In 2010, Little Elm had 3646 residents. Five years later, they had 17,150 residents. If the population grows at this rate, about how many residents will the town have in 2020? Include explanation.


A. 20,800


B. 27,000


C. 30,700


D. 35,400



PLS DON'T PUT LINKS AND WRITE ANSWER, THX! I WILL MARK BRAINLIEST IF YOU WRITE THE ANSWER!

Answers

Answer 1

The answer is option C) 30,700

Why the answer is option C?

The problem involves using linear interpolation to estimate the population of Little Elm in 2020 based on the given data from 2010 and 2015.

To start, we need to calculate the annual growth rate of the population between 2010 and 2015. This can be done by taking the difference between the population in 2015 and the population in 2010, and then dividing that difference by the number of years in that time period:

Annual growth rate = (17,150 - 3,646) / 5 = 2,700

This means that, on average, the population of Little Elm grew by 2,700 people per year between 2010 and 2015.

Next, we can use this annual growth rate to estimate the population of Little Elm in 2020. To do this, we need to add 10 years of growth to the initial population of 3,646 (since we want to estimate the population in 2020, which is 10 years after 2010):

Estimated population in 2020 = 3,646 + (2,700 x 10) = 30,646

Therefore, the estimated population of Little Elm in 2020 is approximately 30,700, which corresponds to answer choice C.

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Related Questions

A builder wishes to fence in 80000 m2 of land in a rectangular shape. for security reasons, the fence along the front part of the land will cost $60 per meter, while the fence for the other three sides will cost $20 per meter.

how much of each type of fence should the builder buy to minimize the cost of the fence?

determine the length of the fence along the front part of the land that will be cost $60 per meter.

(give your answer as a whole or exact number.)

Answers

To minimize the cost of the fence, the builder should use the expensive fence along the shorter side of the rectangular shape, as this will require less length of the expensive fence. Let's say the length of the rectangle is x meters and the width is y meters. Then the area of the rectangle is given by:

A = xy = 80000

And the perimeter of the rectangle is:

P = 2x + 2y

We are given that the cost of the fence along the front part of the land will cost $60 per meter, while the fence for the other three sides will cost $20 per meter. So the total cost of the fence is:

C = 60x + 20(2x + 2y)

Simplifying this expression, we get:

C = 100x + 40y

We can now use the area equation to eliminate one of the variables. Solving for y, we get:

y = 80000/x

Substituting this expression for y into the cost equation, we get:

C = 100x + 40(80000/x)

Simplifying this expression, we get:

C = 100x + 3200000/x

To minimize this function, we need to take its derivative and set it equal to zero:

dC/dx = 100 - 3200000/x^2 = 0

Solving for x, we get:

x = sqrt(32000) = 178.89

So the length of the rectangle should be approximately 178.89 meters, and the width should be:

y = 80000/178.89 = 446.68

Therefore, the amount of expensive fence needed is 178.89 meters, and the amount of cheap fence needed is:

2(178.89) + 2(446.68) - 178.89 = 893.36 meters

Finally, the length of the fence along the front part of the land that will be cost $60 per meter is simply the width of the rectangle, which is:

y = 446.68 meters (rounded to two decimal places)

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Diego has a bag with the letters DOG inside. Diego picks 30 letters from the bag, replacing the letter he picks each time. Is it possible that Diego could draw D 19 times, O 10 times, and G 1 time? Why or why not?

Answers

Therefore, it is possible for Diego to draw D 19 times, O 10 times, and G 1 time when picking 30 letters from the bag with replacement, although it is highly unlikely.

What is probability?

Probability is a measure of the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, with 0 indicating that the event is impossible, and 1 indicating that the event is certain to occur.

Here,

Yes, it is possible for Diego to draw D 19 times, O 10 times, and G 1 time when picking 30 letters from the bag with replacement.

The probability of drawing the letter D on one pick is 1/3, since there is 1 D out of 3 letters in the bag. Similarly, the probability of drawing the letter O on one pick is also 1/3, and the probability of drawing the letter G on one pick is 1/3.

Since Diego replaces each letter he picks, the probability of drawing D 19 times in a row is (1/3)¹⁹, the probability of drawing O 10 times in a row is (1/3)¹⁰, and the probability of drawing G 1 time is 1/3.

The probability of all these events happening in this order is the product of their individual probabilities, which is:

(1/3)¹⁹ * (1/3)¹⁰ * 1/3 = (1/3)³⁰

This probability is very small, but it is still greater than zero.

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Emma is sick a lot and as a result has to go to the doctor regularly. Each time she goes there is a $20 copay that she uses her FSA to pay for. Last month she went to the doctor 9 times. She earns $20 an hour at her job. How many hours (round up) would she have to work to pay these bills without an FSA/HSA? (She pays 17 percent in taxes. )

Answers

She would have to work for 11 hours to pay these bills without her FSA/HSA.

Emma went to the doctor 9 times last month, which means she had to pay a total of 9 x $20 = $180 in copays.

Without her FSA/HSA, she would have to work to earn $180 after taxes. Since she pays 17 percent in taxes, the amount she would have to earn before taxes is $180 / (1 - 0.17) = $216.87.

To earn $216.87, she would have to work for $216.87 / $20 per hour = 10.84 hours.

Rounding up, she would have to work for 11 hours to pay these bills without her FSA/HSA.

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A shipping container is in the shape of a right rectangular prism with a length of 11. 5


feet, a width of 8. 5 feet, and a height of 7 feet. The container is completely filled with


contents that weigh, on average, 0. 32 pound per cubic foot. What is the weight of the


contents in the container, to the nearest pound?

Answers

The weight of the contents in the container is approximately 222 pounds when rounded to the nearest pound.

The weight of the contents in the container can be calculated using the formula:

Weight = Volume x Density

First, we need to find the volume of the container, which is simply the product of its length, width, and height:

Volume = 11.5 x 8.5 x 7 = 696.5 cubic feet

Next, we need to multiply the volume by the density of the contents:

Weight = 696.5 x 0.32 = 222.08 pounds

It's important to note that the weight may vary depending on the actual density of the contents. Additionally, it's also important to consider the weight of the container itself, which would add to the total weight of the shipment.

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Martha went skiing in Arizona she got on the ski lift at the bottom of the mountain which is at 189 feet below sea level the ski lift took her up ascending 790 feet to the very top of the mountain then she skied down part of the mountain down descending 254 feet what elevation is she at now?

Answers

Answer:

Martha started at 189 feet below sea level. She went up 790 feet to the top of the mountain, so her elevation was 790-189 = 601 feet above sea level. She then went down 254 feet, so her elevation is now 601-254 = 347 feet above sea level.

Here is the calculation in equation form:

```

Elevation = (Starting elevation) + (Ascent) - (Descent)

```

```

Elevation = 189 feet + 790 feet - 254 feet

```

```

Elevation = 347 feet

```

Answer: Martha is 347 ft above sea level.

Step-by-step explanation:

At first, she is -189 feet below sea level. She went up by 790 feet, bringing her to 690 feet above sea level. She descended by 254 feet and ended up at 347 feet above sea level.

Question 10 9 pts Let f(c) = x3 +62? 15x + 3. (a) Compute the first derivative of f f'(x) = (c) On what interval is f increasing? interval of increasing = (d) On what interval is f decreasing? interval of decreasing = **Show work, in detail, on the scrap paper to receive full credit. (b) Compute the second derivative of / L'(x) = (e) On what interval is concave downward? interval of downward concavity = () On what interval is concave upward? interval of upward concavity = **Show work, in detail, on the scrap paper to receive full credit.

Answers

(a) The first derivative of f is f'(x) = 3x² - 15.

(b) The second derivative of f is f''(x) = 6x.

(c) f is increasing on the interval (-∞, √5) and decreasing on the interval (√5, ∞).

(d) f is decreasing on the interval (-∞, √5) and increasing on the interval (√5, ∞).

(e) f is concave downward on the interval (-∞, 0) and concave upward on the interval (0, ∞).

(a) To find the first derivative of f, we differentiate each term of the function with respect to x using the power rule. Thus, f'(x) = 3x² - 15.

(b) To find the second derivative of f, we differentiate f'(x) with respect to x. Thus, f''(x) = 6x.

(c) To determine the intervals where f is increasing, we set f'(x) > 0 and solve for x. Thus, 3x² - 15 > 0, which simplifies to x² > 5. Therefore, x is in the interval (-∞, √5) or (√5, ∞). To determine which interval makes f increasing, we can test a point within each interval.

For example, when x = 0, f'(0) = -15, which is negative, so f is decreasing on (-∞, √5). When x = 10, f'(10) = 285, which is positive, so f is increasing on (√5, ∞). Thus, f is increasing on the interval (√5, ∞) and decreasing on the interval (-∞, √5).

(d) To determine the intervals where f is decreasing, we set f'(x) < 0 and solve for x. Thus, 3x² - 15 < 0, which simplifies to x² < 5. Therefore, x is in the interval (-∞, √5) or (√5, ∞). Again, we can test a point within each interval to determine which one makes f decreasing.

For example, when x = 0, f'(0) = -15, which is negative, so f is decreasing on (-∞, √5). When x = 10, f'(10) = 285, which is positive, so f is increasing on (√5, ∞). Thus, f is decreasing on the interval (-∞, √5) and increasing on the interval (√5, ∞).

(e) To determine the intervals of concavity, we examine the sign of the second derivative of f. If f''(x) > 0, then f is concave upward, and if f''(x) < 0, then f is concave downward. If f''(x) = 0, then the concavity changes. Thus, we set f''(x) > 0 and f''(x) < 0 and solve for x. We get f''(x) > 0 when x > 0 and f''(x) < 0 when x < 0.

Therefore, f is concave upward on (0, ∞) and concave downward on (-∞, 0).

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The circumference (C) of a circle is 16 cm. Which formula can you use to find the diameter (d) if you know that C = π
d?

Answers

Answer:

c/π=d

explanation:

d × π = c

divide c to isolate d

Answer: I would multiply pie by a diameter until it equals 16.

(I know this probably isn’t the professional way but it should work.

A controversial issue in the sport of professional soccer is the use of instant replay

Answers

The use of instant replay in professional soccer has been a controversial issue, as it raises questions about the balance between maintaining the flow of the game and ensuring accurate officiating.

Supporters of instant replay, often referred to as Video Assistant Referee (VAR), argue that it helps referees make better decisions, leading to fairer outcomes. By reviewing footage of crucial incidents such as goals, penalties, and red card situations, VAR can help correct errors that could have a significant impact on the final result.

On the other hand, critics of instant replay believe that it disrupts the natural flow of the game and can cause confusion among players, fans, and officials. Soccer is a fast-paced sport, and many argue that interruptions for video reviews can negatively affect the momentum and excitement of the game. Additionally, the technology can still be subjective, as referees have the final say in interpreting the video footage. This can lead to inconsistencies in decision-making, further fueling controversy.

Another concern is that the use of instant replay may undermine the authority of on-field referees. If their decisions are consistently questioned and overturned, their credibility may be damaged. Furthermore, not all soccer leagues and tournaments have the resources to implement VAR, which could lead to disparities between competitions.

In conclusion, while instant replay in professional soccer can contribute to fairer and more accurate officiating, it also has the potential to disrupt the game's flow, create confusion, and challenge the authority of referees. As the debate continues, it is important for soccer's governing bodies to carefully consider the implications of VAR and strive for a solution that upholds the integrity of the sport while minimizing its negative impacts.

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Prepare a mixture of 100g of 8% cream into 200g of 3% cream. What is the resulting concentration?


(Pharmacy technician math)

Answers

The resulting concentration from the mixture will be: 4.67%

How to obtain the concentration of the mixture

To obtain the concentration of the mixture, we will multiply the volumes of the substances by their percentages and then equate the result that we get to the sum of the mixture. This gives us:

100 g * 0.08 + 200 g * 0.03 = (100 + 200) C

8 + 6 = 300C

= 14 = 300 C

C = 14/300

= 0.046

This could be rewritten in the form of a percentage as 4.67%.

So, the resulting concentration of the solution will be 4.67%.

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The Coast Starlight Amtrak train that runs from Seattle to Los Angeles. The mean travel time from one stop to the next on the Coast Starlight is 129 mins, with a standard deviation of 113 minutes. The mean distance traveled from one stop to the next is 108 miles with a standard deviation of 99 miles. The correlation between travel time and distance is 0. 636.


a. ) Write the equation of the regression line from predicting travel time.


b. ) Interpret the slope and the intercept in this context.


c. ) Calculate R2 of the regression line for predicting travel time from distance traveled for the Coast Starlight, and interpret R2 in the context of the application.


d. ) The distance between Santa Barbara and Los Angeles is 103 miles. Use the model to estimate the time it takes for the Starlight to travel between two cities.


e. ) It usually takes the Coast Starlight about 168 mins to travel from Santa Barbara to Los Angeles. Calculate the residual and explain the meaning of this residual value.


f. ) Suppose Amtrak is considering adding a stop to the Coast Starlight 500 miles away from Los Angeles. Would it be appropriate to use this linear model to predict the travel time from Los Angeles to tis point?

Answers

a) The equation of the regression line is Travel Time = β₀ + β₁(Distance Traveled) + ɛ. b) The slope of the regression line indicates the increase in travel time and the intercept represents the estimated travel time. c) R₂ is 0.404. d) Regression equation will be used. e) Residual cannot be calculated. f) No, the given linear model is not appropriate to use.

a) The equation of the regression line for predicting travel time is

Travel Time = β₀ + β₁(Distance Traveled) + ɛ

where β₀ is the intercept, β₁ is the slope, Distance Traveled is the independent variable, and Travel Time is the dependent variable.

b) The slope of the regression line indicates the increase in travel time (in minutes) for every one-mile increase in distance traveled. The intercept represents the estimated travel time (in minutes) when the distance traveled is zero. In this context, the intercept is not meaningful since there cannot be a distance of zero between two stops.

c) To calculate R₂, we need to first calculate the correlation coefficient (r) between Travel Time and Distance Traveled

r = (covariance of Travel Time and Distance Traveled) / (standard deviation of Travel Time × standard deviation of Distance Traveled)

Using the given values, we have

r = (0.636 × 113 × 99) / (113 × 99) = 0.636

Then, we can calculate R₂ as

R₂ = r₂ = 0.6362 = 0.404

R₂ represents the proportion of variance in Travel Time that is explained by Distance Traveled. In this context, R₂=0.404 indicates that 40.4% of the variation in travel time from one stop to the next on the Coast Starlight can be explained by the distance traveled between those stops.

d) To estimate the time it takes for the Starlight to travel between Santa Barbara and Los Angeles, we need to use the regression equation

Travel Time = β₀ + β₁(Distance Traveled)

We know that the distance between Santa Barbara and Los Angeles is 103 miles. So, we plug this value into the equation

Travel Time = β₀ + β₁(103)

To solve for the travel time, we need to know the values of β₀ and β₁. We can use the given mean and standard deviation values to estimate these parameters using linear regression. However, we are not given this information in the question.

e) To calculate the residual, we need to first calculate the predicted travel time based on the regression equation

Travel Time = β₀ + β₁(Distance Traveled)

We are told that the distance between Santa Barbara and Los Angeles is 103 miles, so we can plug this value into the equation to get the predicted travel time

Predicted Travel Time = β₀ + β₁(103)

However, we are not given the values of β₀ and β₁, so we cannot calculate the predicted travel time.

The residual is the difference between the actual travel time and the predicted travel time. In this case, we are told that the actual travel time is 168 minutes, and we do not have the predicted travel time. Therefore, we cannot calculate the residual.

f) It would not be appropriate to use this linear model to predict the travel time from Los Angeles to a point 500 miles away from Los Angeles, because the linear relationship between travel time and distance traveled may not hold beyond the range of distances that were used to estimate the regression equation. The linear model assumes that the relationship between travel time and distance traveled is constant across all distances, which may not be true. Additionally, adding a stop at a point 500 miles away from Los Angeles may affect the relationship between travel time and distance traveled, since there may be other factors that influence travel time at that distance. Therefore, a new regression model would need to be estimated using data that includes stops at or beyond the 500-mile mark.

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which is the range of the relation in the table below?

Answers

The range of the relation is ( 0,2)

What is range of relation?

The set which contains all the second elements, on the other hand, is known as the range of the relation.

For example, the two terms a and b have the following values

a: 1, 2 ,4, 8, 10

b: 1, 4 , 12, 14.

The range of relation between the two values is ( 1 ,4) because the two values are common to both term.

Similarly, looking at the term x and y , we can see that only 0 and 2 are common to both terms.

Therefore the range of relation is (0,2)

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A museum sells stone souvenirs shaped like a cone with a diameter of 4.2 centimeters and a height of 9.5 centimeters. What is the volume of each souvenir? Round to the nearest tenth

PLEASE HURRY

Answers

the volume of each souvenir is  43. 85 cm³

How to determine the volume

The formula for calculating the volume of a cone is represented as;

V = 1/3 πr²h

Given that;

V is the volumer is the radius of the coneh is the height of the cone

Then,

r = diameter/2 = 4.2 /2 = 2.1 centimeters

Substitute the values, we have

Volume = 1/3  × 3.14 × 2.1² × 9.5

find the square, we have;

Volume = 1/3 × 3.14 × 4. 41 × 9.5

Multiply the values

Volume = 131. 5503/3

divide the values

Volume = 43. 85 cm³

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Help with problem in photo

Answers

Check the picture below.

[tex](x)(18)=(x+1)(16)\implies 18x=16x+16\implies 2x=16 \\\\\\ x=\cfrac{16}{2}\implies x=8=RW[/tex]

If you spin a spinner 75 times, how many multiples of 2?

Answers

If you spin a spinner 75 times, the number of multiples of 2 could be either 7 or 38.

Assuming the spinner has an equal chance of landing on any number from 1 to 6, we can find the probability of landing on a multiple of 2 (2, 4, or 6) by dividing the number of multiples of 2 by the total number of possible outcomes:

Number of multiples of 2 = 3
Total number of possible outcomes = 6

So the probability of landing on a multiple of 2 is:

P(multiple of 2) = 3/6 = 1/2

This means that out of 75 spins, we can expect to land on a multiple of 2 about half the time. To find the exact number, we multiply the probability by the number of spins:

Number of multiples of 2 = P(multiple of 2) x Number of spins
Number of multiples of 2 = (1/2) x 75 = 37.5

Since we can't have a fraction of a spin, we need to round to the nearest whole number. In this case, we can round up or down depending on how we interpret the question. I

f we want to know how many times we can expect to land on a multiple of 2 on average, we should round down to 37.

If we want to know the closest integer to the expected value, we should round up to 38.

So depending on the context of the question, the answer could be either 37 or 38.

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The path the rover travels out of the crater is a distance of 180 m and covers a vertical distance of 65 meters, determine the angle of elevation of the room to the nearest thousands of degree

Answers

The angle of elevation of the room is approximately 19.1 degrees.

To determine the angle of elevation of the room, we need to use trigonometry. The angle of elevation is the angle between the horizontal plane and the line of sight from the rover to the room. We can use the tangent function to find this angle:

tan(angle of elevation) = opposite/adjacent

In this case, the opposite side is the vertical distance of 65 meters and the adjacent side is the horizontal distance of 180 meters. So we have:

tan(angle of elevation) = 65/180

To find the angle of elevation, we can take the inverse tangent (or arctan) of both sides:

angle of elevation = arctan(65/180)

Using a calculator, we get:

angle of elevation = 19.1 degrees (rounded to the nearest thousands of degree)

Therefore, the angle of elevation of the room is approximately 19.1 degrees.

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A spinner is divided into 15 identical sectors and labeled 1 through 15.

how many spins are expected for a multiple of 4 to be spun 7 times?

select from the drop-down menu to correctly complete the sentence.
the spinner is expected to have to spin approximately times for a multiple of 4 to be spun 7 times.

Answers

Answer: 35

Step-by-step explanation: The other person is wrong

Hope this helped :)

For each of the following functions find f(- x) and - f * (x) , then determine whether it is even, odd or neither. Justify your answer. F(x)= x^3-7/x

Answers

The function is neither even nor odd.

To find f(-x), we substitute -x for x in the function f(x):

f(-x) = (-x)^3 - 7/(-x) = -x^3 - 7/x

To find -f(x), we multiply the function f(x) by -1:

-f(x) = -1 * (x^3 - 7/x) = -x^3 + 7/x

To determine if the function is even, odd or neither, we compare f(-x) and -f(x).

If f(-x) = f(x), the function is even.

If f(-x) = -f(x), the function is odd.

If neither of these is true, the function is neither even nor odd.

Comparing f(-x) and -f(x), we have:

f(-x) = -x^3 - 7/x

-f(x) = -x^3 + 7/x

Since f(-x) and -f(x) are not equal, and f(-x) is not the negative of -f(x), the function is neither even nor odd.

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What does 9x5 equal to

Answers

Answer:

Step-by-step explanation:

9 groups with 5 in each equals to

45

Answer: 9 x 5 = 45

Step-by-step explanation:

9

18

27

36

45

54

63

72

81

90

99

108

if two samples a and b had the same mean and standard deviation, but sample a had a larger sample size, which sample would have the wider 95% confidence interval?

Answers

As a result of being more dispersed, sample A has a broader 95% confidence interval.

Given that sample A had a higher standard deviation and that we are aware that when standard deviation rises, the margin of error likewise does, widening the confidence interval as a result.

The average squared departure of each observation from the mean is the standard deviation's square root.  In other words, it tells you how much the data points deviate from the average value.

Standard deviation is often used as a tool in statistical analysis to help determine the reliability of data. For example, if you were measuring the heights of a group of people, a low standard deviation would suggest that the majority of the people are around the same height, while a high standard deviation would suggest that there is a wider range of heights in the group.

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Find the value of y

Answers

Step-by-step explanation:

x is the radius.....y is the diameter ...which is two times  'x'

find 'x' via the Pythagorean theorem

x^2 = 3.6^2 + 4^2

x = 5.38

y = 2x = 10.76  units

5 dived by 465 long divsion 6th grade

Answers

Answer: 5 divided by 465 is 0.010752688172

          465 divided by 5 is 93

Step-by-step explanation:

Isabella grows two types of pepper plants. The following dot plots show the numbers of peppers, rounded to the nearest
5
55, per plant for each type. Each dot represents a different plant. Compare the typical number of peppers per plant. In general, the

had more peppers, with

per plant

Answers

The possible values of x that satisfy the equation |x+5| = c are x = c - 5 and x = -c - 5.

what is algebra?

Algebra is a branch of mathematics that deals with mathematical operations and symbols used to represent numbers and quantities in equations and formulas.

A circle with center c(2, 4) has radius 13. a) verify that a(14,9) and b(7, 16) are points on this circle. b) if m is the midpoint of ab, show that cm is perpendicular to ab.

Answers

a) To verify that the points A(14, 9) and B(7, 16) are on the circle with center C(2, 4) and radius 13, we can use the distance formula:

Distance between point A and C:

d_AC = sqrt[(x_A - x_C)^2 + (y_A - y_C)^2]

    = sqrt[(14 - 2)^2 + (9 - 4)^2]

    = sqrt[144 + 25]

    = sqrt(169)

    = 13

Since the distance between point A and C is equal to the radius of the circle, point A is on the circle.

Distance between point B and C:

d_BC = sqrt[(x_B - x_C)^2 + (y_B - y_C)^2]

    = sqrt[(7 - 2)^2 + (16 - 4)^2]

    = sqrt[25 + 144]

    = sqrt(169)

    = 13

Since the distance between point B and C is equal to the radius of the circle, point B is also on the circle.

Therefore, points A and B are on the circle with center C(2, 4) and radius 13.

b) The midpoint of line segment AB can be found using the midpoint formula:

M = [(x_A + x_B)/2, (y_A + y_B)/2]

 = [(14 + 7)/2, (9 + 16)/2]

 = [10.5, 12.5]

The slope of line segment AB can be found using the slope formula:

m_AB = (y_B - y_A)/(x_B - x_A)

    = (16 - 9)/(7 - 14)

    = -7/-7

    = 1

The slope of a line perpendicular to AB will be the negative reciprocal of m_AB:

m_CM = -1/m_AB

    = -1/1

    = -1

The equation of the line passing through points C(2, 4) and M(10.5, 12.5) can be found using the point-slope form:

y - y_C = m_CM(x - x_C)

y - 4 = -1(x - 2)

y = -x + 6

The slope of line CM is -1, which is the negative reciprocal of the slope of line AB. Therefore, line CM is perpendicular to line AB.

Hence, we have shown that line segment CM is perpendicular to line segment AB.

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Someone help me please

Answers

The corresponding values for the triangle in the larger circle are;

1. Perimeter of Δ BSH = 71.4 cm

2. The measure of ∠SBH = 102°.

3.  The area of Δ BSH = 41.54 cm²

4. The length of the circumference of circle B = 52.275 cm

How do you calculate the corresponding values for the triangle in the larger circle, like perimeter?

1. The ratio of the perimeters of similar triangles is equal to the ratio of their corresponding sides. Since OB/OA = 4.25, we have:

Perimeter(Δ BSH) = Perimeter(Δ ARG) × 4.25

Perimeter(Δ BSH) = 16.8 cm × 4.25 = 71.4 cm

2. Since the triangles are similar, their corresponding angles are congruent. Therefore, ∠SBH = ∠RAG = 102°.

3. The ratio of the areas of similar triangles is equal to the square of the ratio of their corresponding sides. Since OB/OA = 4.25, we have:

Area(Δ BSH) = Area(Δ ARG) × (4.25)²

Area(Δ BSH) = 2.3 cm² × (4.25)² = 2.3 cm² × 18.0625 = 41.54 cm²

4. The ratio of the circumferences of similar circles is equal to the ratio of their radii or diameters. Since OB/OA = 4.25, we have:

Circumference(circle B) = Circumference(circle A) × 4.25

Circumference(circle B) = 12.3 cm × 4.25 = 52.275 cm

The above answers are in response to the following questions below;

Dante created the following measurements and calculations:

He then made the following measurements and calculations:

He calculated the ratio OB = 4.25.

                                      OA

He measured the perimeter of Δ ARG, and found it to be 16.8 cm.

He measured ∠RAG = 102°.

He calculated the area of Δ ARG, and found it to be 2.3 cm2.

He calculated the circumference of circle A, and found it to be approximately 12.3 cm.

He would now like to calculate corresponding values for the triangle in the larger circle, and he needs your help.

Calculate the following, using your knowledge that all circles are similar, along with the data already collected by Noah..

5. Find the perimeter of Δ BSH.

6. Find the measure of ∠SBH.

7. Find the area of Δ BSH.

8. Find the length of the circumference of circle B.

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In ΔWXY, x = 4.7 cm, y = 7.9 cm and ∠W=162°. Find the area of ΔWXY, to the nearest 10th of a square centimeter.

Answers

The area of the triangle to the nearest tenth is 5.8cm²

What is area of a triangle?

A triangle is a closed, 2-dimensional shape with 3 sides, 3 angles, and 3 vertices. A triangle is also a polygon. Examples of triangle include, isosceles, equilateral , scalene e.t.c

The area of a triangle is expressed as;

A = 1/2 b h for right angle triangle and A = absinC for others.

Here; x = 4.7, y = 7.9, W = 162

area = 1/2× 4.7 × 7.9 sin162

= 1/2 × 4.7 × 7.9 × 0.31

= 5.8 cm²( nearest tenth)

Therefore the area of the triangle is 5.8cm²

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Willow bought 3 m of denim fabric and 5m of cotton


fabric. The total bill, excluding tax, was $22. Jared


bought 6 m of denim fabric and 2 m of cotton fabric


at the same store for $28. How much does the denim


fabric cost? How much does the cotton fabric cost?



How do I start?

Answers

The denim fabric costs $4 per meter and the cotton fabric costs $3 per meter.

To find out the cost per meter of each type of fabric, we can set up a system of two equations. Let d be the cost per meter of denim fabric and c be the cost per meter of cotton fabric. Then, we have:

3d + 5c = 22 (equation 1)

6d + 2c = 28 (equation 2)

We can use equation 2 to solve for one of the variables in terms of the other. Solving for c, we get:

c = 14 - 3d (equation 3)

We can substitute equation 3 into equation 1 and solve for d:

3d + 5(14 - 3d) = 22

Simplifying this equation, we get:

4d = 3

Therefore, d = 0.75, which means the denim fabric costs $0.75 per meter.

We can then use equation 3 to find the cost per meter of cotton fabric:

c = 14 - 3(0.75) = 11.25/2 = $5.625

Therefore, the cotton fabric costs $5.625 per meter.

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At a music store in New York City, 62 people entering the store were selected at random and were asked to choose their favorite type of music. Of the 62, 14 chose rock, 16 chose country, 8 chose classical and 24 chose something other than rock, country, or classical.


a) Determine the empinical probability that the next person entering the store favors rock music.


b) Determine the empirical probability that the next person entering the store favors country music.


c) Determine the empirical probability that the next person entering the store favors something other than rock, country, or classical music

Answers

(a) The empirical probability that the next person favors rock music is approximately 0.226.
b) The empirical probability that the next person favors country music is approximately 0.258.
c) The empirical probability that the next person favors something other than rock, country, or classical music is approximately 0.387.


a) To determine the empirical probability that the next person entering the store favors rock music, you need to divide the number of people who chose rock (14) by the total number of people surveyed (62).
Empirical Probability (Rock) = Number of Rock Fans / Total Surveyed = 14 / 62 ≈ 0.226
b) To determine the empirical probability that the next person entering the store favors country music, you need to divide the number of people who chose country (16) by the total number of people surveyed (62).
Empirical Probability (Country) = Number of Country Fans / Total Surveyed = 16 / 62 ≈ 0.258
c) To determine the empirical probability that the next person entering the store favors something other than rock, country, or classical music, you need to divide the number of people who chose something other (24) by the total number of people surveyed (62).
Empirical Probability (Other) = Number of Other Fans / Total Surveyed = 24 / 62 ≈ 0.387
In summary:
a) The empirical probability that the next person favors rock music is approximately 0.226.
b) The empirical probability that the next person favors country music is approximately 0.258.
c) The empirical probability that the next person favors something other than rock, country, or classical music is approximately 0.387.

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Solve the following diamond problem by finding the answers that would go in box 1 and box 2
20x?
sot
box2
-9x
box 1 =
box 2 =

Answers

Answer:

Step-by-step explanation:

The missing numbers are: box 1 = -5x and box 2 = 4sot,  A diamond problem is a type of math puzzle that involves finding two missing values in a diamond-shaped diagram.

The top and bottom numbers of the diamond represent a product, and the left and right sides represent two numbers that add up to a middle value. The goal is to find the two missing values that fit into the diamond.

To solve a diamond problem, we need to factor the product of the top and bottom numbers and look for two factors whose sum is equal to the middle value. This is because the product of two numbers can only be made up of factors that multiply together to form the product. Once we find the two factors, we can insert them into the left and right sides of the diamond.

In the given diamond problem, we have 20x? as the top and sot as the bottom. The product of these two numbers is 20x^2sot. To find the factors, we can list all the possible factor pairs of this product and check which of them adds up to -9x, which is the middle value in the diamond. We found that -5x and 4sot are the factors that add up to -9x.

Solving diamond problems can help improve factoring skills and problem-solving abilities. It requires logical thinking and an understanding of how factors and multiples work. Additionally, diamond problems can be used to introduce algebraic concepts to students in a visual and intuitive way, making them a useful tool for teaching math to learners of all ages.

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The function models the amount of money a new business has made over x months. Negative values represent debt. Over what interval is the amount increasing?

Answers

If the line has a positive slope, it means that the amount is increasing, and if it has a negative slope, it means that the amount is decreasing.

Based on the given information, the function models the amount of money a new business has made over x months. Therefore, we can assume that the function is a linear function, and its graph is a straight line.

Given that negative values represent debt, we can assume that the slope of the line is positive over the interval where the function takes positive values. Therefore, the interval over which the amount is increasing is from zero to infinity, which means that the business is making money and not in debt.

It's essential to note that if the function has a negative slope over any interval, then the amount is decreasing, and the business is losing money. However, we cannot determine this information from the given function's information.

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The choir practiced 3 times this week. On Monday,the choir practiced 3/4 hour. On Wednesday, they practiced 1/2 hour more than on Monday. On Friday, they practiced twice as long as on both Monday and Wednesday combined. Altogether,how long did the choir practice this week?

Answers

The choir practice this week for 5 1/4 hours.

On Monday, the choir practiced for 3/4 hour.

On Wednesday, they practiced for 1/2 hour more than on Monday, which is 3/4 + 1/2 = 6/8 + 4/8 = 10/8 = 1 1/4 hours.

On Friday, they practiced twice as long as on both Monday and Wednesday combined, which is 2 * (3/4 + 1 1/4) = 2 * 2 = 4 hours.

To find the total practice time for the week, we can add up the times from each day:

3/4 + 1 1/4 + 4 = 5 + 1/4 = 5 1/4 hours.

Therefore, the choir practiced for 5 1/4 hours in total this week.

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