The random variable X has a p.d.f P(X=x) foe x= 1,2 3 as shown below
E(x)=∑ XiPi
Find
i) E(x)
ii) E(3)
ii) E(x²)
iv) E(5x+3)

The oldest Kim could be 7.

What is inequality?

The occurrence of an unfair and/or unequal distribution of opportunities and resources among the people that make up a society is referred to as inequality. To different people and in various settings, the word "inequality" may indicate different things.

Here,

Given

Josh is 4 years older than 2 times Kim's age.

The sum of their ages is less than 25.

We have to find the age of Kim.

Let Kim's age be x.

Then Josh's age is (2x+4)

The total is

 x + (2x+4) < 25.

Simplify and solve the inequality for x

 3x + 4 < 25

3x < 25-4= 21

 x < 21/3 = 7

Hence,  the oldest Kim could be 7.

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The family monthly payment on annual interest is 1691.

What is annual interest rate?

Calculation of amount payable to the bank

Cost of House  -  350000

Down payment 10%  -  35000

Amount payable  -  315000

]5% Annual interest rate and compounded monthly is 186.28030751

A) family monthly payment= Amount payable/Annuity factor =315000/186.28030751 =1691

B)Total interest paid on loan =293756.40

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The value of the other points in the number line for each case are;

a) M = -2¹/₂

N = -1

R = 4

b) M = -1

P = 1

R = 1.6

c) M = -125

P = 125

N = -50

d) N = -6

P = 15

R = 24

a) We are given that P = 2¹/₂

From the point 0 of the number line to point P is 5 units and as such;

Each unit = 2¹/₂/5 = ¹/₂

Thus;

M = -2¹/₂

N = -1

R = 4

b) We are given that N = -0.4

From the point 0 of the number line to point N is 2 units and as such;

Each unit = 0.4/2 = 0.2

Thus;

M = -1

P = 1

R = 1.6

C) We are given that R = 200

From the point 0 of the number line to point R is 8 units and as such;

Each unit = 200/8 = 25

Thus;

M = -125

P = 125

N = -50

D) We are given that M = -15

From the point 0 of the number line to point N is 5 units and as such;

Each unit = 15/5 = 3

Thus;

N = -6

P = 15

R = 24

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The correlation between the obesity rate and the mortality rate is moderately strong.

In math correlation is defined as the a statistical measure that expresses the extent to which two variables are linearly related

Here we have given that Colorectal cancer (CRC) is the third most commonly diagnosed cancer among Americans (with nearly 147.000 new eases), ami the third leading cause of cancer death (with over 50.000 deaths annually).

Here the Research was done to determine whether there is a link between obesity and CRC mortality rates among African Americans in the United States by county.

And we need to find the correlation between obesity rates and mortality rates.

While we looking into the given question we have identified that the regression analysis was carried out to find the relationship between the obesity and CRC mortality rates so the response variable is mortality rate and input variable is obesity.

Therefore, the correlation is moderately stronger than the analyzed data.

Therefore, option (c) is correct.

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The image of P after the rotation of 90° counterclockwise is (-1, 1)

Here we have the point P = (-1, -1), notice that both values are negative, thus, the point is on the third quadrant.

For any point (x, y) on the third quadrant, if we apply a rotation of 90° counterclockwise the new coordinates of the point (coordinates of the image) after the reflection are (y, -x)

In this case the original coordinates are (-1, -1), so the coordinates after the reflection are (-1, -(-1)) = (-1, 1)

The image after the rotation is  (-1, 1).

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Answer:

-9/47

Step-by-step explanation:

[tex]4 \frac{1}{4}x-\frac{1}{3}x=-\frac{3}{4} \\ \\ \frac{17}{4}x-\frac{1}{3}x=-\frac{3}{4} \\ \\ 51x-4x=-9 \\ \\ 47x=-9 \\ \\ x=-\frac{9}{47}[/tex]

Answer:

Step-by-step explanation:

- 5/12

i did the test lol

Answer: Line 1

Step-by-step explanation:

Without looking at the context given, everything seems to be normal, everything is correct. Inputting n = -11 into line 1 makes it true. But when we take a look at the context given, we can see that the equation that it said "6 less than 4 times a number" meaning we were supposed to take 6 and subtract it from 4 times the number, meaning the actual equation is

4n - 6 = 50

Therefore, line 1 made an error

Answer:

4

Step-by-step explanation:

2/3 • 6

*Multiply 2 and 6 by 3.

= (2 × 6) / 3

= 12/3

*12 divided by 3 is equal to 4.

= 4

___________

hope it helps!

Answer:

Step-by-step explanation:3.5 bytes

Answer:

450J/(kg-°C)​

Step-by-step explanation:

the basic stuff of temperature is 3.0kg×5.0°C ，then assumed to be x

the thermal energy was y

then it was a functions y=kx,the k was the specific heat of the material

[tex]k=\frac{6750}{15}[/tex]=450 J/kg·°C

Answer:

80 Meters by 80 Meters

Step-by-step explanation:

Perimeter is the distance around the rectangle.  60+60+100+100 = 320

The perimeter is 320 meters.

Area = Length times width

The area would be

100x 60 = 6,000 [tex]m^{2}[/tex]

If we change the length and width to 80 meters we would have the same perimeter

80+80+80+80 = 320 Meters, but the area would be larger

Area = 80 x 80 = 6,400 [tex]m^{2}[/tex]

Answer:

Since Adil takes 25 seconds to complete the race, and Tom takes 24 seconds, Tom wins the race.

Step-by-step explanation:

To determine who wins the race, we need to first convert the given information into comparable units. The speed of Adil is given in kilometers per hour, while the time taken by Tom to complete the race is given in seconds. We can convert Adil's speed to meters per second by dividing by 3.6:

28.8 km/hr = 28.8 km/hr * (1 hour / 3600 seconds) * (1000 meters / 1 km)

         = 8 meters/second

We can then use this value to find the time it takes Adil to complete the race:

time = distance / speed

   = 200 meters / 8 meters/second

   = 25 seconds

Since Adil takes 25 seconds to complete the race, and Tom takes 24 seconds, Tom wins the race.

The period of some number of  consecutive days during which the team must  play exactly 14 games should be that 2 games plays at  these days  1,5,10,15,20,25,30 individually....

As there are 30 days in a month.

So we have to arrange these 14 games during this time period of 30 days,

Which will be arranged as:

suppose its 1 st month of 2023,

So,

2 games at day  =    1/1/2023

2 games at day   =    5/1/2023

2 games at day   =    10/1/2023

2 games at day   =    15/1/2023

2 games at day   =    20/1/2023

2 games at day   =    25/1/2023

2 games at day   =    30/1/2023  

So from here we conduct:

2+2+2+2+2+2+2=  14 games

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The perimeter of ΔMNP is calculated as; 130

From the given image, it is clear that some sides are congruent to others as indicated.

Thus, we see the following;

QM is parallel and congruent to RS.

Similarly, we see that QR is parallel and congruent to MS.

PR is parallel and congruent to QS.

NR = PR because of line segment division.

Thus, we can plug in the relevant values to get;

PR = QS = 22 = NR

Similarly, MS = SP = QR = 25

RS = x + 4 and so;

x + 4 + x + 4 = 5x - 34

42 = 3x

x = 14

MN = 5(14) - 34

MN = 36

Thus, the perimeter of ΔMNP = 36 + 25 + 25 + 22 + 22

= 130

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Answer:

y = 3x + 37

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 8, 13 ) and (x₂, y₂ ) = (- 6, 19 )

m = [tex]\frac{19-13}{-6-(-8)}[/tex] = [tex]\frac{6}{-6+8}[/tex] = [tex]\frac{6}{2}[/tex] = 3 , then

y = 3x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (- 8, 13 ) , then

13 = 3(- 8) + c = -24 + c ( add 24 to both sides )

37 = c

y = 3x + 37 ← equation of line

The degree of a polynomial is the highest power of the variable in the polynomial. In this case, the highest power of w is 3, so the degree of the polynomial is 3.

The leading coefficient of a polynomial is the coefficient of the term with the highest degree. In this case, the leading coefficient is 12.

In summary, the polynomial -9-8w+3w+12w³ has degree 3 and leading coefficient 12.

Answer:

Hola cómo te llamas Hola

Moment generating function of a random variable is the expectation of a random variable. The moment generating function of the geometric(p) distribution is given by pe^{t}/ (1 - (1 - p)e^{t}.

A moment generating function can be described as

MGFₓ(t) = E( e^{tx})

For continuous x

E( e^{tx}) = ∫ₓ e^{tx}×f(x)×d(x) where f(x) is the probability density function.

For discrete x

E( e^{tx}) = ∑ₓ e^{tx}×P(x) where P(x) is the probability mass function.

A geometric distribution is a discrete probability distribution that provide us the probability that the 1st occurrence o success would need k independent trials of success probability p each. Thus probability mass function of geometric distribution is

P(X = k) = (1 - p)^{k} × p

So moment generating function can be obtained by

MGFₓ(t) = E( e^{tx}) = ∑ₓ e^{tx}×P(x)

MGFₓ(t) = ∑ₓ (e^{kt} × (1 - p)^{k} × p)

MGFₓ(t) = p×∑ₓ (e^{t} × (1 - p))^{k}

|e^{t} × (1 - p)| < 1 so applying property of sum of infinite geometric progression we have

MGFₓ(t) = p× e^{t}/ (1 - (1 - p)e^{t}

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As calculated from the data (1/6)² is the probability of getting 5 of same number on all the dice.

b.)If we will limit the number of winners then we will be able to provide them with large prizes and that also by taking moderate rate from everyone.

Actually, the likelihood of winning is closer to one-third (25/72).

Carnival game organizers want you to believe, like I did, that a game is fair so that you will participate.

The likelihood that you would win a game was just about 1/3, so you probably wouldn't squander your money.

Therefore,

The likelihood of getting five of the same number on all six dice is (1/6)².

Probabilities are mathematical representations of the likelihood that an event will occur or that a statement is true.

Probability can also be expressed using a tree diagram.

The tree diagram makes it easier to organize and see all of the potential outcomes. The tree's branches and ends are its two primary locations. On each branch is written the probability, and the ends hold the results in the end.

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For automobile traffic, dB=81.987657 dB.

For quiet conversation is 40.33423 dB.

For fender guitar, 115.56302 dB.

For jet engine, 151.98657 dB.

(A)

The intensity of automobile traffic is, I=1.58x10^8 I.

Given: dB=10 log (I/I0)

Substituting the value of I,

dB= 10 log (1.58x10^8 I/I)

=10 log (1.58x10^8)

Using the logarithm property,

=10 (log (1.58)+log (10^8))

=10 (log (1.58)+8 log (10)

=10( log (1.58)+8(1)

=80+1.98657

=81.98657

Thus, for automobile traffic, dB=81.987657 dB.

B)

Quiet conversation, I=10800 I0

dB= 10 log (10800 I0/I0)

=10 log (10800)

=10 log (1.08x10^4)

=10 log (1.08)+log (10^4)

=10 (log (108)+4log (10))

=10 (log (1.08+4*(1))

=40+10 log (1.08)

=40+0.33423

=40.33423 dB.

Thus, for quiet conversation is 40.33423 dB.

C)

Fender guitar, I=3.16x10^11 I0

dB= 10 log (3.16x10^11 I0/I0)

=10 (log (3.16)+11)

=110+10 log (3.16)

=110+5.56302

=115.56302

Thus, for fender guitar, 115.56302 dB.

D)

Jet engine, I=1.58x10^5 I0

dB= 10 log (1.58x10^15 I0/I0)

=10 (log (1.58)+15)

=150+10 log (1.58)

=150+1.98657

=151.98657

Thus, for jet engine, 151.98657 dB.

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Answer:

P (n,r)

Step-by-step explanation:

The correct representation for a permutation is P (n,r).

Answer: Luisa is correct.

Step-by-step explanation: Luisa is correct. To find the solution to the equation, we need to isolate the radical expression on one side of the equation. If we subtract x from both sides, we get √5 + 4x - x = x - x, or √5 = 0. Since the square root of any number is always positive, this equation has no solution. Therefore, the solution is H = 5.

On the other hand, if we square both sides of the equation, we get 5 + 8x + 4x^2 = x^2. If we simplify this equation, we get x^2 + 8x - 5 = 0. This equation can be solved using the quadratic formula, which gives us x = (-8 +/- sqrt(64 + 20))/2. This simplifies to x = (-8 +/- sqrt(84))/2. The solutions to this equation are x = -1 and x = 5. However, since we squared both sides of the original equation, we have to check whether these solutions actually work in the original equation. Substituting x = -1 into the original equation gives us √5 + 4(-1) = -1, or √5 = -1. This is not a valid solution, since the square root of any number is always positive. However, substituting x = 5 into the original equation gives us √5 + 4(5) = 5, or √5 = 0. This is a valid solution, since the square root of any number is always positive. Therefore, the only solution to the original equation is x = 5, which is the solution that Luisa found.

Using the specified oriented surface, the surface integral is F=y³i+8j-xk is a downward-pointing normal is -53/60.

Given that,

We have to find using the specified oriented surface, calculate the surface integral: F=y³i+8j-xk is a downward-pointing normal that is a part of the plane x+y+z=1 in the octant x,y,z≥0.

We know that,

Finding the surface integral of [tex]\int {} \,\int\limits_s {F} \, ds[/tex]

Here,

The surface of the plane's part is x+y+z=1;

In the 1st octant, x,y,z≥0, and the oriented surface F=y³i+8j-xk.

The plane x + y + z = 1

z=1-x-y

dz/dx=-1

dz/dy=-1

So, the surface is oriented downward

dS= (dz/dzi+dz/dyj-k)dxdy

dS=(-i-j-k)dxdy

So, we get

[tex]\int {} \,\int\limits_s {F} \, ds[/tex]

[tex]\int {} \,\int\limits_s {F} \, (dz/dzi+dz/dyj-k)dxdy[/tex]

-53/60

Therefore, Using the specified oriented surface, the surface integral is F=y³i+8j-xk is a downward-pointing normal is -53/60.

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The true statements are

Consider the two points in the line

(-1, 1) and (3, 2)

The slope of the line = (2-1) / (3 -(-1))

= 1/4

The slope intercept form is

y = mx + b

2 = (1/4)3 + b

2 = 3/4 + b

b = 2 - (3/4)

b = 5/4

The equation of the line y = (1/4)x + 5/4

(3, 2) and (-1, 1) are points on the line

Consider the point (1, 3/2)

3/2 = (1/4)1 + 5/4

3/2 = 1/4 + 5/4

3/2 = 3/2

Therefore, (1, 3/2) is the solution of the line

It has infinitely many solutions

Therefore, the correct statements are statements A, B, C, E, F

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Answer:

The answer is (10) 8' and (3) 12 A

Step-by-step explanation:

To build a wall that is 12' long and 8' high, you will need (10) 8' 2x4's and (3) 12' 2x4's. This will give you the necessary length for the bottom and top plates and 10 studs. Each stud should be spaced about 16" on center, so 10 studs will be enough to support the wall.

Answer:

C. $6,500

Step-by-step explanation:

Owner's equity is the amount of the business's assets that are owned by the owner or shareholders. It is calculated by subtracting the total liabilities from the total assets.

Given that Total assets = $34,500 and Total liabilities = $28,000, the owner's equity is:

Owner's equity = Total assets - Total liabilities

= $34,500 - $28,000

= $6,500

Therefore, the correct answer is C. $6,500.

The percentage of miles the car has left in battery charge is 10.77%

Total distance traveled when fully charged = 260 miles

The total charged used by the car = 232 miles of charges

The remaining charges left in the car battery = Total distance traveled when fully charged - The total charged used by the car

Here we have to use the subtraction

Substitute the values in the equation

= 260 - 232

= 28 miles of charges

The percentage of miles the car has left in battery charge = (28/260) × 100

= 10.77%

Therefore, 10.77% miles of charge left in the battery

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Answer:

24

Step-by-step explanation:

(9-3)×4

(6)×4

The answer is 24