The segment joining a vertex to the middle of
the opposite side of a triangle is called the
Select one:
O a. angle bisector
O b. altitude
c. perpendicular bisector
O d. median

The sample is 3, 71, 139, 207, and 275.

The procedure for systematic random sampling involves first dividing the population size by the sample size and rounding the result down to the nearest whole number, m. This value of m is known as the sampling interval. For the given population size of 341 and sample size of 5, the value of m is 68.

Next, a random number, k, between 1 and m is chosen. The given random-number table contains the values 03184, 61921, 87377, 97729, and 79151. Reading the two-digit number at the top left, we get 03, which is equal to 3. Therefore, k = 3.

Finally, the sample is taken from the population in intervals of m. In this case, the sample consists of members of the population numbered 3, 71, 139, 207, and 275. Therefore, the sample is 3, 71, 139, 207, and 275.

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Answer:

B

Step-by-step explanation:

Δy = -10-10= -20

Δx = -12-(-6) = -6

-20/-6= 10/3

The amount Casey invested in the certificate of deposit is; $60,000.

An equation is an expression that shows the relationship between two or more numbers and variables.

Assume that

0.01c -  0.02s = $250---equation 1

c + s = $10,000 ------ equation 2

Where: c = amount invested in the certificate of deposit

s = amount invested in the savings account

Now Multiply equation 2 by 0.01:

0.01c + 0.01s = 100 equation 3

Subtract equation 3 from equation 1:

0.01s = 100

Divide both sides of the equation by 0.01:

s = 100 / 0.01

s = 10,000

Substitute for s in equation 2:

c + 10,000 = 70,000

c = 70,000 - 10,000

c = 60,000

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The angle included by these two sides is (c^2 - 74) / (-70).

What is triangle ?

A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted triangle ABC.

The area of a triangle can be found using the formula:

Area = (1/2) * b * h,

where b is the length of the base and h is the height of the triangle.

Since two of the sides have lengths 5 in and 7 in, we can assume that they are the base and the height of the triangle, respectively. Setting b = 5 in and h = 7 in, we can find the area:

Area = (1/2) * 5 in * 7 in = (1/2) * 35 in^2 = 16 in^2.

This means that the height of the triangle is 7 in and the base is 5 in. To find the angle included by these two sides, we can use the Law of Cosines:

c^2 = a^2 + b^2 - 2ab * cos(C),

where a and b are the lengths of the sides and C is the angle included by these two sides.

Since a = 5 in and b = 7 in, we can find the angle C:

c^2 = a^2 + b^2 - 2ab * cos(C)

c^2 = 5^2 + 7^2 - 2 * 5 * 7 * cos(C)

c^2 = 25 + 49 - 70 * cos(C)

c^2 = 74 - 70 * cos(C)

So , The angle included by these two sides is (c^2 - 74) / (-70).

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The volume of the solid obtained by rotating the region bounded by the curves y = 5[tex]x^5[/tex] and y = 5x about the x-axis is -(8π/21) cubic units.

We have,

To find the volume of the solid obtained by rotating the region bounded by the curves y = 5[tex]x^5[/tex] and y = 5x about the x-axis, we can use the method of cylindrical shells.

The region bounded by the curves is between x = 0 and x = 1.

Let's consider an infinitesimally thin strip of width dx at a distance x from the y-axis.

The height of this strip will be the difference between the two curves:

(5[tex]x^5[/tex]) - (5x).

The circumference of the shell at this distance x is 2πx (since we are rotating about the x-axis).

Therefore,

The volume of this infinitesimally thin shell is given by:

dV = (2πx) x [(5[tex]x^5[/tex]) - (5x)] x dx.

To find the total volume, we integrate this expression over the interval [0, 1]:

V = ∫(0 to 1) (2πx) x [(5[tex]x^5[/tex]) - (5x)] dx.

Simplifying the expression inside the integral:

V = 2π ∫(0 to 1) [(5[tex]x^6[/tex]) - (5x²] dx.

Integrating term by term:

V = 2π [([tex]x^7[/tex])/7 - (x³)/3] evaluated from 0 to 1.

Substituting the limits of integration:

V = 2π [(([tex]1^7[/tex])/7 - (1³)/3) - (([tex]0^7[/tex])/7 - (0³)/3)].

Simplifying:

V = 2π [(1/7 - 1/3) - (0 - 0)].

V = 2π [(3 - 7)/21].

V = 2π (-4/21).

V = -(8π/21).

Therefore,

The volume of the solid obtained by rotating the region bounded by the curves y = 5[tex]x^5[/tex] and y = 5x about the x-axis is -(8π/21) cubic units.

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The absolute minimum value of y =-cos(x) - sin(x) on the closed interval [0, π/2] is  [tex]-\sqrt{2}[/tex]

Consider equation,

y = -cos(x) - sin(x)

Let y = f(x)

Differentiate the function f(x) = -cos(x) - sin(x) with respect to x.

f'(x) = -(-sin(x)) - cos(x)

f'(x) = sin(x) - cos(x)

For f'(x) = 0,

sin(x) - cos(x) = 0

sin(x) = cos(x)

sin(x)/cos(x) = 1

tan(x) = 1                     ..............(tan(θ) = sin(θ)/cos(θ))

x = π/4

For above value of x, the value of function would be,

f(π/4) = -cos(π/4) - sin(π/4)

f(π/4) = [tex]-\frac{1}{\sqrt{2} } -\frac{1}{\sqrt{2} }[/tex]

f(π/4) = [tex]-\sqrt{2}[/tex]

f(0) =  -cos(0) - sin(0)

f(0) = -1

And f(π/2) = -cos(π/2) - sin(π/2)

       f(π/2) = -1

So, the minimum value of f(x) is  [tex]-\sqrt{2}[/tex],  shown in the following graph.

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the general lighting VA requirement be for the building service calculation will be 13500VA.

General lighting, also known as ambient lighting, provides an area with overall, non-specific illumination. Radiating a comfortable level of brightness, General lighting enables one to use and see a space according to its function.

given, you have a 4500 square foot club.

Since,  in the National Electrical Code considers a residence a listed occupancy at 3 VA per square foot; therefore, the general lighting load is determined by multiplying the square footage.

Thus,

General lighting required = 4500*3 VA

General lighting required = 13500VA

therefore,  the general lighting VA requirement be for the building service calculation will be 13500VA.

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The first step in this project is to randomly select several city blocks for interviewing. For example, if one were to select two blocks in a city, one could go door-to-door and interview all the adults who live on the blocks.

This would require the researcher to ask questions about the residents' backgrounds and opinions about their current living environment, as well as any other relevant topics of interest. Furthermore, the researcher should collect demographic information, such as age, gender, and ethnicity, to gain insight into the makeup of the population.

By engaging in this project, the researcher can gain valuable insights into the lives of the people living in the city, as well as their opinions on the quality of life they experience. This data can then be used to inform decision-making processes by city officials, such as public policy and urban development projects.

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The solution of each part of the question is given below:

a. Let C be the event that a person smokes cigars, and let S be the event that a person smokes cigarettes. The percentage of Americans who smoke either cigars, cigarettes, or both can be calculated as P(C U S), where U represents the union of two events. From the given information, P(C) = 15% and P(S) = 35%. The probability that a person smokes both cigars and cigarettes is 7%, so P(C ∩ S) = 7%.

P(C U S) = P(C) + P(S) - P(C ∩ S)

P(C U S) = 15% + 35% - 7% = 43%

So, 43% of Americans smoke either cigars, cigarettes, or both.

b. The percentage of Americans who smoke neither cigars nor cigarettes can be calculated as P(C' ∩ S'), where C' represents the complement of event C (not smoking cigars) and S' represents the complement of event S (not smoking cigarettes).

P(C' ∩ S') = 100% - P(C U S)

P(C' ∩ S') = 100% - 43% = 57%

So, 57% of Americans smoke neither cigars nor cigarettes.

c. The percentage of Americans who smoke cigars but not cigarettes can be calculated as P(C ∩ S').

P(C ∩ S') = P(C) - P(C ∩ S)

P(C ∩ S') = 15% - 7% = 8%

So, 8% of Americans smoke cigars but not cigarettes.

d. The conditional probability that a person smokes cigarettes given that he smokes cigars can be calculated as P(S | C), where S represents the event that a person smokes cigarettes and C represents the event that a person smokes cigars.

P(S | C) = P(S ∩ C) / P(C)

P(S | C) = 7% / 15% = 0.47

So, the conditional probability that a randomly selected person smokes cigarettes given that he smokes cigars is 0.47, or 47%.

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The pedestrian crossing sign is a parallelogram because both pairs of opposite sides are parallel. The Second option is Correct.

A parallelogram is a quadrilateral that has two pairs of parallel sides, meaning that both sets of opposite sides are parallel. This is opposed to a trapezoid, which has only one pair of parallel sides. The pedestrian crossing sign is typically in the shape of a parallelogram, with the top and bottom sides being parallel, and the sides slanting towards each other to form a point at the top.

This design helps the sign to be easily visible from a distance and clearly recognizable as a pedestrian crossing sign. The parallel sides of the sign are an important characteristic that helps drivers and pedestrians to identify and understand the meaning of the sign.

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The solution for the given equation is y=(93-qa)/(q-67).

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

The given equation is q⋅(a+y)=67y+93

Here, qa+qy=67y+93

qy-67y=93-qa

y(q-67)=93-qa

y=(93-qa)/(q-67)

Therefore, the solution for the given equation is y=(93-qa)/(q-67).

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Answer:

1) 40%, increase

2) a)20%

3) True

Step-by-step explanation:

Since not all of the leading coefficients are ones and not all of the rows are in descending order, the above linear equation is not in echelon form.

No, an echelon form does not exist for the given linear system. All leading coefficients must be 1 for the structure to be in echelon form, and all rows must be arranged in decreasing order. The second and third rows in this equation are not in decreasing order, and the leading coefficient in the first row is 2, not 1.

An echelon form cannot be described by the given linear system. All of the leading coefficients in the equations must be 1, and all of the rows must be arranged in descending order for the equation to be in echelon form. The leading coefficient of the first row in the preceding equation is 2, not 1, and the second and third rows are not arranged in descending order. The equation is therefore not in echelon form.

Each row should have one more leading coefficient than the row above it in echelon form, and any row with all zeroes should be at the bottom of the equation. Additionally, all leading coefficients must equal 1. The given equation is not valid since it does not match these requirements.

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Answer:

[tex] \frac{1}{3 {x}^{2} + 4x - 4 } [/tex]

Answer:

y=20*3^x

Step-by-step explanation:

y=20*3^x

Approximately 86.5% of customers will be served in less than 10 minutes and only 13.5% of customers will take more than 10 minutes to check out.

To find the proportion of customers who take more than 10 minutes to check out, we need to calculate the cumulative distribution function (CDF) of an exponential distribution at 10 minutes and subtract it from 1. The CDF for an exponential distribution with mean (lambda) 5 minutes is given by:

CDF = 1 - e^(- λ * x)

Plugging in λ = 0.2 (1/mean) and x = 10, we get:

CDF = 1 - e^(-0.2 * 10) = 1 - e^(-2) = 1 - 0.135 = 0.865

So, approximately 86.5% of customers will be served in less than 10 minutes and only 13.5% of customers will take more than 10 minutes to check out.

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None of the aforementioned goods loads upon P1Q45. This is so that they cannot be loaded onto the same amount since each item is linked to a different one.

None of the aforementioned goods loads upon P1Q45. This is so that they cannot be loaded onto the same component since each item is linked to a different one. For instance, P1Q45 is connected to a particular component, like a printer, whereas P1Q7 is connected to a different component, like a monitor. Likewise, P2Q23 is connected to a third element, such a scanner. Therefore, it is not possible to load these items onto the same component as P1Q45. Furthermore, each of the three objects would need to be loaded separately into the component even if they were all linked to the same one. This is due to the fact that for the component to work effectively, each item needs to be put onto it securely and accurately. The answer to the question is therefore none of the aforementioned options.

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CD=9, C would be between -6 and 21, and D would be at -15 since C and D are points on the number line.

An introduction to arithmetic tool is the number line, which is a visual depiction of real numbers. It is a representation of a strength line. Each real number is used to represent a point on the number line, and each real number is taken to signify a point. On a number line, distances between increments are equal. The question that coincides with the number will define how it is used. B: Speak your mind.

given

as by number line

C+ D = 9 -15 = -6

C - D = 9 + 15 = 21

Given that CD=9, C would be between -6 and 21, and D would be at -15 since C and D are points on the number line.

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A life table provides data on the number of living individuals in a particular age class. Age classes are often represented by a time period of 12 month(s).

A life table delivers data on the number of living individuals in a particular age class. Age classes are often represented by a time period of 1 year.

This means that the data in the life table will reflect the number of individuals who are alive in a specific age group, such as 0-1 year, 1-2 years, 2-3 years, and so on. The data in a life table is used to study mortality patterns, life expectancy, and other demographic measures.

By grouping the data into age classes of 1 year, the life table provides a snapshot of the population at different stages of life, making it easier to analyze trends and patterns in the data.

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--The given question is incomplete; the complete question is

"A life table provides data on the number of living individuals in a particular age class. Age classes are often represented by a time period of ______ month(s)."--

y(t) = 2e^(sin(t) + t) is the antiderivative of the function dy/dt = y cos(t) + y, and satisfies the initial condition y(0) = 2.

This is a first-order linear differential equation, which can be solved by the separation of variables. To do so, we can start by writing:

dy/dt = y cos(t) + y

We can divide both sides by y:

dy/dt / y = cos(t) + 1

Now, we can integrate both sides with respect to t, using the property that d(ln y)/dt = 1/y:

∫(dy/dt / y) dt = ∫(cos(t) + 1) dt

ln|y| = sin(t) + t + C

Where C is the constant of integration. To find its value, we can use the initial condition y(0) = 2:

ln|2| = sin(0) + 0 + C

C = ln|2|

Therefore, the solution of the initial value problem is:

y(t) = 2e^(sin(t) + t)

This is the antiderivative of the function dy/dt = y cos(t) + y and satisfies the initial condition y(0) = 2.

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The number of kilogram in 40 lb would be 18.1437.

A pound is an imperial unit used to measure bulk or weight. A kilogram is a metric measuring unit. The letters lb and lbm stand for pounds. Kilo or kg are used to denote kilograms. 0.4535 kilograms make up one pound.

In both the British imperial system and the United States' customary system, weight is measured in pounds. Measuring a person's weight is one common application of pounds.

The weight of a kilogram is 2.2046 pounds. We convert kilograms (kg) to pounds (lb) using the formula 1 kg = 2.2 lb. By multiplying by 2.2, we may convert a kilogram to a pound. We divide by 2.2 to change a pound into a kilogram.

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Answer:

{28, 25, 22, 19, …}

Step-by-step explanation:

you use the next # minus the previous one

Answer:

Dont see anything

Step-by-step explanation:

Pls put a picture, no picture = can't help

Answer:

What is "this"? You didn't even post a problem.

Step-by-step explanation:

Assuming that the standard deviation remains 0.12 ounces, so 16.251 ounces mean weight should Buckley Farms use.

The total weight of each bag follows an approximately normal distribution with a mean of 16.15 ounces and a standard deviation of 0.12 ounces.

Mean (μ) = 16.15

Standard deviation, (σ) = 0.12

n = 6

Buckley Farms decides to increase the mean weight of each bag of chips so that only 5%(0.05) of the bags have weights that are less than 16 ounces. So

P(X > x) = 0.05

P[(X - μ)/(σ/√n) > (x - μ)/(σ/√n)] = 0.05

1 - P(Z ≤ z) = 0.05

Subtract 1 on both side , we get

P(Z ≤ z) = 0.95

z = 1.96

(x' - μ)/(σ/√n) = 1.645

Now putting the value

(x' - 16.15)/(0.15/√6) = 1.645

(x' - 16.15)/(0.15/2.45) = 1.645

(x' - 16.15)/(0.0612) = 1.645

Multiply by 0.0612 on both side, we get

x' - 16.15 = 0.100674

Add 16.15 on both side, we get

x' = 16.251

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The complete question is:

Buckley Farms produces homemade potato chips that it sells in bags labeled 16 ounces. The total weight of each bag follows an approximately normal distribution with a mean of 16.15 ounces and a standard deviation of 0.12 ounces. Buckley Farms ships its chips in boxes that contain 6 bags. Buckley Farms decides to increase the mean weight of each bag of chips so that only 5% of the bags have weights that are less than 16 ounces. Assuming that the standard deviation remains 0.12 ounces what mean weight should Buckley Farms use?

Answer:

[tex]( - \frac{1}{2 \:} \: - \frac{5}{4} )[/tex]

[tex]( - 0.5 \: \: - 1.25)[/tex]

Radioactivity decay, half-life, and population decay are only a few of the forms of decay that may be calculated using the exponential decay formula.

The term "exponential decay" describes a process in which a quantity diminishes over time at a pace that reduces proportionally as the quantity shrinks.

The population decline and radioactive decay are two examples of exponential decay. The data obtained can be used to make predictions about the population of a city or colony in the future as well as the half-life of radioactive materials.

The exponential decay formula aids in determining the rapid decline over time, or exponential decline. The exponential decay formula is used to calculate various types of decay, including radioactivity decay, half-life, and population decay.

The exponential decay formula is used to calculate various types of decay, including radioactivity decay, half-life, and population decay. The standard form of the equation be f(x) = a (1 - r)x.

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To show the given two triangles are similar, choose option D.

If in two triangles the ratio of corresponding sides are equal, and all corresponding angles are equal then they are considered as similar triangles.

Given that, two triangles are similar Δ STW ~ Δ XYZ,

According to definition of similar triangles,

The ratio of corresponding sides are equal, and all corresponding angles are equal,

Therefore, we have,

ST/XY = TW/YZ = SW/XZ

And,

Angles A, B and C are equal to Angles X, Y and Z respectively.

From the above discussion we can conclude, the correct options are;

To show the given two triangles are similar, we should have all the given sides in equal proportion.

As we are already given that, ST = 27 and XY = 9

The scale factor is 1/3

So, we should consider the option D, SW = 15 and TW = 24

By this we can get, SW/XZ = 3 and TW/YZ = 3

Hence, the correct option is D

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Existence and uniqueness of solutions are guaranteed for all of the given initial value problems.

1. dy/dx = 2x^2y^2: y(1) = -1

Existence and uniqueness of a solution is guaranteed by Theorem I. At the point (x, y) = (1, -1), the function f(x, y) = 2x^2y^2 is continuous and the partial derivative ∂f/∂y is also continuous.

2. dy/dx = x ln y: y(1) = 1

Existence and uniqueness of a solution is guaranteed by Theorem I. At the point (x, y) = (1, 1), the function f(x, y) = x ln y is continuous and the partial derivative ∂f/∂y is also continuous.

3. dy/dx = cubicroot y: y(0) = 1

Existence and uniqueness of a solution is guaranteed by Theorem I. At the point (x, y) = (0, 1), the function f(x, y) = cubicroot y is continuous and the partial derivative ∂f/∂y is also continuous.

4. dy/dx = cubicroot y: y(0) = 0

Existence and uniqueness of a solution is guaranteed by Theorem I. At the point (x, y) = (0, 0), the function f(x, y) = cubicroot y is continuous and the partial derivative ∂f/∂y is also continuous.

5. dy/dx = Squareroot x- y: y(1) = 2

Existence and uniqueness of a solution is guaranteed by Theorem I. At the point (x, y) = (1, 2), the function f(x, y) = Squareroot x - y is continuous and the partial derivative ∂f/∂y is also continuous.

6. dy/dx = Squareroot x - y: y(2) = 2

Existence and uniqueness of a solution is guaranteed by Theorem I. At the point (x, y) = (2, 2), the function f(x, y) = Squarroot x - y is continuous and the partial derivative ∂f/∂y is also continuous.

7. dy/dx = Squareroot x - y: y(2) = 1

Existence and uniqueness of a solution is guaranteed by Theorem I. At the point (x, y) = (2, 1), the function f(x, y) = Squareroot x - y is continuous and the partial derivative ∂f/∂y is also continuous.

8. y dy/dx = x - 1: y(0) = 1

Existence and uniqueness of a solution is guaranteed by Theorem I. At the point (x, y) = (0, 1), the function f(x, y) = x - 1 is continuous and the partial derivative ∂f/∂y is also continuous.

9. y dy/dx = x - 1: y(1) = 0

Existence and uniqueness of a solution is guaranteed by Theorem I. At the point (x, y) = (1, 0), the function f(x, y) = x - 1 is continuous and the partial derivative ∂f/∂y is also continuous.

10. dy/dx = ln(1 + y^2): y(0) = 0

Existence and uniqueness of a solution is guaranteed by Theorem I. At the point (x, y) = (0, 0), the function f(x, y) = ln(1 + y^2) is continuous and the partial derivative ∂f/∂y is also continuous.

11. dy/dx = x^2 - y^2: y(0) = 1

Existence and uniqueness of a solution is guaranteed by Theorem I. At the point (x, y) = (0, 1), the function f(x, y) = x^2 - y^2 is continuous and the partial derivative ∂f/∂y is also continuous.

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Therefore , the solution of the given problem of angle bisector  comes out to be each measurement will be equivalent to 30 degrees,

A bisector exists for each angle. Additionally, it is the symmetry line that connects an angle's two arms, triangle  whose construction facilitates the creation of smaller angles.

Here,

A 30° angle, for example, might be called for. A 60° angle can be made, and it can then be divided, to accomplish this.

The concept of an angle bisector is used to construct angles such as 90 degrees, 45 degrees, 15 degrees, and others.

Examples :

What is each angle's measurement if an angle bisector divides an angle of 80 degrees?

The answer is that 80 degrees is the measure of an angle.

It is common knowledge that the angle is divided into two equal pieces by the angle bisector.

Consequently, 80 degrees is divided into two equal portions, let's call x.

Hence,

x + x = 80°

2x = 80°

x = 80°/2

x = 40°.

The second option is ineffective since it would result in A' being positioned at (-5, 2) after translation A 3 up and 1 left (5, -2).

The third option: spinning A in a clockwise direction 90 degrees places it at (-1, 4), then reflecting it across the y-axis places it at (1, 4).

In the fourth option, A is rotated 90 degrees counterclockwise, putting it at (1, -4), and it is reflected across the x-axis, putting it at (1, 4).

The fifth option is to rotate A 180 degrees, which positions it at (-3, -4), after translating 3 down & 1 right (3, 4). B(-5, -5) (-5, -5)  Translated results in (-4, -8), and rotated results in (4, 8). Translation of C(-3, -4) results in (-2, -7), and rotation results in (2, 7).

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