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3 years ago

10

What is the length of a diagonal of a cube with a side length of 3 cm? cm cm cm cm

1 answer:

Evgen [1.6K]3 years ago

4 0

Answer:

5.2cm

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

I WILL GIVE BRAINIEST!!

Vikki [24]

In order to prove that this quadrilateral is a parallelogram, we need to get the opposite sides to be parallel.

The answer would be D because it shows 2 triangles to be equal. If they are equal then they must have corresponding sides.

5 0

3 years ago

Income tax returns show that the mean income of self-employed persons in a particular year was £15,000, with a standard deviatio

DochEvi [55]

Answer:

Yes, There is significant difference.

Step-by-step explanation:

Null Hypothesis , H0 : Mean income = 15000

Alternate Hypothesis , H1 : Mean income ≠ 15000

t = (x - u) / ( s / √n)

x = sample mean = 14500 here, u = population mean = 15000 here , s = standard deviation = 975 here , n = sample size

t = (14500 - 15000) / (975 / √169)

-500 / 75 = - 6.66

As calculated t value in absolute terms is > 1.96 , ie tabulated value at 95% significance level (two sided). So we reject the null hypothesis in favor of alternate hypothesis. Hence, we state that 'Mean Income ≠ 15000'

6 0

2 years ago

How do you graph y=6x-3

diamong [38]

y=6x-3

put a point on (0,-3) this is your y intercept

go up 6 and over 1 this should land you at (1,0) do this again and your at (2,6)

go back to the y intercept now go down 6 and over 1, this should land you (-1,-6)

continue to do this until you graph is filled

3 0

2 years ago

<img src="https://tex.z-dn.net/?f=%5Chuge%5Ccolor%7Byellow%7D%5Cunderline%20%5Ccolorbox%7Bviolet%7D%20%7B%5Ccolor%7Bred%7D%7BQUE

Paladinen [302]

Answer:

FALSE
TRUE
TRUE

Step-by-step explanation:

<u>1.</u>

Non-standard units can be used to measure volume
Examples : m³, in³, cm³, mm³, L

<u>2.</u>

The volume of a rectangular prism can be found by multiplying the length, width, and height
<u>V = lwh</u>

<u />

<u>3.</u>

If there are smaller units, then naturally more of the units will be used
If there are larger units, then less of the units will be used

8 0

2 years ago