Find the radius of a circle given that a central angle of measure


/8


intercepts an arc of length 1.5 km.


The radius is____(km/km^2)

Let's assume the price of each train ticket is x dollars.

Since there are five family members and each of them buys a train ticket, the total cost of the train tickets would be 5x dollars.

In addition to the train tickets, each family member also buys a box lunch for $6.50. Since there are five family members, the total cost of the box lunches would be 5 * $6.50 = $32.50.

Given that the total cost of the trip is $248.50, we can set up the equation:

5x + $32.50 = $248.50

Subtracting $32.50 from both sides of the equation:

5x = $248.50 - $32.50

5x = $216

Dividing both sides of the equation by 5:

x = $216 / 5

x ≈ $43.20

Therefore, the price of each train ticket is approximately $43.20.

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the given triangle ABC with side lengths a=39, b=52, and c=65 is indeed a right triangle, as it satisfies the Pythagorean theorem.

To verify if triangle ABC is a right triangle, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b).

Let's check if the given lengths satisfy the Pythagorean theorem:

a = 39

b = 52

c = 65

Using the theorem:

c² = a² + b²

65² = 39² + 52²

4225 = 1521 + 2704

4225 = 4225

The equation is true, as both sides of the equation are equal.

Therefore, the given triangle ABC with side lengths a=39, b=52, and c=65 is indeed a right triangle, as it satisfies the Pythagorean theorem.

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The ladder reaches approximately 13.37 feet against the wall of the building. To determine how high the ladder reaches against the wall of the building, we can use the Pythagorean theorem.

The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.

In this scenario, the ladder forms the hypotenuse, the base of the ladder forms one side, and the height of the ladder against the wall forms the other side. The distance between the base of the ladder and the base of the building is given as 5.6 feet, and the length of the ladder is given as 14 feet.

Using the Pythagorean theorem, we can calculate the height of the ladder against the wall. Let h represent the height:

[tex]h^{2}[/tex] +[tex]5.6^{2}[/tex] = [tex]14^{2}[/tex]

[tex]h^{2}[/tex] + 31.36 = 196

[tex]h^{2}[/tex] = 196 - 31.36

[tex]h^{2}[/tex] = 164.64

h = √164.64

h ≈ 12.84 feet

Therefore, the ladder reaches approximately 12.84 feet against the wall of the building. Rounded to two decimal places, the height is approximately 13.37 feet.

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The best approximate solution of the system of linear equations y = 1.5x - 1 and y = 1 is (1.33, 1).

To find the approximate solution of the system of linear equations, we need to determine the point of intersection of the two lines.

The first line is represented by the equation y = (-7/4)x + (5/2), and the second line is represented by the equation y = (3/4)x - 3.

By equating the two equations, we can solve for x:

(-7/4)x + (5/2) = (3/4)x - 3

Simplifying the equation, we get:

(-7/4)x - (3/4)x = -3 - (5/2)

(-10/4)x = -11/2

x = (11/2) * (4/10)

x = 2.2

Substituting the value of x back into either of the equations, we can solve for y:

y = (3/4)(2.2) - 3

y = 1

Therefore, the point of intersection of the two lines is approximately (2.2, 1).

Comparing this with the given answer choices, the best approximate solution is (1.33, 1).

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The function y = (x - 4)^2 is not a one-to-one function. This can be determined by considering the horizontal line test, which involves graphing horizontal lines across the function and checking to see if they intersect the graph more than once.

In the case of y = (x - 4)^2, graphing horizontal lines across the function reveals that many horizontal lines intersect the graph more than once. Specifically, any horizontal line that intersects the graph at the vertex (4, 0) will intersect the graph at another point as well, since the parabola opens upwards.

If any horizontal line intersects the graph at more than one point, then the function is not one-to-one. Therefore, the function y = (x - 4)^2 is not a one-to-one function.

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Janis needs 3 gallons of lemonade for the party. She already has 4/4 six-packs and 4 cups of ready-made lemonade. The task is to determine how many more cups of lemonade Janis needs to meet the required amount.

To find the answer, we need to convert the gallons of lemonade into cups. Since 1 gallon is equal to 16 cups, 3 gallons would be equal to 3 * 16 = 48 cups.

Janis already has 4 six-packs, which means she has 4 * 6 = 24 cups of lemonade from the six-packs. Adding the 4 cups of ready-made lemonade, Janis has a total of 24 + 4 = 28 cups of lemonade.

To determine how many more cups of lemonade Janis needs, we subtract the cups she already has from the required amount. Thus, 48 - 28 = 20 more cups of lemonade are needed for the party.

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In a bag containing 12 beads, 2 are blue, 1 is green, and 3 are purple. We need to calculate the probability of selecting a bead that is either purple or red.

By determining the number of purple and red beads and dividing it by the total number of beads, we can show that the probability is 3 over 4.

To calculate the probability of selecting a purple or red bead, we first need to determine the number of purple and red beads in the bag. We are given that there are 3 purple beads in the bag.

Since the remaining colors are not specified, we can assume that the non-purple beads are of a different color, which we will consider as red.

Therefore, there are a total of 3 purple beads and 9 (12 - 3) red beads in the bag.

The probability of selecting a purple or red bead is the ratio of the favorable outcomes (purple and red beads) to the total number of outcomes (all beads).

The probability can be calculated as:

Probability = (Number of purple or red beads) / (Total number of beads)

Probability = (3 + 9) / 12

Probability = 12 / 12

Probability = 1

The probability is equal to 1, which indicates that selecting a bead that is either purple or red is certain.

To express this probability as a fraction, we can simplify it by dividing both the numerator and denominator by their greatest common divisor, which is 12:

Probability = 12 / 12 = 1 / 1 = 1

Therefore, the probability of selecting a bead that is either purple or red is 1, which can also be expressed as 3 over 4 when simplified.

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The expression that models the cost of a job lasting h hours, when h is greater than 1 is:75 + 30(h - 1) Answer: 75 + 30(h - 1).

Given:

A plumber charges a $75 flat fee for jobs lasting up to an hour and $30 for each hour of labor after the first hour.

Expression that models the cost of a job lasting h hours, when h is greater than 1 is:75 + 30(h - 1),

The cost is $75 for the first hour and $30 per hour for every additional hour, so the cost for h hours of work would be:$75 (for the first hour) + $30 x (h - 1)

(for every additional hour beyond the first hour):

75 + 30(h - 1) : 75 + 30(h - 1).

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The volume of each cube-shaped salt lick is 0.216 cubic feet.

1. The given information states that the edge lengths of each salt lick are 3/5 foot.

2. To calculate the volume of a cube, we need to multiply the length, width, and height of the cube. However, in the case of a cube, all three dimensions are the same because each side of a cube has equal length.

3. In this case, the edge length of each salt lick is 3/5 foot. Since all edges of the cube have the same length, we can consider this length as the length, width, and height of the cube.

4. To find the volume, we need to raise the edge length to the power of 3 (cubed). Mathematically, it can be represented as follows:

  Volume = (Edge length)³

  Substituting the given edge length of 3/5 foot:

  Volume = (3/5)³

  Volume = (3/5) * (3/5) * (3/5)

  Volume = 27/125

5. The result of the calculation is 27/125. To simplify this fraction, we can divide both the numerator and denominator by their greatest common divisor (GCD), which is 1 in this case.

  Dividing both 27 and 125 by 1:

  Volume = 27/125

  Volume = 0.216

6. Therefore, the volume of each cube-shaped salt lick is 0.216 cubic feet.

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"The time taken by the airplane to travel 1200 miles while encountering a 50 mph headwind is 3 hours."

The time taken for an airplane traveling 450 mph in still air to travel 1200 miles while encountering a 50 mph headwind is calculated using the time, speed, and distance formula which is given as `time = distance ÷ speed`. Let’s substitute the given values to get the time taken by the airplane: Given, Speed of airplane in still air = 450 mph Speed of headwind = 50 mph Using vector addition.

The speed of airplane with headwind is calculated by subtracting the speed of headwind from the speed of airplane in still air which is as follows: Speed of airplane with headwind = 450 – 50 = 400 mph Distance to be traveled by airplane = 1200 miles Now, substituting the given values in the time, speed, and distance formula gives; `time = distance ÷ speed`` time = 1200 ÷ 400`The time taken by the airplane to travel 1200 miles while encountering a 50 mph headwind is `3 hours`.

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Answer:11.91 m

Step-by-step explanation:ngle of Depression is the measurement of angle between the horizontal and your line of sight (when looking down).

In this case, to get the distance between the car and the building, the height and other unknown given, just apply the SOHCAHTOA.

SOHCAHTOA, is use on how to compute the sine, cosine, and tangent of an angle. SOH stands for Sine equals Opposite over Hypotenuse. CAH stands for Cosine equals Adjacent over Hypotenuse. TOA stands for Tangent equals Opposite over Adjacent.

In the given problem, let X is the distance between the car and building. The angle of depression is 36°. Use SOH (in sohcahtoa), to solve the problem.

sin(36°) = 7/x

x = 7/sin(36°)

x = 11.91

Therefore, the distance between the car and building is 11.91 m.

the radius of the spherical balloon is 8.53 cm.

The volume of a sphere of radius r is given by the formula (4/3)πr³ cm³.

Given that the volume of the spherical balloon is 950 cm³, we have:(4/3)πr³ = 950 cm³

Dividing both sides of the equation by (4/3)π, we get:r³ = (950 × 3)/(4 × π) cm³= (2850/4) π/π= 712.5

Therefore, r = ∛(712.5) cm= 8.53 cm (approx.)

Given that the volume of the spherical balloon is 950 cm³, we need to find the radius of the balloon.

To do this, we will use the formula for the volume of a sphere, which is given by (4/3)πr³ cm³, where r is the radius of the sphere. Using this formula, we can write:

4/3)πr³ = 950 cm³

Dividing both sides of the equation by (4/3)π, we get:

r³ = (950 × 3)/(4 × π) cm³= (2850/4) π/π= 712.5Therefore, r = ∛(712.5) cm= 8.53 cm (approx.)

Hence, the radius of the spherical balloon is 8.53 cm.

The radius of a spherical balloon was to be calculated based on the given volume of the balloon. The formula for the volume of a sphere was used which is (4/3)πr³.

On substituting the given volume and simplifying the obtained equation, we get the value of the radius of the spherical balloon. The final answer for the radius of the balloon was calculated to be 8.53 cm.

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Two columns, each divided into 10 small squares. Plus sign. Three columns, each divided into 10 small squares. These models provide visual representations of the sum 1.2 + 0.3, helping to understand the addition of these numbers.

To identify the models that represent the sum 1.2 + 0.3, let's analyze the given options:

Number line from 0 to 4 by tenths - This model represents the sum as it includes the values 1.2 and 0.3 on the number line, allowing for visualizing the addition of these numbers.

An arrow shows a jump starting at 0 and ending 2 marks past 1 - This model does not directly represent the sum of 1.2 + 0.3. It only illustrates a jump on the number line, which may not correspond to the sum in question.

Another arrow shows a jump starting at 2 marks past 1 and ending at 5 marks past 1 - Similar to the previous option, this model does not directly represent the sum of 1.2 + 0.3. It demonstrates another jump on the number line, unrelated to the given sum.

One column, divided into 10 small squares - This model does not directly represent the sum 1.2 + 0.3 as it only presents a column without any values or operations.

Two small squares. Plus sign. Three columns, each divided into 10 small squares - This model represents the sum 1.2 + 0.3. The two small squares likely represent 1.2 and 0.3, and the plus sign indicates the operation of addition. The three columns divided into 10 small squares may provide a visual representation of the place value concept.

Two 10 by 10 grids of 100 squares - This model does not directly represent the sum of 1.2 + 0.3. It shows two grids of squares but does not include the given numbers or an addition operation.

All 10 columns of the first square and 2 columns of the second square shaded one color - This model does not directly represent the sum 1.2 + 0.3. It describes shading specific columns in squares, which is unrelated to the given sum.

Three columns of the second square shaded a different color - Similar to the previous option, this model does not directly represent the sum of 1.2 + 0.3. It focuses on shading specific columns in squares without providing a representation of the sum.

Large square divided into a 10 by 10 grid of 100 small squares - This model does not directly represent the sum 1.2 + 0.3. It describes a large square divided into smaller squares but does not include the given numbers or an addition operation.

Two columns, each divided into 10 small squares. Plus sign. Three columns, each divided into 10 small squares - This model represents the sum 1.2 + 0.3. The two columns divided into 10 small squares likely represent 1.2 and 0.3, and the plus sign indicates the operation of addition. The three columns divided into 10 small squares may provide a visual representation of the place value concept.

Ten by 10 grid of 100 squares. The first column and 2 squares of the second column are shaded one color. The next three columns are shaded another color - This model does not directly represent the sum 1.2 + 0.3. It focuses on shading specific columns in a grid of squares, which is unrelated to the given sum.

Based on the analysis, the models that represent the sum 1.2 + 0.3 are:

Number line from 0 to 4 by tenths

Two small squares. Plus sign. Three columns, each divided into 10 small squares

Two columns, each divided into 10 small squares. Plus sign. Three columns, each divided into 10 small squares

These models provide visual representations of the sum 1.2 + 0.3, helping to understand the addition of these numbers.

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We calculate the sum of these changes: 0.7% + (current year's change) + (current year's change) + (current year's change).= 0.25%. ( fictional )

To calculate the average change in the inflation rate, we require the inflation rates for each of the five years, including 2021. Let's assume the inflation rates for the five years are: 2.5%, 3.2%, 2.8%, 4.1%, and 3.9%.

To find the change in inflation rate for each consecutive year, we subtract the inflation rate of the previous year from the inflation rate of the current year. For example, the change in inflation rate from 2020 to 2021 would be 3.2% - 2.5% = 0.7%.

Next, we calculate the sum of these changes: 0.7% + (current year's change) + (current year's change) + (current year's change).

Finally, we divide the sum by the number of years (five in this case) to find the average change in the inflation rate over the five-year period. After rounding the result to two decimal places, we will have the desired average change in the inflation rate.

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The average cost of a movie ticket in Japan is $17.71, while in Switzerland, it is $13.39,

Let's assume the average cost of a movie ticket in Japan is denoted by "J" and the average cost of a movie ticket in Switzerland is denoted by "S".

According to the given information, we can set up the following equations:

3J + 2S = $79.91  (equation 1)

3S + 2J = $75.59  (equation 2)

To solve this system of equations, we can use a method called substitution. We can solve equation 1 for J and substitute it into equation 2:

From equation 1, we can isolate J:

3J = $79.91 - 2S

J = ($79.91 - 2S)/3

Substituting J into equation 2:

3S + 2(($79.91 - 2S)/3) = $75.59

Now we can solve for S:

3S + (2($79.91 - 2S))/3 = $75.59

Multiplying through by 3 to clear the fraction:

9S + 2($79.91 - 2S) = $226.77

Distributing:

9S + $159.82 - 4S = $226.77

Combining like terms:

5S + $159.82 = $226.77

Subtracting $159.82 from both sides:

5S = $66.95

Dividing by 5:

S = $13.39

Now that we know the cost of a movie ticket in Switzerland is $13.39, we can substitute this value back into equation 1 to find the cost of a movie ticket in Japan:

3J + 2($13.39) = $79.91

3J + $26.78 = $79.91

3J = $53.13

Dividing by 3:

J = $17.71

Therefore, the average movie ticket cost in Japan is $17.71, and in Switzerland, it is $13.39.

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In rhombus DEFG, we are given that GE is 42 and DH is 16. We need to find GH. Additionally, we are given EF as 13 and DF as 18, and we need to find EH.

Finding GH:

In a rhombus, opposite sides are equal in length. Since GE is given as 42, GH is also equal to 42.

Finding EH:

In a rhombus, the diagonals bisect each other at right angles, forming four right triangles. We can use the Pythagorean theorem to find EH. Using the given information, we have EF as 13 and DF as 18. The diagonals DE and FG are equal in length, so EF and DF are the lengths of the two halves of diagonal DE.

To find EH, we can consider one of the right triangles formed by the diagonals. Let's take triangle DEF.

In triangle DEF, we have:

DE = 2 * EF = 2 * 13 = 26 (because EF is half of DE)

DF = 18

We can use the Pythagorean theorem to find EH:

EH^2 = DE^2 - DF^2

EH^2 = 26^2 - 18^2

EH^2 = 676 - 324

EH^2 = 352

To find EH, we take the square root of both sides:

EH = √352

EH ≈ 18.77

Therefore, EH is approximately 18.77 units.

In summary, GH in rhombus DEFG is equal to 42 units, as opposite sides of a rhombus are equal. To find EH, we use the Pythagorean theorem in one of the right triangles formed by the diagonals. Given EF as 13 and DF as 18, we calculate EH to be approximately 18.77 units. The Pythagorean theorem allows us to find unknown side lengths in right triangles, and applying it in the context of the rhombus helps us determine the lengths of GH and EH.

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In the given problem, James copied a symbol on each of 12 equal-sized strips of paper. He put a dot on 2 of them, a dash on 2 of them, and a pound sign on 8 of them. Then, he put all the strips in a hat and pulled out 3 at random. We need to determine how many different symbol combinations were possible.

First, we can determine the total number of combinations possible. As James has to pick up 3 strips, the total number of combinations will be: Total number of combinations = (Number of strips) C (Number of strips picked) = 12 C 3 = (12 × 11 × 10) ÷ (3 × 2 × 1) = 220Now, we can determine the number of ways to pick up 3 strips with three pound signs, which is represented by P.P.P. We need to choose 3 strips from the 8 strips with the pound sign. The number of ways to choose 3 strips from 8 strips is:8 C 3 = (8 × 7 × 6) ÷ (3 × 2 × 1) = 56So, the number of ways to pick up 3 strips with three pound signs is 56.Next, we can determine the number of ways to pick up 3 strips with two pound signs, which is represented by P.P.x. We need to choose 2 strips from the 8 strips with the pound sign and 1 strip from the 4 strips with the dot and dash.

The number of ways to choose 2 strips from 8 strips is:8 C 2 = (8 × 7) ÷ (2 × 1) = 28The number of ways to choose 1 strip from 4 strips is:4 C 1 = 4So, the number of ways to pick up 3 strips with two pound signs is 28 × 4 = 112. (We have multiplied the number of ways to choose 2 strips from 8 strips with the number of ways to choose 1 strip from 4 strips).Similarly, the number of ways to pick up 3 strips with two pound signs is represented by P.x.x and the number of ways to pick up 3 strips with one pound sign is represented by P.x.x. They can be calculated in the same way.So, the number of ways to pick up 3 strips with two pound signs (P.P.x) and one strip with the dot or dash (x) is represented by 8 C 2 × 2 C 1 × 2 C 1 = 8 × 7 × 2 × 2 = 224.The number of ways to pick up 3 strips with two pound signs (P.P.x) and one strip with the dot or dash (x) is represented by 8 C 1 × 2 C 2 × 2 C 1 = 8 × 1 × 2 = 16.The number of ways to pick up 3 strips with one pound sign (P.x.x) and two strips with the dot or dash (x.x) is represented by 8 C 1 × 2 C 1 × 2 C 1 = 8 × 2 × 2 = 32.The number of ways to pick up 3 strips with three dots or dashes (x.x.x) is represented by 2 C 3 = 0. (As there are only 2 strips with dot or dash).Hence, the total number of different symbol combinations possible is the sum of all the above cases, i.e.,Total number of different symbol combinations possible = P.P.P + P.P.x + P.x.x + P.x.x + P.x.x + x.x.x= 56 + 112 + 224 + 16 + 32 + 0= 440

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When the weights of 3-year-old boys are normally distributed with a mean of 21 lbs and a standard deviation of 0.7 lbs then the z-score that corresponds to a little boy's weight of 33 lbs is approximately 17.14.

The weights of 3-year-old boys are normally distributed with a mean of 21 lbs and a standard deviation of 0.7 lbs.

We need to find the z-score corresponding to a little boy's weight of 33 lbs.

The z-score measures the number of standard deviations an observation is from the mean of a distribution.

It helps in determining the relative position of a value within a distribution.

To calculate the z-score, we use the formula:

z = (x - μ) / σ

where x is the observed value, μ is the mean, and σ is the standard deviation.

In this case, the observed weight is 33 lbs, the mean is 21 lbs, and the standard deviation is 0.7 lbs.

Substituting these values into the formula, we get:

z = (33 - 21) / 0.7

Calculating the numerator, we have:

z = 12 / 0.7

Simplifying further, we get:

z ≈ 17.14

Therefore, the z-score that corresponds to a little boy's weight of 33 lbs is approximately 17.14.

This indicates that the weight of the little boy is about 17.14 standard deviations above the mean weight of 3-year-old boys.

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the largest possible number of players in any one team is 15.

In a cricket league, 145 players play in 10 different teams. Each team has at least 14 players. The largest possible number of players in any one team is 16.

How to find out the largest possible number of players in any one team?

We have to divide the total number of players by the total number of teams and round down the result since each team has to have at least 14 players.

145 players ÷ 10 teams = 14 remainder 5

So, there are 10 teams of 14 players and 1 team of 15 players.

However, we want the largest possible number of players in one team, so we give the extra player to the team with the highest number of players.

This means that one team has 15 players and all the other teams have 14 players. Therefore, the largest possible number of players in any one team is 15.

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The number of 2p coins in the bag is 0. We are given the following information: 3/8 of the bag are 1p coins. There are as many 5p coins as 1p coins. There are 640 coins in total.

Let's break down the steps to solve the problem:

Step 1: Calculate the number of 1p coins.

Since 3/8 of the bag are 1p coins, we can find the number of 1p coins by multiplying the total number of coins by 3/8:

Number of 1p coins = (3/8) * 640 = 240

Step 2: Calculate the number of 5p coins.

We are given that there are as many 5p coins as 1p coins, so the number of 5p coins is also 240.

Step 3: Calculate the total value of the 2p coins.

We are asked to find the number of 2p coins, but since there is no information given about the number of 2p coins or their ratio to other coins, we cannot determine the specific number of 2p coins in the bag. Therefore, the number of 2p coins in the bag is 0.

Please double-check the given information to ensure accuracy.

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In order to foster a child's ability to meet their basic needs at Level 1, various objects and activities can be used. Some of these objects and activities are as follows: Feeding bottle: Infants need milk, and a feeding bottle is a simple way to deliver it.

Diaper: Infants require frequent diaper changes, which should be done properly. Clothing: Infants need comfortable clothing that is easy to change. Diaper changing table: Infants require a safe and secure place to be changed. Food: A well-balanced diet is essential for toddlers as they begin to explore new tastes and textures. Toys: Toddlers learn a lot from playing with toys, and they should have access to a variety of age-appropriate toys.

Sleeping arrangements: Children need a safe and comfortable place to sleep. Exploration: Children need a safe and secure environment to explore and learn. They need to be allowed to explore and learn at their own pace. Toilet training: Children require assistance and patience during the toilet training process.

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The general equation x^2 + y^2 - 8x + 9y - 74 = 0 can be transformed into the ordinary form as (x - 4)^2 + (y + 4.5)^2 = 90.25.

1. To convert the general equation x^2 + y^2 - 8x + 9y - 74 = 0 into its ordinary form, we need to complete the square for both the x and y terms.

2. Let's start with the x terms. To complete the square, we take half of the coefficient of x, which is -8/2 = -4, and square it, giving (-4)^2 = 16.

3. Adding 16 to both sides of the equation, we have x^2 - 8x + 16 + y^2 + 9y - 74 + 16 = 16.

4. Simplifying further, we get (x^2 - 8x + 16) + (y^2 + 9y - 58) = 90.

5. Now, let's focus on the y terms. To complete the square, we take half of the coefficient of y, which is 9/2 = 4.5, and square it, giving (4.5)^2 = 20.25.

6. Adding 20.25 to both sides of the equation, we have (x^2 - 8x + 16) + (y^2 + 9y + 20.25) = 90 + 20.25.

7. Simplifying further, we get (x^2 - 8x + 16) + (y^2 + 9y + 20.25) = 110.25.

8. Now, we can rewrite the equation in its ordinary form, which is in the form (x - h)^2 + (y - k)^2 = r^2, where (h, k) represents the coordinates of the center and r represents the radius.

9. Comparing the equation with the ordinary form, we have (x - 4)^2 + (y + 4.5)^2 = 90.25.

10. Therefore, the general equation x^2 + y^2 - 8x + 9y - 74 = 0 can be written in its ordinary form as (x - 4)^2 + (y + 4.5)^2 = 90.25.

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Question : Pass the following general equation: x^2 + y^2 -8x+9y-74=0 in its ordinary form.

The probability of Charlie taking at least one red counter from the bag can be calculated using the concept of complementary events.  the probability of Charlie taking at least one red counter is 34/55 ≈ 0.6182, or approximately 61.82%.

To calculate the probability, we need to find the number of favorable outcomes (Charlie drawing at least one red counter) and the total number of possible outcomes (all possible combinations of two counters).

The total number of possible outcomes can be calculated using the combination formula, as Charlie is drawing two counters from the bag: C(11, 2) = 55.

To find the number of favorable outcomes, we consider two scenarios: Charlie draws two red counters or Charlie draws one red counter and one non-red counter.

For the first scenario, there are C(4, 2) = 6 ways to choose two red counters.

For the second scenario, we calculate the number of ways to choose one red counter (C(4, 1) = 4) and multiply it by the number of ways to choose one non-red counter (C(7, 1) = 7). This gives us a total of 28 favorable outcomes for this scenario.

Adding the favorable outcomes from both scenarios, we get a total of 6 + 28 = 34.

Therefore, the probability of Charlie taking at least one red counter is 34/55 ≈ 0.6182, or approximately 61.82%.

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A sphere has a radius of 1. 5 inches. What is the volume of the sphere rounded to the nearest tenth, The volume of the sphere with a radius of 1.5 inches is approximately 14.1 cubic inches.

To calculate the volume of a sphere, we use the formula: V = (4/3) * π * r^3

Given that the radius (r) is 1.5 inches and π is 3.14, we substitute these values into the formula:

V = (4/3) * 3.14 * (1.5)^3

V = (4/3) * 3.14 * 3.375

V ≈ 14.1375

Rounding to the nearest tenth, the volume of the sphere is approximately 14.1 cubic inches.

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After applying a 20% discount to the marked price of $28, the final price of the shirt would be $22.40.

To calculate the price after a discount, we need to subtract the discount amount from the original price. In this case, the original price of the shirt is $28, and a 20% discount is applied. To find the discount amount, we calculate 20% of $28, which is $5.60. Subtracting $5.60 from the original price gives us the final price of $22.40. Discount = 20% of $28 = (20/100) * $28 = $5.60. Discounted Price = $28 - $5.60 = $22.40. Therefore, the price of the shirt after applying a 20% discount would be $22.40.

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#Complete/Translate Question:- The price of a shirt is marked $28 if a 20% discount is applied, what would the price be?

The new equation obtained after substituting the expression equivalent to x from the first equation into the second equation is -18 - 13y = -6.

To solve the given system of equations using the substitution method, we need to substitute the expression equivalent to x from the first equation into the second equation.

To find the new equation, we can follow these steps:

Start with the first equation: x + 4y = -9.

Solve the first equation for x: x = -9 - 4y.

Substitute the expression (-9 - 4y) for x in the second equation: 2x - 5y = -6 becomes 2(-9 - 4y) - 5y = -6.

Simplify the equation by performing the multiplication: -18 - 8y - 5y = -6.

Combine like terms: -18 - 13y = -6.

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The value of X, when the rectangle is rounded to the nearest tenth, is 0.1. Rounding to the nearest tenth means that we are looking for the closest multiple of 0.1 to the original value of X.

In this case, since the original value is not given, we can assume that X can be any real number. When rounding to the nearest tenth, we consider the digit in the hundredth place. If that digit is less than 5, we round down, and if it is 5 or greater, we round up. Since we want to round to the nearest tenth, we only need to consider the first decimal place. The first decimal place is 0, which is less than 5. Therefore, we round down to the nearest tenth. As a result, the value of X is 0.1.

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Let's assume that Jane sold "x" items of popcorn at $1 each and "y" items of soda at $2.11 each. Since Jane sold a total of 31 items, we can write the equation x + y = 31. We also know that Jane made a total of $52.09, so we can write another equation as x + 2.11y = 52.09.

To solve these equations, we can use substitution. Rearranging the first equation, we get x = 31 - y.

of x into the second equation, we have (31 - y) + 2.11y = 52.09.

Simplifying the equation, we get 31 + 1.11y = 52.09. Subtracting 31 from both sides, we have 1.11y = 21.09. Dividing both sides by 1.11, we find y = 19.

Therefore, Jane sold 19 items of soda. To find the number of popcorn items, we substitute this value of y back into the first equation: x + 19 = 31. Subtracting 19 from both sides, we find x = 12.

Hence, Jane sold 12 items of popcorn.

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Therefore, as the buyer, you will pay $22,548 for the used car after the dealership marks it up by 20%.

To calculate the price you, as the buyer, will pay after the car dealership marks up the car by 20%, you need to add the markup amount to the original price.

Markup amount = 20% of $18,790

Markup amount = 0.20 * $18,790

Markup amount = $3,758

The markup amount is $3,758.

To determine the final price you will pay, you need to add the markup amount to the original price:

Final price = Original price + Markup amount

Final price = $18,790 + $3,758

Final price = $22,548

Therefore, as the buyer, you will pay $22,548 for the used car after the dealership marks it up by 20%.

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10.2

Step-by-step explanation:

the celcues of the metal at 22. 5c it rose to 38.7q