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The expectation of X, when X is log-normal and log(X) follows a normal distribution with mean m and standard deviation k, is exp(m + k²/2).

Therefore the answer is exp(m + k²/2).

The log-normal distribution is a probability distribution of a random variable whose logarithm is normally distributed. In other words, if X is log-normal, then log(X) follows a normal distribution with mean m and standard deviation k.

The expectation of a random variable is the expected value of the variable, which is a measure of the central tendency of the distribution. For a continuous probability distribution, the expectation is also known as the population mean. The expected value of X can be calculated using the probability density function (PDF) of X.

The expectation of X is calculated as the integral of X × f(X) over the range of X. Where f(X) is the probability density function of X and X is the random variable.

For log-normal distribution, the expectation of X is calculated as follows:

E(X) = exp(m + k²/2)

where m is the mean of log(X) and k is the standard deviation of log(X).

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The number of calories per cup of popcorn is 28 oz and the number of calories per ounce of soda is 14 oz.

A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.

Let the number of calories per cup of popcorn be x and the number of calories per ounce of soda be y.

Roselle has 3 cups of popcorn and 6 oz of soda for a total of 162 calories.

3x+6y=162 ------(I)

Carmel has 1 cup of popcorn and 11 oz of soda for a total of 162 calories.

x+11y=182

x=182-11y------(II)

Substitute equation (II) in equation (I), we have

3(182-11y)+6y=162

546-33y+6y=162

546-162-27y=0

384-27y=0

384=27y

y=384/27

y=14

Substitute y=14 in equation (II), we get

x=182-11(14)

x=28

Therefore, the number of calories per cup of popcorn is 28 oz and the number of calories per ounce of soda is 14 oz.

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"Your question is incomplete, probably the complete question/missing part is:"

Roselle has 3 cups of popcorn and 6 oz of soda for a total of 162 calories. Carmel has 1 cup of popcorn and 11 oz of soda for a total of 182 calories. Determine the number of calories per cup of popcorn and per ounce of soda

Answer:

general sherman is the biggist

Step-by-step explanation:

grant and sherman - 5900

washington and sherman -4650

Answer:

72.38

Step-by-step explanation:

When converting from mm to cm divide the length value by 10

Answer:

B

Step-by-step explanation:

Did this problem yesterday

Answer:

[tex]x = 21[/tex]

Step-by-step explanation:

Apply triangle interior theorem,

[tex]71 + 88 + x = 180[/tex]

[tex]159 + x = 180[/tex]

[tex]x = 21[/tex]

One of the way by which we can solve equivalent questions is by multiplying both the numerator and the denominator by a same number .

The number chosen for the purpose should be same and should be a non zero number. Example, if we want to find the equivalent of 2/8 then we can simply multiply 2 and 8 which are the numerator and the denominator by a same number say 3 .

Then we will get the result as 2 x 3 /8 x 3 = 6 / 24 .

The result will be a number equivalent to the given fraction. This can be checked by reducing the result to its lowest terms.

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The rule to find the cost and the cost of 7 packages can be given as 15n and $105 respectively.

When two quantities have some dependence in their values they can be said proportional to each other.

It can be of two types such as direct and indirect.

The direct proportionality means the values of both the quantities are increasing or decreasing at the same time while the indirect proportionality implies value of one quantity is increasing while the other is decreasing.

The table for the given case can be written as follows,

Packages of Golf Balls                                     Cost

        1                                                                  $15

        2                                                                 $30

        3                                                                 $45

        4                                                                 $60

The relation for proportionality can be obtained as,

15/1 = 30/2 = 45/3 = 60/4 = 15

(A) Suppose n be the number of packages.

Then, the cost is given as 15n.

(B) The cost of 7 packages is as below,

⇒ 15 × 7 = $105

Hence, the answers to both part can be given as 15n and $105 respectively.

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Answer:

a

Step-by-step explanation:

In the given diagram beside a coffee, the value of x is 38.

A diagram is a visual, symbolic representation of data. Diagrams have been used on cave walls since prehistoric times, but they became more common during the Enlightenment. The method occasionally employs the projection of a three-dimensional visualisation onto a two-dimensional surface. Sometimes the word "graph" is used in place of the word "diagram."

We know that all angles here add up to 360°

And with the vertical angles theorem we get the equation

2(36°) + 2(78 - x)° + 2(3x - 10) = 360°

2(36 + 78 - x + 3x - 10) = 360°

2(104 + 2x) = 360°

208 + 4x = 360°

4x = 360 - 208

4x = 152

x = 152/4

x = 38

Thus, In the given diagram beside a coffee, the value of x is 38.

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Answer:

18 is the original number.

Step-by-step explanation:

Let the number be x.

A/Q:-

3 (x-14)= 2/3x

Multiplying by 3 we get

9(x-14)=2x

9x-126=2x

9x-2x=126

7x=126

x =126/7

x=18

Answer:

Let the no. be x

3 (x-14) =

Question 1

The area of the fairway between two streams on a golf course cannot be determined without additional details such as the dimensions or measurements of the fairway and the streams.

Question 2

A. Triangle

To find the area of the fairway, you could separate it into figures whose areas you can find using formulas.

Step 1: Draw a diagram of the fairway, including the two streams and any other relevant features such as bunkers or trees.

Step 2: Divide the fairway into two sections, one on either side of the streams.

Step 3: Measure the width and length of each section of the fairway.

Step 4: Use the formula for the area of a rectangle to find the area of each section. (Area = width x length)

Step 5: Add the areas of the two sections together to find the total area of the fairway between the two streams.

The base of the trapezoid would be the width of the fairway and the width of the stream, and the height would be the distance between the fairway and the stream. The area of a trapezoid is (a+b)h÷2, where a and b are the lengths of the bases and h is the height. The triangle would be formed by the side of the trapezoid that is the distance between the fairway and the stream, and the width of the stream. The area of a triangle is base×height÷2.

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The weighted average of Shenandoah's test scores is 82.3.

What is the weighted average?

To find a weighted average, multiply each number by its weight, then add the results. If the weights don't add up to one, find the sum of all the variables multiplied by their weight, then divide by the sum of the weights.

To calculate a weighted average, we need to multiply each score by its corresponding weight, and then add those products up and divide by the sum of all the weights.

To calculate a  non-weighted average such as a mean average, all we need to do is, sum up, the scores and divide this sum by the number of scores. For a weighted average, each score must have a frequency attached to it. This frequency is called specific weight.

So in this case,

Weighted average = (701 + 803 + 805 + 904) / (1+3+5+4) = (70 + 240 + 400 + 360) / 13 = 1070/13 = 82.3

Hence, The weighted average of Shenandoah's test scores is 82.3

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The example of an associative property is a+(b+c) = (a+b) + c for additional operation and a × (b × c) = (a × b) × c for the multiplication operation. The associative property is used to solve an equation or expression of real numbers.

What are the properties of real numbers?

In the number system, real numbers are only the fusion of rational and irrational numbers. These numbers can generally be used for all arithmetic operations and can also be expressed on a number line.

The four primary characteristics of real numbers are as follows:

Commutative property

Associative property

Distributive property

Identity property.

Associative property: The associative property is applicable on two arithmetic operations. They are multiplication and addition.

For multiplication operations: a × (b × c) = (a × b) × c

For additional operation: a+(b+c) = (a+b) +

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On solving the provided question, we can say that - the slope of the following will be slope, m = [tex]4-6/4-2 = -2/2 = -1[/tex]

A line's steepness is determined by its slope. The "gradient overflow" is a mathematical expression for the gradient (the change in y divided by the change in x). The ratio of the vertical change (rise) between two points to the horizontal change (run) between the same two places is referred to as the slope. The slope-intercept form of an equation is used to represent each time a straight line's equation is stated as y = mx + b. The line's slope is m. b is b at the point where the y-intercept is, and (0, b). As an illustration, the equation y = 3x - 7 has a slope of 3, and its y-intercept is (0, 7).

here,

(x1,x2) = (6,4)

(y1,y2) = (2,4)

slope, m = 4-6/4-2 = -2/2 = -1

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On solving the provided question, we can say that - the slope of the following will be slope, m = -1

what is slope?

A line's steepness is determined by its slope. The "gradient overflow" is a mathematical expression for the gradient (the change in y divided by the change in x). The ratio of the vertical change (rise) between two points to the horizontal change (run) between the same two places is referred to as the slope. The slope-intercept form of an equation is used to represent each time a straight line's equation is stated as y = mx + b. The line's slope is m. b is b at the point where the y-intercept is, and (0, b). As an illustration, the equation y = 3x - 7 has a slope of 3, and its y-intercept is (0, 7).

here,

(x1,x2) = (6,4)

(y1,y2) = (2,4)

slope, m = 4-6/4-2 = -2/2 = -1

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Answer:

a) 45/2,25=20 km per hour

b) 45 minutes

c) 45/3=15 km per hour

The slope is $125 and the slope tells the annual due payment of $125.

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,

m = Δy/Δx where, m is the slope

Given:

Take two points from the graph as (2, 400) and (4, 650)

Then, the slope of line is

slope, m = ( 650- 400) / ( 4- 2)

slope, m = 250 /2

slope , m = 125

Hence, the slope is 125.

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Answer:

y intercept at (0,-1) and line runs through the points (-6,3) and (-3,4)

Step-by-step explanation:

Answer:

20

Step-by-step explanation:

110 -70 = 40 40/2= 20

Answer:

[tex] \sf \: x = {20}^{o} [/tex]

Step-by-step explanation:

Let's take the value of y as,

→ y = 90°

(Because, it is a right angle)

Forming the equation,

→ x + y + 70° = 180°

Now the value of x will be,

→ x + y + 70° = 180°

→ x + 90° + 70° = 180°

→ x + 160° = 180°

→ x = 180° - 160°

→ [ x = 20° ]

Hence, the value of x is 20°.

Answer in explanation:

although there's an addition sign, you subtract the two because a

(+) + (-) = (-) subtract

[This is a general rule, writing down the "rules" for reference is a good way to help if your having trouble]

subtract to find your answer (you keep the sign of 1.8 because it's the larger number.)

1.3 + (-1.8) =

-0.5

-0.5 is your answer

Hope this is clear!

Answer:

In a square or other rectangle, all pairs of adjacent sides are perpendicular. A right trapezoid is a trapezoid that has two pairs of adjacent sides that are perpendicular. Each of the four maltitudes of a quadrilateral is a perpendicular to a side through the midpoint of the opposite side.

Step-by-step explanation:

Answer:

391

explanation:somehow it is 391. just somehow.

Answer:

The median of the data is 1

Hello there!

Answer:

$400'000

Step-by-step explanation:

Estate -- $2.4 million or $2'400'000

Springfield University will receive: 10% * $2'400'000 = 0.1 * $2'400'000 = $240'000

First Church of Springfield will receive: 15% * $2'400'000 = 0.15 * $2'400'000 = $360'000

Wife will receive $600'000

Total: $240'000 + $360'000 + $600'000 = $1'200'000

Children will receive at total: $2'400'000 - $1'200'000 = $1'200'000

So each child will receive: $1'200'000 / 3 = $400'000

Answer: Each child of Homer Simpson gets $400000.

Step-by-step explanation:

Homer Simpson left 10% of his estate, or (10/100)  x $2.4 million

= $ (10/100)x2400000= $240000

$240,000 to Springfield University.

He left 15% of his estate, or (15/100) x $2.4 million = $(15/100)2400000

= $360000

So 360,000 to the First Church of Springfield.

So in total, he left $240,000 + $360,000 + $600,000 = $(240000+360000+600000)

=$1200000

 $1,200,000 to organizations and his wife.

That means the remainder of the estate, $2.4 million - $1,200,000

= $2400000-1200000

= $1200000

1,200,000, was divided among his three children. So each child received $1,200,000 / 3 = $1200000/3

=$400000

Answer: $400000.

Answer:

24 mg find the whole area then subtract 16 boom!

Answer:

Cement = 20

Step-by-step explanation:

2x6=12

2x4=8

12+8=20

Answer:

A)one solution (3, -3)

B)no solution

C)infinite solution

Step-by-step explanation:

A) The two equations intersect at a point. This point satisfies both equations.

B) The two equations are parallel and never intersect. Therefore no solution.

C) The two equations are stacked on top of one another. No matter with point of the like is chosen, the point will satisfy both equations.