.7\text{ feet}^3

Hence the total volume of the building is 185553.7\text{ feet}^3                                      

5 0
3 years ago
I.
Kaylis [27]
It’s A because (-2)2+(4)2-2(-2)+4(4)+8=0
-4+8+4+-16+8
(8+8) (-4+4) (-16)
16 -16 =0
4 0
3 years ago
In circle o, the length of radius OL is 6 cm and the length
AlekseyPX

Answer:

14.2cm

Step-by-step explanation:

The diagram representing the circle and its attributes has been attached to this response.

<em>As shown in the diagram;</em>

The circle is centered at o,

The length of radius OL = 6cm

The length of the arc LM = 6.3cm

The angle MON = 75°

The angle LOM = θ

<em>Remember that;</em>

The length, L, of an arc is given by;

L = (θ / 360) x (2πr)         -------------(i)

Where;

θ is the angle subtended by the arc

r = radius of the circle.

Using the formula in equation (i), let's calculate the angle θ subtended by arc LM as follows;

L = (θ / 360) x (2πr)  

Where;

L = length of arc LM = 6.3cm

r = radius of the circle = length of radius OL = 6cm

<em>Substitute these values into the equation to get;</em>

6.3 = (θ / 360) x (2 x π x 6)

6.3 = (θ / 360) x (12 x π)

6.3 = (θ / 30) x (π)              [Take π = 22/7]

6.3 = (θ / 30) x (22 / 7)

θ = \frac{6.3*30*7}{22}

θ = 60.14°

Therefore, the angle subtended by arc LM is 60.14°

Now, from the diagram,

The angle subtended by arc LMN is;

θ + 75° = 60.14° + 75° =  135.14°

Let's now calculate the length of arc LMN using the same equation (i)

L = (θ / 360) x (2πr)  

Where;

L = length of arc LMN

θ = angle subtended by LMN = 135.14°

r = radius of the circle = length of radius OL = 6cm

<em>Substitute these values into the equation;</em>

L = (135.14° / 360°) x (2 x π x 6)             [Take π = 22/7]

L = 14.15cm

Therefore, the length of arc LMN is 14.2cm to the nearest tenth.

6 0
3 years ago
(GIVING BRAINLIEST!!!!!!)<br><br> Solve 1 ÷ 1/2 = ________<br><br> A) 2<br> B) 3<br> C) 4<br> D) 5
Tcecarenko [31]

Answer:

B

Step-by-step explanation:

Becuase 1 divide 1/2

You make the division sign a multiplication sign

1 time 1/2

get the recipricol of 1/2 wich is 2

1 times 2/1

is 2

5 0
3 years ago
The article on the next page from the San Francisco Chronicle, January 27, 1996, describes very serious problems of subsidence,
Mekhanik [1.2K]

Answer:

246.3%

the complete question is found in the attached document

Step-by-step explanation:

1st step:

using 1936 data,

w1= 356% = 3.56(356/100) , H= 79 feet

specific gravity = 2.65

Sₓ= 100%= 1

initial void ratio(e₀)= (w1 x specific gravity)/Sₓ

=3.56 x 2.65/1 = 9.434

2nd step

using 1996 data

ΔH= 22ft

ΔH/H = Δe/(1 + e₀)

22/79 = Δe/(1+9.434)

0.278=Δe/10.434

Δe= 0.278 x 10.434

Δe= 2.905

Δe= e₀ - eₓ

eₓ= e₀-Δe

eₓ= 9.434 - 2.905

eₓ= 6.529

3rd step

calculating water content in 1996

eₓ =6.529, specific gravity= 2.65, Sₓ= 100%

W2 X 2.65 = 1 x 6.529

w2 = 6.529/2.65 = 2.463 = 246.3%

6 0
3 years ago
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