What three regular polygons have special triangles formed by their radius and apothem and what are the special triangles?

The scale factor was used for each dilation are-

A transformation that changes the size of a figure is called a dilatation. This indicates that the preimage as well as image are similar and have been scaled up or down, respectively.

A dilatation that results in a reduction (imagine shrinking) or an enlargement (think stretching) produces a smaller or larger image, respectively.

Part a: For ΔABC

Length AB = 2 units

Length A'B' = 4 units

A'B' = 2 *AB

Thus,  For ΔABC - scale factor = 2

Part b: For ΔDEF -

Length DF = 2 units

Length D'F' = 1  units

D'F' = 1/2 DF

Thus, For ΔDEF - scale factor = 1/2

Part c: For ΔGHJ -

Length GH = 3 units

Length G'H' = 1  units

G'H' = 1/3 GH

Thus,  For ΔGHJ - scale factor = 1/3

Part d: For ΔKML -

Length KM = 2 units

Length K'M' = 6  units

K'M' = 3*KM

Thus, For ΔKML - scale factor = 3

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The soft drink vendor's maximum profit per day is $5250, and he must sell 1500 cans of soda pop to reach the maximum profit.

To find the maximum profit per day for the soft drink vendor, we need to use the formula P(x) = 0.001x^2 + 3x + 1800, where x is the number of cans of soda pop sold in one day.

To find the maximum profit, we need to find the vertex of the parabola represented by the profit function. The x-coordinate of the vertex is given by -b/2a, where a = 0.001 and b = 3. Plugging in these values, we get x = -3/(2*0.001) = -1500.

Since the soft drink vendor cannot sell a negative number of cans, we know that the maximum profit occurs at the closest whole number to x = -1500, which is x = 1500.

To find the maximum profit per day, we can plug in x = 1500 into the profit function:

P(1500) = 0.001(1500)^2 + 3(1500) + 1800 = $5250

Therefore, the soft drink vendor's maximum profit per day is $5250, and he must sell 1500 cans of soda pop to reach the maximum profit.

To find the maximum profit per day and the number of cans needed to reach that profit, we'll first need to find the critical point of the given quadratic profit function, P(x) = -0.001x^2 + 3x - 1800.

Step 1: Find the derivative of P(x) with respect to x. This will give us the rate of change of profit as the number of cans sold changes.

P'(x) = -0.002x + 3

Step 2: Set the derivative equal to zero and solve for x. This will give us the critical point where the maximum profit occurs.

-0.002x + 3 = 0

x = 1500 cans

Step 3: Substitute the critical point (x = 1500) back into the profit function P(x) to find the maximum profit.

P(1500) = -0.001(1500)^2 + 3(1500) - 1800

P(1500) = $600

So, the maximum profit per day is $600, and the soft drink vendor must sell 1500 cans to reach the maximum profit.

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The maximum profit per day is $4800, and the vendor must sell 1500 cans of soda pop to reach this maximum profit.

The profit function for the soft drink vendor is given by:

P(x) = [tex]0.001x^2 + 3x + 1800[/tex]

To find the maximum profit, we need to find the vertex of the parabola represented by this function. The x-coordinate of the vertex can be found using the formula:

x = -b / (2a)

where a = 0.001 and b = 3. Substituting these values, we get:

x = -3 / (2 * 0.001) = -1500

Since the value of x cannot be negative in this context, we know that the maximum profit occurs at x = 1500. To find the maximum profit, we substitute this value of x into the profit function:

P(1500) =[tex]0.001(1500)^2 + 3(1500) + 1800 = $4800[/tex]

Therefore, the maximum profit per day is $4800, and the vendor must sell 1500 cans of soda pop to reach this maximum profit.

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There are almost 8 different dessert options that can be served.

Given that there are four fruit alternatives (watermelon, cantaloupe, pineapple and mango) and two ice cream selections (lemon or piquin chilli), the question asks how many different dessert options are offered. We can utilise the multiplication principle of counting. In this case, there are 4 ways to choose a fruit and 2 ways to choose an ice cream flavor. Using the multiplication principle, we can multiply these choices to find the total number of dessert options:

4 (fruit options) x 2 (ice cream options) = 8

Therefore, there are 8 different dessert options that can be served.

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--The complete Question is, Today's dessert is any of these fruits: watermelon, cantaloupe, pineapple or mango, accompanied by lemon or piquin chili ice cream. How many different desserts can be served? --

The statement "When eliminating a loop-carried dependency that adds a constant, the closed-form direct solution will likely contain a multiplication" is true because eliminating a loop-carried dependency that adds a constant simplifies the equation, but to obtain a closed-form direct solution, we need to express the result as a function of the current iteration's variables only

When eliminating a loop-carried dependency that adds a constant, the closed-form direct solution will likely contain a multiplication. This is because the loop-carried dependency adds a constant to the result of the previous iteration, which means that the current iteration's result is a function of both the current iteration's variables and the previous iteration's result.

By eliminating this dependency, we remove the need to use the previous iteration's result, which simplifies the equation. However, to obtain a closed-form direct solution, we need to express the result as a function of the current iteration's variables only, which often involves a multiplication. This is because multiplication is a fundamental mathematical operation that allows us to combine variables in a way that preserves their individual values.

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True. When eliminating a loop-carried dependency that adds a constant, the closed-form direct solution will likely contain a multiplication. This is because the loop-carried dependency is typically expressed as an addition, and removing it would result in a product of the loop index and the constant.

when eliminating a loop-carried dependency that adds a constant, the closed-form direct solution will likely contain a multiplication. This is because the process often involves applying mathematical transformations that result in multiplications to simplify the loop and eliminate dependencies.

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The value of x is given as follows:

x = 17.

We obtain the value of x for this problem considering that the sum of the measures of the internal angles of a triangle is of 180º.

The internal angles of the triangle is given as follows:

The sum of the measures of the angles is of 180º, hence the value of x is given as follows:

4x + 3 + x + 7 + 5x = 180

10x + 10 = 180

10x = 170

x = 17.

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The branch of mathematics that analyzes situations in which players must make decisions and then receive payoffs most often used by economists is "game theory". So, option C is the correct answeer.

Game theory is a branch of mathematics that studies how people or organizations interact in situations where there are choices to be made and where the outcome of each choice depends on the choices made by others. It is often used in economics to model the behavior of firms and consumers in markets, and to analyze strategic interactions between competitors in oligopolistic industries.

One of the most famous examples of game theory is the prisoner's dilemma, which is a simple model that illustrates how two individuals might not cooperate, even if it appears that it is in their best interest to do so.

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To construct a 98% confidence interval,  the critical value is 2.624.

We have,

98% Confidence Interval

Sample size, n= 15

At 98%,

Degree = n-1

             = 15-1= 14

So, For a 98% confidence level with 14 degrees of freedom, the critical value is 2.624.

Therefore, to construct a 98% confidence interval, the critical value is 2.624.

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The steps for each expression here is

a.

Step 1: (x)-2

Step 2: 9-2

Step 3: 7

b.

Step 1: 3(y)+2

Step 2: 3*7+2

Step 3: 23

c.

Step 1: 8+((r)/6)

Step 2: 8+(24/6)

Step 3: 12

What is meant by expression?

An expression is a representation of a mathematical equation, logical statement, or string of characters using symbols, numbers, and operators. It can be evaluated to produce a value or result. In programming, expressions can be used to assign values to variables, perform mathematical operations, or compare values. They are an essential part of most programming languages and play a crucial role in the execution of computer programs.

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The y-intercept of 0 indicates that if the musician does not exchange any pounds, they will not receive any dollars.

In the given equation, y = 1.25x, the slope is 1.25, and the y-intercept is 0.

The slope represents the exchange rate between pounds and dollars. Specifically, it tells us that for every pound exchanged, the musician receives 1.25 dollars.

The y-intercept of 0 indicates that if the musician does not exchange any pounds, they will not receive any dollars.

Keep in mind that positive numbers in this context reflect bank deposits, whereas negative numbers represent bank withdrawals

. As a result, a positive value for y indicates money received, whereas a negative value for y indicates money taken out.

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The associative property of addition:

[tex](a + b) + c = a + (b + c)[/tex]

We now apply the associative property of addition to the expression in this problem.

[tex](4+9)+11=4+(9+11)[/tex]

Now we follow the correct order of operations by adding the numbers inside the parentheses first.

[tex]= 4 + 20[/tex]

[tex]= 24[/tex]

Answer: B

Answer:

[tex].28(22) + 3 = 9.16[/tex]

The predicted width of a foot with a length of 22 centimeters is 9.16 centimeters.

Required value of x is 201.52 ft.

What is Trigonometric ratio?

Trigonometric ratios are defined as the values of all trigonometric functions based on the value of the ratio of the sides of a right triangle. The ratio of the sides of a right triangle to its acute angles are called the trigonometric ratios of that particular angle.

For example,tan(θ) = opposite/adjacent where θ is the angle between the hypotenuse and the base.

We want to solve for x, the length of the adjacent side. We also know that the hypotenuse is 500 ft and the height is y.

Here by the given figure, it is clear that angle between height and hypotenuse is (90°-29°) = 61°

So, θ = 61°

[tex]tan( {61}^{o} ) = \frac{y}{x} [/tex]

Simplifying this expression,

[tex]x = \frac{y}{tan(61°)}[/tex]

To solve for y, for the right angle triangle

[tex]y^2 + x^2 = 500^2[/tex]

Substituting the expression for x from the first equation,

y² + (y/tan(61°))² = 500²

Solving for y, we get:

y = 500 / √(1 + (1/tan(61°))²)

y ≈ 357.98 ft

Finally, we can substitute this value of y into the expression for x that we derived earlier,

x = y/tan(61°)

x ≈ 201.52 ft

Therefore, the value of x is approximately 201.52 ft.

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The given function of the growth decay is decreasing.

What in mathematics is an exponential?

The formula for an exponential function, often known as an exponential function, is f (x) = axe, where "x" is a variable and "a" is a constant that serves as the function's basis and must be greater than 0.The transcendental number, abbreviated e, which is roughly equivalent to 2.71828, is the most often used exponential function basis.

We have given that,

Y=400(.99)^x

Exponential growth is a process that increases quantity over time. decreases over time, and is said to be undergoing exponential decay instead.

Therefore, The given function of the growth decay is decreasing.

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Answer:

To find the button's radius, we need to divide its diameter by 2, since the radius is half the size of the diameter.

radius = diameter ÷ 2

Given that the diameter of Ted's button is 10 millimeters, we can substitute it into the above formula to get:

radius = 10 mm ÷ 2

radius = 5 mm

Therefore, the button's radius is 5 millimeters.

The y-component of the force that the wall exerts on the beam (f) is -400.5 N.

The y-component of the force that the wall exerts on the beam (f) can be found using the following steps:

Step 1: Calculate the magnitude of the force (f):

f = √[f_x² + f_y²]

f = √[(-500 N)² + (-300 N)²]

f = 600 N

Step 2: Calculate the angle of the force relative to the y-axis:

θ = tan-1(-300 N/500 N)

θ = -53.13°

Step 3: Calculate the y-component of the force (fy):

fy = f × sin(θ)

fy = 600 N × sin(-53.13°)

fy = -400.5 N

Therefore, the y-component of the force that the wall exerts on the beam (f) is -400.5 N.

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The square of the centimeter of the area is calculated by the square of the centimeter. The area of the rectangle is calculated by the formula width x length. So the rectangles area is 94cm  

Squares have only one side that is squared to find the area of the shape. But in rectangle there will be two sides given that width and length of the shape. So to find the area the width and the length of the rectangle is given so the numerical must be multiplied. In the given question the width of the rectangle is 8.5 and the length of the rectangle is 11.

o the area of the rectangle can be found by the formula= w x l

=8.5 x 11

=93.5

approximately can be taken as 94 cm.

A rectangle can is a four sided shape that includes the length, width and height and that opposites sides are equal in the rectangle. The adjacent sides of the rectangle is perpendicular and the angle is right angle that is it is measured as 90 degree. A rectangle can be a parallelogram but parallelogram can not be equal to the rectangle.

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The question has an area because the square because the square has only one side and the area of the square can be found by squaring one side of square. So the actual question should be What is the area, in rectangle centimeters, of an 8.5 inch by 11 inch sheet of paper?

the nicknames of the four friends are:

Andre: Boss

Bilal: Buzz

Glenna: Cosmo

Juanita: Tiger

From clue 1, we realize that Juanita's moniker isn't Tiger or Buzz, and Tiger's epithet isn't Chief or Cosmo. Along these lines, Juanita's epithet should be Cosmo or Chief, and Tiger's moniker should be Buzz or Tiger.

From clue 2, we realize that Glenna's moniker isn't Chief or Buzz, and Tiger's epithet isn't Cosmo or Tiger (currently disposed of in the past step). In this way, Glenna's moniker should be Cosmo, and Tiger's epithet should be Buzz.

From clue 3, Cosmo's nickname has already been determined to be Glenna, and we are aware that Andre's nickname cannot be Boss, Buzz, or Tiger (all of which have been eliminated). Boss has to be Andre's nickname.

From clue 4, Cosmo's nickname has already been identified as Glenna, and we are aware that Juanita's nickname cannot be Buzz or Tiger (both of which have already been eliminated). Therefore, Juanita must go by the name Boss.

So, the nicknames of the four friends are:

Andre: Boss

Bilal: Buzz

Glenna: Cosmo

Juanita: Tiger

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Answer:

10.12

Step-by-step explanation:

440=(x)(4x+3)

=10.11979...

Answer:

Step-by-step explanation:

The estimated total number of fur seal pups in Rookery A is 8905 (rounded to the nearest whole number).

Proportion refers to the relationship between the part and the whole. It is a measure that expresses the size of one subset (part) relative to the size of the entire population (whole). A proportion is usually expressed as a fraction or a percentage.

A whole number is a number that does not have any fractional or decimal part. It is a positive integer (1, 2, 3, ...) or zero (0). Whole numbers are used to count objects or things that cannot be divided into parts.

To estimate the total number of fur seal pups in Rookery A, we can use the proportion of tagged pups in the sample to the total tagged pups in the rookery.

The proportion of tagged pups in the sample is 244/500 = 0.488.

Assuming that the proportion of tagged pups in the sample is representative of the proportion of tagged pups in the entire rookery, we can set up a proportion:

0.488 = (number of tagged pups in Rookery A) / (total number of pups in Rookery A)

Solving for the total number of pups in Rookery A, we get:

(total number of pups in Rookery A) = (number of tagged pups in Rookery A) / 0.488

(total number of pups in Rookery A) = 4350 / 0.488

(total number of pups in Rookery A) ≈ 8905

Therefore, the estimated total number of fur seal pups in Rookery A is 8905 (rounded to the nearest whole number).

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The values of a that make (x - a) a factor of x^4 - 5x³ - 21x² - 23x - 8 are given as follows:

a = 8 and a = -1.

The polynomial is given as follows:

f(x) = x^4 - 5x³ - 21x² - 23x - 8

By the factor theorem, x - a is a factor of a polynomial f(x) if f(a) = 0.

The numeric value at x = a is given as follows:

f(a) = a^4 - 5a³ - 21a² - 23a - 8.

Hence the values of a are obtained solving the equation presented as follows:

a^4 - 5a³ - 21a² - 23a - 8 = 0.

Using a calculator, the values of a are given as follows:

a = 8 and a = -1.

(the root of -1 has a multiplicity of 3).

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For the given problem, The correct answer will be option 2: The IQR of 13 is the most accurate to use, since the data is skewed.

The Interquartile Range (IQR) is a measure of variability that compares the 25th percentile (Q1) to the 75th percentile (Q3) of a dataset (Q3). It is frequently used to describe the distribution or variability of data that may contain outliers or is not regularly distributed.

The data in the histogram is not evenly distributed in this example because there are many donations at the higher end of the scale (16 to 20), resulting in a positively skewed distribution. Using a range of 20, which indicates the difference between the greatest and lowest value in the dataset, may not adequately depict the data's variability since it is significantly impacted by outliers at the extremes.

For the given dataset, IQR can be calculated as:

Arrange the dataset in ascending order:

[tex]5, 5, 6, 8, 10, 15, 18, 20, 20, 20, 20, 20, 20[/tex]

Find the median (Q2), i.e. the middle value of given dataset:

Median (Q2) = 15

Find the lower quartile (Q1), which is the median of the lower half of the dataset:

[tex]Q1 = Median of (5, 5, 6, 8, 10) = 6[/tex]

Find the upper quartile (Q3) i.e. median of the upper half of dataset:

[tex]Q3 = Median \;of (15, 18, 20, 20, 20, 20, 20) = 19[/tex]

[tex]IQR = Q3 - Q1 = 19 - 6 = 13[/tex]

Utilizing the IQR of 13, which represents the range between the 25th percentile (Q1 = 6) and the 75th percentile (Q3 = 19), would provide a more accurate measure of variability that is less impacted by outliers at the higher end of the data. It would also offer a better indication of the organization's typical donations because it captures the middle 50% of the data.

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The coefficient of variation for SAT scores at this school is 11.21%. This means that the standard deviation of the SAT scores is about 11.21% of the mean score.

The coefficient of variation (CV) is a measure of relative variability, defined as the ratio of the standard deviation to the mean of a dataset. It is expressed as a percentage and provides a way to compare the variability of datasets with different means.

To calculate the CV for SAT scores at this particular college, we first need to calculate the standard deviation of the dataset. We are given that the average SAT score for incoming freshmen is 535 with a standard deviation of 60. Therefore, the standard deviation (s) is 60.

Next, we need to calculate the mean of the dataset. We are given that the mean (μ) is 535.

The coefficient of variation is then given by:

CV = (s / μ) x 100%

Substituting the values, we get:CV = (60 / 535) x 100%

= 0.1121 x 100%

= 11.21%

Therefore, the coefficient of variation for SAT scores at this school is 11.21%. This means that the standard deviation of the SAT scores is about 11.21% of the mean score. This information can be useful in comparing the variability of SAT scores between different colleges, even if their mean scores are different.

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The coefficient of variation for SAT scores at this school is approximately 11.21%.

The coefficient of variation for SAT scores at this school can be calculated using the following formula:

Coefficient of Variation = (Standard Deviation / Mean) x 100

Given the average math SAT score for incoming freshmen at this particular college is 535 and the standard deviation is

60, we can plug these values into the formula:

Coefficient of Variation = (60 / 535) x 100

Now, let's perform the calculations:

Coefficient of Variation ≈ 11.21 %

So, the coefficient of variation for SAT scores at this school is approximately 11.21%.

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Answer: Its the last one

Step-by-step explanation:

Answer: The angle of depression from Jesenia to the duck is 25.17°. The solution has been obtained by using trigonometry.

What is trigonometry?

Right-angled triangles, their sides, angles, and connections are the main topics of the mathematical field of trigonometry.

We are given that that Jesenia is standing on a pedestrian bridge that is 9.5 feet above the lake and the duck is 4.5 feet away from jesenias position on the bridge.

This means that perpendicular is 9.5 and base is 4.5.

We know that tan θ is value of opposite side to adjacent side.

So, we get

⇒ Tan θ =

⇒ Tan θ = 0.47

⇒ θ = 25.17°

Hence, the angle of depression from Jesenia to the duck is 25.17°.

Step-by-step explanation:

Welcome!

Answer:

Step-by-step explanation:

On Monday, the total amount paid for CDs = 149 * $9 = $1341

On Tuesday, the total amount paid for CDs = 263 * $9 = $2367

Therefore, the total amount paid for CDs on these two days = $1341 + $2367 = $3708.

The number of students who had zero brothers or sisters is 1.

The probability of students with zero brothers or sisters is calculated from the ratio of the total number of students to the number of students with zero brothers or sisters.

Total number of students = 65

Number of zero siblings = 1

The probability = 1 / 65

So based on this information, we can conclude that in the sixth-grade class and based on the collected data, the number of students who had zero brothers or sisters is 1.

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the cost per mile over the course of a year for a $24,000 car that depreciates 20%, with costs shown in the table, and that has been driven for 10,000 miles is $0.59 per mile. Answer B is correct.

To calculate the cost per mile, we need to add up all the expenses for the car and divide by the total miles driven.

First, we need to calculate the total depreciation for the car:

Depreciation = 20% * $24,000 = $4,800

Next, we can calculate the total expenses for the car:

Total expenses = Gas + Insurance + Oil + Registration + Depreciation

Total expenses = $550 + $400 + $90 + $100 + $4,800

Total expenses = $5,940

Finally, we can calculate the cost per mile:

Cost per mile = Total expenses / Miles driven

Cost per mile = $5,940 / 10,000

Cost per mile = $0.594 or $0.59 (rounded to the nearest cent)

Therefore, the cost per mile over the course of a year for a $24,000 car that depreciates 20%, with costs shown in the table, and that has been driven for 10,000 miles is $0.59 per mile. Answer B is correct.

Note: Option D is not a possible answer because the cost per mile cannot be greater than the total expenses divided by the miles driven, which in this case is $0.594.

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Answer:

105

cause you do

P arenthaces

E xponents

M ultiplication D ivision

A dd

S ubtract