find the volume of the largest right circular cylinder that can be inscribed in a sphere of radius 3

The angles and their relationships are -

a) ∠x = 135° (corresponding angles), ∠y = 135° (vertical angles)

b) ∠y = 45° (liner pair angles), ∠x (not enough information provided)

c) ∠x = 135° (corresponding angles), ∠y = 45° (liner pair angles)

d) ∠x = 45° (liner pair angles), ∠y (not enough information provided)

What is angle pair relationship?

In Geometry, there are five fundamental angle pair relationships:

Complementary Angles

Supplementary Angles

Adjacent Angles

Linear Pair

Vertical Angles

a) In the first diagram -

∠x = ∠a as they are both corresponding angles to each other.

So, ∠x = 135°.

Similarly, ∠y = ∠x as they both are vertically opposite angles to each other.

So, ∠y = 135°.

b) In the second diagram -

∠y + ∠a =180° as they are both form a linear pair of angles.

So, ∠y = 180° - ∠a

∠y = 180° - 135°

∠y = 45°.

Now, ∠x cannot be deduced and no proper information is given in the image.

c) In the third diagram -

∠x = ∠a as they are both corresponding angles to each other.

So, ∠x = 135°.

Now, ∠y + ∠x =180° as they are both form a linear pair of angles.

So, ∠y = 180° - ∠x

∠y = 180° - 135°

∠y = 45°.

d) In the fourth diagram -

∠x + ∠a =180° as they are both form a linear pair of angles.

So, ∠x = 180° - ∠a

∠x = 180° - 135°

∠x = 45°.

Now, ∠x cannot be deduced and no proper information is given in the image.

Therefore, all the angles are and their relationships are found.

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By using properties for angles we can find and solve some linear equations, there we can see that x = 30°.

Remember that the sum of the interior angles of a triangle must give 180°, and we also know that the angle defined by a line is 180°.

Let's define N as the angle located at vertex N of the right triangle in the left side, we then can write:

2x + 90° + N = 180°

And we also can write the linear equation:

105° + 45° + N = 180°

Solving this one, we can find the value of N.

N = 180° - 45° - 105°  =30°

N = 30°

Replacing that in the equation with x we will get:

2x + 90° + 30°  =180°

2x = 180° - 90° - 30°

2x = 60°

x = 60°/2 = 30°

The value of x is 30°.

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An undecidable problem is one that should have a "yes" or "no" answer but has no algorithm that can correctly answer on all inputs.

According to the theories of computational complexity and computability, an undecidable problem is one for which it has been demonstrated that it is impossible to create an algorithm that always yields the right yes-or-no response. As an illustration, it can be shown that there is no algorithm that can accurately predict whether arbitrary programmes will eventually halt when run.

Any question that is simply yes or no on an infinite list of inputs is a decision problem. It is customary to define the decision problem as the set of inputs for which the problem returns yes because of this. Natural numbers as well as values of other kinds, such as strings in a formal language, can be used as these inputs.

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The equations of the commissions are

From the question, we have the following parameters that can be used in our computation:

Also from the question, we have:

This means that:

Commission = Unit rate * Commission proportion * Number of pieces

Using the above as a guide, we have the following:

Sara: y = 25 * 60% * x

Ravi: y = 2000 * 25% * x

Evaluate

Sara: y = 15x

Ravi: y = 500x

See attachment for the graph of the commission equations

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∠BCE is drawn, line segment CA is drawn,  Ray CA is drawn, For Circle C is drawn, Ray BE is not drawn.

A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.

Given that Circle C is inscribed with 5 lines

Point C is at the center of the circle

3 lines come out of point C and make points D, A, and B on the edge of the circle.

Another line comes out of point C and goes past the edge to point E.

For ∠ABC

The geometric figure is not drawn.

For ∠BCE

The geometric figure is drawn.

For line segment CA

The geometric figure is drawn.

For Ray CA

The geometric figure is drawn.

For Circle C

The geometric figure is drawn.

For Ray BE

The geometric figure is not drawn.

For Line segment AE

The geometric figure is not drawn.

Hence,  ∠BCE is drawn, line segment CA is drawn,  Ray CA is drawn, For Circle C is drawn, Ray BE is not drawn.

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The missing part is 1/5. The complete expression is 1/7 of 1/5 is 1/35.

An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.

We have the expression:

1/7 of (...) = 1/35

To find the missing fraction:

Let n be the number.

So,

1/7(n) = 1/35

n = 7/35

n = 1/5

Therefore, 1/5 is the missing part.

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Answer:

Step-by-step explanation:

We know that : Percentage means 'divided by 100'

therefore, 1/2 percent = 1 / 2 ÷ 100 = 0.5 ÷100 = 5÷1000= 0.005

The rate of change, y=−√x−4 +5 , is expressed as 1/5−2i/5 .The square root of a number is the number itself.

A number can be obtained by multiplying the square root by itself. Square root is represented by the symbol sqrt, which stands for square root of, end square root. The reverse of squaring an integer is finding its square root. The result of multiplying a number by itself yields its square value, whereas the square root of a number can be found by looking for a number that, when squared, yields the original value. If 'a' is the square root of 'b,' then a a = b.

given

Use the average rate of change formula to substitute.

(√1)−(√−4) / (1)−(−4)

Condense the phrase.

1/5−2i/5

The rate of change, y=−√x−4 +5 , is expressed as 1/5−2i/5 .The square root of a number is the number itself.

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The constant of proportionality is 2

From the question, we have the following parameters that can be used in our computation:

1 scoop of ice cream = 1/2 cup of milk

5 scoops of ice cream = 2.5 cups of milk

The constant of proportionality (k) is then calculated as

k = Scoop of ice cream/Cup of milk

So, we have

k = 5/2.5

Evaluate

k = 2

In (a), we have:

k = 2

A proportional relationship is represented as

s = km

Where

s = scoop of ice cream

m = cup of milk

So, we have

s = 2m

In (b), we have

s = 2m

To graph the relationship, we start by generating a table of values and then plot the points

Recall that

s = 2m

So, we have

18 = 2m

Divide by 2

m = 9

Hence, the number of cups is 9

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Answer: $52.57 for each basic yearbook and $153.5 for each deluxe yearbook

Step-by-step explanation:

First, do Mr. Boyer's class to find out how much each deluxe yearbook is:

2,763 ÷ 18 = $153.5

Then do, Mrs. Wu's class: First, multiply 153.5 by the 6 deluxe yearbooks ordered;

153.5 x 6 = 921

After, subtract 921 from 2,025:

2,025 - 921 = 1104

The remaining $1104 is the total cost of the 21 basic yearbooks ordered. Divide the total cost by the number of yearbooks ordered to find the unit price:

1104 ÷ 21 = 52.5714285714

Round to the nearest hundredth: $52.57

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The solution of the expression 3x² - 4 = 0 is x = ±2/√3.

The term expression in math is defined as a sentence with a minimum of two numbers or variables and at least one math operation

Here we have the expression 3x² - 4 = 0.

Now, we have to solve this one by using the following steps:

First we have to add 4 to both sides of the equation, then we get the expression as,

=> 3x² = 4

Now, we have to Divide each term by 3 and simplify, then we get

=> x² = 4/3

Then we have to take the specified root of both sides of the equation to eliminate the exponent on the left side,

=> x = √4/3

When we simplify this one further, then we get

=> x = ±2/√3.

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After making the subject of [tex]$n^2=4 \mathrm{~d}+t^3 / t^3$[/tex] could be [tex]$\mathrm{t}=\sqrt[3]{4 d / n 2-1}$[/tex]

An expression is a combination of symbols, such as numbers and operators, that represent a computation or a value. Expressions can be used to perform calculations, assign values to variables, and control the flow of a program. They are a fundamental concept in computer programming.

Simplification is the process of making an expression or equation simpler, while still maintaining its meaning or function. This can be done by combining like terms, combining or removing unnecessary elements, or applying mathematical rules or identities.

For example, in algebra, simplifying an expression might involve combining the coefficients of similar terms (such as 2x + 3x = 5x), or factoring out a common factor from multiple terms (such as 2x^2 + 4x = 2x(x+2)).

Glven expression,

[tex]$$\begin{aligned}& n^2=4 \mathrm{~d}+t^3 / t^3 \\& n^2=4 \mathrm{~d} / t^3+t^3 / t^3 \\& n^2=4 \mathrm{~d} / t^3+1 \\& n^2-1=4 \mathrm{~d} / t^3 \\& t^3=4 \mathrm{~d} / n^2-1 \\& \mathbf{t}=\sqrt[3]{4 d / n 2-1}\end{aligned}$$[/tex]

Hence after making [tex]$\mathbf{t}$[/tex] the subject of[tex]$n^2=4 \mathrm{~d}+t^3 / t^3$[/tex] could be

[tex]$$\mathrm{t}=\sqrt[3]{4 d / n 2-1}$$[/tex]

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The product of the two polynomials is (8x³)(4x⁷) = 32x¹⁰.

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1

To find an unknown number we can use properties of equality.

Algebraic Method

Another word to describe an unknown number is "variable". For the equation, I will call this variable x. Any variable can be used, but x is the most common.

We can write an equation to describe the situation. The statement says that the product of 15 and x is 15. This means that 15 * x = 15. Now we can use algebra to solve this equation.

To find x, divide both sides by 15.

Identity Property of Multiplication

Additionally, if you know all the properties of equality, you can answer this question without doing any math. One of the properties of equality is the identity property of multiplication. The identity property states:

This means that any number multiplied by 1 is itself. So, since the factor and product are equal, the other factor must be 1. If you plug 15 in for a, you can see how this property applies to this situation.

The function form of the given function would be  [tex]f(x)=log_b(x)[/tex].

What is a function?

In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.

The given function is f(x) = logbx.

So the function form would be the function of x is equal to the logarithmic of x having base b.

so this can be written as

       [tex]f(x)=log_b(x)[/tex]

Hence, the function form of the given function would be  [tex]f(x)=log_b(x)[/tex].

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The function form of the given function would be  [tex]f(x)=log_b(x)[/tex].

What is a function?

In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.

The given function is f(x) = logbx.

So the function form would be the function of x is equal to the logarithmic of x having base b.

so this can be written as

[tex]f(x)=log_b(x)[/tex]

Hence, the function form of the given function would be  [tex]f(x)=log_b(x)[/tex].

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Answer:

y = 1

Step-by-step explanation:

locate x = - 4 on the x- axis, go vertically up to meet the graph at (- 4, 1 ), so

when input x = - 4 the output is y = 1

To identify the solutions in solving linear inequalities in two variables, you can first graph the equation on a coordinate plane. Then, you can use the boundary line to identify which regions of the plane satisfy the inequality.

Any points in the shaded regions will be solutions to the inequality. Additionally, you can use the boundary line to identify the points that are not solutions by finding the points that lie on the boundary line.

Example:

x + 2y ≥ 4

The graph of this inequality is a line with a slope of -2/1 and a y-intercept of 4/2. The line will be shaded on the side of the line containing the greater values, which in this case is the side containing the origin.

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The slope of a line is a measure of its steepness and can be calculated using the formula:

slope = (y2 - y1) / (x2 - x1)

In this case, the points (0,3) and (36,0) represent the coordinates of two points on the ramp. To find the slope of the ramp, we can plug these values into the formula:

slope = (0 - 3) / (36 - 0) = -3 / 36 = -1/12

The slope of the ramp is -1/12. This indicates that the ramp is relatively flat, as a negative slope means that the line is sloping downward.

To find the slope of the second ramp, represented by the function g(x) = -1/4x + 2, we can take the derivative of the function. The derivative of a function represents the slope of the function at any given point, and it is calculated using the formula:

derivative = f(x) = -1/4

The derivative of the function g(x) is a constant value of -1/4, which means that the slope of the second ramp is also -1/4. This is a steeper slope than the first ramp, as the value of the derivative is larger in magnitude.

We found that translations have the following three properties: line segments are taken to line segments of the same length;

angles are taken to angles of the same measure; and. lines are taken to lines and parallel lines are taken to parallel lines.

Properties of Translations

- Distance Where the lengths of the segments stay the same.

-Angle Measures These remain the same.

-Parallelism Where the parallel lines will stay parallel.

-Collinearity The points will stay on the same line.

-Orientation The order of the letters will stay the same.

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The value of d in the equation is 13 and it is equal to the number of dresses made by her.

The total amount paid by Mr. Hubble to make some custom dresses is 1677 dollars.

The price paid to make one dress is 129 dollars.

The equation that represents this situation is given to be 1677 = 129d

Where d is the number of dresses made,

Now, using simple algebra,

1677 = 129d

d = 1677/129

d = 13

So, she has made a total number of dress she made is 13 and the value of d is the equation is also 13.

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Answer: Lyda wants to score 80% on a test that is worth 50 points. To figure out how many points she needs to accomplish her goal, we can set up a proportion using her desired percentage as the proportion of points she wants to score over the total number of points on the test.

score / total points = percentage / 100

To figure out the number of points Lyda needs to score, we can use the proportion above and cross-multiply:

score * 100 = percentage * total points

We know that percentage=80 and total points =50, so we can substitute these values:

score * 100 = 80 * 50

score = (80*50) / 100 = 40

So Lyda needs to score 40 points to accomplish her goal of 80%.

The proportion would be score / total points = x/100 = percentage/100 = 40/50 = 8/10

It's worth to mention that scoring 80% on a test means she scored 40 points on a test worth 50, the minimum score to pass is 30 so she got a good grade already.

Step-by-step explanation:

As a professional artist and judging from the current sales ratio and commission rates, one would earn more if one apprenticed for Sara.

As evident in the task content; the current ratio of Sara's sales to Ravi's sale is 100 : 2.

Since Sara's pieces of art sell for $25, the total earnings is; 25 × 100 = $2500.

Hence, since the commission rate is 60%, it follows that the commission earned on sales of Sara's pieces is; 60% of 2500 = 0.6 × 2500 = $1500.

Also, since Ravi's pieces each cost $2000, it follows that for 2 pieces, the total earnings is; 2 × $2000 = $4,000.

Hence, since the commission rate for Ravi's pieces is 25%, the commission earned is therefore; 25% of 4000 = 0.25 × 4000 = $1000.

On this note, one would earn more if one apprenticed for Sara.

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Answer: To divide two rational expressions, you need to first find the least common denominator (LCD) of the two expressions. The LCD is the least common multiple of the two denominators.

In this case, the rational expressions are x/(3x-1) and (x-2)/(2x). The LCD of these two expressions is (3x-1)(2x), which can be factored as 6x(x-1).

To divide the two rational expressions, you need to express each expression as a fraction with the LCD as the denominator.

The first expression, x/(3x-1), can be rewritten as (x * (2x))/(3x-1 * (2x)) = (2x^2)/(6x^2-2x).

The second expression, (x-2)/(2x), can be rewritten as ((x-2) * (3x-1))/(2x * (3x-1)) = (3x^2-3x+2)/(6x^2-2x).

To divide these two expressions, you can divide the numerators and the denominators separately:

(2x^2)/(6x^2-2x) ÷ (3x^2-3x+2)/(6x^2-2x)

= (2x^2) ÷ (3x^2-3x+2)

= (2/3)x^2 ÷ (x^2-x+2/3)

Therefore, the quotient of the rational expressions x/(3x-1) and (x-2)/(2x) is (2/3)

Step-by-step explanation:

Manuel was incorrect, because the perimeter of a flower bed is [tex]51\frac{1}{4}[/tex] feet not [tex]25\frac{5}{8}[/tex] feet.

The perimeter of a rectangle is the total distance of its outer boundary. It is twice the sum of its length and width and it is calculated with the help of the formula: Perimeter = 2(length + width).

Given that, Manuel says [tex]25\frac{5}{8}[/tex] feet of fencing is enough for a rectangular flower bed that measures [tex]9\frac{7}{8}[/tex] feet by [tex]15\frac{3}{4}[/tex] feet

Here, perimeter =2([tex]9\frac{7}{8}[/tex] +  [tex]15\frac{3}{4}[/tex]) feet

= 2(79/8 + 63/4)

= 2(79/8 + 126/8)

= 2(205/8)

= 410/8

= [tex]51\frac{1}{4}[/tex] feet

Manuel was incorrect, because the perimeter of a flower bed is [tex]51\frac{1}{4}[/tex] feet not [tex]25\frac{5}{8}[/tex] feet.

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Answer: y<-5x+9

Step-by-step explanation:

Slope is -5, y-intercept is 9 and the shaded area is on the left side (meaning y is less than the line). The line is dotted which means that the answer will less than but not equal to.

Answer:

Step-by-step explanation:

the first equation we konw x=-2y-1,

then -2y-1=y+5

so, y = -2, x=3

Answer:

y = -2

x = 3

Step-by-step explanation:

y + 5 + 2y = -1 (substitute)

3y + 5 = -1        (Simplify)

3y = -6            (Get rid of 5)

y = -2                 (Divide)

x = -2 + 5         (plug in y)

x = 3                 (simplify)

hope this helps :)

Therefore, amu (atomic mass unit) and Avogadro's number are not the same things.

A unit of measurement for atomic and molecular weight is the atomic mass unit (amu).

Molecular weight, commonly known as molecular mass, is the mass of a substance's molecules, calculated using the atomic weight of carbon-12, which is 12.

No, amu and Avogadro's numbers are not the same things because An atomic mass unit (amu) is a unit of measurement for atomic and molecular weight. It is defined as one twelfth of the mass of a neutral atom of carbon-12. It is commonly used in chemistry to express the masses of atoms and molecules While Avogadro's number (N) is a fundamental constant of nature that relates the number of atoms or molecules in a sample to the mass of that sample. It is defined as the number of atoms or molecules in one mole of a substance. It is approximately 6.022 x 10^23 atoms or molecules per mole.

So, amu is a unit of measurement for atomic and molecular weight, while Avogadro's number is a constant that relates the number of atoms or molecules in a sample to the mass of that sample.

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Answer:

The two answers would be 0 and ln (7)

Step-by-step explanation:

Hope it helps:)

Using the method of simple random sampling, The answer is we select sample before collecting data.

Random sampling is a method of selecting a sample from a population in such a way that each member of the population has an equal probability of being selected. This ensures that the sample is representative of the population, and reduces bias in the sampling process. In simple random sampling, a random sample is drawn from a larger population by using random number generators, tables of random numbers, or other methods that ensure that each member of the population has an equal chance of being selected.

A sample is a portion or a subset of a population that is selected for the purpose of studying characteristics of the population. The sample is used to make inferences or conclusions about the population from which it was drawn. The sample is usually smaller in size than the population, and it is selected through a process called sampling. The process of sampling is used to select a sample that is representative of the population, meaning that the sample has similar characteristics as the population.

In simple random sampling, the sample size is determined before collecting data. There are several ways to determine the sample size, but one common method is to use a sample size calculation formula, such as: n = (z^2 * p * (1-p)) / e^2

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