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andreev551 [17]

3 years ago

14

If two lines are parallel and one has a slope of 8, what is the slope of the other line

1 answer:

tresset_1 [31]3 years ago

6 0

Answer: 8

Parallel lines always have the same slope.

[I attached a picture that might help show you]

The lines do NOT Intersect.

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The length of a rectangle is twice the width. If the perimeter of the rectangle is 60 units, find the area of the rectangle.

Snowcat [4.5K]

200

Let width = x
Let length = 2x
Let’s area = a

x+2x+x+2x=60

Combine the terms

6x = 60

Divide both sides by 6

x = 10

Width = 10
Length = 2*10 = 20

Area = 10*20 = 200

7 0

3 years ago

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

3 years ago

Which Heinz Ketchup offer is the better deal? (Assume the price stays proportional and the Ketchup is

Andrew [12]

B because you get more for a cheaper price.

7 0

3 years ago

5. A life insurance policy costs $16.00 for every $1,000.00 of insurance. At

attashe74 [19]

Answer:

800.00

Step-by-step explanation:

so you give me a hint that was for every 16.00 it was 1000.00

i did 16x50=800

i got 50 from <u>50</u> in 50000 and the 16 from <u>16.00 so then i times 16 from 50 which is 800</u>

5 0

3 years ago

Question 16 (Essay Worth 7 points)<br><br> Verify the identity.<br><br> tan (x + π/2) = -cot x

Rus_ich [418]

Step-by-step explanation:

We know that tan=sin/cos, so tan(x+π/2)=

$\frac{sin(x+pi/2)}{cos(x+pi/2)}$

Then, we know that sin(u+v)=sin(u)cos(v)+cos(u)sin(v),

so our equation is then

$\frac{sin(x)cos(\pi/2)+cos(x)sin(\pi/2)}{cos(x+\pi/2)} = \frac{cos(x)}{cos(x+\pi/2) }$

Then, cos(u+v)=cos(u)cos(v)-sin(u)sin(v), so our expression is then

$\frac{cos(x)}{cos(x)cos(\pi/2)-sin(x)sin(\pi/2)} = \frac{cos(x)}{-sin(x)} = -cot(x)$

6 0

3 years ago