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a_sh-v [17]
3 years ago
15

The formula for the circumference of a circle is C = 2 pi r. Determine the circumference when the radius r is 10 cm.

Mathematics
1 answer:
liq [111]3 years ago
6 0

Answer:

D 100cm

Step-by-step explanation:

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Canadians who visit the United States often buy liquor and cigarettes, which are much cheaper in the United States. However, the
fenix001 [56]

Answer:

(a): Marginal pmf of x

P(0) = 0.72

P(1) = 0.28

(b): Marginal pmf of y

P(0) = 0.81

P(1) = 0.19

(c): Mean and Variance of x

E(x) = 0.28

Var(x) = 0.2016

(d): Mean and Variance of y

E(y) = 0.19

Var(y) = 0.1539

(e): The covariance and the coefficient of correlation

Cov(x,y) = 0.0468

r \approx 0.2657

Step-by-step explanation:

Given

<em>x = bottles</em>

<em>y = carton</em>

<em>See attachment for complete question</em>

<em />

Solving (a): Marginal pmf of x

This is calculated as:

P(x) = \sum\limits^{}_y\ P(x,y)

So:

P(0) = P(0,0) + P(0,1)

P(0) = 0.63 + 0.09

P(0) = 0.72

P(1) = P(1,0) + P(1,1)

P(1) = 0.18 + 0.10

P(1) = 0.28

Solving (b): Marginal pmf of y

This is calculated as:

P(y) = \sum\limits^{}_x\ P(x,y)

So:

P(0) = P(0,0) + P(1,0)

P(0) = 0.63 + 0.18

P(0) = 0.81

P(1) = P(0,1) + P(1,1)

P(1) = 0.09 + 0.10

P(1) = 0.19

Solving (c): Mean and Variance of x

Mean is calculated as:

E(x) = \sum( x * P(x))

So, we have:

E(x) = 0 * P(0)  + 1 * P(1)

E(x) = 0 * 0.72  + 1 * 0.28

E(x) = 0   + 0.28

E(x) = 0.28

Variance is calculated as:

Var(x) = E(x^2) - (E(x))^2

Calculate E(x^2)

E(x^2) = \sum( x^2 * P(x))

E(x^2) = 0^2 * 0.72 + 1^2 * 0.28

E(x^2) = 0 + 0.28

E(x^2) = 0.28

So:

Var(x) = E(x^2) - (E(x))^2

Var(x) = 0.28 - 0.28^2

Var(x) = 0.28 - 0.0784

Var(x) = 0.2016

Solving (d): Mean and Variance of y

Mean is calculated as:

E(y) = \sum(y * P(y))

So, we have:

E(y) = 0 * P(0)  + 1 * P(1)

E(y) = 0 * 0.81  + 1 * 0.19

E(y) = 0+0.19

E(y) = 0.19

Variance is calculated as:

Var(y) = E(y^2) - (E(y))^2

Calculate E(y^2)

E(y^2) = \sum(y^2 * P(y))

E(y^2) = 0^2 * 0.81 + 1^2 * 0.19

E(y^2) = 0 + 0.19

E(y^2) = 0.19

So:

Var(y) = E(y^2) - (E(y))^2

Var(y) = 0.19 - 0.19^2

Var(y) = 0.19 - 0.0361

Var(y) = 0.1539

Solving (e): The covariance and the coefficient of correlation

Covariance is calculated as:

COV(x,y) = E(xy) - E(x) * E(y)

Calculate E(xy)

E(xy) = \sum (xy * P(xy))

This gives:

E(xy) = x_0y_0 * P(0,0) + x_1y_0 * P(1,0) +x_0y_1 * P(0,1) + x_1y_1 * P(1,1)

E(xy) = 0*0 * 0.63 + 1*0 * 0.18 +0*1 * 0.09 + 1*1 * 0.1

E(xy) = 0+0+0 + 0.1

E(xy) = 0.1

So:

COV(x,y) = E(xy) - E(x) * E(y)

Cov(x,y) = 0.1 - 0.28 * 0.19

Cov(x,y) = 0.1 - 0.0532

Cov(x,y) = 0.0468

The coefficient of correlation is then calculated as:

r = \frac{Cov(x,y)}{\sqrt{Var(x) * Var(y)}}

r = \frac{0.0468}{\sqrt{0.2016 * 0.1539}}

r = \frac{0.0468}{\sqrt{0.03102624}}

r = \frac{0.0468}{0.17614266944}

r = 0.26569371378

r \approx 0.2657 --- approximated

8 0
2 years ago
Anyone happen to know the answer?
WINSTONCH [101]

Answer:

6.85 is the answer to this.

Step-by-step explanation:

356*24*60=525,600 minutes in a year

Birth rate

3,600,000/525,600 = 6.85

6 0
3 years ago
Hurry please<br> I need the answer to this one in 2 minutes
adoni [48]

Answer:

125

Step-by-step explanation:

45 ÷9=5

5² or 5×5=25

25×5=125

Hope this helps!

7 0
2 years ago
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The image for this is attached for reference. This problem can be used by the Pythagorean equation.  To make solving convenient, let us see only one part of the tent. Hence, one side is half of the tend width which is 16/2ft. Height is 12 ft. The unknown side is the hypotenuse. The answer is: 
a^{2} + b^{2}  = c^{2}    8^{2} + 12^{2}  = c^{2}   c = 14.4

7 0
3 years ago
Four mathematicians, three physicists, and an engineer are to be seated equally spaced around a circular table. How many differe
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First, we can choose the seats for the four mathematicians.  Then we seat the physicits, then the engineer.  There are 4! ways to seat the mathematicians, then 3! ways to seat the physicists, then 1! ways to seat the engineer.  But then we must divide by 8, because we can rotate the table, so there are 8!*4!*3!/8 = 725760 ways to seat everyone.

3 0
3 years ago
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