Pls help this one question is worth 25 points !!!
3. (05. 04 MC)Circle A has a diameter of 7 inches, a circumference of 21. 98 inches, and an area of 38. 465 square inches. The diameter of circle B is 6 inches, the circumference is 18. 84 inches, and the area is 28. 26 square inches. Part A: Using the formula for circumference, solve for the value of pi for each circle. Part B: Use the formula for area and solve for the value of pi for each circle. Part C: What observation can you make about the value of pi for circles A and B?

"Elementary and Middle School Mathematics: Teaching Developmentally" is a widely used textbook for teaching math at elementary and middle school levels.

What is developmentally ?

In education, the term "developmentally" refers to the idea that students should be taught in a way that is appropriate for their developmental level. Developmental teaching is a student-centered approach that takes into account the students’ abilities, interests, and needs as they learn.

Elementary and Middle School Mathematics: Teaching Developmentally is a textbook that provides an overview of the principles and practices of teaching mathematics in the elementary and middle school levels. It is designed to help teachers understand the mathematical concepts and skills that students need to learn at each grade level, as well as the best ways to teach those concepts and skills. The book covers a wide range of topics, including number sense and operations, algebra, geometry, measurement, and data analysis. It also provides strategies for differentiating instruction, using technology, and assessing student learning. The book is written by John A. Van de Walle and Karen S. Karp, and it is widely used as a textbook for teacher education programs and professional development workshops.

"Elementary and Middle School Mathematics: Teaching Developmentally" is a widely used textbook for teaching math at elementary and middle school levels.

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The value of (a)  125 / 78125 and  (b)  1296 / 7776.

What is exponential power?

In mathematics, power defines a base number raised to the exponent, where the base number is the factor that is multiplied by itself and the exponent denotes the number of times the same base number is multiplied.

To solve 5³ * 5⁻⁷, we can simplify the exponents first:

5³ = 125

5⁻⁷ = 1 / 5⁷

So, the expression simplifies to:

125 * (1 / 5⁷) = 125 / 78125

To solve 6⁴ * 6⁻⁵, we can simplify the exponents first:

6⁴ = 1296

6⁻⁵ = 1 / 6⁵

So, the expression simplifies to:

1296 * (1 / 6⁵) = 1296 / 7776

Hence, The value of (a)  125 / 78125 and  (b)  1296 / 7776.

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The measurements in (a) 3 inch, 5 inch, 7 inch  produce a triangle. Other two measurements do not produce a triangle.

A triangle is a three-sided polygon that consists of three edges and three vertices.

The properties of the triangle are:

Using second properties we find that which of the following measures produce a triangle.

In a) 3 inch, 5 inch, 7 inch, the sum of the length of two smallest sides are

3 + 5 = 8 inch, which is greatest from the third side.

So this measures produce a triangle because the sum of the length of the two sides of a triangle is greater than the length of the third side.

In b) 5cm, 7cm, 13 cm, the sum of the length of two smallest sides are

5 + 7 = 12 cm, which is smallest from the third side

So this measures does not produce a triangle because the sum of the length of the two sides of a triangle is smaller than the length of the third side.

In c) 14.23ft, 18.23ft, 36.23ft, the sum of the length of two smallest sides are

14.23 + 18.23 = 32.46ft, which is smallest from the third side.

So this measures does not produce a triangle because the sum of the length of the two sides of a triangle is smaller than the length of the third side.

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The probability that a student, chosen at random, does not study Chemistry is 0.49.

What is Probability?

Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is.

From the Venn diagram -

The number of students that study biology and physics = 2

The number of students that study biology and chemistry = 6

The number of students that study chemistry and physics = 4

The number of students that study only physics = 5

The number of students that study only biology = 7

The number of students that study only chemistry = 8

The number of students that study all the subjects = 3

The number of students that study none = 6

So, the total number of students a = 2 + 6 + 4 + 5 + 7 + 8 + 3 + 6 = 41

The number of students that study chemistry = 8 + 6 + 3 + 4 = 21

The number of students that do not study chemistry b = 41 - 21 = 20 students

The probability chosen at random that child does not study chemistry =  b/a -

= 20/41

= 0.49

Therefore, the probability value is 0.49.

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Answer:

Step-by-step explanation:

THE OUTLINER IS 28!

Answer:

x=40 HZ

..............

Answer: number c I think

Step-by-step explanation:

Answer: The 2nd table (blue)

Step-by-step explanation:

The interest on the spent of $2000 will be $60.

The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.

Given that Skarleth is considering whether to apply for a credit card or debit card at her bank. The credit card will charge 3% interest if she does not pay her balance in full each month. If she spends $2,000.

The amount of interest will be calculated as:-

Amount = 2000 x 3%

Amount = ( 2000 x 3 ) / 100

Amount = $60

Therefore, the interest on the spent of $2000 will be $60.

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The value of x is 28.4°. The solution has been obtained using the law of cosines.

What is law of cosines?

The law of cosines, commonly referred to as the cosine rule or the cosine formula, in trigonometry essentially connects the length of the triangle to the cosines of one of its angles.

Law of Cosines: c² = a² + b² - 2ab cos C

We are given a= 37, b=23 and x= 20

Using the law of cosines,

⇒x² = a² + b² - 2ab cos x

⇒20² = 37² + 23² - 2(37)(23) cos x

⇒20² = 37² + 23² - 2(37)(23) cos x

⇒400 = 1369 + 529 - 1702 cos x

⇒400 = 1898 - 1702 cos x

⇒1702 cos x = 1498

⇒cos x = 1498 /1702

⇒cos x = 0.88

⇒x = [tex]cos^{-1} (0.88)[/tex]

⇒x = 28.4°

Hence, the value of x is 28.4°.

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The distance between the point (-5, 6) to the origin is 61 units.

Regardless of direction, an object's distance is defined by its total velocity.

Distance is the amount of space an object has traveled, regardless of where it began or concluded.

Knowing an object's distance from us allows us to determine its true size.

The following formula is widely used to determine the distance between two points: d=((x2 - x1)2 + (y2 - y1)2)

The given point is thus:

(-5, 6)

Assume that (0, 0) serves as the origin and that the given position is at (-5, 6).

d=((-5 - x1)2 + (6 - y1)2)

d=((-5)2 + (6)2)

d=25+36

d=61 units

Therefore, the distance between the point (-5, 6) to the origin is 61 units.

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Answer:

All except shift up.

The slope of the line is 0.05. This indicates that the diver ascends at a rate of 0.05 m/s.

The slope is defined as the ratio of the vertical change between two points, the rise, to the horizontal change between the same two points, the run.

Given that, the graph shows a scuba diver ascent over time.

We see that,

He goes up 2 meters in every 40 seconds,

then, in 20 seconds, he will go 1 meter up

so,

1/20 = 0.05

Hence, the slope of the line is 0.05. This indicates that the diver ascends at a rate of 0.05 m/s.

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The table which has the correct values for A, B, and C is;

A. Donuts    2        4          5           8

   Cost      15.80  31.60   39.50   63.20

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

y = kx

Where:

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

Constant of proportionality, k = y/x

Constant of proportionality, k = 31.60/4

Constant of proportionality, k = 7.9

When the value x = 2, the value of A can be calculated as follows;

y = kx

A = 7.9 × 2

A = 15.80

When the value y = 39.50, the value of B can be calculated as follows;

x = k/y

B = 39.50/7.9

B = 5.

When the value x = 8, the value of C can be calculated as follows;

y = kx

C = 7.9 × 8

C = 63.20.

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The ratios 40/18 and 27/11 are not equal because 20/9 and 3/1 are different fractions. They stand for various proportional connections between two quantities, in other words.

We need to see if the ratios of 40/18 and 27/11 fall to the same fraction when the numerator and denominator are both divided by their largest common factor (GCF).

Given that the GCF of 40 and 18 is 2, we can obtain 20/9 by reducing both the numerator and denominator of 40/18 by 2. Since the GCF of 27 and 11 is also 11, we obtain 3/1 when we divide the numerator and denominator of 27/11 by 11.

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One small container fills 1/15 gallons of water. Therefore, if the fish bowl can hold 1/3 gallons of water, then one small container can hold 1/15 gallons of water.

1/3 gallons of water in the fish bowl divided by 5 smaller containers = 1/15 gallons of water in one small container.

Andrew purchased a fish bowl that has the capacity to hold 1/3 gallons of water. To fill the fish bowl with water, he used smaller containers. It took him 5 of these smaller containers to fill the fish bowl. This means that each small container filled 1/15 gallons of water. Therefore, if the fish bowl can hold 1/3 gallons of water, then one small container can hold 1/15 gallons of water.

One small container fills 1/15 gallons of water.

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The value of √14 lies between 3.70 and 3.75.

The √ symbol that is used to denote square root or nth roots. Radical Expression - A radical expression is an expression containing a square root.

Given:

We have to √14.

So, the value of √14 ≈ 3.74

Now, we can solve for all the answer .

A) 19/6 = 3.1666...

22/7 = 3.1428...

So, It cannot be the answer.

B) Doesn't need to be solved.

3.17

3.71

So, It cannot be the answer.

C)√4 = 2

√9 = 3

So, It cannot be the answer.

D) Doesn't need to be solved.

3.70

3.75

So, It can be the answer.

Hence, √14 lies between 3.70 and 3.75

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The starting temperature would be 29 degrees.

What are the initial value and final value?

Initial value refers to the starting value or the value of a variable at the beginning of a process or time period. Final value refers to the end value or the value of a variable at the end of a process or time period. In the context of a mathematical function, the initial value would be the value of the function at the beginning of the domain and the final value would be the value of the function at the end of the domain.

If the temperature outside dropped 23 degrees in 6 hours. The final temperature was -6,

The starting temperature would be 29 degrees (-6 + 23).

Hence, the starting temperature would be 29 degrees.

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The inequality can be rewritten into:

x > 4 or x < -4

And the graph can be seen in the image at the end.

We want to solve the inequality below and then graph it, the inequality is:

|x| + 3 > 7

moving the 3 to the right side we get:

|x| > 7 - 3

|x| > 4

Now we can break the absolute value part into two:

x > 4

x < -4

That is the solution:

x > 4 or x < -4

The graph is the one below.

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Domain: Real numbers.

Range: Set of output value.

What is the Range and domain of the function?

The domain of the function is the set of all input values, or the set of x-values, for which the function is defined.

The range of the function is the set of all possible output values, or the set of y-values, that the function can produce.

The domain of the function is all real numbers since there are no restrictions on the input x.

The range of the function is the set of output values, which in this case is {5}.

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The relationship between the volume of a sphere with a radius that equals to y and the volume of a sphere with a radius equal to 2y is V₂ = 8V₁.

The volume of a thing is the area that it takes up in three dimensions. Simply said, a thing occupies space.

The volume of the sphere,

= 4/3πr³, with the radius r.

So, if the radius of the sphere is y.

Then the volume of the sphere,

V₁ = 4/3πy³.

So, if the radius of the sphere is 2y.

Then the volume of the sphere with the radius 2y,

V₂ = 4/3π(2y)³.

= 8(4/3)π(y)³.

= 8 x the volume of the sphere with the radius y.

= 8V₁

Therefore, the relationship is V₂ = 8V₁.

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There is the average decrease in temperature which is -2.5 degrees per hour.

For the given data:

So,

Difference in temperature =  32.7 - 45.2

                                            =  -12.5

Total time from 8:00 pm to 1:00 am = 5 hours.

Then,

Average change in temperature per hour = -12.5 / 5 = -2.5 degrees.

Thus, there is the average decrease in temperature which is -2.5 degrees per hour.

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Answer: x= 4 and y= 540

You should read the corresponding values inorder to figure out the other value

The completing square form of the equation is  [tex](x+1)^2=-25[/tex].

What is completing square method?

By altering the equation's form so that the left side is a perfect square trinomial, a quadratic equation can be solved using the "Completing the Square" approach. One approach to locating the roots of the given quadratic equation is to complete the square method.

Here the equation [tex]x^2+2x=-26[/tex]

To completing the square of the equation add 1 on both sides then,

=> [tex]x^2+2x+1=-26+1[/tex]

=> [tex]x^2+2.x.1+1^2=-25[/tex]

=> [tex](x+1)^2=-25[/tex]

Hence the completing square of the equation is  [tex](x+1)^2=-25[/tex].

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The best method for solving a quadratic equation depends on the specific equation and the context in which it is being used. However, the quadratic formula is a universally applicable method and it is one of the most widely used methods for solving quadratic equations.

The quadratic formula is a method for solving a quadratic equation, which is an equation of the form ax^2 + bx + c = 0, where a, b, and c are constants.

The quadratic formula is:

x = (-b ± √(b^2 - 4ac))/(2a)

It allows to find the solutions or roots, x, of a quadratic equation of the form ax^2 + bx + c = 0, where a, b, and c are constants.

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The slope of the line is undefined.

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

Two points on the line are (-4, 6) and (-4, 1)

Now,

Since, The equation of line passes through the points (-4, 6) and (-4, 1)

So, We need to find the slope of the line.

Hence, Slope of the line is,

m = (y₂ - y₁) / (x₂ - x₁)

m = (1 - 6) / (-4 - (-3))

m = - 5 / 0

m = ∞

Thus, The slope of the line is undefined.

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Answer:

y=2

Step-by-step explanation:

Answer:

The sentence "Eight more than the quotient of a number and 4 equals 5" can be translated into the following equation:

(b / 4) + 8 = 5

Where b is the unknown number, and 4 is the divisor.

Answer:

b = - 12

Step-by-step explanation:

let the number be b

the quotient ( division ) of b and 4 is [tex]\frac{b}{4}[/tex] , then

[tex]\frac{b}{4}[/tex] + 8 = 5 ← equation

to solve for b

subtract 8 from both sides

[tex]\frac{b}{4}[/tex] = - 3 ( multiply both sides by 4 to clear the fraction )

b = - 12 ← value of b

For the linear function y = 0.7x, option A: An additional day on the medicine is associated with 0.7 pounds of weight gain is the correct answer.

What is a linear function?

A linear function is a function that, when plotted, creates a straight line. Typically, it is a polynomial function with a maximum degree of 1 or 0. Nevertheless, calculus and linear algebra are also used to represent linear functions.

The given linear function is y = 0.7x.

Where x represents the number of days on the medicine.

y represents the weight gain, in pounds.

The slope intercept form is y = mx + b, where m is slope.

So, the slope of y = 0.7x is m = 0.7.

If x = 2 , then y will be -

y = 0.7(2)

y = 1.4

If x = 3 , then y will be -

y = 0.7(3)

y = 2.1

Therefore, it can be seen that when the number of days on the medicine is increased the weight gain also increases with 0.7 pounds.

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Ten balls in five lines Puzzle – Solution The puzzle Place 10 balls in 5 rows in such a way that each row contains exactly 4 balls below figures are:

A puzzle is a sport, trouble, or toy that examines a person's ingenuity or understanding. In a puzzle, the solver is anticipated to position pieces together (or take them aside) in a logical manner, so that you can arrive at the appropriate or a laugh solution to the puzzle. There are special genres of puzzles, which include crossword puzzles, phrase-search puzzles, variety puzzles, relational puzzles, and good judgment puzzles. the academic take look at puzzles is referred to as enigmatology.

Puzzles are often created to be a form of leisure however they can also get up from critical mathematical or logical problems. In such cases, their solution can be a substantial contribution to mathematical research. Puzzles expand memory competencies, as well as the capability to devise, check ideas and solve troubles. even as completing a puzzle, children want to recollect shapes, colors, positions, and techniques to complete them.

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