Pythagorean theorem help quickly please

The ages of the​ teacher's three children whose product is 72 will be 3,3,8.

Let the age of three children be x, y, z

x × y × z = 72

x + y + z = No. of rooms

Now possible answers can be three numbers whose product is 72

There are two possible answers in which the product of the number is 72 and the sum of the number is also same

1) 2 × 6 × 6 = 72  and 2 + 6 + 6 = 14

2) 3 × 3 × 8 = 72  and 3 + 3 + 8 = 14

Now teacher gave a hint that his oldest child is good at math

Oldest means one of the three child is oldest so the only possible answer could be 3,3,8

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The simplified expression for p(z), the profit the company earns, in dollars is: p(z) = -3z² + 18z

The set X is known as the domain of the function, and the set Y is known as the codomain of the function. A function from a set X to a set Y assigns each element of X to exactly one element of Y. Originally, functions were an idealization of how one variable depends on another.

First, let's substitute the expressions for r(z) and c(z) in the expression for p(z):

p(z) = r(z) - c(z)

p(z) = 60z - (3z² + 42z)

p(z) = 60z - 3z² - 42z

p(z) = -3z² + 18z

Therefore, the simplified expression for p(z), the profit the company earns, in dollars is:

p(z) = -3z² + 18z

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The value of measure of RU is,

⇒ 149°

We have to given that;

In circle,

m RS = 88 degree

m ST = 35 degree

Hence, We can formulate;

The value of measure of RU is,

⇒ 360° - ( 88° + 35° + 88°)

⇒ 360° - 211°

⇒ 149°

Thus, The value of measure of RU is,

⇒ 149°

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The solution for the differential equation is y = (23/48) x + 4.

(A) Re-writing the differential equation in terms of differentials, we get:

dy = (23/48) dx

Here, dy and dx represent infinitesimal changes in the variables y and x, respectively.

(B) Integrating both sides of the equation with respect to their respective variables, we get:

∫dy = ∫(23/48)dx

On the left-hand side, the integral of dy is simply y (plus a constant of integration), while on the right-hand side, we can pull the constant factor (23/48) outside the integral:

y + C1 = (23/48) ∫dx

Integrating the right-hand side with respect to x, we get:

y + C1 = (23/48) x + C2

where C1 and C2 are constants of integration.

(C) To solve for y, we can isolate it on one side of the equation by subtracting C1 from both sides:

y = (23/48) x + (C2 - C1)

Next, we can use the initial condition y(0) = 4 to solve for the constant C2 - C1:

y(0) = (23/48) (0) + (C2 - C1) = C2 - C1

Since y(0) = 4, we have:

4 = C2 - C1

Therefore, C2 - C1 = 4, and we can substitute this back into the expression for y to get the final solution:

y = (23/48) x + 4

So the solution for the differential equation with initial condition y(0) = 4 is y = (23/48) x + 4.

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The probability that a student gets a lunch with chips and apple juice is 1/12, and the probability that a student gets a lunch without chips is 1/2.

There are 3 choices of sandwiches, 2 choices of sides, and 2 choices of drinks, so there are a total of 3x2x2 = 12 possible lunch combinations. To find the probability that a student gets a lunch that includes chips and apple juice, we need to count the number of lunch combinations that include chips and apple juice, and then divide by the total number of possible lunch combinations.

Number of lunch combinations that include chips and apple juice = 1 (chips and apple juice is only one combination)

Total number of possible lunch combinations = 12

Probability of getting a lunch that includes chips and apple juice = 1/12

To find the probability that a student gets a lunch that does not include chips, we need to count the number of lunch combinations that do not include chips, and then divide by the total number of possible lunch combinations,

Number of lunch combinations that do not include chips = 6 (3 choices of sandwiches x 2 choices of drinks) Total number of possible lunch combinations = 12, probability of getting a lunch that does not include chips = 6/12 = 1/2

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The annual rate of inflation between the two time periods is approximately 3.05%.

To calculate the annual rate of inflation, we can use the formula:

Annual Inflation Rate = ((Current Price - Past Price) / Past Price) * 100 / Number of Years

Plugging in the values, we have:

((3.25 - 1.75) / 1.75) * 100 / 20 ≈ 0.153 * 100 / 20 ≈ 3.05%

Therefore, the annual rate of inflation between the two time periods is approximately 3.05%.

Inflation refers to the general increase in prices over time, which leads to a decrease in the purchasing power of money. In this case, the cost of a gallon of milk has increased from $1.75 to $3.25 over 20 years. By calculating the annual rate of inflation, we find that prices have been rising at an average rate of 3.05% per year during this period.

This means that the cost of goods and services, including milk, has increased by an average of 3.05% each year due to inflation. It highlights the importance of considering inflation when comparing prices and understanding the impact it has on the value of money over time.

In conclusion, based on the given information, the annual rate of inflation between the two time periods is approximately 3.05%, indicating the increase in the cost of a gallon of milk over 20 years.

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For function f(x,y) = x² e^{3xy} ,  fx = 2xe^{3xy} + 3x²y e^{3xy}, fy = 3x² e^{3xy}

The given function is f(x,y) = x² e^{3xy}.

To find the partial derivatives of f(x,y) with respect to x and y,

we differentiate the function with respect to each variable while treating the other variable as a constant.

To find fx, we differentiate the function f(x,y) with respect to x while treating y as a constant.

The derivative of x² is 2x, and the derivative of e^{3xy} is e^{3xy} times the derivative of 3xy with respect to x, which is 3y.

Therefore, we get:

fx = (d/dx)(x² e^{3xy}) = 2xe^{3xy} + 3x²y e^{3xy}

To find fy,

we differentiate the function f(x,y) with respect to y while treating x as a constant.

The derivative of e^{3xy} with respect to y is e^{3xy} times the derivative of 3xy with respect to y, which is 3x². Therefore, we get:

fy = (d/dy)(x² e^{3xy}) = 3x² e^{3xy}

Hence, the partial derivatives of f(x,y) are fx = 2xe^{3xy} + 3x^2y e^{3xy} and fy = 3x² e^{3xy}.

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The correct answer is option c i.e. the value of the function decreases as x approaches positive infinity.

The function g(x) = -4 log(x – 8) has the following features:

a. The domain is x > 8, because the expression x - 8 must be greater than 0 for the logarithm to be defined. Therefore, x must be greater than 8, so the domain is x > 8.

b. is incorrect because the range of the function is y < 0, not y > -8.

c. The value of the function decreases as x approaches positive infinity. As x gets larger and larger, the expression x - 8 gets larger and larger, so log(x - 8) gets larger and larger, approaching infinity. Multiplying by -4 makes the function more and more negative, so the value of the function decreases as x approaches positive infinity.

d. The value of the function does not increase as x approaches positive infinity, because as we just explained, the value of the function actually decreases as x approaches positive infinity. Therefore, option d is not correct.

Therefore, the correct answer is option c

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The rate of change between August and October is

Rate is how a quantity changes over a period of time.

Therefore rate = change in quantity/change in time.

For example acceleration is defined as the rate of change of velocity with time. This means that acceleration = change in velocity/time

change in quantity = 85-81 = 4

change in time = 2 months

therefore rate of change = 4/2 = $2 per month

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The total surface area of the figure shown as a rectangular prism is 208. 6 cm

The formula for calculating the total surface area of a rectangular prism is expressed as;

TSA =  2 (lh +wh + lw )

Such that the parameters are;

Now, substitute the values, we have;

TSA = 2(2(9) + 7.9(9) + 2(7.6)

expand the bracket, we have;

TSA = 2(18 + 71.1 + 15.2)

add the values

TSA = 2(104. 3)

TSA = 208. 6

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If the vertex of a parabola is at (5,0) and it opens UPWARD, it will have one solution.

Since the parabola opens upward, its vertex is the minimum point, and therefore, it will have only one solution.

A parabola is a U-shaped curve in mathematics that can be formed by the graph of a quadratic function. It is a type of conic section, along with circles, ellipses, and hyperbolas.

Mathematically, a parabola can be defined as the set of all points in a plane that are equidistant from a fixed point called the focus and a fixed line called the directrix. The focus lies on the axis of symmetry of the parabola, and the directrix is perpendicular to the axis of symmetry.

If the vertex of a parabola is at (5,0) and it opens UPWARD, it will have one solution.

Your answer: one

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The equation would be: y = 3 + x

To include the terms you mentioned, we can set up an equation to represent the relationship between the number of weeks Stacy volunteers (x) and the number of cards she has (y).

Since Stacy starts with 3 collector's cards and receives 1 more card each week she volunteers, the equation would be:

y = 3 + x

In this equation, x represents the number of weeks Stacy volunteers, and y represents the total number of collector's cards she has.

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Answer: 0 g * m/s

Step-by-step explanation:

You first want to multiply 100g, by 12 m/s. This gives you the momentum of the first bird, the answer being 1200 g * m/s

Second, You was to multiply 30g, by 40 m/s. This gives you the momentum of the second bird, The answer also being 1200 g * m/s.

Then, subtract The final answers, and you get 0 g * m/s.

=(100 g)(12 m/s​)+(30 g)(−40 m/s​)

=1200 g⋅ m/s​+(−1200 g⋅ m/s​)

=0 g⋅ m/s

I am not an expert, so I may have gotten some things incorrect.

If this doesn't make sense please consult an expert :,)

The relative speed of the birds is 52 m/s.

We are given that;

Number of blackbirds= 100g

Speed= 12m/s

Now,

The relative speed of the blackbird as seen by the bluebird is:

vblackbird relative to bluebird​=vblackbird​−vbluebird​

vblackbird relative to bluebird​=−12−40

vblackbird relative to bluebird​=−52 m/s

This means that the blackbird is moving to the left at 52 m/s as seen by the bluebird. The relative speed of the bluebird as seen by the blackbird is:

vbluebird relative to blackbird​=vbluebird​−vblackbird​

vbluebird relative to blackbird​=40−(−12)

vbluebird relative to blackbird​=52 m/s

This means that the bluebird is moving to the right at 52 m/s as seen by the blackbird. The relative speed of either bird is equal to the magnitude (absolute value) of their relative velocity.

Therefore, by the speed the answer will be 52 m/s.

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Answer:

x = 4 and y = 9

Step-by-step explanation:

Let x and y be the two numbers. Also,

Let the first number be x and the second number be y.

Converting the word expressions to an equation we get:

                   y = x + 5

               3x + 2y = 30

Only thing left is to substitute y = x + 5 into the second equation

     3x + 2y = 30

     3x + 2(x + 5) = 30   (substituting y as x + 5)

     3x + 2x + 10 = 30   (multiplying by both x and 5)

     5x = 30 - 10     (collecting like terms to one side)

     5x = 20

     [tex]\frac{5x}{5} = \frac{20}{5}[/tex]     (divide both sides by 5 to get the value of x)

     x = 4

 Now that we know the value of x, we can find y.

      y = x + 5

      y = 4 + 5

      y = 9

If you want to make sure your answer is correct, substitute x and y into the equation.

  3x + 2y = 30

  3(4) + 2(9) = 30

  12 + 18 = 30

  30 = 30

The value of m by the given data is m=2

We are given that;

Number of elephants= 125000gram

The mass of african elephant= 3 x 10

Now,

To find the values of b and c, we need to write the given masses in scientific notation, which means that the coefficient must be between 1 and 10. For example, 6 x 10 grams is not in scientific notation, because 6 is not between 1 and 10. To fix this, we need to move the decimal point one place to the left and increase the exponent by one. We get:

6x106 grams=6.0x106 grams=6.0x106−1×101 grams=6.0x105×101 grams=6.0x105+1 grams=6.0x107 grams

Similarly, for the silverback gorilla, we get:

2x105 grams=2.0x105 grams=2.0x105−1×101 grams=2.0x104×101 grams=2.0x104+1 grams=2.0x105 grams

Therefore, the values of b and c are b=7,c=5

To find the value of m, we need to divide the mass of the African elephant by the mass of the silverback gorilla and write the result in scientific notation. We get:

Mass of silverback gorillaMass of African elephant​=2.0x105 grams6.0x107 grams​=2.06.0​×105107​=3.0×107−5=3.0×102

Therefore, by unitary method the answer will be m=2.

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The minimum and maximum measurements taken by Joshua is 44.5 inches and 45.5 inches, under the condition that Joshua is building a model airplane that measures 45 inches.

Now in order to find the scale factor necessary to find the minimum and maximum measurements of Joshua's model airplane, we have to apply the given information.
The given information include that the difference in measurements of the model vary by 0. 5 inches.
Therefore,
Minimum measurement = 45 - 0.5 = 44.5 inches
Maximum measurement = 45 + 0.5 = 45.5 inches

Hence, the minimum measurement is 44.5 inches and the maximum measurement is 45.5 inches.

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The mass of the lamina that occupies the region D is 31/2 units and the center of mass is located at (1/2, 2/e).

We can find the mass of the lamina by integrating the density function over the region D:

m = ∫∫D p(x,y) dA

where dA is the area element in polar coordinates, which is equal to r dr dθ. The region D can be described as 0 ≤ x ≤ 1 and 0 ≤ y ≤ e, so the integral becomes:

m = ∫0^1 ∫0^e 31y dy dx

Solving the integral, we get:

m = 31/2

To find the center of mass, we need to find the x-coordinate and y-coordinate separately:

x = (1/m) ∫∫D x p(x,y) dA

y = (1/m) ∫∫D y p(x,y) dA

For the x-coordinate, we have:

x = (1/m) ∫0^1 ∫0^e x(31y) dy dx

Simplifying, we get:

x = (1/m) ∫0^1 31/2 x dx

x = 1/2

For the y-coordinate, we have:

y = (1/m) ∫0^1 ∫0^e y(31y) dy dx

Simplifying, we get:

y = (1/m) ∫0^1 31/3 e^3 dx

y = (2/e)

Therefore, the center of mass is located at (1/2, 2/e).

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The opposite angles in an inscribed quadrilateral are supplementary, meaning their sum is 180 degrees.

An inscribed quadrilateral is a quadrilateral whose vertices all lie on a circle. Let's label the vertices of the quadrilateral as A, B, C, and D, in clockwise order.

Draw the circle that contains all four vertices, and label the center of the circle as O.

Now, draw chords AC and BD that cross at point P. Each chord divides the quadrilateral into two triangles. Notice that angle AOC and angle BOD are both central angles that subtend the same arc, CD.

Therefore, these angles have the same measure, and we can write:

angle AOC = angle BOD = x

Similarly, we can show that angle AOB = angle COD = y.

Now, consider the two triangles APC and BPD. These triangles share the side P D and have the same angle APD, which is equal to angle AOC + angle BOD, or 2x.

Therefore, by the angle-sum property of triangles, the other angles in each triangle must also be equal. We can write:

angle APC = angle BPD = (180 - 2x)/2 = 90 - x

Similarly, consider the two triangles APB and CPD. These triangles share the side P C and have the same angle APC, which we just found to be 90 - x.

Therefore, by the angle-sum property of triangles, the other angles in each triangle must also be equal. We can write:

angle APB = angle CPD = (180 - (90 - x))/2 = 90 + x/2

Finally, notice that angle APB + angle CPD = (90 + x/2) + (90 - x/2) = 180, so the opposite angles in the quadrilateral are indeed supplementary.

Therefore, the main answer is: The opposite angles in an inscribed quadrilateral are supplementary, meaning their sum is 180 degrees.

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37.5% of the students collected between 49 and 98 kilograms of newspapers for the recycling project. Percentage method can be used here.

To answer this question, we need to determine the number of students who collected between 49 and 98 kilograms of newspapers and then calculate what percentage of the total number of students that represents.

First, we need to gather the data and sort it into categories. We can create a frequency table with intervals of 10 kilograms:
Mass Range | Number of Students
   0-9 kg               3
   10-19 kg            5
  20-29 kg           7
  30-39 kg           4
  40-49 kg           6
  50-59 kg           8
  60-69 kg           5
  70-79 kg           2
  80-89 kg           1
  90-99 kg           2

To find the number of students who collected between 49 and 98 kilograms of newspapers, we need to add up the frequencies for the 50-59, 60-69, and 70-79 kg categories. That gives us a total of 15 students.
To calculate the percentage of students who collected between 49 and 98 kilograms of newspapers, we need to divide the number of students in that range by the total number of students and then multiply by 100. In this case, we have 15 students in the range and a total of 40 students overall, so:
15/40 * 100 = 37.5%.

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Using area formula for rectangles, we can find the new area of the rectangle to be 7350m².

The new dimensions are:

Length = 105m

Breadth = 70m

A rectangle is a quadrilateral with parallel opposite sides and equal angles. There are a lot of rectangular objects all around us. Each rectangle's two defining characteristics are its length and breadth. A rectangle's longer and shorter sides are its width and length, respectively.

Here in the question,

Dimensions of the rectangle are as follows:

Length, l = 42m.

Width, w = 28m.

Scale factor here is 1: 5/2

Now,

Let the new width be x.

The new width will be:

28/x = 1/ (5/2)

Cross multiplying:

⇒ 28 × 5/2 = x

⇒ x = 70m.

So, new width = 70m.

Now, let new length be x.

So,

42/x = 1/ (5/2)

Cross multiplying:

⇒ x = 42 × 5/2

⇒ x = 105m.

So, the new length = 105m.

Now new area will be:

70 × 105

= 7350m².

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The lowest price she can charge per gift box to earn $2,000 in profit in her first month is approximately $3.2.

Jill is starting her own business called Fuzzy Socks Box, where she'll knit and sell gift boxes of fuzzy socks online.

Jill's profit per gift box is x - 2 dollars. To earn $2,000 in profit in her first month, she needs to sell

2000 / (x - 2) gift boxes.

According to her survey, the number of gift boxes she'll sell is

-10x + 350

Setting these two expressions equal to each other, we can find the lowest price Jill can charge per gift box to earn $2,000 in profit

-10x + 350 = 2000 / (x - 2)

Multiplying both sides by (x - 2), we get

-10[tex]x^{2}[/tex] + 12x - 470 = 0

Solving this quadratic equation, we find that

x = (6 +[tex]\sqrt{196[/tex] )/5 ≈ 3.2

or

x = (6 -[tex]\sqrt{196[/tex] )/5 ≈ 0.7

Since Jill cannot charge a negative price for her gift boxes, the lowest price she can charge per gift box to earn $2,000 in profit in her first month is approximately $3.2.

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If the school district surveyed 500 families to see if they were satisfied or not satisfied with the new district website. the maximum number of families who are satisfied with the new district website is approximately 130,771.

First, we need to calculate the confidence level, which is 1 minus the margin of error:

Confidence level = 1 - margin of error

Confidence level = 1 - 0.027

Confidence level = 0.973

Next, we can use the proportion of satisfied families in the sample to estimate the proportion in the population:

Proportion satisfied in population = Proportion satisfied in sample

Proportion satisfied in population = 480/500

Proportion satisfied in population = 0.96

Now we can use this proportion and the confidence level to calculate the maximum number of satisfied families in the population:

Maximum number of satisfied families = Proportion satisfied in population x Total number of families x Confidence level

Maximum number of satisfied families = 0.96 x 140,000 x 0.973

Maximum number of satisfied families ≈ 130,771

Therefore, the maximum number of families who are satisfied with the new district website is approximately 130,771.

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The image of point (-3, 8) after a rotation of 180 counterclockwise about the origin is (3, -8)

Transformation is the movement of a point in the coordinate plane from one location to another. Transformation can either be reflection, rotation, translation and dilation.

Rotation is the flipping of a figure about a point in the coordinate plane; this point of rotation is usually origin.

(x, y) → (-x, -y) represents a rotation 180° counterclockwise.

The image of point (-3, 8) after a rotation of 180 counterclockwise about the origin is (3, -8)

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Answer:

This relation is a function.

Algebraically, this function is written as

y = 5x.

The two letters in which the new point lie include the following: C. between G and H.

In Geometry, a number line simply refers to a type of graph that is composed of a graduated straight line, which typically comprises both negative and positive numerical values (numbers) that are located at equal intervals along its length.

This ultimately implies that, all number lines would primarily increase in numerical value (number) towards the right from zero (0) and decrease in numerical value (number) towards the left from zero (0).

From the number line shown in the image attached below, we can logically deduce the following point:

|J - E| = 45% of x

|J - E| = 0.45x

|J - E| = GH

In conclusion, 45% is almost half way or 50% between E and J, which makes the distance between the two letters G and H, the new point.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Emilia make an error in step 3 she didn't use an x and y from the same coordinate pair.

In step 1 : point 1 : (5, 2.15)  point 2 : (12, 3.06)

In step 2 : m = [tex]\frac{12-5}{3.06-2.15}[/tex]

m = 7/0.91

m = 7.69

In Step 3 : y = mx + b

m = slope

Point used by Emilia (2.15 , 5)

But the point should be used be Emilia is (5, 2.15)

2.15 = 5(7.69) + b

b = y intercept

b = -36.3

step 3 is wrong she didn't use right coordinates of x and y

In step 4 : y = mx +b

y = 7.69x -36.3

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Answer:

Option B.

Step-by-step explanation:

Angle SOB and Angle VOK are vertical angles, and thus congruent because all vertical angles are congruent.

Lines SB and KV are parallel, cut by the transversal SV, and Angle S and Angle V are Alternate Interior Angles.  So, Angle S and Angle V are congruent by Alternate Interior Angle congruence.

Therefore, Triangle SOB and Triangle VOK are similar by Angle Angle similarity postulate.

The inequality that is true is Negative 2 and three-fourths less-than negative 1 and one-half.

The first inequality from the number line can be shown to be :

( 1 / 4 ) < - 1 1 / 2

This is not possible as a negative cannot be larger than a positive.

The second inequality is:

- 2. 75 < - 1. 5

This is true as larger negative numbers are lower than smaller negative numbers.

The third inequality is:

- 2. 25 > - 1. 25

This is not possible for the reason explained.

In conclusion, option B is correct.

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If Holly cuts 6 ribbons into fifths for her craft project, after cutting, she has a total of 30 one-fifth-size ribbons (6 ribbons x 5 cuts each).

Holly has cut 6 ribbons into fifths for her craft project. This means that she has a total of 30 ribbons, each with a size of one-fifth. To understand this better, we can break it down into fractions. Each ribbon is one-fifth of a whole ribbon, and since Holly has cut 6 ribbons, she has 6 times one-fifth, which equals 30. So, to answer the question, Holly has 30 ribbons, each with a size of one-fifth. These ribbons can be used for various crafts, such as creating bows, wrapping presents, or decorating cards. The possibilities are endless, and with 30 ribbons, Holly can get creative and make a lot of beautiful crafts.

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The probability that the mean weight of the sample of horses would differ from the population mean by greater than 18lbs if 41 horses are sampled at random from the large stable is approximately 0.131 or 13.1%.

Suppose the horses in a large stable have a mean weight of 807lbs and a variance of 5776. We want to find the probability that the mean weight of a sample of 41 horses would differ from the population mean by greater than 18lbs.

Step 1: Calculate the standard deviation of the population.
Standard deviation (σ) = √variance = √5776 = 76lbs.

Step 2: Calculate the standard error of the mean.
Standard error (SE) = σ / √n = 76 / √41 ≈ 11.88lbs, where n is the sample size (41 horses).

Step 3: Calculate the z-score for the difference of 18lbs.
z = (difference - 0) / SE = (18 - 0) / 11.88 ≈ 1.51

Step 4: Find the probability corresponding to the z-score.
Using a z-table, we find that the probability corresponding to a z-score of 1.51 is approximately 0.9345.

Step 5: Calculate the probability of the mean weight differing by more than 18lbs.
Since we are looking for the probability of the mean weight differing by more than 18lbs (in either direction), we need to consider both tails of the distribution.
P(z > 1.51) = 1 - 0.9345 = 0.0655
P(z < -1.51) = 0.0655 (since the distribution is symmetric)

Total probability = P(z > 1.51) + P(z < -1.51) = 0.0655 + 0.0655 = 0.1310

So, the probability that the mean weight of the sample of horses would differ from the population mean by greater than 18lbs if 41 horses are sampled at random from the large stable is approximately 0.131 or 13.1%.

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