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2 years ago

14

A box contains a total of 30 paper clips with colors in the ratio red:white:blue = 2:5:3. Suppose that one paper clip of each co

lor is removed from the box and not replaced. What is the probability that the next paper clip chosen will be blue?
A: 5/27
B: 2/7
C: 8/27
D: 3/10

1 answer:

faust18 [17]2 years ago

4 0

Answer:

C.8/27

Step-by-step explanation:

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12 spheres of the same size are made from melting a solid cylinder of 1 cm diameter and 2 cm height. Find the diameter of each s

mars1129 [50]

The answer is: The diameter is 4 centimeters.

The explanation is shown below:

1. The volume of the cylinder is:

$Vc=r^{2}h \pi$

Where $r$ is the radius ( $r=\frac{16cm}{2}=8cm$ ) and $h$ is the height ( $h=2cm$ ).

Then:

$Vc=(8cm)^{2}}(2cm)\pi\\Vc=128\pi$

2. The total volume of the 12 spheres is:

$Vs=12(\frac{4}{3}r^{3}\pi)\\Vs=16r^{3}\pi$

3. The volume of the cylinder and the total volume of all the 12 spheres, are equal, therefore:

$Vc=Vs\\128\pi=16r^{3}\pi$

4. Now, you must solve for the radius:

$r=\sqrt[3]{\frac{128\pi}{16\pi}}\\r=2cm$

5. The diameter is:

$d=2r\\d=2(2cm)\\d=4cm$

5 0

3 years ago

Suppose I have an urn with 9 balls: 4 green, 3 yellow and 2 white ones. I draw a ball from the urn repeatedly with replacement.

Mrrafil [7]

Answer:

$E(X_n)=\frac{2(n-1)}{27}$

$E(y)=\frac{14}{9}$

Step-by-step explanation:

From the question we are told that:

Sample size n=9

Number of Green $g=4$

Number of yellow $y=4$

Number of white $w=4$

Probability of Green Followed by yellow P(GY) ball

$P(GY)=\frac{4}{9}*\frac{3}{9}$

$P(GY)=\frac{4}{27}$

Generally the equations for when n is even is mathematically given by

$Probability of success P(S)=\frac{4}{27}$

$Probability of Failure P(F)=\frac{27-4}{27}$

$Probability of Failure P(F)=\frac{23}{27}$

Therefore

$E(X_n)=\frac{n}{2}*P$

$E(X_n)=\frac{n}{2}*\frac{4}{27}$

$E(X_n)=\frac{2n}{27}$

Generally the equations for when n is odd is mathematically given by

$\frac{n-1}{2}$

$E(X_n)=\frac{n-1}{2}*\frac{4}{27}$

$E(X_n)=\frac{2(n-1)}{27}$

b)

Probability of drawing white ball

$P(w)=\frac{2}{9}$

Therefore

$E(w)=\frac{1}{p}$

$E(w)=\frac{1}{\frac{2}{9}}$

$E(w)=\frac{9}{2}$

Therefore

$E(y)=[E(w)-1]\frac{4}{9}$

$E(y)=[\frac{9}{2}-1]\frac{4}{9}$

$E(y)=\frac{14}{9}$

5 0

3 years ago

Is this question correct?

Andrews [41]

Answer:

10^20

3^11

3^24

10^12

Step-by-step explanation:

(10^2)^10=10^2*10=10^20

3^3*3^8=3^3+8=3^11

(3^3)^8=3^3*8=3^24

10^2*10^10=10^2+10=10^12

6 0

3 years ago

Which system of the equation is represents by the graph?<br><br><br>

pashok25 [27]

Sorry just needed points to use this app

3 0

2 years ago

(8+2b)+(-4+6x)+(6+9m)

ANTONII [103]

Answer:

2 b + 9 m + 6 x + 10

Step-by-step explanation:

2 b + 4 + 6 x + 6 +9 m

2 b + 6 x + 10 + 9m

2 b + 6 x + 9 m + 10

= 2 b + 9 m + 6 x + 10

3 0

3 years ago

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