a rectangle is drawn around a sector of a circle as shown. if the angle of the sector is 1 radian and the area of the sector is , find the dimensions of the rectangle, giving your answers to the nearest millimetre

The simplified polynomial, with each term written in standard form, is: 36a^3b - 6a^2b^3 + 11a^2b

To simplify the given polynomial, we need to expand and combine like terms.

First, we can distribute the coefficients of the first term:

12a^2 · 3ba = 36a^3b

Next, we can simplify the second term by multiplying the coefficients and adding the exponents:

-2ab · 3ab^2 = -6a^2b^3

Finally, we can combine the like terms:

36a^3b - 6a^2b^3 + 11a^2b

To write each term in standard form, we arrange the terms in decreasing order of exponents of 'a' and 'b':

36a^3b - 6a^2b^3 + 11a^2b

So, the simplified polynomial, with each term written in standard form, is:

36a^3b - 6a^2b^3 + 11a^2b

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Answer:

Show that, the sum of an infinite arithmetic progressive sequence with a positive common difference

is +∞

Step-by-step explanation:

To show that the sum of an infinite arithmetic progressive sequence with a positive common difference is +∞, we can use the formula for the sum of the first n terms of an arithmetic sequence:

Sn = n/2 [2a + (n-1)d]

where a is the first term, d is the common difference, and n is the number of terms in the sequence.

Now, if we let n approach infinity, the sum of the first n terms of the sequence will also approach infinity. This can be seen by looking at the term (n-1)d in the formula, which grows without bound as n becomes larger and larger.

In other words, as we add more and more terms to the sequence, each term gets larger by a fixed amount (the common difference d), and so the sum of the sequence increases without bound. Therefore, the sum of an infinite arithmetic progressive sequence with a positive common difference is +∞.

Answer:

yes it is right now you can write it

If a customer purchases 3 of the products, the probability of getting at least one that is defective is 38.59%.

In order to determine the probability of getting at least one defective product if a customer purchases three products with a defective rate of 7.5%, we can use the concept of complementary probability.

The probability of getting at least one defective product can be calculated as the complement of the probability of getting none defective products.

So, the probability of getting no defective products is:

P(none defective) = (1 - 0.075)³ = 0.6141

Therefore, the probability of getting at least one defective product is:

P(at least one defective) = 1 - P(none defective) = 1 - 0.6141 = 0.3859 or 38.59%

.So, the probability of getting at least one that is defective is 38.59%.

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Answer:

To indicate that we want both the positive and the negative square root of a radicand

Answer:

Because a negative number times a negative number has a positive answer

Step-by-step explanation:

The inequalities which the number lines represent are as follows;

x > 3

x <= 2.

A mathematical comparison and expression of the relationship between two expressions is known as an inequality.

It can be seen as a generalization of an equation and is denoted by a symbol like ">", "", "", or "".

In contrast to an equation, which only has one solution, an inequality may have several answers or none at all.

The values that give rise to an inequity are its remedies.

The range of potential values for a variable is one example of how inequality models limits or limitations in the real world.

They can also be used to describe how two variables relate to one another, such as when one is more than or less than the other.

According to our question-

the inequality is; x <= 2

the inequality is; x > 3

x > 3

x <= 2

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The equation of line B is y = (1/5)x + 0, which can be simplified to y = (1/5)x.

An equation is a statement that shows the equality between two expressions. It typically contains one or more variables and may involve mathematical operations such as addition, subtraction, multiplication, division, exponentiation, or roots. An equation can be solved by finding the value(s) of the variable(s) that make the equation true. Equations are used extensively in mathematics, science, engineering, and other fields to describe relationships between different quantities and to make predictions or solve problems.

Here,

Since line B is perpendicular to line A, the product of their gradients is -1. Therefore, the gradient of line B is 1/5.

a) To find the y-intercept of line B, we need to know a point on the line. Since we don't have one, we can use the fact that the y-intercept is the point where the line intersects the y-axis. To find this point, we can set x = 0 in the equation of line B:

y = (1/5)x + c

0 = (1/5)(0) + c

c = 0

Therefore, the y-intercept of line B is (0,0).

b) The equation of line B is y = (1/5)x + 0, which can be simplified to y = (1/5)x.

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The calculated value of x in the similar triangles is 14 and it is calculated from the ratio 10 : x = 20 : 28

Given the triangle

The triangle is a superset of similar triangles

So, we have the following equivalent ratio that can be used to determine teh value of x

The set up of teh ratio is

10 : x = 10 + 10 : 28

Evaluating the like terms, we get

10 : x = 20 : 28

So, we have

x/10 = 28/20

Multiply both sides by 10

x = 14

Hence, the value of x is 14

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Answer:

I hope this helps please rate my answer

Step-by-step explanation:

2/5×60

2×12=24

Therefore, 15% of the beads on Tiana's necklace are blue.

Percentage is a way of expressing a fraction or a proportion out of 100. It is denoted by the symbol "%". For example, if we say that 50% of the students in a class are girls, it means that 50 out of every 100 students are girls.

Percentage can be calculated by dividing the given quantity by the total and multiplying by 100. For example, if there are 20 girls out of a total of 40 students in a class, the percentage of girls in the class can be calculated as follows:

Percentage of girls = (number of girls / total number of students) x 100%

= (20 / 40) x 100%

= 50%

by the question.

Tiana's necklace has a total of 3 + 17 = 20 beads.

To find the percentage of blue beads, we need to divide the number of blue beads by the total number of beads and then multiply by 100 to get the percentage:

percentage of blue beads = (number of blue beads / total number of beads) x 100

percentage of blue beads = (3 / 20) x 100

percentage of blue beads = 15

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Step-by-step explanation:

a) Area=144m²

side²= 144

side=12m

b) perimeter=32m

4×side=32

side=32/4

side=8m

The following equation can be used to represent the sentence:

7 + (x/4) = 5 where x stands for a number.

A straight line on a graph is represented by a linear equation. It has a constant slope and y-intercept, one or more variables, typically expressed by x and y. Several different real-world situations can be represented by linear equations, such as estimating the cost of goods based on the quantity purchased or calculating a car's distance traveled based on speed and time. Finding the value of the variable that causes the equation to be true is the first step in solving a linear equation. In mathematics, science, engineering, and economics, linear equations are frequently employed.

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The length of a side of the square is 8 cm.

What do you mean by perimeter of a rectangle and square?

When a wire is bent into the shape of a rectangle, its length becomes the perimeter of the rectangle. Similarly, when the wire is reshaped into a square, its length becomes the perimeter of the square.

The perimeter of a rectangle is given by the formula [tex]P=2(l+w)[/tex] , where [tex]l[/tex] is the length and [tex]w[/tex] is the width.

The perimeter of a square is given by the formula [tex]P=4s[/tex] , where [tex]s[/tex] is the length of a side.

Calculating the length of a side of the square:

The length of the rectangle is 11 cm and the width is 5 cm.

Therefore, the perimeter of the rectangle is [tex]P=2(11+5)=32[/tex] cm.

Since the wire is reshaped into a square, the perimeter of the square is also 32 cm.

Using the formula [tex]P=4s[/tex], we can solve for the length of a side of the square:

[tex]32 = 4s[/tex]

[tex]s = 32/4[/tex]

[tex]s = 8[/tex]

Therefore, the length of a side of the square is 8 cm.

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For equation a, x = 3

For equation b, x = -11/4.

For equation c, x = 1.

For equation d, x = -7/3.

For equation e, x = 9.

For equation f, x = 1/2.

To solve this equation, we need to isolate the variable x on one side of the equation.

7x - 6 = 6x + 3

Subtracting 6x from both sides:

x - 6 = 3

Adding 6 to both sides:

x = 9

Therefore, the solution to the equation is x = 9.

In the other equations:

a) 4x + 7 = 2x + 13

Subtracting 2x from both sides:

2x + 7 = 13

Subtracting 7 from both sides:

2x = 6

Dividing by 2:

x = 3

Therefore, the solution to the equation is x = 3.

b) x - 2 = 10 + 5x

Subtracting x from both sides:

-2 = 9 + 4x

Subtracting 9 from both sides:

-11 = 4x

Dividing by 4:

x = -11/4

Therefore, the solution to the equation is x = -11/4.

c) -3x - 8 = -7x - 4

Adding 7x to both sides:

4x - 8 = -4

Adding 8 to both sides:

4x = 4

Dividing by 4:

x = 1

Therefore, the solution to the equation is x = 1.

d) 2t + 5 = 5t + 12

Subtracting 2t from both sides:

5 = 3t + 12

Subtracting 12 from both sides:

-7 = 3t

Dividing by 3:

t = -7/3

Therefore, the solution to the equation is t = -7/3.

f) 15x = 7x + 4

Subtracting 7x from both sides:

8x = 4

Dividing by 8:

x = 1/2

Therefore, the solution to the equation is x = 1/2.

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Complete Question:

Find X for each equation.

A) 4 x + 7 = 2 x + 13 ;

b) x – 2 = 10 + 5 x ;

c) – 3 x – 8 = – 7 x – 4 ;

d) 2 t + 5 = 5 t + 12 ;

e) 7 x – 6 = 6 x + 3

f) 15 x = 7 x + 4

Answer:

58 degrees

Step-by-step explanation:

51+27=58 degrees

second one is 56 degrees

132-76=56 degrees

The possible widths for the rectangular mural are between 10 and 15 feet. We can also list the number of possible widths within this range, which is six. They are 10 feet, 11 feet, 12 feet, 13 feet, 14 feet, and 15 feet.

To determine the possible widths for the rectangular mural with an area of 60 square feet, we can use the formula for the area of a rectangle, which is length multiplied by width. Since the area is given as 60 square feet and the length should be between 4 and 6 feet, we can set up inequality as follows:

4w ≤ 60 ≤ 6w

where w is the width of the mural in feet. Solving this inequality for w, we get:

10 ≤ w ≤ 15

It is important to consider the dimensions carefully to ensure that the mural meets the requirements and fits in the desired space. By having multiple possible widths, the class can select the most suitable one based on the available resources and space.

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Complete question:

Our class is planning to paint a rectangular mural with an area of 60 square feet, it should be at least 4 feet high but not more than 6 feet in length and width, and list a number of possible widths for our class. Planning to paint a rectangular mural with an area of 60 square feet, it should be at least 4 feet high but not more than 6 feet in length and width, and list the number of possible widths for it.

The smallest positive integer n so that,

$$\renewcommand{\arraystretch}{1.5} \begin{pmatrix} -\frac{\sqrt{2}}{2} \frac{1}{n} \\ \frac{\sqrt{2}}{2} \frac{1}{n} \end{pmatrix}$$is a column matrix that contains integers,

we can write it as follows. $$\begin{pmatrix} -\frac{\sqrt{2}}{2} \frac{1}{n} \\ \frac{\sqrt{2}}{2} \frac{1}{n} \end{pmatrix} = \begin{pmatrix} -\frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{2}} \end{pmatrix} \frac{1}{n}.$$Since n has to be an integer, we have to find the smallest positive integer n for which the right-hand side is a column matrix containing integers. Since the left-hand side has a factor of 1/n, we can see that the smallest value of n must be a divisor of the denominator of the left-hand side. The denominator of the left-hand side is $\sqrt{2}/2$. If we multiply this by 100, we get 70.710678.

Therefore, the smallest positive integer n that satisfies the equation is the smallest divisor of 70.710678. This is 2, and it gives us the column matrix $$\begin{pmatrix} -\frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{2}} \end{pmatrix}.$$Therefore, the smallest positive integer n is 2.

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Answer: 20

Step-by-step explanation:

Using the Pythagorean theorem, we know that:

c² = a² + b²

Substituting the given values, we get:

c² = 12² + 16²

c² = 144 + 256

c² = 400

Taking the square root of both sides, we get:

c = √400

c = 20

Therefore, the length of the hypotenuse in the right triangle is 20.

Compute P(x ≤ 15) = (15-10)/(20-10) = 5/10 = 0.5.

Compute P(12 ≤ x ≤ 18) = (18-12)/(20-10) = 6/10 = 0.6.

Compute E(x): The expected value of x is: E(x) = (a+b)/2 = (10+20)/2 = 15

Compute Var(x):The variance of x is: Var(x) = (b - a)^2/12 = (20 - 10)^2/12 = 100/12 = 8.33.

The probability density function is as follows: As the random variable x is uniformly distributed between 10 and 20. Thus, f(x) = 1/(20-10) = 1/10 for 10 ≤ x ≤ 20.Compute P(x ≤ 15):Thus, P(x ≤ 15) = (15-10)/(20-10) = 5/10 = 0.5.Compute P(12 ≤ x ≤ 18):Thus, P(12 ≤ x ≤ 18) = (18-12)/(20-10) = 6/10 = 0.6.Compute E(x):The expected value of x is: E(x) = (a+b)/2 = (10+20)/2 = 15.Compute Var(x):The variance of x is: Var(x) = (b - a)^2/12 = (20 - 10)^2/12 = 100/12 = 8.33.

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The probability that the gambler has to play at least 3 rounds of the game before getting his first win is equal to 3/4.

The probability that the gambler has to play at least n rounds of the game before getting his first win is equal to 1 - (the probability of winning in the first n-1 rounds). To calculate the probability of winning in the first n-1 rounds, use the following formula:
P = (1/2)^(n-1)
Where P is the probability of winning in the first n-1 rounds.
For example, if the gambler has to play at least 3 rounds of the game, the probability of winning in the first 2 rounds is equal to (1/2)^(3-1) = (1/2)^2 = 1/4.

So, the probability that the gambler has to play at least 3 rounds of the game before getting his first win is equal to 1 - (1/4) = 3/4.

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Answer:

Step-by-step explanation:

71/8*9 which it 639/8 feet long

X = 2 is the solution of  the given equation for "x".

What does a math equation mean?

An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. For instance, 3x + 5 = 14 is an equation where 3x + 5 and 14 are two expressions separated by the 'equal' sign.

                           A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. By solving for x, we discover that x equals 7, which is the value for the variable.

8ˣ = (25)

 8ˣ =  (5)²

  X = 2

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Answer:

Step-by-step explanation:

This can be solved by taking X as the magnification

8*x = 12cm *10

x= 120/8

x= 30/2= 15

the magnification = 15 times

Answer:

Proofs attached to answer

Step-by-step explanation:

Proofs attached to answer

The valid proof approaches are: b. Show P(0), P(1),P(-1) and that Vk E Z P(k) → P(k + 1) and e. Show P(0), P(1),P(-1) and that Vk e Z+ P(k) → P(k + 1) and Vk e Z+ P(-k) → P(-(k + 1))

Approach a is invalid because it only shows that P holds for some integers, but not for all integers.

Approach c is invalid because it only shows that P holds for non-negative integers, but not necessarily for negative integers.

Approach d is invalid because it only shows that P holds for non-negative integers and negative even integers, but not necessarily for negative odd integers.

Approach f is invalid because it only shows that P(0) and P(1) imply P(-k) for all positive integers k, but not necessarily for all integers.

Approach b is a valid proof approach because it establishes a base case for P(0), and then shows that P holds for P(1) and P(-1), and that if P holds for an arbitrary integer k, then it also holds for k+1.

Approach e is also a valid proof approach because it establishes a base case for P(0), and then shows that P holds for P(1), P(-1), and that if P holds for a positive integer k, then it also holds for k+1, and if it holds for a negative integer -k, then it also holds for -(k+1).

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The answer of the given question based graph of function on finding the initial value of the function the answer is the initial value of the function is 2.

A graph is  visual representation of data that displays  relationship between variables. It consists of points or vertices connected by lines or arcs that represent relationships between  variables. Graphs can be used to represent various types of data, like numerical, categorical, and ordinal data.

Graph are commonly used in mathematics, science, engineering, and social sciences to help people understand complex data and relationships. Different types of graphs like  bar graphs, line graphs, scatter plots, pie charts, and histograms. Graphs are powerful tool for data analysis and visualization, and they can help people identify patterns, trends, and outliers in data.

If the function intersects both the x-axis and y-axis at the point (2,4), then the function can be written in the form:

y = a(x - 2)(x - 4)

where a is some constant.

To find the value of a, we can use the fact that the function passes through the point (0,2). Substituting x = 0 and y = 2 into the equation above, we get:

2 = a(0 - 2)(0 - 4)

2 = 8a

Solving for a, we get:

a = 2/8 = 1/4

Therefore, the function is:

y = (1/4)(x - 2)(x - 4)

To find the initial value of the function, we need to determine the value of the function when x is equal to zero. Substituting x = 0 into the equation above, we get:

y = (1/4)(0 - 2)(0 - 4)

y = (1/4)(8)

y = 2

Therefore,  initial value of  function is 2.

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Answer:

What is the measure of angle F?

Step-by-step explanation:

You're welcome.

The answer of the given question based on the changing the denominator of fraction the answer is the fraction a+3/6-2a can be rewritten with a denominator of 2(a²-9) as (3 + a)/(2(a - 3)).

In mathematics,  formula is  mathematical expression or equation that describes  relationship between two or more variables or quantities. A formula can be used to solve problems or make predictions about particular situation or set of data.

Formulas often involve mathematical symbols and operations, like addition, subtraction, multiplication, division, exponents, and square roots. They may also include variables, which are typically represented by letters, and constants, which are fixed values that do not change.

To change the denominator of the fraction a+3/6-2a to 2(a²-9), we need to factor the denominator of the original fraction and then use algebraic manipulation to rewrite it in the desired form.

First, we can factor the denominator of the original fraction as follows:

6 - 2a = 2(3 - a)

Next, we can rewrite the denominator using the difference of squares formula:

2(a² - 9) = 2(a + 3)(a - 3)

Now, we can use the factored form of the denominator to rewrite the original fraction:

(a + 3)/(6 - 2a) = (a + 3)/(2(3 - a)) = -(a + 3)/(-2(a - 3)) = (3 + a)/(2(a - 3))

Therefore, the fraction a+3/6-2a can be rewritten with a denominator of 2(a²-9) as (3 + a)/(2(a - 3)).

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The area of the quadrilateral ABCD for this case is of 4 square units.

The quadrilateral ABCD in the context of this problem represents a diamond, hence it's area is given by half the product of the diagonal lengths of the diamond.

The lengths for each diagonal of the diamond are given as follows:

The product of the diagonal lengths is given as follows:

AC x BD = 2 x 4 = 8 square units.

Hence half the product of these diagonal lengths, representing the area of the quadrilateral, is given as follows:

0.5 x 8 square units = 4 square units.

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Answer: 61 kg

Step-by-step explanation:

To find the average mass of the other 5 people, we need to subtract the mass of the lightest person from the total mass of all six people and then divide by 5 (since we're looking for the average of the other 5 people). Here are the steps:

   Find the total mass of all six people:

   To find the total mass of all six people, we can multiply the average mass by 6:

Total mass of all six people = 58 kg/person x 6 people = 348 kg

   Subtract the mass of the lightest person:

   We need to subtract the mass of the lightest person (43 kg) from the total mass of all six people:

Total mass of the other 5 people = Total mass of all six people - Mass of the lightest person

Total mass of the other 5 people = 348 kg - 43 kg = 305 kg

   Find the average mass of the other 5 people:

   Finally, we divide the total mass of the other 5 people by 5 to find the average mass:

Average mass of the other 5 people = Total mass of the other 5 people / 5

Average mass of the other 5 people = 305 kg / 5 = 61 kg

Therefore, the average mass of the other 5 people is 61 kg.