help anyone ?????????????

A. The probability that exactly 5 adults meet the criteria for hypertension is approximately 0.0916 or 9.16%.

B. The probability that none of the adults meet the criteria for hypertension is approximately 0.0255 or 2.55%.

C.  The probability that less than or equal to 7 adults meet the criteria for hypertension is approximately 0.9999 or 99.99%.

To calculate the probabilities,

Use the binomial probability formula.

The binomial probability formula is,

P(X = k) = C (n ,k) × \(p^k\) × \((1 - p)^{(n - k)\)

Where,

P(X = k) is the probability of exactly k successes

n is the number of trials

k is the number of successes

p is the probability of success in a single trial

(1 - p) is the probability of failure in a single trial

C(n, k) represents the binomial coefficient,

which can be calculated as n! / (k! × (n - k)!)

A. To calculate the probability that exactly 5 adults meet the criteria for hypertension,

n = 15 (number of adults assessed)

k = 5 (number of adults meeting the criteria)

p = 0.30 (probability of meeting the criteria)

A. Probability that exactly 5 adults meet the criteria for hypertension,

n = 15

k = 5

p = 0.30

P(X = 5) = C( 15, 5) × 0.30⁵ × (1 - 0.30)¹⁵⁻⁵

Using the binomial coefficient formula C (n ,k) = n! / (k! × (n - k)!), we have,

(¹⁵C₅) = 15! / (5! × (15 - 5)!) = 3003

P(X = 5) = 3003 × 0.30⁵ × 0.70¹⁰

Calculating the probability,

P(X = 5) = 0.0916 (approximately)

B. Probability that none of the adults meet the criteria for hypertension,

n = 15

k = 0

p = 0.30

P(X = 0) = (¹⁵C₀) × 0.30⁰× (1 - 0.30)¹⁵⁻⁰

(¹⁵C₀) = 1 (since choosing 0 from any set results in 1)

P(X = 0) = 1 × 0.30⁰ × 0.70¹⁵

Calculating the probability,

P(X = 0) = 0.0255 (approximately)

C. Probability that less than or equal to 7 adults meet the criteria for hypertension,

n = 15

k = 0, 1, 2, 3, 4, 5, 6, 7

p = 0.30

P(X ≤7) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7)

Calculate each individual probability using the binomial probability formula and sum them up.

P(X ≤7) = (¹⁵C₀) × 0.30⁰ × 0.70¹⁵ + ¹⁵C₁× 0.30¹× 0.70¹⁴+ (¹⁵C₂) × 0.30²× 0.70¹³ + (¹⁵C₃) × 0.30³ × 0.70¹² + (¹⁵C₄) ×0.30⁴ × 0.70¹¹ + (¹⁵C₅) × 0.30⁵× 0.70¹⁰ + (¹⁵C₆) × 0.30⁶× 0.70⁹ + (¹⁵C₇) × 0.30⁷ ×0.70⁸

Calculating the probability,

P(X ≤ 7) ≈ 0.9999

Therefore, the probabilities for different conditions are,

A. For exactly 5 adults is 0.0916 or 9.16%.

B. For none of the adults is 0.0255 or 2.55%.

C. less than or equal to 7 adults is 0.9999 or 99.99%.

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The value of n that solves the equation and represents the width of the box is 9 inches.

In order to solve the equation 8(n + 2)(n + 4) = 1,144 for the variable n, you can follow these steps:

Expand the equation:

8(n + 2)(n + 4) = 1,144

8(n² + 4n + 2n + 8) = 1,144

8(n² + 6n + 8) = 1,144

Distribute 8 to each term inside the parentheses:

8n^2 + 48n + 64 = 1,144

Move 1,144 to the other side of the equation:

8n²+ 48n + 64 - 1,144 = 0

8n² + 48n - 1,080 = 0

Divide the entire equation by 8 to simplify it:

n² + 6n - 135 = 0

Now you have a quadratic equation in standard form. To solve it, you can either factor it or use the quadratic formula.

Factoring method:

n² + 6n - 135 = 0

(n + 15)(n - 9) = 0

Setting each factor equal to zero:

n + 15 = 0 or n - 9 = 0

Solving for n:

n = -15 or n = 9

The possible solutions for n are -15 and 9. However, since n represents the width of a box, it cannot be negative. Therefore, the only valid solution is n = 9.

Alternatively, you can use the quadratic formula to find the solution:

The quadratic formula is given by:

n = (-b ± √(b² - 4ac)) / (2a)

For our equation n² + 6n - 135 = 0, we have:

a = 1, b = 6, c = -135

Plugging these values into the quadratic formula:

n = (-6 ± √(6² - 4 * 1 * -135)) / (2 * 1)

n = (-6 ± √(36 + 540)) / 2

n = (-6 ± √(576)) / 2

n = (-6 ± 24) / 2

Solving for n:

n = (-6 + 24) / 2 or n = (-6 - 24) / 2

n = 18 / 2 or n = -30 / 2

n = 9 or n = -15

As before, the only valid solution is n = 9.

Therefore, the value of n that solves the equation and represents the width of the box is 9 inches.

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Answer:

1/3n=12

Step-by-step explanation:

The reason why it is 1/3n=12, is because you know that the number in front of n is 1/3. By figuring that out, you have already ruled out 3n=12 and 3n=-12. Finally, you know that 12 is a positive number leaving you with 1/3n=12.

The least expensive rectangular storage container without a lid, with a volume of 10 cubic meters, has a length three times its width.  The total cost of the least expensive box is $750.  

Let's assume the width of the rectangular container is x meters. According to the given information, the length of the base is three times the width, so the length is 3x meters. The height of the box can be determined by dividing the volume by the area of the base, giving us a height of 10/(3x^2) meters.  

The cost of the base can be calculated by multiplying the area of the base (3x * x = 3x^2) by the cost per square meter ($20). Therefore, the cost of the base is 3x^2 * $20 = $60x^2.

The cost of the sides can be calculated by finding the area of the four sides (2 * 3x * 10/(3x^2) + 2 * x * 10/(3x^2)), which simplifies to 20/x. Multiplying this by the cost per square meter ($10) gives us a cost of $200/x.

To find the total cost, we sum the cost of the base and the cost of the sides: $60x^2 + $200/x. To minimize the cost, we can take the derivative with respect to x, set it equal to zero, and solve for x. The result is x = √(100/3). Substituting this value back into the cost equation, we find the minimum cost is approximately $750.

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Which of these values for x make the value of the expression (x-5)(x+7) the greatest? ​

This is a quadratic equation (vertical parabola) open upward

the vertex is a minimum

the greatest value of this expression is for the greater value of x in absolute value

we have

that -9 is the greater value in absolute value

therefore

the answer is -9

Given:

The graph passes through the given points (4,-2) and (2,0).

To find:

The quadratic function \(y=a(x-h)^2\).

Solution:

We have, quadratic function

\(y=a(x-h)^2\)            ...(i)

The graph passes through the given points (4,-2) and (2,0). It means the equation must be true for these points.

Putting x=4 and y=-2 in (i), we get

\(-2=a(4-h)^2\)         ...(ii)

Putting x=2 and y=0 in (i), we get

\(0=a(2-h)^2\)          ...(iii)

Divide (iii) by (ii).

\(\dfrac{0}{-2}=\dfrac{a(2-h)^2}{a(4-h)^2}\)

\(0=\dfrac{(2-h)^2}{(4-h)^2}\)

\(0=(2-h)^2\)

\(0=2-h\)

\(h=2\)

Putting h=2 in (ii), we get

\(-2=a(4-2)^2\)

\(-2=a(2)^2\)

\(-2=a(4)\)

Divide both sides by 4.

\(\dfrac{-2}{4}=a\)

\(\dfrac{-1}{2}=a\)

Putting \(a=-\dfrac{1}{2}\) and h=2 in (i), we get

\(y=-\dfrac{1}{2}(x-2)^2\)

Therefore, the required quadratic function is \(y=-\dfrac{1}{2}(x-2)^2\).

\(~\hfill \stackrel{\textit{\large distance between 2 points}}{d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}}~\hfill~ \\\\[-0.35em] ~\dotfill\\\\ A(\stackrel{x_1}{5}~,~\stackrel{y_1}{5})\qquad B(\stackrel{x_2}{2}~,~\stackrel{y_2}{4}) ~\hfill AB=\sqrt{[ 2- 5]^2 + [ 4- 5]^2} \\\\\\ AB=\sqrt{(-3)^2+(-1)^2}\implies \boxed{AB=\sqrt{10}} \\\\[-0.35em] ~\dotfill\\\\ B(\stackrel{x_1}{2}~,~\stackrel{y_1}{4})\qquad C(\stackrel{x_2}{4}~,~\stackrel{y_2}{1}) ~\hfill BC=\sqrt{[ 4- 2]^2 + [ 1- 4]^2}\)

\(BC=\sqrt{2^2+(-3)^2}\implies \boxed{BC=\sqrt{13}} \\\\[-0.35em] ~\dotfill\\\\ C(\stackrel{x_1}{4}~,~\stackrel{y_1}{1})\qquad D(\stackrel{x_2}{6}~,~\stackrel{y_2}{1}) ~\hfill CD=\sqrt{[ 6- 4]^2 + [ 1- 1]^2} \\\\\\ CD=\sqrt{2^2+0^2}\implies \boxed{CD=2} \\\\[-0.35em] ~\dotfill\\\\ D(\stackrel{x_1}{6}~,~\stackrel{y_1}{1})\qquad A(\stackrel{x_2}{5}~,~\stackrel{y_2}{5}) ~\hfill DA=\sqrt{[ 5- 6]^2 + [ 5- 1]^2}\)

\(DA=\sqrt{(-1)^2+4^2}\implies \boxed{DA=\sqrt{17}} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{\Large Perimeter}}{\sqrt{10}~~ + ~~\sqrt{13}~~ + ~~2~~ + ~~\sqrt{17}}~~ \approx ~~ 12.89\)

Answer:

The total volume of water in the pool  =-2 (x-11)(x+5) ft^3

Step-by-step explanation:

a) (2x^2 + 12x + 10) - (4x^2-100)

= 2x^2+12x+10-4x^2+100

= -2x^2+12x+110

b)

Lets simplify first by taking the GCF out:

= -2 (x^2-6x-55)

Now Just simplify by finding the product of a and c

I used -11 and 5 because when you multiply -11x5 you get -55, and when you do -11+5 you get -6.

= -2 (x-11)(x+5) ft^3

Answer:

Given expressions

Deep end:   \(2x^2+12x+10\)

Shallow end:  \(4x^2-100\)

a) Difference between the deep end and shallow end

⇒ difference = deep end - shallow end

                     \(=(2x^2+12x+10)-(4x^2-100)\)

b) simplifying:

                     \(=2x^2+12x+10-4x^2+100\)

                     \(=(-2x^2+12x+110) \textsf{ ft}^3\)

Answer:

I think it;s 9.8

Step-by-step explanation:

You divide 35 and 28 i think

The magnitude of the expected shortfall at a 95% confidence level is not provided. Please provide the necessary information to calculate the expected shortfall.

The expected shortfall at a specific confidence level, we need additional information, such as the distribution of returns or loss data. The expected shortfall, also known as conditional value-at-risk (CVaR), represents the average value of losses beyond a certain threshold.

Typically, the expected shortfall is calculated by taking the average of the worst (1 - confidence level) percent of losses. However, without specific data or parameters, it is not possible to determine the magnitude of the expected shortfall at a 95% confidence level.

To calculate the expected shortfall, we would need a set of data points representing returns or losses, as well as a specified distribution or methodology to estimate the expected shortfall. Please provide the necessary details so that the expected shortfall can be calculated accurately.

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Answer:

I think the answer is A. 45m - 30 over 4 ≥ 275

The mean of a binomial probability distribution with p = 0.32 and n = 150 is 48

The binomial distribution is a probability distribution that describes the number of successes in a fixed number of independent trials, where each trial has the same probability of success, denoted by p. In the case of a binomial distribution with n trials and probability of success p, the mean, or expected value, is equal to the product of the number of trials and the probability of success, which is np.

In this case, the problem provides the values of p and n, which are p = 0.32 and n = 150, respectively. Therefore, the mean can be calculated by multiplying these two values

μ = np = 150 x 0.32 = 48

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Answer:

Yes

Step-by-step explanation:

The difference of 18 and 3 is 15 which can be expressed as fraction, so its a rational number.

Answer:

Yes, it is a rational number.

Step-by-step explanation:

A rational number is a number that can be expressed in fractional form. A rational number consists of:

Since the difference of 18 and 3 is 15 and the number 15 can be expressed as 15/1. Therefore, 15 or the difference of 18 and 3 is a rational number.

The eigenvector corresponding to the eigenvalue λ = 59 - 4 is the zero vector [0, 0, 0].

To find an eigenvector corresponding to the eigenvalue λ = 59 - 4 for the given matrix, we need to solve the equation: (A - λI) * v = 0,

where A is the given matrix, λ is the eigenvalue, I is the identity matrix, and v is the eigenvector.

Let's set up the equation:

[(10 - 59) 0 351] [v₁] [0]

[409 (116 - 59) -412] [v₂] = [0]

[189 189 (134 - 59)] [v₃] [0]

Simplifying:[-49 0 351] [v₁] [0]

[409 57 -412] [v₂] = [0]

[189 189 75] [v₃] [0]

Now we have a system of linear equations. We can use Gaussian elimination or other methods to solve for v₁, v₂, and v₃. Let's proceed with Gaussian elimination:

Multiply the first row by 409 and add it to the second row:

[-49 0 351] [v₁] [0]

[0 409 -61] [v₂] = [0]

[189 189 75] [v₃] [0]

Multiply the first row by 189 and subtract it from the third row:

[-49 0 351] [v₁] [0]

[0 409 -61] [v₂] = [0]

[0 189 -264] [v₃] [0]

Divide the second row by 409 to get a leading coefficient of 1:

[-49 0 351] [v₁] [0]

[0 1 -61/409] [v₂] = [0]

[0 189 -264] [v₃] [0]

Multiply the second row by -49 and add it to the first row:

[0 0 282] [v₁] [0]

[0 1 -61/409] [v₂] = [0]

[0 189 -264] [v₃] [0]

Multiply the second row by 189 and add it to the third row:

[0 0 282] [v₁] [0]

[0 1 -61/409] [v₂] = [0]

[0 0 -315] [v₃] [0]

Now we have a triangular system of equations. From the third equation, we can see that -315v₃ = 0, which implies v₃ = 0. From the second equation, we have v₂ - (61/409)v₃ = 0. Substituting v₃ = 0, we get v₂ = 0. Finally, from the first equation, we have 282v₃ = 0, which also implies v₁ = 0. Therefore, the eigenvector corresponding to the eigenvalue λ = 59 - 4 is the zero vector [0, 0, 0].

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Answer:

19.7 miles

Step-by-step explanation:

29-9.3=19.7

For the equations y = 2x and y = -x + 6, the solution is (2,4) which is represented by point A in graph of option C.

What is an equation?

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").

We can solve this system of equations by substituting one equation into the other and solving for the remaining variable.

Let's solve for y -

y = 2x (equation 1)

y = -x + 6 (equation 2)

Since both equations are equal to y, we can set them equal to each other -

2x = -x + 6

Adding x to both sides -

3x = 6

Dividing both sides by 3 -

x = 2

Now that we have found the value of x, we can substitute it back into either equation to solve for y.

Let's use equation 1 -

y = 2x

y = 2(2)

y = 4

Therefore, the solution to the system of equations is (2, 4).

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By answering the presented question, we may conclude that As a result, probability the likelihood that none of the three households chosen have a cat is 0.314, or around 31.4%.

Probability is a measure of how likely an event is to occur. It is represented by a number between 0 and 1, with 0 representing a rare event and 1 representing an inescapable event. Switching a fair coin and coin flips has a chance of 0.5 or 50% since there are two equally likely outcomes. (Heads or tails). Probabilistic theory is an area of mathematics that studies random events rather than their attributes. It is applied in many disciplines, including statistics, economics, science, and engineering.

If 32% of families have a cat, that leaves 68% of families without a cat.

The likelihood that one household lacks a cat is 0.68, and the probability that all three families lack a cat equals the sum of the probabilities that each family lacks a cat.

As a result, the likelihood that none of the three households chosen have a cat is:

0.68 x 0.68 x 0.68 = 0.314

As a result, the likelihood that none of the three households chosen have a cat is 0.314, or around 31.4%.

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Answer:  1/9 of a mile per hour

=========================================================

Explanation:

6 & 3/4 = 6 + 3/4 = 24/4 + 3/4 = (24+3)/4 = 27/4

The work crew paves 3/4 of a mile in 27/4 hours. Divide those two fractions:

(3/4) divide (27/4)

(3/4) times (4/27)

(3*4)/(4*27)

3/27

1/9

The unit rate is 1/9 of a mile per hour. In other words, for each hour, they are able to pave 1/9 of a mile on average. So we should expect it takes about 9 hours to pave a full mile.

Answer:

-4

Step-by-step explanation:

Simplify:

5 - 4 - 7 + 2

Simplify more:

1 - 5

Celebrate:

-4

To solve for x in an angle, you first need to identify what type of angle you are dealing with. Depending on the type of angle, you will use different formulas to solve for x. For example, if you are dealing with a right angle, you can use the Pythagorean Theorem to solve for x.

1. Identify the given information:-

First, identify the type of triangle and the angles that are given.

2. Use the appropriate formula:-

If it is a right triangle, use the Pythagorean Theorem to solve for the missing side. If it is an isosceles triangle, use the law of sines to solve for the missing angle.

3. Substitute the given values into the appropriate formula:-

Substitute the given values into the appropriate formula and simplify.

4. Solve for the unknown:-

Solve the equation for the unknown value (x).

5. Check your answer:-

Check your answer by plugging it back into the original equation to make sure it is correct.

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Answer:

1x + 46 or x + 46

Step-by-step explanation:

4(-8x + 5) – (-33x – 26)

-32x + 20 + 33x + 26

1x + 46

or x + 46

∠

Trapezoid PRST

Lines PR and TS are parallel crossed by a perpendicular line PT.

If you link both paralel lines with an F shaped line, you'll get that ∠P and the external angle ∠T' are corresponding angles, this means that they are congruent.

Now these angles are a linear pair, this means that they share a vertex (T) and a line (TS) and both add up to 180º (i.e. they are supplementary), so that

∠T+∠T'=180º

From this expression you can calculate the value of the inner angle ∠T

7(x+2)

Let's find the common term in this expression to factor it out. it is 7.

Factoring is the opposite of distributing.

If we distribute, we will get the original expression.

Next:

45-27k

Here, the common term is 9:

9(5-3k)

12ab+7b - the common term is b:

b(12a+7)

y^2-9y.

Here the common term is y:

y(y-9)

8r-32r² the common term here is 8r:

8r(1-4r)

16gh+28gh: the Common Term is 4gh:

4gh(4+7)

21w²-77wx The common term is 7w:

7w(3w-11x)

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Answer:

278.4 dollars

Step-by-step explanation:

So you know that each month is 29.00 dollars

You mutilpy that by 12 to find out the total cost for paying each month

That would be 348 dollars

So if you pay upfront that takes 20 percent off

So you take the 348 and take 20 percent off

That would be 69.6

So then to find the amount saved you subtract 69.6 from 348

Which would be 278.4 dollars

They saved 278.4 dollars

The lines y = 2 and x = 4 are neither parallel nor perpendicular.

The given lines are y = 2 and x = 4.

The line y = 2 is a horizontal line because the value of y remains constant at 2, regardless of the value of x. This means that all points on the line have the same y-coordinate.

On the other hand, the line x = 4 is a vertical line because the value of x remains constant at 4, regardless of the value of y. This means that all points on the line have the same x-coordinate.

Since the slope of a horizontal line is 0 and the slope of a vertical line is undefined, we can determine that the slopes of these lines are not equal. Therefore, the lines y = 2 and x = 4 are neither parallel nor perpendicular.

Parallel lines have the same slope, indicating that they maintain a consistent distance from each other and never intersect. Perpendicular lines have slopes that are negative reciprocals of each other, forming right angles when they intersect.

In this case, the line y = 2 is parallel to the x-axis and the line x = 4 is parallel to the y-axis. Since the x-axis and y-axis are perpendicular to each other, we might intuitively think that these lines are perpendicular. However, perpendicularity is based on the slopes of the lines, and in this case, the slopes are undefined and 0, which are not negative reciprocals.

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Answer:

1/2

Step-by-step explanation:

There are 4 odd numbers on the wheel and 8 numbers total; therefore your ratio is 4/8, which can be reduced to 1/2.

HTH :)

Pilot should take reverse bearing, calculated using atan2(East,North),converted in degrees.

What is radian ?

A radian is a unit of measurement for angles. It is defined as the ratio of the length of an arc of a circle to the radius of that circle. One radian is approximately 57.3 degrees. Radians are often used in mathematics, physics, and engineering because they allow for a more natural way of measuring angles and help simplify certain calculations.

To find the bearing, we can use the formula ,

Bearing = atan2(East, North)

Where East is the number of miles east of the airport and North is the number of miles north of the airport.

The atan2 function is a variation of the arctangent function, which returns the angle (in radians) whose tangent is the quotient of its two arguments. This function is defined for all real arguments and returns a value between -π and π.

So you can convert the bearing from radians to degrees using the formula ,

degrees = bearing * (180/π)

Pilot should take reverse bearing, calculated using atan2(East,North),converted in degrees.

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