Triangle def is similar to triangle abc solve for y DEF 37. 5 20 27. 5 ABC y 12 16. 5​

The slant height of the right cone is 24.2 units, rounded to the nearest tenth.

What is the Pythagorean Theorem?

The Pythagorean theorem is a mathematical theorem that states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. It can be expressed as c² = a²+ b².

The slant height of a right cone can be found by using the Pythagorean Theorem. The radius of the circular base is half the diameter, which is 6/2 = 3 units. The volume of the cone can be found using the formula:

V = (π/3)r²h

Where r is the radius, and h is the height of the cone. Plugging in the given values, we have:

72π = (π/3)r²h

72π = (π/3)3²h

72π = (π/3)9h

72π = 3πh

24 = h

Using the Pythagorean Theorem, we can find the slant height as follows:

c² = a² + b²

Where a and b are the height and radius of the cone, and c is the slant height. Plugging in the values we have:

c² = 24² + 3²

c² = 576 + 9

c² = 585

c = 24.2

Hence, the slant height of the right cone is 24.2 units, rounded to the nearest tenth.

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Answer:

x>-3

Step-by-step explanation:

Divide both sides by 5

x > -3

-15/5 = -3

Lines AB and CD are parallel to each other because the lines make the same angle as the transversal line.

When the distance between the lines is constant then the lines are called parallel lines. The lines do not intersect when they are separated from each other. And the slope of the lines is equal.

Let the transversal line be EF to line AB and CD.

Line AB and line CD make the same angle as the transversal line. Then we can say that the lines AB and CD are parallel to each other.

The diagram is given below.

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The 95% confidence interval for the mean number of shoes owned by female students is (95.58, 195.14).

Calculate the sample mean:  

Total number of shoes = 45+31+3125+62+15+29+27+28+35+18+55+18+39+28+35+44+18+10+55+50+40+38+22+16 = 3634

Sample mean = 3634/25 = 145.36

Calculate the standard deviation:

Standard deviation = √[(45-145.36)² + (31-145.36)² + (3125-145.36)² + … + (16-145.36)²]/24 = 586.33

Calculate the margin of error:

Margin of error = 1.96∗586.33/√25 = 49.78

Calculate the 95% confidence interval:

Lower bound = 145.36 - 49.78 = 95.58

Upper bound = 145.36 + 49.78 = 195.14

Since the sample mean is not an integer, we must round the lower and upper bounds to the nearest integer, which gives us (29.73, 40.27) as the 95% confidence interval for the mean number of shoes owned by female students.

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a) The slope is 1

b) The equation of the tangent line is x-y=20.

What is slope?

Slope is calculated using the slope of a line formula, the ratio of "vertical change" to "horizontal change" between two different locations on a line is determined. The difference between the line's y and x coordinate changes is known as the slope of the line.Any two distinct places along the line can be used to determine the slope of any line.

a) To find the slope of the curve, the derivative of a function f(x) at the given point is a slope of the curve

Slope of the given curve y = x at the point P(25, 5) is the derivative f'(x) at P(25,5)

=>m = f'(x) = dy/dx

=>1

Since the derivative of x is 1

f'(x) at P(25, 5) is 1

= > Slope = 1

b) To find an equation of the tangent line at P (25,5) for the curve y = x.

The equation of tangent line in for the function f(x) at P ([tex]x_1,y_1[/tex]) is (y - [tex]y_1[/tex]) = m (x - [tex]x_1[/tex])

Given:

[tex]x_1[/tex] = 25 and  [tex]y_1[/tex] = 5, f(x) =x and slope of tangent m = 1

The equation of the tangent line is (y - 19) = - 24(x - 2)

⇒ y - 5 = 1(x -25)

=> y=x-25+5

=> y=x-20

=> x-y=20

The equation of tangent is x-y=20.

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The light post's height is 21 metres higher than the structure,

A lamp post is 45 feet away from where you are. You are standing at a 36" angle and are 5 feet tall as you stare up at the top of the light post.

tan 60 degrees is equal to 36/x sqrt(3),

36/x, and 36/(sqrt(3))*m. sqrt (3)

36/3 = 36 - h

h = 36 - 12

h = 24m

The distance between AB and CD is thus

60/(sqrt(3)) * 1.

The light post is 24 metres tall.

The light post's height is 45 -24 =21 metres higher than the structure, which is 21 metres higher.

The light post's height is 21 metres higher than the structure,

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randomly choosing a male first and randomly choosing a male second are independent events.

Sample Space:

M1, M2, M3, M4, F1, F2, F3, F4, F5

Independent Events:

M1, M2, M3, M4, M1, M2, M3, M4

The sample space includes all of the possible outcomes of picking two contestants from the audience of 5 females and 4 males. Since the order of choosing does not affect the outcome, the sample space does not change regardless of which gender is chosen first. Therefore, randomly choosing a male first and randomly choosing a male second are independent events.

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100 kilograms (kg) converts to 220.463 pounds (lb).

Conversion. 100 kilograms (kg) converted to pounds (lb). 100 kilograms (kg) equals 220.463 pounds (lb). A kilogram weighs approximately 2.2046226218 pounds. The method for converting kilos to pounds is pretty straightforward. All you have to do is multiply the kilogram amount by 2.2046226218.

The term “pound” derives from the ancient Roman libra pondo, which means “a pound by weight.” According to the BBC, the English term “pound” is derived from the pondo component of the sentence. However, the abbreviation “lb” is taken from the word libra.

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The solution of the given equation is y = y = e^(6x -∞) ,y = e^(6x)

The given equation is a first-order linear differential equation with constant coefficients. Applying the integrating factor, we get:

[tex]I = e^(int (6 dy/6y)) = e^(ln y)[/tex]

Multiplying both sides of the equation by I:

[tex]Iy' = 6y5/6 ⇒ dy/y = 6/6 dy ⇒ ln y = 6x + c[/tex]

Therefore, the general solution of the given equation is:

y = e^(6x + c)

Substituting the initial condition, y(0) = 0 to the above equation, we get:

[tex]0 = e^(6(0) + c) ⇒ c = -∞[/tex]

Therefore, the solution of the given equation is:

y = e^(6x -∞)

Solution 2:

The given equation is a first-order linear differential equation with constant coefficients. Applying the integrating factor, we get:

[tex]I = e^(int (6 dy/6y)) = e^(ln y)[/tex]

Multiplying both sides of the equation by I:

Iy' = 6y5/6

⇒ dy/y = 6/6 dy

⇒ ln y = 6x + c

Therefore, the general solution of the given equation is:

y = e^(6x + c)

Substituting the initial condition, y(0) = 0 to the above equation, we get:

0 = e^(6(0) + c)

⇒ c = 0

Therefore, the solution of the given equation is:

y = e^(6x)

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Hz (Hertz) is a unit of frequency, which measures the number of events or occurrences of a certain phenomenon per second. In this case, the tape timer creates 28 dots per second, which means that the frequency of dot creation is 28 Hz.

To find the time interval between 3 successive dots, we need to calculate the time it takes for the tape timer to create 3 dots. This can be done by dividing the total time by the number of dots created.

Since the tape timer creates 28 dots per second, the time interval between 3 dots can be calculated as follows:

Time interval = 1 second / 28 dots = 1/28 seconds

So, the time interval between 3 successive dots created by the tape timer is 1/28 seconds, which is the amount of time that elapses between the creation of each dot.

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The study design of selecting 50 trees using random latitude/longitude coordinates may result in sampling error and measurement error, which could affect the accuracy of the results.

The error that is likely to result from this study design is known as "sampling error" because the sample of 50 trees is not necessarily representative of the entire population of white pine trees in the national forest as these trees were selected by chance.

If the sample of 50 trees were selected from a particular area of the forest where the trees were smaller in diameter, the study results would not accurately reflect the average diameter of all the white pine trees in the forest.

Moreover, there is a possibility of measurement error if the diameter of the trunks were not measured consistently. This could also contribute to the overall error in the study results.

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The sample space may be limited or infinite, depending on the nature of the experiment. A sample point is a component of the sample space that symbolizes one potential experiment result.

The sample space may be limited or infinite, depending on the nature of the experiment. A sample point is a component of the sample space that symbolises one potential experiment result.

The sample space is a set in probability theory that includes all potential results of a random experiment. The set of all potential outcomes or outcomes of a random experiment is referred to as a sample space. The set 1, 2, 3, 4, 5, and 6 might be the sample space, for instance, if we are rolling a die.

A sample space is a group of items that in set theory represents all potential outcomes of a random event. Depending on the situation, either a finite or infinite sample space

A sample space is a group of items that in set theory represents all potential outcomes of a random event. Depending on the nature of the experiment, the sample space may be either finite or limitless. A sample point is a component of the sample space that symbolises one potential result of the experiment. As it offers a framework for defining and computing probabilities, the sample space is a basic idea in probability theory.

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78.740 inches in 2 meters. 2 meters equals 6.56168 ft. One meter is equivalent to 3.28084 ft.

2 meters into inches

1 inch = 39.370

2 meters = 2 × 39.370

Then we get ,

= 78.740 inches

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Answer:

the answer is 48 i believe

Step-by-step explanation:

............

47.) The angle between the plane is 0 degrees.

48.) The angle between the plane is 180 degrees.

What is the angle between the plane?

To find the angle between two planes, we need to find the normal vectors of each plane and then find the cosine of the angle between the normal vectors using the dot product.

First, let's find the normal vectors for the two planes:

Plane 1: x + y = 1

The normal vector for this plane can be found by taking the coefficients of x, y, and z and forming a vector:

n1 = ⟨1, 1, 0⟩

Plane 2: 2x + y - 2z = 2

The normal vector for this plane can be found in the same way:

n2 = ⟨2, 1, -2⟩

Next, we will find the cosine of the angle between the normal vectors using the dot product:

cosθ = (n1 • n2) / (|n1| * |n2|)

where |n1| and |n2| are the magnitudes of the normal vectors.

Calculating the dot product and magnitudes:

n1 • n2 = 1 * 2 + 1 * 1 + 0 * -2 = 3

|n1| = sqrt(1^2 + 1^2 + 0^2) = sqrt(2)

|n2| = sqrt(2^2 + 1^2 + (-2)^2) = sqrt(9)

Substituting into the formula:

cosθ = 3 / (sqrt(2) * sqrt(9)) = 3 / (3) = 1

Since cosθ = 1, θ = 0, so the angle between the two planes is 0 degrees or a coincident plane.

Next, let's find the normal vectors for the two planes:

Plane 1: 5x + y - z = 10

The normal vector for this plane can be found by taking the coefficients of x, y, and z and forming a vector:

n1 = ⟨5, 1, -1⟩

Plane 2: x - 2y + 3z = -1

The normal vector for this plane can be found in the same way:

n2 = ⟨1, -2, 3⟩

Next, we will find the cosine of the angle between the normal vectors using the dot product:

cosθ = (n1 • n2) / (|n1| * |n2|)

Calculating the dot product and magnitudes:

n1 • n2 = 5 * 1 + 1 * (-2) + -1 * 3 = -3

|n1| = sqrt(5^2 + 1^2 + (-1)^2) = sqrt(27)

|n2| = sqrt(1^2 + (-2)^2 + 3^2) = sqrt(14)

Substituting into the formula:

cosθ = -3 / (sqrt(27) * sqrt(14)) = -3 / (3 * sqrt(2)) = -sqrt(2) / sqrt(2) = -1

Since cosθ = -1, θ = 180 degrees, so the angle between the two planes is 180 degrees, or perpendicular.

Hence,

47.) The angle between the plane is 0 degrees.

48.) The angle between the plane is 180 degrees.

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The series of transformations that would map polygon ABCDE onto polygon A'B'C'D'E' will be Dilation and Reflection.

A point, line, or mathematical figure can be converted in one of four ways, and each has an effect on the object's structure and/or position.

Dilation is the process of increasing the size of an item without affecting its form. Depending on the scale factor, the object's size can be raised or lowered. There is no effect of dilation on the angle.

Then the scale factor about the origin is given as,

Scale factor = 2 / 4

Scale factor = 1/2

The reflection does not change the shape and size of the geometry. But flipped the image.

Reflection of the image over the y-axis.

The series of transformations that would map polygon ABCDE onto polygon A'B'C'D'E' will be Dilation and Reflection.

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The value of the sum of the series is 160

In an arithmetic series, the sum of the first "n" terms (Sn) is given by the formula:

Sn = n/2 * (a1 + an)

Where "a1" is the first term and "an" is the nth term.

In this series, n = 25, a1 = -20, and an = 148.

Plugging these values into the formula, we get:

Sn = 25/2 * (-20 + 148)

= 25/2 * 128

= 25 * 64

= 1600

So, the sum of the first 25 terms of the arithmetic series is 1600.

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On solving the linear equations 14x + 5y = 975 and 10x + 4y = 750, the price for small ad and full page ad is obtained as $25 and $125 respectively.

What is a linear equation?

A linear equation is one that has a degree of 1 as its maximum value. No variable in a linear equation, thus, has an exponent greater than 1. A linear equation's graph will always be a straight line.

The two linear equations given are -

14x + 5y = 975 .... (1)

10x + 4y = 750 .... (2)

Here, x represents the price of small ad and y represents the price of a full-page ad.

To get the value of x and y solve the system of linear equations -

Multiply equation (1) by 4 and (2) by 5 -

4 (14x + 5y) = 4 × 975

56x + 20y = 3900 .... (3)

5 (10x + 4y) = 5 × 750

50x + 20y = 3750 .... (4)

Subtract equation (4) from (3) -

56x + 20y - (50x + 20y) = 3900 - 3750

56x + 20y - 50x - 20y = 3900 - 3750

6x = 150

x = 150/6

x = 25

Substitute the value of x in equation (1) -

14(25) + 5y = 975

350 + 5y = 975

5y = 975 - 350

5y = 625

y = 625/5

y = 125

So , the prices of small ad is $25 and prices of full-page ad is $125.

Therefore, the values for x and y are $25 and $125 respectively.

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The capacity of the airplane is 105 passengers.

Since 90 passengers is to 6/7 of the capacity, then 90/6 people is 1/7 of the capacity. And, 90 / 6 = 15

So, 15 people is 1/7 of the capacity. It means, the full capacity is 7/7.

Full capacity = 15 * 7 = 105

Hence, the capacity of the airplane is 105 passengers.

Capacity of passengers are the total number of seats and berths and the total number of authorized standing places which available in a passenger vehicle when doing the service for what it is intended. The maximum passenger capacity in airplane means the maximum number of passenger seats for that an aircraft is configured.

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Although part of your question is missing, you might be referring to this full question: An airplane is carrying 90 passengers, which is 6/7 of the capacity of the airplane. What is the capacity of the airplane?

Fe-59 concentrates in the spleen with a biological half life of approximately 600 days, and an effective half life of approximately 42 days.

Define half life?

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The values of x in the triangles are 38.9 and 43.3 degrees

The complete question is added as an attachment

Triangle 1

The value of x can be calculated using the following sine ratio

sin(x) = 15/24

Evaluate the quotient

sin(x) = 0.625

Take the arc sin of both sides

x = 38.9

Triangle 2

The value of x can be calculated using the following cosine ratio

cos(x) = 8/11

Evaluate the quotient

cos(x) = 0.7273

Take the arc cos of both sides

x = 43.3

Hence, the solution is 43.3 degrees

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The spillage refer to Cyber Awareness Challenge 2022 is explained below.

The Cyber Awareness Challenge 2022 is an important event that focuses on raising awareness about the dangers and risks associated with the use of technology and the internet.

In this context, spillage refers to the accidental or unintentional release of sensitive information. This can be caused by a variety of factors, including human error, technical glitches, and malicious attacks.

In addition, the challenge will explore the consequences of spillage, such as identity theft, financial loss, and reputational damage. This is why it is so important to take the challenge seriously and to understand the importance of cyber awareness and security.

By participating in the Cyber Awareness Challenge 2022, students will gain valuable skills and knowledge that will help them protect themselves and their information in the digital world

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The critical values of the given function are 0, +2, and -2.

According to the question

Given function f(x) = y^2(4-y^2)

Setting the partial derivatives of the function y2(4-y2) to zero and solving for y will reveal where the function's crucial points are.

The partial derivatives of y^2(4-y^2) with respect to y are:

⇒ d/dy (y^2) = 2y

⇒ d/dy (4-y^2) = -2y

⇒ d/dy (y^2(4-y^2)) = 2y(-2y) + 2(y^2)

⇒ -4y^2 + 4y^2 = 0

Setting the partial derivative equal to zero:

-4y^2 + 4y^2 = 0

Solving for y:

y = 0 or y = ±2

The critical values are therefore y = 0 and y = 2. Using the second derivative test or by examining the behavior of the function close to these locations, these key points can be categorized as local minima, local maxima, or inflection points.

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Answer:

f'(x)=16x³+69x²+86x+33

Answer: q = 16

Step-by-step explanation:

When given the equation 3(q - 7) = 27,  you would solve for the variable.

The variable in this equation is q, so we need to isolate the variable.

Solving process:

3(q - 7) = 27

lets distribute, due to the orders of PEMDAS.

PEMDAS stands for: Parenthesis, Exponents, Multiplication, Division, Addition, and Subtraction.

3(q - 7) = 27

distributing is multiplying the number correlated outside of the parenthesis with the inside components.

3q - 21 = 27

lets add 21 to both sides

3q = 48

now lets divide by 3 (we are trying to get q by itself)

q = 16

----

To check if your solution is correct, you replace the value (16) of the variable (q) within the original equation:

3 (16 − 7) = 27

Following PEMDAS you get:

3(9) = 27

27 = 27 (meaning that the solution is correct)

Thank you.

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Maximum or the upper limit of the amount of water leaked in 2 hours will be r(2) since t = 2 hrs.

The lower bound or limit will be zero if the leaked is fixed or the amount of water is zero.

Each element of X receives precisely one element of Y when a function from one set to the other is used. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. Initially, functions represented the idealized relationship between two changing quantities.

The set of integers x for which a function has a valid definition is known as its domain. A closed interval is referred to as a function's domain if it is specified across the interval a≤ x ≤b.

A function's range can be used to describe one of two related ideas: The function's codomain a representation of the action A binary relation f between two sets X and Y is a function if there is precisely one y in Y such that f connects x to y for every x in X.

The tank is leaking in the function of time givenas

r(t), where t is measured in hours

Maximum or the upper limit of the amount of water leaked in 2 hours will be r(2) since t = 2 hrs.

The lower bound or limit will be zero if the leaked is fixed or the amount of water is zero.

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Considering the other two sides, i.e. 5ft, 25ft, The unknown side length is 24.5 ft.

The unknown side length can be found using the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.

In this case, we have one side with a length of 5 ft and another side with a length of 25 ft. To find the length of the third side, we can use the formula: [tex]c^2 = a^2 + b^2[/tex], where c is the length of the hypotenuse and a and b are the lengths of the other two sides.

Substituting the given values, we have

[tex]25^2 = 5^2 + b^2[/tex],

[tex]b^2[/tex]= 625 - 25 = 600.

Taking the square root of both sides, we have c = √600 = 24.4949. Rounding to the nearest tenth, the unknown side length is 24.5 ft.

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Complete Question:

Find the unknown side length. Round to the nearest tenth.

a = 5 ft

b = ?

c = 25 ft

Therefore , the solution of the given problem of triangle comes out to be it is unsolvable as the all the information is not given option A is correct.

Polygons include triangles since they have four sides or more. It has a simple, geometric shape. The letters ABC make up a triangle, which is a square angle. Euclidean geometry results in a single rectangle or square so when sides remain not coincident. Because they have 3 components and three corners, triangles are polygons. A triangle's corners are where its three sides meet. The total of the angles in a triangle is 180 degrees.

Here,

Given :

=> α = 60°

=> β = 60°

=> γ = 60°

To solve the triangle we need to know the angles,

Since all the angles are equal to 60 degree

it seems it is an equilateral triangle having all the same sides

So,

it can be option b,c and d

but here is not mentioned the side length.

Thus, it is unsolvable.

Therefore , the solution of the given problem of triangle comes out to be it is unsolvable as the all the information is not given option A is correct.

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The probability P that all the students with A’s and B’s are female and all the students with C’s and D’s are male is 0.0000907 or 0.00907%.

To determine the probability P, we can use the formula for combinations:

P = (number of ways to select A's and B's from the females) * (number of ways to select C's and D's from the males) / (number of ways to assign grades to all students)

Let's first find the number of ways to select A's and B's from the females:

There are 2 ways to select 2 A's from 7 females.

There are 7 choose 5 ways to select 5 B's from 7 females, which is 21.

So, there are 2 * 21 = 42 ways to select A's and B's from the females.

Next, let's find the number of ways to select C's and D's from the males:

There are 8 ways to select 8 C's from 11 males.

There are 11 choose 3 ways to select 3 D's from 11 males, which is 165.

So, there are 8 * 165 = 1320 ways to select C's and D's from the males.

Finally, let's find the number of ways to assign grades to all students:

There are 18 choose 2 ways to select 2 A's from 18 students, which is 153.

There are 18 choose 5 ways to select 5 B's from 18 students, which is 18564.

So, there are 153 * 18564 = 2827672 ways to assign grades to all students.

Putting it all together, the probability P is:

P = (42) * (1320) / (2827672) = 0.0000907

Therefore, the probability P that all the students with A’s and B’s are female and all the students with C’s and D’s are male is 0.0000907 or 0.00907%.

Complete Question:

An EEOC investigation into course grading encountered the following situation. In a course with eighteen students, 7 females and 11 males, grades were assigned as follows: 2 A’s, 5 B’s, 8 C’s, and 3 D’s. Determine the probability P that all the students with A’s and B’s are female and all the students with C’s and D’s are male.

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