If the two triangles in the map below are similar, what is the distance from Arrow Road to the end of the forest (x)?

According to the equation of the trend line the population will reach 52900 in 27831 years.

A mathematical statement known as an equation is a combination of two expressions joined together by the equal sign.

The equation of the trend line is:

y = 1.9x + 21

where, y is the population and x indicate the year.

To find the number of years in which the population reach 52900, substitute y = 52900.

y = 1.9x + 21

52900 = 1.9x + 21

52900 - 21 = 1.9x

52879/ 1.9 = x

x = 27831

Hence, according to the equation of the trend line the population will reach 52900 in 27831 years.

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The radius of such a cylinder will be 8 and height=8/3.

What is a cylinder?

Cylinder is one of the basic 3d shapes, in geometry, which has two parallel circular bases at a distance. The two circular bases are joined by a curved surface, at a fixed distance from the center. The line segment joining the center of two circular bases is the axis of the cylinder. The distance between the two circular bases is called the height of the cylinder. LPG gas-cylinder is one of the real-life examples of cylinders.

Since, the cylinder is a three-dimensional shape, therefore it has two major properties, i.e., surface area and volume. The total surface area(TSA) of the cylinder is equal to the sum of its curved surface area and area of the two circular bases. The space occupied by a cylinder in three dimensions is called its volume(V).

V=πr²h and TSA=2πr²+2πrh where r=radius and h=height.

Now,

In any case, we can let the radius of the inscribed cylinder be x

. That must therefore mean that the height of the cylinder is 8−4/6x

. This makes the volume of the cylinder

V=πx^2(8−2/3x)=π(8x^2−2/3*x^3)

To find the maximum volume of the cylinder we take the derivative of V

with respect to x

and set it to 0

dV/dx=π(16x−2x^2)=0⇒16x−2x^2=2x(8−x)=0

x=0  leads to a trivial case, which leaves us with x=8

. This means that the height is 8−2/3*8=8/3

, and the volume is therefore

V=π⋅8^2⋅8/3

V=512/3π.

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The fewest number of straight cuts needed to divide a flat pancake into 16 pieces is 5. This can be done by cutting the pancake into 4 pieces, then the 4 pieces into 4, and the resulting 16 pieces into 2.

The fewest number of straight cuts needed to divide a flat pancake into 16 pieces is 5. To do this, start by making one straight cut to divide the pancake into two equal pieces. Then make two more cuts, spaced evenly around the circumference, to divide the pancake into 4 equal pieces. Next, make two more cuts, spaced evenly around the circumference, to divide the 4 pieces into 4 even smaller pieces. Finally, make one last cut, spaced evenly around the circumference, to divide the 16 pieces into 2 equal pieces, giving you a total of 16 pieces. With this method, you can divide a flat pancake into 16 pieces with just 5 straight cuts.

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The frequency table has been created in the attachment

Given that 56 respondents did not belong to any clubs, we know that the number of 7th graders who belong to zero clubs is 56.

Given that twice as many 7th graders belonged to one club as no clubs, we can set up the equation:

x = 2 * 56

Given that 10 fewer 7th graders belonged to more than one club than no clubs, we can set up the equation:

y = 56 - 10

Given that twice as many 8th graders belonged to one club as more than one club, we can set up the equation:

z = 2*w

Now we have the following system of equations:

x = 2 * 56

y = 56 - 10

z = 2*w

x+z = 150

y+w = 150

By solving the above system of equations we get:

x = 112

y = 46

z = 112

w = 56

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The number of student tickets sold are 109.

As per the given data a high school drama department sold 238 tickets for their performance.

An adult ticket cost $6. 75.

A student ticket cost $3. 50.

Let the number of adult tickets be x.

Let the number of student tickets be y.

Then we know that the total number of tickets is 238.

x + y = 238 ... (1)

If we multiply the cost of a ticket by the number of tickets we can also get the total.

6. 75x + 3. 50y = 1252. 25(....... (2))

Now we have two equations and two unknowns and we can find the value for these unknowns

Lets use substitution method.

x + y = 238

x = 238 - y

Substitute x = 238 - y in equation (2)

6. 75(238 - y) + 3. 50y = 1252. 25

1606.5 - 6.75y + 3. 50y = 1252. 25

- 3.25y = - 354.25

3.25y =  354.25

y = 109

Substitute y = 109 in equation (1)

x + 109 = 238

x = 129.

Therefore number of student tickets are 109.

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The cost of 1 mall candle = $1 while the cost of 1 large candle = $5

Let the cost of 1 mall candle = x

Let us assume that the cost of 1 large candle = y

So, in case 1,

As I can buy,

4 mall candles and 2 large candles for $14

So, framing the equation,

We can rewrite it as:

4x+2y = 14-------(1)

As my friend can buy 5 mall candles and 3 large candles for $20

Now again framing the equation,

We can write it as:

5x+3y=20 -------(2)

From (1) and (2), for determining the value of x, we will first make the coefficient of y equal in both cases.

So, multiply the first equation by 3 and the second by 2

We will get,

12x+6y=42 -----(3)

10x+6y=40------(4)

Now subtracting (4) from (3)

We will get,

2x=2

=>x=1

So, for determining the value of y,

We will put the value of x in (1)

So,  4x+2y = 14-------(1)

=> 4+2y=14

=>2y=10

=>y=5

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The cost of a small candle is equal to $1, and the cost of each large candle is $5..

When I buy the candles,

Cost of 4 small and 2 large candles = $14

but when my friend purchse the candles , cost of 5 small and 3 large candles= $ 20 .

Let the cost of each small candle and each large candle be $x and $y respectively.

From first condition, when I can buy the candles,

Cost of 4 smalll candles = $4x

Cost of 2 large candles= $2y

=> $4x + $2y = $14

Reduce the equation, 2x + y = 7 ---(1) ( since, divided by 2)

In case Second, when my friend buy the candles,

Cost of 5 small candles= $5x

Cost og 3 large candles= $ 3x

=> $5x + $3y = $20 or 5x + 3y = 20 --(2)

Now, equation (1) and (2) made a system of linear equations. Linear equations are in two variables x and y . To solve the system of linear equation, we can use Elimination Method,

To make the same cofficient of y variable in both equtions, multiply the equation (1) by 3

=> 3(2x + y ) = 3× 7

=> 6x + 3y = 21 --(3)

Subtracts the eqution (2) from (3) to eliminate y,

=> 6x + 3y - ( 5x + 3y) = 21 - 20

=> 6x + 3y - 5x - 3y = 21 - 20

=> x = 1

from (1) , 2x + y = 7 => 2×1 + y = 7

=> y = 5

Hence, the cost of one small candle and one large candle are $1 and $5.

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I think this is it if not I'm sorry

78264 in

Correct option is D, the fraction of area of square region ABCD is 1/4.

A + B + C = D + E + F since diagonal QS divides the square into two equal portions.

We can see that the areas of regions A and F must be equal because they have the exact same measurements and form. Similar reasoning leads us to the conclusion that the areas of regions D and C are equal.

As a result, it follows that the size of regions E and B must likewise be equal. Due to the fact that URPT is a parallelogram, its area equals (base)(height)=(1)(2)=2.

Area of region E = Area of region B = 1 as a result.

The percentage of the square PQRS's area is represented by the darkened region 1/4 is a fraction.

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Complete question -

According to the information in the table, the value of B is 50 (option B)

To find the value of B we must calculate the constant, for that we have to perform the following operation:

In this case, we use the values of another column to identify the constant that applies to all the values in the table and the result is the following:

Additionally, to find the value of B we must perform the following operation:

According to the above, the correct answer would be 50 (option B).

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A geometric sequence begins with 72, 36, 18, 9, is Of(n) is 72(2)+1.

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Answer:

f(n) = 72(0.5)n−1

Step-by-step explanation:

Got right.

The z score that corresponds to the 90th percentile is 1.28. Option D

A z-score (also called a standard score) gives you an idea of how far from the mean a data point is. But more technically it’s a measure of how many standard deviations below or above the population mean a raw score is.

The 90th percentile refers to the value above 90 percent of the data. This is illustrated in the figure.

Therefore, using a z-table (also attached) or a technology, we can solve that  getting the  z=1.28.

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Distance of the race is 500 feet.

Given that tortoise moves at 50 feets per hour and hare moves at 250 feets per hour.

So speed of tortoise = 50 feets per hour.

Speed of hare = 250 feets per hour.

Let hare takes T hours to complete the race

Than tortoise will take (T + 8) hours to complete the race.

Total distance traveled by hare = speed * time = 250T

Total distance traveled by tortoise = speed * time = 50(T + 8)

Total distance traveled by both is same.

250T = 50(T + 8)

250T = 50T + 400

250T – 50T = 400

200T = 400

T = 2 hours

So, total distance of the race = 250T = 250 * 2 = 500 feet.

Therefore, total distance of the race is 500 feet.

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If Chris takes the 2:20 train, then he will get to willow lake at 2:28.

If Chris takes the 2:20 train, then we have to find at what time he will get to willow lake.

The distance from where Chris lives to willow lake is 48 miles.

Chris will take the train to willow lake. The train goes 60 miles an hour.

The distance = 48 miles

The speed of train = 60 miles an hour

Time = distance/speed

Time = 48/60

Time = 0.8 minutes

The train reach after 8 minutes in willow lake.

So the train reach 2:28.

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4 cups of mayonnaise should be used if 1 cup of pecans is used.

As per the given data:

A recipe calls for  [tex]$1\frac{1}{2}[/tex] cups of mayonnaise and [tex]$\frac{3}{8}[/tex] cups of pecans.

First, convert the mixed fraction to an improper fraction.

[tex]$1\frac{1}{2}[/tex] cups of mayonnaise = [tex]$\frac{3}{2}[/tex]

Here we have to determine how much mayonnaise should be used if 1 cup of pecans is used.

This can be determined by using the unitary method.

We may determine the value of one unit from the value of many units and the value of many units from the value of one unit using the unitary technique.

The ratio of the amount of pecans comparing reality and the recipe is:

[tex]$= \frac{1}{\frac{3}{8} }[/tex]

= [tex]$\frac{8}{3}[/tex]

To find the amount of mayonnaise that should be added:

= [tex]$\frac{8}{3}[/tex] × [tex]$\frac{3}{2}[/tex]

= 4

Therefore 4 cups of mayonnaise is required.

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The relative frequencies for the car riders are given as follows:

A relative frequency is obtained with the division of the number of desired outcomes by the number of total outcomes.

The total number of car riders is given as follows:

78.

The number in each grade is given as follows:

Hence the relative frequencies are given as follows:

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In order to leave an equal space between shelves, the distance between each shelf should be 9 feet 10 inches.

1. The floor-to-ceiling clearance is 9 feet 10 inches.

2. Each shelf is 10 inches thick.

3. To leave an equal space between shelves, the distance between each shelf should be the same as the floor-to-ceiling clearance, which is 9 feet 10 inches.

In order to ensure that there is an equal space between each of the shelves, the distance between each shelf should be 9 feet 10 inches. This is because the floor-to-ceiling clearance is 9 feet 10 inches, and the thickness of each shelf is 10 inches.

Therefore, in order to have an equal space between shelves, the total distance between each shelf should be 9 feet 10 inches. This is the best way to ensure that each shelf is equally spaced from the next.

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The slope of the line AB and the perpendicular bisector are reciprocal to each other and the equation of the line is 3y + - 4x = 18.  

A line is known as a perpendicular bisector when it divides a specified line segment in half, by creating a 90° angle at the intersection.

The intersection of a line segment's midpoint with a perpendicular bisector. It can be built with a compass and a ruler.

On both sides of the line segment being divided, it forms a 90° angle.

Here we have

On the grid below segment AB is shown with endpoints A(-1,-1) and B(7,5). It's midpoint M. The coordinates of M (3, 2).  

Slope from A(-1,-1) and B(7,5)  

=> [ 5 + 1]/[7 + 1 ] = 6/8 = 3/4

When we draw a perpendicular bisector of AB on the grid. It will pass through the point (0, 6)  

The slope of the perpendicular bisector i.e from (0, 6) to (3, 2)  

=> [2 - 6]/[3 - 0] = - 4/3

Let the equation of the bisector is y = mx + c

=> y = (-4/3)x + c

=> 3y = - 4x + 3c           [ ∵ Slope = -4/3 ]

As we know the bisector will pass through (3, 2)

=> 3(2) = -4(3) + 3c

=> 3c = 12 + 6

=> 3c = 18

Hence, the required equation of the line is 3y = - 4x + 18  

Therefore,

The slope of the line AB and the perpendicular bisector are reciprocal to each other and the equation of the line is 3y + - 4x = 18.  

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Answer:

The gravitational force acting on the 6-kg bowling ball at the top of the 120-meter tall building is approximately 58.64 Newtons.

Step-by-step explanation:

After solving, 1.53 pints of blue paint she used to paint her bedroom walls.

Irene uses 6.1 pints of white paint and blue paint to paint her bedroom walls.

3/4 of this amount is white paint, and the rest is blue paint.

The combined amount of blue and white paint = 6.1 pints

Quantity of white paint applied to bedroom walls = 3/4

Quantity of blue paint applied to bedroom walls = 1 - 3/4

Quantity of blue paint applied to bedroom walls = 4/4 - 3/4

Quantity of blue paint applied to bedroom walls = (4 - 3)/4

Quantity of blue paint applied to bedroom walls = 1/4

Hence, 

Blue paint were used to paint the bedroom's walls = 1/4 × 6.1

Blue paint were used to paint the bedroom's walls = 1.53

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The complete question is:

Irene uses 6. 1 pints of white paint and blue paint to paint her bedroom walls. 3/4 of this amount is white paint, and the rest is blue paint. How many pints of blue paint did she use to paint her bedroom walls?

In step 2. the addition property of equality was applied.

In step 2. the subtraction property of equality was applied.

We have solved the equation x/4 + 5 = 23.

In step second we subtract 5 on both side, this is the property of equality of addition.

In step 3 the expression is x/4 = 23

In step 4 we multiply 4 on both side, again using the property of equality of subtraction.

Now the value of x is 72.

Hence, using the property of equality in step 2 and 4 we solve the equation.

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The complete question is given below:

Answer:

100° and 40°

Step-by-step explanation:

In an isosceles, 2 interior angles are equal.

If one angle is 40°, another one of its angles must be also 40°.

Fact of a triangle

Sum of interior angles of a triangle is 180°.

Let the unknown angle be x.

x + 40° + 40° = 180°

x + 80° = 180°

x = (180 - 80)°

x = 100°

So, the other angle is 100°

Hence,

100° and 40° are the possible measures for the other two triangles.

A graph of the ordered pairs (time, distance) for the rows in the ratio table is shown in the image attached below.

In Mathematics, a proportional relationship is a type of relationship that produces equivalent ratios and it can be modeled or represented by the following mathematical expression:

y = kx

Where:

Next, we would determine the constant of proportionality (k) for the data points on this graph as follows:

Constant of proportionality, k = y/x

Constant of proportionality, k = 2/10

Constant of proportionality, k = 0.2

When time x = 20, the distance (y) is given by:

y = 20(0.2)

y = 4 miles.

When time x = 30, the distance (y) is given by:

y = 30(0.2)

y = 6 miles.

When time x = 40, the distance (y) is given by:

y = 40(0.2)

y = 8 miles.

Next, we would use an online graphing calculator to plot the ordered pairs as shown in the graph attached below.

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Heat loss, according to Newton's cooling curve, is exponential. Like a half-life, it operates.

Cake temperature and ambient temperature varied by 140 F. The cake has lost half of that difference after 30 minutes, thus that is the half-life. It will shed another half or 35 F in the next 30 minutes, bringing the temperature to 105 F. It will shed 17.5 F in about 30 minutes, leaving 87.5 F.

The temperature is between the last two, at 100 F, so it will be between an hour and an hour and a half. You get an interpolated result of about an hour and ten minutes.

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She needs to go to the swimming pool about 14 times for it to be worth paying the membership fee.

To determine how many times you need to go to the swimming pool to make the membership fee worth paying, you can use the following formula:

Number of visits = membership fee / (cost without the membership - cost with membership)

Plugging in the values, we get:

Number of visits = $50 / ($5 - $3.50)

The savings from the membership's lower entrance price will have surpassed the cost of the membership after 14 visits.

Hence, she needs to go to the swimming pool about 14 times for it to be worth paying the membership fee.

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The area of figure composing a parallelogram and two semicircles is 399.06 units².

What is a parallelogram?

A quadrilateral with two sets of parallel sides is referred to as a parallelogram. In a parallelogram, the opposing sides are of equal length, and the opposing angles are of equal size. Additionally, the interior angles that are additional to the transversal on the same side.

The base of the parallelogram is = 18 units

The height of the parallelogram is = 11 units

The area of a parallelogram is given as -

Area = Base × Height

Area = 18 × 11

Area = 198 units²

The diameter of the semicircle is = 16 units

The radius of semicircle is = 8 units

The area of the semicircle is given as -

Area = (1/2)πr²

Area = (1/2)π(8)²

Area = (1/2)π × 64

Area = 32π units²

The total area of the figure is given as -

Total Area = Area of Parallelogram + 2 (Area of semi-circle)

Total Area = 198 + 2(32)π

Total Area = 198 + 64π

Total Area = 198 + 201.06

Total Area = 399.06 units²

Therefore, the area of the figure is 399.06 units².

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Answer: To solve the equation -3(x+2)^2-4 = 5 by factoring, we can follow these steps:

Move all the terms to one side of the equation by adding 3(x+2)^2 and 4 to both sides: -3(x+2)^2-4+3(x+2)^2+4 = 5+3(x+2)^2

Combine like terms: 3(x+2)^2 = 5

Take the square root of both sides of the equation: (x+2)^2 = 5/3

Isolate x+2 on one side of the equation by taking the square root of both sides: x+2 = ±sqrt(5/3)

Solve for x by subtracting 2 from both sides of the equation: x = ±sqrt(5/3) - 2

So the solutions to the equation -3(x+2)^2-4 = 5 by factoring is x = ±sqrt(5/3) - 2.

It's important to note that the square root of a fraction is a positive and negative solution, so the solutions are x = sqrt(5/3) - 2 and x = -sqrt(5/3) - 2

Step-by-step explanation:

The expression that shows John's score will be 2x + 9.

It is vital to note that an expression is simply used to show the relationship between the variables that are provided or the data given regarding an information.

In this case, it is vital to note that they have at least two terms which have to be related by through an operator.

In this case, Mai has a score of x while John has 9 more than twice mai's score.

The expression for this relationship will be:

= (2 × x) + 9

= 2x + 9

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Complete question

Mai has a score of x. John has 9 more than twice mai's score. Illustrate the expression for Johnsc score.

The linear equation parallel to y=(2/3)x+1 that passes through (3, 0) is:

y = (2/3)*x - 2

A general linear equation can be written in the slope-intercept form as:

y = m*x + b

Where m is the slope and b is the y-intercept.

Particularly, two linear equations are parallel only if both equations have the same slope and different y-intercepts.

Then a line parallel to:

y = (2/3)*x + 1

Is of the form:

y = (2/3)*x + b

And we want this line to pass through the point (3, 0), replacing these values we will get:

0 = (2/3)*3 + b

0 = 2 + b

-2 = b

Then the linear equation is:

y = (2/3)*x - 2

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Answer:

55°

Step-by-step explanation:

For the line including the 110°, the angle of the supplementary angle is 70° which is the 'non-equivalent' length of the isosceles triangle. Then do:

(180°-70°)/2 = 55° to get x

Answer:

Supplementary angles, x = 55

Step-by-step explanation:

Supplementary angles: straight line means both angles add up to 180, this if the outside angle is 110 then the inside angle is 180° - 110° = 70°

Since it is an isosceles triangle, it means both angles are equal to x therefore

[tex]180 - 70 = 2x\\110 = 2x\\\frac{110}{2} = x\\x = 55[/tex]

Work Shown:

|x - 5| < 3

-3 < x-5 < 3

-3+5 < x-5+5 < 3+5

2 < x < 8

The graph will have open circles at 2 and 8, then shade between the open circles. The open circles indicate "do not include this endpoint". This is why choice A is the final answer.