Find the value of X in the diagram. (See below)

1. 25
2. 10
3. 180
4. 50

The probability of having a boy when a couple has six ​children is 63 / 64.

The ratio of good outcomes to all possible outcomes of an event is known as probability. A lot of successful results for an experimental with 'n' results can be represented by the symbol x.

Given:

A couple has six ​children, n = 6

The wanted event, p = 1 / 2

Calculate the probability of having a boy given by the following formula,

\(P(X) = nC_x px (1-p)n-x\)

Here, \(X\) = number of boys,

So,

P(X >= x) = 1 - P(X = 0)

P (X) = 1 - 6C₀ × (1 / 2) 0 × (1/2) 6

P (X) = 63 / 64

Therefore, the probability of having a boy when a couple has six ​children is 63 / 64.

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After 2 years there will be 6257 research papers published from now if the Dr. Carey's area of expertise has been increasing by 3% every year.

It is defined as the function that rapidly increases and the value of the exponential function is always a positive. It denotes with exponent \(\rm y = a^x\)

where a is a constant and a>1

We have:

The number of research papers in Dr. Carey's area of expertise has been increasing by 3% every year.

We are assuming there is exponential increase.

So,

After 2 years the published research papers (a)

a = 34,176(1 + 0.03)²

Because increasing by 3%(0.03) every year.

a = 34176(1.03)²

a = 36257.31 ≈ 36257 research papers

Thus, after 2 years there will be 6257 research papers published from now if the Dr. Carey's area of expertise has been increasing by 3% every year.

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The firm should produce good  x₁ = 4 and x₂ = 8 to minimize cost of C = x₁² + x₂² .

What is Lagrange multipliers ?

Lagrange multipliers is a method used in optimization problems to find the maximum or minimum value of a function subject to one or more constraints. The method involves introducing a Lagrange multiplier, which is a scalar variable, to the objective function and the constraint(s). This forms the Lagrangian function, which is then optimized with respect to the original variables and the Lagrange multiplier.

To minimize the cost C = x₁² + x₂²

We can use the method of Lagrange multipliers to solve this problem. Let's define the Lagrangian function L as:

L(x₁, x₂, λ) = x₁²+ x₂² + λ(400 - 5x₁²- 8x₁x₂ - 15x₂²)

Taking partial derivatives of L with respect to x₁, x₂, and λ, we get:

∂L/∂x₁ = 2x₁ - 10λx₁ - 8λx₂ = 0

∂L/∂x₂ = 2x₂ - 30λx₂ - 8λx₁ = 0

∂L/∂λ = 400 - 5x₁² - 8x₁x₂ - 15x₂² = 0

Solving these equations simultaneously, we get:

x₁ = 4

x₂ = 8

λ = 1/20

Hence, the firm should produce a combination of x₁ = 4 and x₂ = 8 to minimize the cost of C = x₁² + x₂² while satisfying the production quota of 400.

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The graph of g(x) is obtained from the graph of f(x) by the following transformations:

- A horizontal stretch by a factor of 9. This is because the graph of g(x) is 9 times wider than the graph of f(x).

- A vertical translation down by 2 units. This is because the graph of g(x) is 2 units lower than the graph of f(x).

In other words, to obtain the graph of g(x) from the graph of f(x), we stretch the graph horizontally by a factor of 9 and then translate it down by 2 units.

Here is a more detailed explanation of the transformations:

- Horizontal stretch by a factor of 9: To stretch the graph horizontally by a factor of 9, we multiply all of the x-coordinates by 9. This means that every point on the graph of f(x) will be moved 9 units to the right on the graph of g(x).

- Vertical translation down by 2 units: To translate the graph down by 2 units, we subtract 2 from all of the y-coordinates. This means that every point on the graph of f(x) will be moved 2 units down on the graph of g(x).

The solution of the expression is x=0 and it is the only solution that is an integer.

An expression in mathematics is a combination of numbers, variables, and mathematical operations that evaluates to a numerical value or an algebraic expression.

To do this, we need to pick a range of x values and substitute them into each equation to find the corresponding y values.

Next, we need to find the points of intersection between the two curves. These are the x values where the two curves cross each other and have the same y value. To find these points, we will set the two equations equal to each other and solve for x:

=> x=5x−x³

Expanding this equation, we get

=> 4x³+x=0.

Factoring this equation, we get

=> x(4x²+1)=0.

This gives us two solutions, x=0 and x=±i√(1/4), where i is the imaginary unit. Since x can only take on real values, x=0 is the only solution that is an integer.

Complete Question:

Use the open space to show all of your work. This includes: sketching the curves, finding and labeling the points of intersection, setting up the appropriate definite integral(s), and evaluating them. Place your numerical answer for the area of the region in the box. Leave your answer in exact form.

y = x,

y = 5x−x³

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Step-by-step explanation:

A B D

I did it and this was the correct answers

multiply the numbers

a)

The equation of a line in the slope intercept form is expressed as

y = mx + c

where

m is the slope

c is the y intercept

The given equation of the line is

5x - 3y = 15

3y = 5x - 15

Dividing both sides by 3,

y = 5x/3 - 5

By comparing this equation with the slope intercept equation,

slope, m = 5/3

If two lines are parallel, it means that they have the same slope. This means that the slope of the line passing through the point (3/8, - 1) and parallel to the given line is 5/3

We would find the y intercept of the line by substituting m = 5/3, x = 3/8 and y = - 1 into the slope intercept equation. We have

- 1 = 5/3 * 3/8 + c

- 1 = 5/8 + c

c = - 1 - 5/8 = (- 8 - 5)/8

c = - 13/8

We would substitute m = 5/3 and c = - 13/8 into the slope intercept equation. Thus, the equation of the line is

y = 5x/3 - 13/8

b) If two lines are perpendicular, it means that the slope. This means that the slope of the line passing through the point (3/8, - 1) and perpendicular to the given line is - 3/5

We would find the y intercept of the line by substituting m = - 3/5, x = 3/8 and y = - 1 into the slope intercept equation. We have

- 1 = - 3/5 * 3/8 + c

- 1 = - 9/40 + c

c = - 1 + 9/40 = (- 40 + 9)/40

c = - 31/40

We would substitute m = - 3/5 and c = - 31/40 into the slope intercept equation. The equation of the line is

y = - 3x/5 - 31/40

\(\huge\text{Hey there!}\)

\(\huge\textbf{Equation:}\)

\(\mathsf{n^2 = 5n - 4}\)

\(\huge\textbf{Convert:}\)

\(\mathsf{5n - 4 = n^2}\)

\(\huge\textbf{Subtract }\boxed{\bf n^2}\huge\textbf{ to both sides:}\)

\(\mathsf{5x - 4 - n^2 = n^2 - n^2}\)

\(\huge\textbf{Simplify it:}\)

\(\mathsf{-n^2 + 5x - 4 = 0}\)

\(\huge\textbf{Factor the LEFT side of the equation:}\)

\(\mathsf{(-n + 1)\times (n - 4) = 0}\)

\(\huge\textbf{Simplify that as well:}\)

\(\mathsf{-n + 1 = 0 \ or\ even\ \ n - 4 = 0}\)

\(\huge\textbf{Lastly, simplify that as well:}\)

\(\mathsf{n = 1\ or\ n = 4}\)

\(\huge\textbf{Therefore, your answer should be: }\)

\(\huge\boxed{\frak{n = 1\ or \ n = 4}}}\huge\checkmark\)

\(\huge\text{Good luck on your assignment \& enjoy your day!}\)

~\(\frak{Amphitrite1040:)}\)

Answer:

Area="10"

Step-by-step explanation:

The reason for this is because the fromula for finding an area of a rectangle is LxW or Length mutiplied by with.And in this situation the length is 5 and the with is 2.Mutiply them and you get your answer  5x2="10"

Answer:

(-5, 4)

Step-by-step explanation:

Recall that in a reflection across the x-axis the x coordinate stays the same, while the y coordinate flips its sign.

Therefore

(-5, -4)  converts under reflection into (-5, 4)

Question attached

Answer and explanation:

Here we would use the two sample t test. In finding the hypotheses for a two sample t test we test the sample mean of one group against the other group to determine if there is a statistical difference or they are equal. We have this to compare the mean finger tapping rate of the two groups being tested in the question. Our null and alternative hypotheses here are:

H0: u1 = u2 null hypothesis

H1: u1 > u2 alternative hypothesis

Where u1 and u2 are the sample means for each group in the caffeine experiment

Answer:

55

Step-by-step explanation:

a triangle adds up to 180°

25+30+x= 180

55+x=180

x=180-55

x=125

x and y is a straight line so it adds up to 180°

x=125 y=?

x+y=180

125+y=180

y=180-125

y=55°

y= 55°

Step-by-step explanation:

OUT of  35 spins   4 + 15 + 3  = 22   were blue or green or purple

 22/35 probability  = 63%

Answer:

169

Step-by-step explanation:

360-[36+160]-36

360-160-72

169

Answer:

28

Step-by-step explanation:

14x2=28

Therefore x=28

9514 1404 393

Answer:

  100 runs from Macon

Step-by-step explanation:

A graph of the requirements shows the feasible region is bounded by a polygon with vertices (Macon, Jonestown) = (0, 180), (40, 60), and (100, 0).

Checking costs of these solutions, we find the lowest cost to be obtained when ...

  100 production runs should be ordered from Macon

Using distributive property, the solution to the given expression is: 50v - 40w + 20

The Distributive Property is a term which is an algebra property which is used to multiply a single term and two or more terms inside a set of parentheses.

For example:

4(3 + 5)

According to the distributive property, you first have to multiply out the bracket to get:

4*3 + 4*5 = 12 + 20

= 32

Thus:

5(10v - 8w + 4) = (5 * 10v) - (5 * 8w) + (5 * 4)

= 50v - 40w + 20

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Answer:38

Step-by-step explanation:

The proportional relationship used to find B, the area of the base with a volume of V, is given as follows:

B = V/6.

A proportional relationship is a type of relationship between two quantities in which they maintain a constant ratio to each other.

The equation that defines the proportional relationship is given as follows:

y = kx.

In which k is the constant of proportionality, representing the increase in the output variable y when the constant variable x is increased by one.

From the table given in the image at the end of the answer, we have that the base area is a sixth of the volume, hence the equation is:

B = V/6.

The table is given by the image presented at the end of the answer.

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The expression that is equivalent to the given value would be = 18-i . That is option C.

An equivalent expression is defined as the type of expression that is similar to a given value when simplified.

The given expression = ( 3 + 4i) ( 2 - 3i)

Expand the given expression by removing the brackets as follows:

= =2(3+4i)−3i(3+4i)

=(6+8i)−(9i−12)

= (6+12)+i(8−9)

=18−i.

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Answer:

I canot answer this

Step-by-step explanation:

The probability of getting exactly one tail when a fair coin is tossed three times is 3/8.

Probability is the measure of the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, where 0 indicates an impossible event and 1 indicates a certain event.

In the given question,

There are 8 possible outcomes, and we want to find the probability of getting exactly one tail. We can list the outcomes with exactly one tail as HHT, HTH, and THH.

So, the probability of getting exactly one tail is:

P(exactly one tail) = P(HHT) + P(HTH) + P(THH)

We know that each individual toss of a fair coin has a probability of 1/2 of resulting in either heads or tails. Using the multiplication rule of probability, we can find the probabilities of each of these outcomes:

P(HHT) = (1/2) * (1/2) * (1/2) = 1/8

P(HTH) = (1/2) * (1/2) * (1/2) = 1/8

P(THH) = (1/2) * (1/2) * (1/2) = 1/8

So, the probability of getting exactly one tail is:

P(exactly one tail) = P(HHT) + P(HTH) + P(THH) = 1/8 + 1/8 + 1/8 = 3/8

Therefore, the probability of getting exactly one tail when a fair coin is tossed three times is 3/8.

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Answer:

A watermelon my woman

Step-by-step explanation:

Answer:

about -1

Step-by-step explanation:

0.9999999999 minus 2

word form: one million, three thousand, four hundred ninety eight

number form : 1,003,498

expaned form 1000000 + 30000 + 400 + 90 + 8

i would so base form but i cant

The quantity of gallons that would be sold per hour when the price is $2.20 per gallon would be = 1288 gallons

When charges is $2.05 per gallon the number of gallons sold = 1200 gallons

When the charges is $2.45 per gallon the number of gallons sold = 900 gallons per hour.

That is;

$2.05 = 1200 gallons

$2.20 = X gallons

Make X gallons the subject of formula;

X gallons = 2.20×1200/2.05

= 2640/2.05

= 1287.8 gallons

= 1288 gallons ( approximately)

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Answer:

The bubble on the left should be 0.01.  The bubbles on the right should be: (top to bottom) 7, 0.1, 0.07, 0.004.

Step-by-step explanation:

You're just supposed to break the decimal into parts.  It like breaking 178 into hundreds, tens, and ones (100 + 70 + 8)

a Answer:

Explanation:

Here, we want to know the number of different cards that can be made

From the question, she wants to make four-digit identification card

For the first digit, there are 6 choices, so also for the second to the fourth digit. This is because repetition is allowed

Thus, the total number of different cards possible will be: