The button on Ted's jacket has a diameter of 10 millimetres. What is the button's radius?

The  explicit formula for nth term geometric sequence is aₙ = a x rⁿ⁻¹.

let a geometric series is of the form

a, a², a³, a⁴ a⁵, ....

where a₁ = a = first term and other terms are obtained by multiplying by

r.

Now, each term is r times of previous term.

So, to get the nth term we have to multiply (n-1) by r.

Thus, the explicit formula for nth term geometric sequence is

aₙ = a x rⁿ⁻¹

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Answer: The formula for the volume of a cone is V=1/3hπr²

Step-by-step explanation: The volume or capacity of a cone is one-third of its corresponding cylinder. This means that when a cone and a cylinder have the same base dimension and height, the volume of the cone is one-third of the volume of the cylinder.

Answer: To calculate the mean square treatment (MST), we need to have the sums of squares for treatment (SST) and the degrees of freedom for treatment (dfT).

Assuming that there are k treatment groups and a total of n observations, we can calculate SST and dfT as follows:

SST = Σ(xi - x_bar)^2 - Σ(yi - y_bar)^2 / n

where xi is the dried weight of plants for the i-th treatment group, x_bar is the mean dried weight of plants for all treatments combined, yi is the dried weight of plants for the control group, and y_bar is the mean dried weight of plants for the control group.

dfT = k - 1

Once we have calculated SST and dfT, we can find MST by dividing SST by dfT:

MST = SST / dfT

Note that SST is the sum of squares for treatment, which represents the variation in the response variable that is due to the different treatment conditions. MST represents the average amount of variation in the response variable that can be attributed to the treatment conditions.

Without knowing the specific values for the dried weight of plants, it is not possible to calculate SST and dfT, and therefore the MST.

Step-by-step explanation:

Answer: 3.45meters

Step-by-step explanation:

To find the range of the length of pipe that the plumber can cut, we need to write an absolute value inequality that expresses the condition that the length of the pipe must be within 0.09 meters of the required length. Let's call the required length L.

The plumber can cut a pipe that is within 0.09 meters of the required length, so the length of the pipe must be between L - 0.09 and L + 0.09. We can express this as:

|3.36 - L| ≤ 0.09

To solve this inequality, we need to consider two cases: when 3.36 - L is positive and when it is negative.

Case 1: 3.36 - L ≥ 0

In this case, the absolute value of 3.36 - L is equal to 3.36 - L. So we can write:

3.36 - L ≤ 0.09

Solving for L, we get:

L ≥ 3.36 - 0.09

L ≥ 3.27

Therefore, if 3.36 - L is positive, the length of the pipe must be greater than or equal to 3.27 meters.

Case 2: 3.36 - L < 0

In this case, the absolute value of 3.36 - L is equal to -(3.36 - L), or L - 3.36. So we can write:

L - 3.36 ≤ 0.09

Solving for L, we get:

L ≤ 3.36 + 0.09

L ≤ 3.45

Therefore, if 3.36 - L is negative, the length of the pipe must be less than or equal to 3.45 meters.

Putting these two cases together, we get:

3.27 ≤ L ≤ 3.45

Therefore, the range of the length of pipe that the plumber can cut is between 3.27 meters and 3.45 meters.

The simplified rational expression for this problem is given as follows:

[tex]\frac{3\sqrt{21} + 13}{12}[/tex]

The rational expression in the context of this problem is defined as follows:

[tex]\frac{\sqrt{7} + \sqrt{3}}{2\sqrt{3} - \sqrt{7}}[/tex]

The first step in simplifying the expression is removing the root from the denominator, multiplying numerator and denominator by the conjugate, as follows:

[tex]\frac{\sqrt{7} + \sqrt{3}}{2\sqrt{3} - \sqrt{7}} \times \frac{2\sqrt{3} + \sqrt{7}}{2\sqrt{3} + \sqrt{7}}[/tex]

Applying the subtraction of perfect squares, the denominator is given as follows:

2² x 3 - 7 = 12.

The numerator is:

[tex](\sqrt{7} + \sqrt{3})(2\sqrt{3} + \sqrt{7}) = 2\sqrt{21} + 7 + 6 + \sqrt{21} = 3\sqrt{21} + 13[/tex]

Thus the simplified expression is:

[tex]\frac{3\sqrt{21} + 13}{12}[/tex]

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It would take Rafael approximately 9.05 hours to run a 50-mile marathon in Washington D.C. at the same pace he ran the Boston Marathon.

What is distance?

Distance is the measure of how far apart two objects or locations are from each other. It is usually measured in units such as meters, kilometers, miles, or feet.

To solve this problem, we can use the concept of the average speed or pace, which is given by the formula:

pace = time / distance

where pace is the time it takes to cover one unit of distance (e.g., one mile), time is the time taken to cover the distance, and distance is the distance covered.

We can rearrange this formula to find the time it would take to cover a given distance at a given pace:

time = pace * distance

Using this formula, we can find the pace at which Rafael ran the Boston Marathon:

pace = time / distance

pace = 4.75 hours / 26.2 miles

pace = 0.181 hours/mile

Now we can use this pace to find the time it would take Rafael to run a 50-mile marathon:

time = pace * distance

time = 0.181 hours/mile * 50 miles

time = 9.05 hours

Therefore, it would take Rafael approximately 9.05 hours to run a 50-mile marathon in Washington D.C. at the same pace he ran the Boston Marathon.

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An association class is frequently required for a many-to-many relationship.

In object-oriented programming, an association class is a class that is used to represent an association between two or more other classes. An association class is typically used when the relationship between the other classes is many-to-many, which means that each instance of one class can be associated with multiple instances of another class, and vice versa.

For example, consider a database that stores information about students and the courses they are enrolled in. Each student can be enrolled in multiple courses, and each course can have multiple students.

To represent this many-to-many relationship between students and courses, we can create an association class called "Enrollment" that has attributes such as the date of enrollment and the grade received. The Enrollment class would have a many-to-one relationship with both the Student class and the Course class.

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An association class is frequently required for a "c. many to many" relationship. therefore, option c. many to many is correct.

In this type of relationship, multiple instances of one class can be associated with multiple instances of another class.

The association class helps to capture additional information about the relationship between these instances.

An association class is most commonly required for a many-to-many relationship between two classes.

a relationship that explains the causes of the relationship and the rules that control it between two classifiers, such as

classes or use cases.

An association class is frequently required for a "c. many to many" relationship. therefore, option c. many to many is correct.

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Using the laws of outside angle, we can find the value of the angle x° to be = 77°.

The measure of an exterior angle is equal to the sum of the measures of the two distant interior angles of the triangle, according to the external angle theorem. According to the exterior angle inequality theorem, any triangle's outside angle has a measure bigger than either of its opposing interior angles.

Here in the question,

The measure of the 2 arcs is given as 85° and 172°.

The measure of the 3rd arc that is subtended by the tangents is:

360° - 85° - 172°

= 103°

As per the outside angle theorem,

x° = 180° - 103°

= 77°

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The total amount of water Keisha drinks in 12 days is 12 + 18 = 30 quarts.

Algebra is a branch of mathematics that involves using letters and symbols to represent numbers and quantities in mathematical equations and formulas. It includes a variety of topics, such as solving equations, manipulating expressions, working with functions and graphs, and studying abstract structures such as groups and rings.

At its core, algebra is about understanding the relationships between numbers and how they can be manipulated using various operations such as addition, subtraction, multiplication, and division. Algebraic expressions can be used to model real-world situations and solve problems in fields such as physics, engineering, and finance.

To find the total amount of water Keisha drinks in 12 days, we need to add up the amounts of water she drinks each day:

1 1/2 + 2 1/4 + 2 + 1 1/2 + 1 3/4 + 1 1/2 + 1 1/4 + 2 + 2 1/4 + 1 1/2 + 2 + 1 1/2

We can simplify the mixed numbers by converting them to improper fractions:

3/2 + 9/4 + 2 + 3/2 + 7/4 + 3/2 + 5/4 + 2 + 9/4 + 3/2 + 2 + 3/2

Then we can add the fractions together:

(3/2 + 3/2 + 3/2 + 2 + 2 + 2) + (9/4 + 7/4 + 5/4 + 9/4 + 3/2 + 3/2)

Simplifying the sum of the whole numbers, we get:

12

Simplifying the sum of the fractions, we get:

(18/4 + 14/4 + 10/4 + 18/4 + 6/4 + 6/4) = 72/4 = 18

So the total amount of water Keisha drinks in 12 days is:

12 + 18 = 30 quarts.

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The complete  question is:

For 12 days, Keisha keeps track of how much water she drinks per day. 1 1/2 quarts, 2 1/4 quarts, 2 quarts, 1 1/2 quarts, 1 3/4 quarts, 1 1/2 quarts, 1 1/4 quarts, 2 quarts, 2 1/4 quarts, 1 1/2 quarts, 2 quarts, 1 1/2 quarts. What is the total amount of water that Keisha drinks the 12 days?

Answer: for future k-12 kids :)

Step-by-step explanation:

Answer:

  (a)  x² +y² -2x -6y -26 = 0

Step-by-step explanation:

You want the equation for the circle with center (1, 3) and radius 6 written in general form.

The standard form equation for a circle with center (h, k) and radius r is ...

  (x -h)² +(y -k)² = r²

The radius and center are found from the graph, attached. For the circle centered at (h, k) = (1, 3) and radius r = 6, this is ...

  (x -1)² +(y -3)² = 6²

Expanding this equation gives ...

  x² -2x +1 +y² -6y +9 = 36

Written in general form, the equation becomes ...

  x² +y² -2x -6y -26 = 0 . . . . matches choice A

__

Additional comment

There is an image of this question showing the correct answer choice is the third one. However, that answer choice shows up first on this instance of the question. You will need to read and compare answer content to make sure you have the correct choice. You cannot go by the order of the the answers.

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In circle L in which secant lines TQ and SQ intersect at point Q outside the circle value of x = 54°, m ST = 143°, m PR = 79°

∠PQR = 1/2( ST - PR)

∠PQR = 32°

m ST = (3x - 19)°

m PR = (x + 25)°

Putting the value in the equation we get

32 = 1/2( 3x - 19 - (x + 25) )

32 × 2 = 3x -19 -x -25

64 = 2x - 44

64 + 44 = 2x

108 = 2x

x = 54°

m ST = (3x - 19)°

m ST = 3(54) -19

m ST = 162 - 19

m ST = 143°

m PR = (x + 25)°

m PR = 54 + 25

m PR = 79°

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Using Pythagoras Theorem, we have the solutions as:

3) Length of AB = 32 in

4) x = 24

5) Perimeter of PRQ = 35

Pythagoras Theorem is the way in which you can find the missing length of a right angled triangle.

3) Using Pythagoras theorem, we can say that:

Radius = √(16² - 5²)

Radius = √231

Radius = 15.2

Thus, AB will be twice the measurement of 16 as the perpendicular distance to bth chords are the same. Thus:

AB = 16 * 2 = 32 in

4) Using Pythagoras theorem,

x = √((18 + 7)² - 7²)

x = √(625 - 49)

x = 24

5) Using Pythagoras theorem, we can say that:

PC = 8.66

RC = √((14² - 8.66²)

RC = 11

Thus:

Perimeter of PRQ = 14 + 10 + 11 = 35

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The population from which the manager should choose a sample to answer her question is: B. The list of customers who purchased plants from the nursery.

A population is a term that goes by the definition of it being the entire group that we specifically intend to get conclusions about. Meanwhile, we ca sample is defined as the specific group that you will collect data from. The size of the given sample is normally always less than  that of the total size of the given population. In research, it is noticed that a population doesn't always mean we are referring to people.

Now, we are told that the manager wants to know which types of plants his customers buy most often.

Looking at the options, the most appropriate population from which a sample could be gotten from is the list of customers who purchased plants from the nursery.

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The percent of change in the price of the book is 50%.

To calculate the percent of change, we first need to find the difference between the original price and the new price. In this case, the original price of the book was $10, and the new price is $5. To find the difference, we can subtract the new price from the original price, which is:

$10 - $5 = $5

Now, we need to express this difference as a percentage of the original price. To do this, we divide the difference by the original price and then multiply by 100. In other words, we need to find the percentage that the original price has changed by. This can be represented mathematically as:

Percent of change = (Difference / Original price) x 100

Plugging in the values we found earlier, we get:

Percent of change = ($5 / $10) x 100

Percent of change = 0.5 x 100

Percent of change = 50%

This means that the price of the book has decreased by 50% from the original price of $10 to the sale price of $5.

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The side of the house which the ladder will reach now is equal to 14.2 feet.

In Mathematics and Geometry, Pythagorean's theorem is represented or modeled by the following mathematical equation:

x² + y² = z²

Where:

x, y, and z represents the length of sides or side lengths of any right-angled triangle.

In order to determine how far up the side of the house will the ladder reach, we would have to apply Pythagorean's theorem as follows;

21² + y² = 35²

y² = 1,225 - 441

y² = 784

y = √784

y = 28 feet.

Since Elijah grabs the ladder at its base and pulls it 4 feet farther from the house, we have:

New Length = 28 + 4 = 32 feet.

Therefore, the required length is given by;

Distance = √(35² - 32²)

Distance = 14.2 feet.

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Sev needs to run 9 miles as per the below calculations to complete his target.

The target that Sev needs to achieve is 18 miles in a week. A week has 7 days. Sev is already done running for 5 days.
Day 1: 1.4 miles

Day 2: 1.4 miles

Day 3: 1.4 miles

Day 4: 2.4 miles

Day 5: 2.4 miles

Thus, Sev has run for 1.4*3 = 4.2 miles in the first 3 days.

Sev has run for 2.4*2 = 4.8 miles in the last 2 days.

So far, she has run 4.2 + 4.8 = 9 miles. Since her goal is to run 18 miles, she needs to run an additional: 18 - 9 = 9 miles to meet her goal.

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Answer:

The top right graph shows the solution to this system of linear equations.

The probability of winning something from the Pepsi sales promotion with winning symbols under the caps of 10% of all Pepsi bottles in a six-pack is 46.9%.

The probability of winning something from the Pepsi sales promotion depends on the total number of bottles in the six-pack and the percentage of bottles with winning symbols under the caps.

Assuming that the six-pack contains six bottles, and 10% of all Pepsi bottles have winning symbols under the cap, the probability of winning something from the promotion can be calculated using the following formula:

Probability of winning = Number of bottles with winning symbols / Total number of bottles

Since 10% of all Pepsi bottles have winning symbols, the probability of finding a winning symbol under one bottle cap is 10%. Therefore, the probability of winning from a six-pack is the same as finding at least one winning bottle cap in six bottles.

To calculate the probability of winning, we can use the complement rule, which states that the probability of an event occurring is equal to one minus the probability of the event not occurring.

So, the probability of not winning from a single bottle is 1 - 0.1 = 0.9. The probability of not winning from all six bottles is 0.9^6 = 0.531. Therefore, the probability of winning something from a six-pack is 1 - 0.531 = 0.469 or 46.9%.

In conclusion, the probability of winning something from the Pepsi sales promotion with winning symbols under the caps of 10% of all Pepsi bottles in a six-pack is 46.9%. This means that nearly half of the customers who buy a six-pack are likely to win something from the promotion.

However, it is important to note that this probability may vary depending on the total number of bottles and the percentage of winning symbols used in the promotion.

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When we factor the expression, we are going to obtain the result;

9a(9a + 4) + 4

Factoring an expression involves breaking it down into simpler parts that can be multiplied together to obtain the original expression. The specific method used to factor an expression depends on the type of expression.

It's important to note that factoring can sometimes be a challenging process, and not all expressions can be factored using real numbers.

We can carry out this factorization by the use of the nesting method, Hence;

81a^2 + 36a + 4

(81a^2 + 36a ) + 4

9a(9a + 4) + 4

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The solutions to the equation are z = 1 and z = 1/3. We can mark these solutions on a number line is {1/3, 1}.

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. It involves the study of variables, expressions, equations, and functions.

We can solve this equation by considering two cases:

Case 1: 3z-2 = 1

Solving for z, we get:

3z-2 = 1

3z = 3

z = 1

Case 2: 3z-2 = -1

Solving for z, we get:

3z-2 = -1

3z = 1

z = 1/3

Therefore, the solutions to the equation are z = 1 and z = 1/3. We can mark these solutions on a number line as follows:

The solution set is {1/3, 1}.

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The value of x, obtained using the property of bisected angles is 10

Bisected angles are angles that are split by a line segment in two to create two angles of the same measure.

The specified information indicates;

[tex]\overrightarrow{GI}[/tex] bisects ∠DGH

m∠DGI = x - 3

m∠IGH = 2·x - 13

The angle addition postulate indicates that we get;

m∠DGH = m∠DGI + m∠IGH

The definition of the bisected angle ∠DGH indicates that we get;

∠DGI = ∠IGH

Therefore;

x - 3 = 2·x - 13

2·x - 13 = x - 3

2·x - x = 13 - 3 = 10

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The height of the center of the Ferris wheel 51 m.

The height of capsule M is 51 m and the height of capsule T is 102 m.

Using this information, we can calculate the height of the center of the Ferris wheel, the height of capsule M, and the height of capsule T.

Height of the center of the Ferris wheel:

The center of the Ferris wheel is the midpoint of its diameter. Therefore, the height of the center of the Ferris wheel is half of the height of the top of the wheel above the ground.

Height of center of Ferris wheel = 102 meters / 2 = 51 meters.

Height of capsule M:

Since capsule M is at the same height as the center of the Ferris wheel, the height of capsule M is also 51 meters.

Height of capsule T:

Since capsule T is at the very top of the Ferris wheel, its height above the ground is equal to the height of the top of the Ferris wheel above the ground.

Height of capsule T = 102 meters.

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4 is the correct value from the set {1, 2, 3, 4} which is the solution to the equation 3x + 3 = 15.

A solution of an equation refers to a value or values that satisfy the given equation. It is the value or values that make the equation true when substituted for the variable(s) in the equation. Equations are mathematical expressions that contain an equals sign and can have one or more variables. A solution is typically represented as a number, but it can also be a set of numbers, a range of values, or an expression. Finding the solutions of an equation is an important part of solving mathematical problems and has many practical applications in fields such as engineering, physics, and finance.

Solution of the given equation 3x + 3 = 15 means when we put a value in x we should get the result as 15, that is left hand side of the equation should be equal to the right hand side of the equation.

Solving the equation we get,

3x + 3 - 3 = 15 - 3

3x = 12

x = 4

Therefore, the value 4 is a solution to the equation.

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Answer:

Step-by-step explanation:

see it simple it's not asking quite much if I do my calculation right it would be 8[tex]\pi[/tex]

The scale factor used to create the image include the following: C. 2.

In Mathematics and Geometry, a scale factor can be calculated or determined through the division of the dimension of the image (new figure) by the dimension of the original figure (pre-image).

Mathematically, the formula for calculating the scale factor of any geometric object or figure is given by:

Scale factor = side length of image/side length of pre-image

By substituting the given side lengths or dimensions into the formula for scale factor, we have the following;

Scale factor = 2/1

Scale factor = 2.

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The calculated value of each boy's share is shown below

Let's call the amount of oranges the third boy gets "x".

According to the problem, the second boy gets twice the amount of oranges as the third boy, so he gets 2x oranges.

And the first boy gets twice more oranges than the second boy, so he gets 2(2x) = 4x oranges.

So the total number of oranges is x + 2x + 4x = 7x, and we need to divide this equally among the three boys.

Therefore, the first boy gets 4/7 of the total oranges, which is 4x/3, the second boy gets 2/7 of the total oranges, which is 2x/3 and the third boy gets 1/7 of the total oranges, which is x/3.

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Y = 3(-3) + 4 = -5 when x is equal to 3. Hence, the final set of negative x- and y-coordinates is (-3, -5).

A set of numbers known as coordinates describes a point or object's location in a given space or coordinate system. When representing a spot's location in a plane or three-dimensional space, coordinates are frequently expressed as x or triples in mathematics. Depending also on system being utilised, several values can be used to represent coordinates, although often, integers or real numbers are used to express them.

given

We can substitute negative values for x and solve for y to obtain three pairs of negative x and y coordinates that lie on the line y = 3x + 4.

With x = 1, y = 3(-1), plus 4, equals 1. Hence, one set of negative x and y coordinates is (-1, 1).

Y = 3(-2) + 4 = -2 when x is equal to 2. In light of this, another set of negative x- and y-coordinates is (-2, -2).

Y = 3(-3) + 4 = -5 when x is equal to 3. Hence, the final set of negative x- and y-coordinates is (-3, -5).

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