Its calculus. I need help for (i). Thank you.​

The random variable X has a pdf P(X=x) for x = 1,2,3 then,

1) E(x)= 2.2

2) E(3) = 0.9

3) E(x²) = 2.26    

4) E(5x + 3)= 14.

Probability Density Function (pdf) is a statistical expression that defines a probability distribution for a discrete random variable as opposed to a continuouse random variable.

We have given that,  

E(x) = ∑xipi

1) E(x) = ∑xipi

         = x₁p₁ + x₂p₂ + x₃p₃

         = 1(0.1) + 2(0.6) + 3(0.3)

         = 0.1 + 1.2 + 0.9

  E(x) = 2.2

2)E(3) = x₃p₃

          = 3(0.3)

   E(3) = 0.9

3) E(x²) = ∑xi²pi²

           = x₁²p₁² + x₂²p₂² + x₃²p₃²

           = 1(0.1)² + 4(0.6)² + 9(0.3)²

           = 0.01 + 1.44 + 0.81

   E(x²) = 2.26

4) E(5x + 3) = ∑5(xipi) + 3

                  = (5x₁p₁ + 5x₂p₂ + 5x₃p₃) + 3

                  = (5(0.1) + 10(0.6) + 15(0.3)) + 3

                  = 0.5 + 6 + 4.5 + 3

   E(5x + 3) = 14

Therefore the random variable X has a pdf P(X=x) for x = 1,2,3 is

E(x) = ∑xipi then E(x) = 2.2, E(3) = 0.9, E(x²) = 2.26 and E(5x + 3) = 14.

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We will get y = -7x + 6  in graph y-intercept 6 and slope-7.

The equation of the line with a y-intercept of 6 and a slope of -7 can be written in slope-intercept form as:

y = mx + b

where m is the slope and b is the y-intercept.

Substituting the given values, we get:

y = -7x + 6

So the equation of the line is y = -7x + 6.

slope -7 and y - intercept 6.

Slope intercept form: y = mx + b, m=slope, b = y-intercept

y = -7x + 6

Just plug in a value for x and solve for y

x     y=-7x+6

------------------

0           6

1          -1

If you plot these two points and draw a straight line through them,

that is the graph of the line.

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The x value is first and the y value is second.point A is at (-3,-6)

Answer:

7

Step-by-step explanation:

The sum of the two number is 10 + x, which when doubled equals 36. Divide the 36/2, which gets to 18. Move the 10 to the other side which gets 18-10 to get 8. 20 years from now, so add 20. 20+8 is 28. 4 times my present age. So do the inverse and you will get 28/4 which equals 7. You're present age is 7.

Answer:

0.4 / 41=0.009760

It starts to repeat the same numbers

Step-by-step explanation:

Answer:

I think 5 tomatoes cost $1.80

Answer:

Ralphs.

Step-by-step explanation:

Ralphs:

5 tomatoes = $1.80

    1 tomato = $0.36

Vons:

3 tomatoes = $1.14

    1 tomato = $0.38

Hence, Ralphs would be a better buy.

Answer:

Step-by-step explanation:

Let the number of games be x

Inequality:

Since there should be more than 0 left, another inequality for it:

So 13 < x < 15, which leaves us with 14

Answer:

See below.

Step-by-step explanation:

1)

So we have:

\(\exists x\in\mathbb{N},y\in\mathbb{Z}|x^2=y^2\)

This can be interpreted as:

"There exists a natural number x and an integer y such that x² is equal to y²."

2)

So we want even numbers are in the set of integers.

\(\{2n:n\in\mathbb{Z}\}\in\mathbb{Z}\)

This is interpreted as:

"The set of even numbers (2n such that n is an integer) is in the set of integers"

No, the rank of the product of two n by n square matrices A and B, denoted as AB, cannot be less than n-1 if both A and B have ranks of n-1.

According to the Rank-Nullity theorem, for any matrix M, the sum of its rank and nullity is equal to the number of columns in M. In this case, the number of columns in AB is n, so the sum of the rank and nullity of AB must be n.

If rank(A) = rank(B) = n-1, it means that both A and B have nullity 1. The nullity of a matrix is the dimension of its null space, which consists of all vectors that get mapped to the zero vector when multiplied by the matrix. Since both A and B have rank n-1, their null spaces consist only of the zero vector.

Now, considering AB, if the rank of AB were less than n-1, it would mean that the nullity of AB is greater than 1.

However, this would violate the Rank-Nullity theorem since the sum of the rank and nullity of AB must be n, which is the number of columns.

Therefore,  if rank(A) = rank(B) = n-1, the rank of AB cannot be less than n-1.

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Answer: 22.4402

Step-by-step explanation:

Answer:

84.4% of 23 is 19.412.

Step-by-step explanation:

Let the unknown number be x.

Now, 84.4% of x = 19.412.

∴ (84.4 ÷ 100) × x = 19.412.

By simplifying the equation,

x = (19.412 × 100) ÷ 84.4

x = 1941.2 ÷ 84.4

∴ x = 23

Thus, 84.4% of 23 is 19.412.

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Answer:

a^2+b^2+2|a||b|≥a2+b2+2ab(|a|+|b|)2≥|a+b|2(∵∀x∈R;x2=|x|2)∴|a|+|b|≥|a+b|\

Step-by-step explanation:

Answer:

I dont know but I can direct.

Step-by-step explanation:

The median is a middle number in a sorted, ascending or descending, list of numbers.

The quartile measures the spread of values above and below the mean by dividing the distribution into four groups.

The interquartile range describes the middle 50% of values when ordered from lowest to highest.

Answer: median: 133.5

               first quartile: 128

              third quartille: 139

             interquartille range: 11

Step-by-step explanation:

Answer:

19

Step-by-step explanation:

Using a system of equations, it is found that:

------------------------

\(x + y = 108\)

Since \(x = 2y\)

\(2y + y = 108\)

\(3y = 108\)

\(y = \frac{108}{3}\)

\(y = 36\)

\(x = 2y = 2(36) = 72\)

Zoe is 36 inches tall.

Claire is 72 inches tall.

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The coordinates of point A are (7/5, 0), and the perpendicular line that also passes through that point is:

y = 0.

Here we want to get a line perpendicular to:

5x - 7 = 0

Solving this for x, we get:

5x = 7

x = 7/5.

This is a vertical line, so the perpendicular line will be a horizontal line, which is of the form:

y = a.

We know that the line:

x = 7/5.

Cuts the x-axis at point A.

Remember that the x-axis as coordinates (x, 0).

So the coordinates of point A are (7/5, 0).

Now, the perpendicular line:

y = a

Needs to pass through the point (7/5, 0), so the value of a must be zero, then the line is:

y = 0.

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Answer:

C

Step-by-step explanation:

You are required to provide the measurement in inches for each measurement given on the left column. The first one is solved thus;

Therefore we shall use the same conversion rate of 12 inches equals 1 foot to solve the others as follows;

Answer:

The average rate of change of f on the interval [-4, -2] is -11.

Step-by-step explanation:

Recall that the average rate of change of a function over an interval is simply the slope of the line connecting the two endpoints.

Therefore, the average rate of change of f on the interval [-4, 2] equals:

\(\displaystyle f_\text{avg}(x) = \frac{f(2)-f(-4)}{2-(-4)}\)

Evaluate:
\(\displaystyle \begin{aligned} f_\text{avg}(x) & = \frac{f(2)-f(-4)}{2-(-4)} \\ \\ & = \frac{(-3)-(63)}{6} \\ \\ &= -11 \end{aligned}\)

In conclusion, the average rate of change of f on the interval [-4, -2] is -11.

The fraction 13/7 lies between the fractions 6/6 and 6/7.

We have,

Between the fractions 6/6 and 6/7, there are infinitely many fractions.

To find a fraction that lies between these two fractions, we can take their average.

The fraction 6/6 simplifies to 1, and the fraction 6/7 cannot be simplified further.

To find the average, we add the two fractions and divide the sum by 2:

(6/6 + 6/7) / 2

To add the fractions, we need a common denominator, which is the least common multiple (LCM) of 6 and 7, which is 42.

Converting the fractions to have a common denominator:

(6/6) x (7/7) + (6/7) x (6/6) / 2

Simplifying the expression:

(42/42 + 36/42) / 2

Combining the numerators:

(78/42) / 2

Dividing:

78/42 = 13/7

Thus,

The fraction 13/7 lies between the fractions 6/6 and 6/7.

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Answer: D) y = -3x + 5

Step-by-step explanation:

Move x.

3y = -9x + 15

Divide by 3.

y = -3x + 5

Hope it helps :) and let me know if you want me to elaborate.

Answer:

D. y = -3x + 5

Step-by-step explanation:

Subtract 9x from both sides

3y = 15 - 9x

y = 15/3 - 9x/3

y = 5 - 3x

y = -3x + 5

A.  The payback period is 7.2 years. The net present value of the proposed investment is 3720.55.

B. No, the project does not meet the company's cash payback criteria.

C.  Yes, the project does meet the net present value criteria for acceptance.

A. The truck costs $55,440 and generates annual cost savings of $7,700. So the payback period is the cost of the truck divided the expected amount the truck will generate.

                $55,440 / $7,700 = 7.2 years

To solve for the net present value, we say

Net Present Value = ∑ [(Cash inflow in period t) / (1 + \(r^{t}\)] - Initial Investment.

NPV = (($7,700 / (1 + 0.08)¹) = 7 129.63

+ ($7,700 / (1 + 0.08)²) = 6601.51

+ .($7,700 / (1 + 0.08)³ = 6112.51

+ ($7,700 / (1 + 0.08)⁴) = 5659.73

+ ($7,700 / (1 + 0.08)⁵) = 5240.49

+ ($7,700 / (1 + 0.08)⁶) = 4 852.31

+ ($7,700 / (1 + 0.08)⁷) = 4492.88

+($7,700 / (1 + 0.08)⁸)  = 4160.07

+ ($27,600 / (1 + 0.08)⁸)) = 14911.42

- $55,440

We add all these values together and subtract by  $55,440

7 129.63 + 6601.51 + 6112.51 + 5659.73 + 5240.49 +4 852.31 + 4492.88 + 4160.07 + 14911.42 - $55,440

59160.55 - 55,440

NPV = 3720.55

B. The cash payback period of the project is 7.2 years. The company's cash payback criteria state that a project should not be accepted unless it has a payback period that is less than 50% of the asset's estimated useful life, which would be 4 years which is 50% of 8 years. Since 7.2 years is greater than 4 years, the project does not meet the company's cash payback criteria.

C. The positive NPV of $3,720.55 shows that embarking on the prooject will be valuable to the company. This means the project meets the NPV criteria for acceptance.

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The slope of the line on the graph is - 2

The given parameter is the line on the graph

From the above graph, we have the following points

(x₁, y₁) = (0, 0)

(x₂, y₂) = (3, -6)

The slope of a line can be calculated using the following slope formula

Slope = (y₂ - y₁)/(x₂ - x₁)

Where

(x₁, y₁) = (0, 0) and (x₂, y₂) = (3, -6)

Substitute the known values in the above equation

So, we have the following equation

Slope = (-6 - 0)/(3 -0)

Evaluate the quotient

Slope = -2

Hence, the slope is -2

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Answer:

RT = 81

Step-by-step explanation:

RT = RS+ST

13y – 23 = ( 6y+2) + (3y+7)

13y – 23 = 9y +9

13y – 9y = 9+23

4y = 32

y = 32/ 4

y=8

RT= 13y – 23 = 13 (8) – 23 = 104 – 23 = 81

___o___o___

If you want RS , ST

RS = 6y +2 = 6(8)+2 = 48 +2=50

ST = 3y +7 = 3(8) +7 = 24 + 7 =31

I hope I helped you^_^

The value of side length x (DF) in the triangle is 4.

The figures in the image is that of two similar triangle.

Triangle ABC is similar to triangle DEF.

From the diagram:

Leg 1 of the smaller triangle DE = 5

Leg 2 of the smaller triangle DF = x

Leg 1 of the larger triangle AB = 30

Leg 2 of the larger triangle AC = 24

To find the value of x, we take the ratio of the sides of the two triangle since they similar:

Hence:

Leg DE : Leg DF = Leg AB : Leg AC

Plug in the values:

5 : x = 30 : 24

5/x = 30/24

Cross multiplying, we get:

30x = 5 × 24

30x = 120

x = 120/30

x = 4

Therefore, the value of x is 4.

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Answer:

159

Step-by-step explanation:

by expansion and simplifying:

100+64-5=159

Answer:

159

Step-by-step explanation:

You need to remember BIDMAS

B - brackets

I - indecieas 4 to the power of 5 for example

D - divide

M - multiply

A - add

S - subtract

Its the order in which you have to do everything.

So first do the brackets

3 + 5 = 8 and then do the indecies so 8 squared = 64

then do 10 cubed which is 100

for the moment we have 100 + 64 - 5

so the answer is 159

Hope this helps :D

The total cost needed to tile the training room with an area of 100 m² is R110.

An equation is an expression that shows the relationship between two or more numbers and variables.

Let assume that the area of the trainig room is 100 m² and one box can complete 50 m², hence:

number of box needed = 100 m² / 50 m² = 2

Total  cost = R55 per box * 2 box = R110

The total cost needed to tile the training room with an area of 100 m² is R110.

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Answer:

Step-by-step explanation:

-206

when you divide those two numbers you get a negative number and a decimal because you are dividing by a decimal with a negative sign.

Answer:

-21

...

I think, let me know if I'm wrong

Answer: 691

Step-by-step explanation:

(17 + 6 + 9) × (19 + 16) - 19 × 7 - 6 × 4 - 16 × 17 = 691