The average weekly salary of two employees is $5250. One makes $500 more than the other. Find their salaries.

Answer:

(a): Marginal pmf of x

[tex]P(0) = 0.72[/tex]

[tex]P(1) = 0.28[/tex]

(b): Marginal pmf of y

[tex]P(0) = 0.81[/tex]

[tex]P(1) = 0.19[/tex]

(c): Mean and Variance of x

[tex]E(x) = 0.28[/tex]

[tex]Var(x) = 0.2016[/tex]

(d): Mean and Variance of y

[tex]E(y) = 0.19[/tex]

[tex]Var(y) = 0.1539[/tex]

(e): The covariance and the coefficient of correlation

[tex]Cov(x,y) = 0.0468[/tex]

[tex]r \approx 0.2657[/tex]

Step-by-step explanation:

Given

x = bottles

y = carton

See attachment for complete question

Solving (a): Marginal pmf of x

This is calculated as:

[tex]P(x) = \sum\limits^{}_y\ P(x,y)[/tex]

So:

[tex]P(0) = P(0,0) + P(0,1)[/tex]

[tex]P(0) = 0.63 + 0.09[/tex]

[tex]P(0) = 0.72[/tex]

[tex]P(1) = P(1,0) + P(1,1)[/tex]

[tex]P(1) = 0.18 + 0.10[/tex]

[tex]P(1) = 0.28[/tex]

Solving (b): Marginal pmf of y

This is calculated as:

[tex]P(y) = \sum\limits^{}_x\ P(x,y)[/tex]

So:

[tex]P(0) = P(0,0) + P(1,0)[/tex]

[tex]P(0) = 0.63 + 0.18[/tex]

[tex]P(0) = 0.81[/tex]

[tex]P(1) = P(0,1) + P(1,1)[/tex]

[tex]P(1) = 0.09 + 0.10[/tex]

[tex]P(1) = 0.19[/tex]

Solving (c): Mean and Variance of x

Mean is calculated as:

[tex]E(x) = \sum( x * P(x))[/tex]

So, we have:

[tex]E(x) = 0 * P(0) + 1 * P(1)[/tex]

[tex]E(x) = 0 * 0.72 + 1 * 0.28[/tex]

[tex]E(x) = 0 + 0.28[/tex]

[tex]E(x) = 0.28[/tex]

Variance is calculated as:

[tex]Var(x) = E(x^2) - (E(x))^2[/tex]

Calculate [tex]E(x^2)[/tex]

[tex]E(x^2) = \sum( x^2 * P(x))[/tex]

[tex]E(x^2) = 0^2 * 0.72 + 1^2 * 0.28[/tex]

[tex]E(x^2) = 0 + 0.28[/tex]

[tex]E(x^2) = 0.28[/tex]

So:

[tex]Var(x) = E(x^2) - (E(x))^2[/tex]

[tex]Var(x) = 0.28 - 0.28^2[/tex]

[tex]Var(x) = 0.28 - 0.0784[/tex]

[tex]Var(x) = 0.2016[/tex]

Solving (d): Mean and Variance of y

Mean is calculated as:

[tex]E(y) = \sum(y * P(y))[/tex]

So, we have:

[tex]E(y) = 0 * P(0) + 1 * P(1)[/tex]

[tex]E(y) = 0 * 0.81 + 1 * 0.19[/tex]

[tex]E(y) = 0+0.19[/tex]

[tex]E(y) = 0.19[/tex]

Variance is calculated as:

[tex]Var(y) = E(y^2) - (E(y))^2[/tex]

Calculate [tex]E(y^2)[/tex]

[tex]E(y^2) = \sum(y^2 * P(y))[/tex]

[tex]E(y^2) = 0^2 * 0.81 + 1^2 * 0.19[/tex]

[tex]E(y^2) = 0 + 0.19[/tex]

[tex]E(y^2) = 0.19[/tex]

So:

[tex]Var(y) = E(y^2) - (E(y))^2[/tex]

[tex]Var(y) = 0.19 - 0.19^2[/tex]

[tex]Var(y) = 0.19 - 0.0361[/tex]

[tex]Var(y) = 0.1539[/tex]

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

Covariance is calculated as:

[tex]COV(x,y) = E(xy) - E(x) * E(y)[/tex]

Calculate E(xy)

[tex]E(xy) = \sum (xy * P(xy))[/tex]

This gives:

[tex]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)[/tex]

[tex]E(xy) = 0*0 * 0.63 + 1*0 * 0.18 +0*1 * 0.09 + 1*1 * 0.1[/tex]

[tex]E(xy) = 0+0+0 + 0.1[/tex]

[tex]E(xy) = 0.1[/tex]

So:

[tex]COV(x,y) = E(xy) - E(x) * E(y)[/tex]

[tex]Cov(x,y) = 0.1 - 0.28 * 0.19[/tex]

[tex]Cov(x,y) = 0.1 - 0.0532[/tex]

[tex]Cov(x,y) = 0.0468[/tex]

The coefficient of correlation is then calculated as:

[tex]r = \frac{Cov(x,y)}{\sqrt{Var(x) * Var(y)}}[/tex]

[tex]r = \frac{0.0468}{\sqrt{0.2016 * 0.1539}}[/tex]

[tex]r = \frac{0.0468}{\sqrt{0.03102624}}[/tex]

[tex]r = \frac{0.0468}{0.17614266944}[/tex]

[tex]r = 0.26569371378[/tex]

[tex]r \approx 0.2657[/tex] --- approximated

Answer:

A) can be used to conduct a test about a hypothesized population regression function slope.

Step-by-step explanation:

A least squares regression line is a standard technique in regression analysis used to make the vertical distance obtained from the data points running to the regression line to become very minimal or as small as possible.

In Mathematics, residuals are used to measure or determine whether or not the line of regression is a good fit or match for the data by subtracting the difference between them i.e the predicted y value and the actual y value, for the x value respectively.

The confidence interval for the sample regression function slope can be used to conduct a test about a hypothesized population regression function slope.

Answer: 1 = 90 2=58 3=90 6=58 7=8

Step-by-step explanation:

I don’t know what 4 and 5 are

9514 1404 393

Answer:

  7.7 seconds

Step-by-step explanation:

The solution is given by the quadratic formula.

For ax² +bx +c = 0, the roots are ...

  x = (-b±√(b²-4ac))/(2a)

We want the positive root, so ...

  x = (-113 -√(113² -4(-16)(74)))/(2(-16)) = (113 +√17505)/32 ≈ 7.6658

The rocket will hit the ground about 7.7 seconds after it is launched.

Answer:

angle BOC

Step-by-step explanation:

complementary angles add up to 90 degrees

Answer:

option 2

Step-by-step explanation:

a colored in dot is less than or equal to or greater than or equal to while an uncolored dot is less then or greater than. arrow going left of the number is less than arrow going right is greater than. the problem is a is greater than 4/5 so an uncolored dot shout be on 4/5 going to the right

Answer:

Part A: Rewrite the expression by factoring out the greatest common factor. (4 points)

answer:

2y(x³+4x-2x²-8)

Part B: Factor the entire expression completely. Show the steps of your work. (6 points)

answer:

2y(x³+4x-2x²-8)

2y(x³-2x²+4x-8)

2y(x²(x-2)+4(x-2))

2y(x²+4)(x-2)

Answer:

Wassup what do you need help with

Answer:

About 131.95 (you may have to round up)

Step-by-step explanation:

Volume of a cone = pi(r^2)(h/3)

= pi(3^2)(14/3)

= pi(9)(4 & 4/5)

= pi(43.2)

If your teacher wants an exact number, you have to multiply 43.2 y whatever your teacher says to shorten pi to, usually 3.14. The about 131.95 is from 43.2*3.14 I think.

Answer:

Step-by-step explanation:

150 -12.2 -rounded

350 -18.4.

add or subtract

Step-by-step explanation:

1st quadrant is(+,+)

2nd quadrant is(+,-)

3rd quadrant is (-,-)

4th quadrant is (-,+)

Answer:

Number 4 is a right triangle whether 3 isnt.

Step-by-step explanation:

I just know this because a right triangle is always gonna have a 90 degree angle whether that number 3 doesnt have one

Answer:

1

Step-by-step explanation:

Answer:

The balance after 4 years would be $1,380.05.

Step-by-step explanation:

Given that you deposit $ 1,200 in a bank account, to find the balance after 4 years in the account pays 3.5% annual interest compounded monthly, the following calculation must be performed:

1,200 x (1 + 0.035 / 12) ^ 4x12 = X

1,200 x 1.00291666 ^ 48 = X

1,380.05 = X

Therefore, the balance after 4 years would be $1,380.05.

Answer:

The balance after 4 years in account pays 3.5% annual interest compounded monthly is 1308.05$

Answer:

[tex]2 \times (7 \times 3 + {3.5}^{2} \times \pi \times 0.5) + (7 + 6 + (7 \times \pi \times 0.5)) \times 9[/tex]

Answer:

2  3   5

Step-by-step explanation:

Answer:-1

Step-by-step explanation:

Answer:

-1

Step-by-step explanation:

Answer:2 and 3

Step-by-step explanation:

They just aren't correct im not sure how to explain

Answer:

Each of the 4 people will get 1/24 of the original cake

Step-by-step explanation:

The fractional part of cake left out is 1/6

This remaining cake is to be divided among four people.

Thus, each person will get

fractional part of cake left/total number of people

i.e 1/6/4

= 1/24

Each of the 4 people will get 1/24 of the original cake

Answer:

Radius is 9

Formula of a circumference is:

2πr

we can use pie/π as 3.14

3.14 x 2 x 9 (radius) = 56.52

Step-by-step explanation:

If there is a diameter only do half of that and that would be your radius.

Answer:

18π inches (or approximately 56.549 inches)

Step-by-step explanation:

The formula to find circumference is 2πr (or πd). Since we are given the radius (which is half of a circle), we will use 2πr, and the radius (or r) is equal to 9. So you just plug that into the circumference formula, and get:

2*π*9 = 18π

So, the circumference is 18π inches or approximately 56.549 inches (when rounded to the nearest thousandths).

Answer:

521,400

Step-by-step explanation:

660 times 790

The area of the rectangular park which having 660 meter and 790 meter is  521400 m².

A = l b is the formula for the Area of a Rectangle. Once the length and width of a rectangle are known, the area is calculated. The area of a rectangle can be calculated by multiplying its length and width.

The area is the amount of space covered by a flat surface of a specific shape. It is expressed as a "number of" square units. The number of unit squares that can fit into a rectangle is defined as its area. Rectangular shapes include the flat surfaces of laptop monitors, blackboards, painting canvas, and so on. The space occupied by these objects can be calculated using the area of a rectangle formula.

In this figure 1 cm = 100 m

6.6 cm * 100m = 660 m

7.9 cm * 100m = 790 m

Area of the park =  521400 m²

To learn more about area refer :

https://brainly.com/question/25292087

#SPJ2

Answer:

So happy you are with brainly

Step-by-step explanation:

34

Answer:

Do 16 times pi.

Step-by-step explanation:

The closest answer is D.

Answer:

8 (option 1)

Step-by-step explanation:

Mark it as option 1 => 8 is the crt answer

2pi r = 16

r = 8

Answer:

exponent

Step-by-step explanation:

Answer:

power or exponent it can be both, but being specific here, choose exponent

Step-by-step explanation:

i studied this concept trust me

Answer:

B

Step-by-step explanation:

Answer: It’s C

Step-by-step explanation:

Answer:

we all know that perimeter is the total distance around us.so the perimeter of a trapezoid is the sum of the lengths of its four sides.if one side is missing use the pythagoras theory.

Step-by-step explanation:

if am wrong please tell me right away

Answer:

i think it would be a) 1/8

Step-by-step explanation:

sorry if its wrong