The radius of a spherical balloon increases from 7 cm to 14 cm as air is being pumped into it. Find the ratio of surface areas of the balloon in the two cases. *

Answer:488441

Step-by-step explanation:

Luc is correct in stating that the line will remain the same with certain dilation centers, such as the origin (0, 0) and the point (3, -4). These centers of dilation will cause a scale factor of 2, but the line will remain the same.

To check if Luc is correct, we can calculate the points of the dilation with scale factor 2.

For the origin (0, 0):

Point A: (x, y) = (0, 3)

Point B: (x, y) = (-4, -3)

Dilated Point A: (x, y) = (0, 6)

Dilated Point B: (x, y) = (-8, -6)

Equation of the dilated line: y = -4x + 6

This shows that the line is dilated with scale factor 2, but is the same line.

For the point (3, -4):

Point A: (x, y) = (3, -1)

Point B: (x, y) = (-1, -7)

Dilated Point A: (x, y) = (6, -2)

Dilated Point B: (x, y) = (-2, -14)

Equation of the dilated line: y = -4x + 3

This shows that the line is dilated with scale factor 2, but is the same line.

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The value of volume of pyramids is 448 cubic meter.

A triangular pyramid's volume can be calculated using the formula Volume= 1/3 Base area Height. The side, height, and slant height of a triangular pyramid are the three parameters needed to calculate its surface area.

The basic formula for volume is length, breadth, and height, as opposed to length, width, and height for the area of a rectangular shape. The calculation is unaffected by how you refer to the various dimensions; for instance, you can use "depth" instead of "height."

Given,

Length=12m

Width=7m

height=16m

volume =l * w * h / 3

= 12*7*16/3

= 448 cubic meter

Therefore volume of pyramid is 448 cubic meter .

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The design has a total area of 116 cm² when measured using the area of a square.

The area is the total amount of space that an object's shape or a flat (2-D) surface occupies.

Create a square on paper by using a pencil.

Two dimensions make it up.

A shape's area on paper is the space it takes up.

Given that a square has equal sides, we can calculate its area as follows:

A = s²

The photograph below illustrates the three square-shaped pieces of fabric that Jordan used to create the design.

Find the area of each square-shaped piece of fabric and add them all up to get the total pattern area.

Inferring the area of a square, the total area would be as follows:

Total Area = 4² + 6² + 8²

Total Area = 116 cm²

Therefore, the design has a total area of 116 cm² when measured using the area of a square.

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the answer to your question is 36

No, isosceles triangles do not always have to have 90-degree angles.

An isosceles triangle is a triangle with two sides of equal length. While the two sides are equal, they can be of any length. This means that the angles of the isosceles triangle can vary, and the triangle does not always have to have 90-degree angles. In fact, an isosceles triangle can have angles that range from 0 to 180 degrees. The only requirement for an isosceles triangle is that it must have two sides of equal length. As such, an isosceles triangle can have angles that are greater than 90 degrees, angles that are less than 90 degrees, or even angles that are equal to 90 degrees.

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Answer:

7/2

Step-by-step explanation:

7x – 2y = 10

using ( y = mx + b) as our guideline

where m is the slope

7x – 2y = 10

subtract 7x from both sides

7x – 7x – 2y = 10 – 7x

–2y = 10x – 7x

when arranged in slope form

–2y = –7x + 10

divide both sides by (–2) to get y

[tex] \frac{ \\ - 2y}{ - 2} = \frac{ - 7x}{ - 2} + \frac{10}{ - 2} [/tex]

[tex]y = \frac{ \\ 7y}{2} - 5[/tex]

[tex]the \: slope \: will \: be \: \frac{ \\ 7}{2} [/tex]

This is our answer.

i hope i

Answer:

30

Step-by-step explanation:

perimeter is the outside of a shape so just add them all together honestly

Answer:

surface area ---> i

volume ---> b

radius ---> d

Step-by-step explanation:

surface area= 4πr² =4x3.14x14²=2461.76cm²

volume= (4÷3)πr³= (4÷3)x3.14x14³=11488.21cm³

radius = half the diameter = 14cm

The sample space between A to C is A,B,C

The likelihood that a sample point will occur is quantified by its probability.

The likelihood of a sample point

According to tradition, statisticians have adopted the following guidelines.

Any sample point's probability can be between 0 and 1.

The probability of every sample point in a sample space added together is 1.

Let's say we run a straightforward statistical experiment. One coin is flipped. Heads or tails are the possible results of the coin flip. These results taken as a whole serve as our experiment's sample space. Each result stands in for a single sample point in the sample space. What is each sample point's probability?

Solution: the total of all sample points' probability

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To find the percentage increase of the slave population from 1800 to 1860, we can use the following formula:

What does math's % mean?

In essence, percentages are fractions with a 100 as the denominator. We place the percent symbol (%) next to the number to indicate that the number is a percentage. For instance, you would have received a 75% grade if you answered 75 out of 100 questions correctly on a test (75/100).

percentage increase = (new value - original value) / original value x 100

We know that in 1800 the slave population was 893,602 and in 1860 the slave population was 1,953,760. So we can plug in these values into the formula:

percentage increase = (1,953,760 - 893,602) / 893,602 x 100

percentage increase = (1,060,158) / 893,602 x 100

percentage increase = 1.1885 x 100

percentage increase = 118.85

So, the slave population increased by 118.85% from 1800 to 1860.

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In most cases, the inverse of a linear function is also a linear function.

The term "linear function" in mathematics applies to two different but related ideas: A polynomial function of degree zero or one that has a straight line as its graph is referred to as a linear function in calculus and related fields.

A function with the formula f(x) = ax + b, where a and b are real values, is referred to as a linear function.

Here, stands for the line's gradient and b for the y-axis intercept (which is sometimes called the vertical intercept).

These functions' graphs are mirror images of one another when viewed along the line y=x.

As a result, the points on the graph of f(x) are the points on the graph of f(x) that have been turned around.

A linear function's inverse is typically also a linear function.

Therefore, in most cases, the inverse of a linear function is also a linear function.

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The missed value in the frequency tree is 224.

Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.

Given that 400 people are asked if they drink tea.

7/10  say Yes and  20% of the people who say Yes drink at least 3 cups each day

7/10 of 400 is 280

Which means 280 people drink tea.

The remaining people does not drink tea.

Remaining =400-280=120.

Now let us find 20% of 280

20/100×280

0.2×280=56

So 56 drink at least 3 cups each day.

280-56=224

So 224 people drink tea but not three cups.

Hence, the missed value in the frequency tree is 224.

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Answer:

Center: = (-1,-3)

Radius: = 1

Step-by-step explanation:

No, triangle ABC is not a right triangle. The equation of a line BC "y=x-11" is a line with slope of 1, which means it has an angle of 45 degrees with respect to the x-axis. The segment AB has a slope of 0, which means it is parallel to the x-axis. A right triangle's legs must be perpendicular, therefore a line with a slope of 1 and a line with a slope of 0 cannot be the legs of a right triangle.

A right triangle is a triangle in which one of the angles is 90 degrees. In order for a triangle to be a right triangle, the two sides (or legs) that form the 90-degree angle must be perpendicular to each other. Perpendicular lines have slopes that are negative reciprocals of each other.

In this case, the equation of the line segment AB is "y = -6", which means it is parallel to the x-axis. The slope of a line parallel to the x-axis is 0. On the other hand, the equation of the line BC is "y = x - 11", which means it has a slope of 1. A slope of 1 means that the line is at a 45 degree angle with respect to the x-axis.

Since the slopes of the two lines are not negative reciprocals of each other (0 and 1), the legs of the triangle cannot be perpendicular. Therefore, triangle ABC cannot be a right triangle.

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solving sin ( 4x ) = √3 / 2 , the value of x is 15°

Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle. The ratios of sides of a right-angled triangle with respect to any of its acute angles are known as the trigonometric ratios of that particular angle.

For angle of 30° and 60°

sin 30° = 1/2

cos 60° = √3/2

tan60° = √3

for angle 60 °

sin60° = √3/2

cos 60° = 1/2

tan60° = 1/√3

since sin(4x) = √3/2

and sin 60° = √3/2

sin60° = sin(4x)

this means 60° = 4x

divide both sides 4

x = 60/4

x = 15°

therefore the value of x is 15°

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Answer: 32x

Step-by-step explanation:

4x (3 + 5)

add 3 and

⇒ 4x (8)

⇒ 32x answer .

hope that helps...

In the transaction, he will receive $374 more in sales of buttered popcorn than caramel popcorn.

An operation, often known as an "operand" or "argument," is a function in mathematics that converts zero or more input values into a clearly defined output value. In mathematics, addition, subtraction, multiplication, division, and modular forms are the five basic operations.

Given, Derek owns a snack shop where he sells tins of buttered and caramel popcorn. The table shows the number of each type of popcorn sold over w weeks.

Popcorn Sales     Popcorn Cost ($)      Number Sold Over w Weeks

Buttered                   11                                        8w+9

Caramel                    11                                        6w−1

After 12 weeks of total buttered popcorn, he will make the sale

= $11 * (8*12 + 9)

= 11 * (96 + 9)

= $1,155

After 12 weeks of total caramel popcorn, he will make the sale

= $11 * (6*12 - 1)

= $11* (71)

=$781

In the sale, he will get more sales in buttered popcorn than sales in caramel popcorn by 1,155 - 781 = $374

Therefore, He will make $374 more in sales of buttered popcorn than caramel popcorn during the sale.

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The length of the sides of ΔABC are; AB = 2√5, BC = √13, and AC = √17

The length of the sides of ΔDEF are; DE = 2√5, EF = √13, and DF = √17

By the SSS Congruence Theorem, ΔABC ≅ ΔDEF

We are given the coordinates of Triangles ABC and DEF as;

A(5, 3), B(7, 7), C(9, 4)

D(-8, 6), E(-12, 8), F(-9, 10)

The formula for distance between two coordinates is;

Distance = √[(y₂ - y₁)² + (x₂ - x₁)²]

Thus;

AB = √[(7 - 3)² + (7 - 5)²]

AB = √20

AB = 2√5

Similarly;

BC = √[(4 - 7)² + (9 - 7)²]

BC = √13

AC = √[(4 - 3)² + (9 - 5)²]

AC = √17

Likewise;

DE = √[(8 - 6)² + (-12 + 8)²]

DE = √20

DE = 2√5

Similarly;

EF = √[(10 - 8)² + (-9 + 12)²]

EF = √13

DF = √[(10 - 6)² + (-9 + 8)²]

DF = √17

Since the corresponding sides of the two triangles are equal and as such they can be said to congruent by SSS Congruency.

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The plot for histogram is given below. Through digits distribution it can be seen that last digit of height of many students are same and the heights appear to be reported.

What is frequency distribution?

To make the information easier to understand, frequency distributions are visual displays that organise and present frequency counts. Absolute frequencies as well as relative frequencies, such as percentages or ratios, can be displayed in frequency distributions.

The table of data is given below.

According to the table the histogram is plotted.

The graphic representation of data points arranged into user-specified ranges is called a histogram. The histogram, which resembles a bar graph in appearance, condenses a data series into an intuitive visual by collecting numerous data points and organising them into logical ranges or bins.

The digits distribution show that the maximum number of students have a height whose last digit is 3.

The heights appears to be reported by the students and not actually measured as maximum of them are having same last digit which corresponds to the possibility that the first digit might be different. This is a possible example of a survey.

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On solving the provided question, we can say that since it it is right angled triangle so the relation that be formed is  [tex]m^2 = p^2 + z^2[/tex]

A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.

since it it is right angled triangle

so the relation that be formed is

[tex]m^2 = p^2 + z^2[/tex]

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Answer:

-8.52, -8.15, 0.55, 8.25

Step-by-step explanation:

The lowest of negatives goes first, and the highest of positives goes last.

Answer:

from the least to the highest which is:

-8.52

-8.15

0.55

8.25

Answer:

215/100

Step-by-step explanation:

it is asking for improper fraction

improper fractions are just the bottom number multiplied by the number outside of the fraction so in this case it is

2*100 which is 200 then add that to the top number

which leaves you with 215/100

Answer:

no, it's not correct

Step-by-step explanation:

volume or the cube = L³

so if we doubled the side lengths

They would be 2L

then the volume= (2L)³ = 8L³

so that would make the volume 8 times the first value not double

The original amount placed in the account is $320.

What is simple interest ?

Simple interest is calculated based on a loan's principal or the initial deposit into a savings account. Simple interest doesn't compound, therefore a creditor will only charge interest on the principal sum, and a borrower will never be required to pay further interest on the interest that has already accrued.

The simplest way to compute interest is as a percentage of the principal. For instance, if you borrow $100 from a friend and agree to pay back the money with 5% interest, the interest you would have to pay would simply be 5% of $100, or $5.

Simple Interest is the amount repaid for using the borrowed funds over a predetermined amount of time.

The interest earned is calculated as follows:

I = P*r*t

Where:

I = Interest

P = initial principal balance

r = interest rate

t = time

Marvin is saving money in a savings account with a simple interest rate of r=7.5%=0.075. It's known that after t=12 years, the account had earned $288 interest.

Substituting in the formula:

288 = P*0.075*12

Calculating:

288 = 0.9P

Dividing by 0.9:

P = $320

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When two inner angles are stated as 61° and 52° in the sixth figure, x and y are both set to 67°.

A circle is created in the plane by each point that is a specific distance from another point (center). Thus, it is a curve made up of points that are separated from one another by a defined distance in the plane. Additionally, it is rotationally symmetric about the center at every angle. Every pair of points in a circle's closed, two-dimensional plane are evenly spaced apart from the "center." A circular symmetry line is made by drawing a line through the circle. Additionally, it is rotationally symmetric about the center at every angle.

given

in 6th figure

61° + 52° + x = 180° ( sum of exterior angle )

113° + x = 180°

x = 67°

y = 67°

When two inner angles are stated as 61° and 52° in the sixth figure, x and y are both set to 67°.

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The depiction of numbers as an equilateral triangle organized in a series is known as a triangular number sequence. These numerals follow a 1, 3, 6 order.

A number that may be expressed as the sum of the initial n positive integers is referred to as a triangular number.

Thus, the first three triangular numbers 1, 3, 6.

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Let's say we have an expression P^A then the negation of  P^A  will be not(  P^A  ). This is an example of negation.

As the name suggests negation means the negative of a term or expression and it comes under the branch of mathematical logical reasoning.

When not word is added in front of an expression it becomes the opposite , this is how we negate something. A statement is only admissible if it is always true or always false.

It is sometimes required in mathematics to find the inverse of a particular mathematical statement, this is when negation is used. Negation thus, refers to the process of determining the inverse of a given assertion.

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The height of the mt. Everest in miles exists 5.499 miles.

By changing the unit of measurement, a quality can be expressed differently. In contrast to distance, which can be stated in miles, kilometers, feet, or any other unit of length, time can also be expressed in minutes rather than hours.

By multiplying or dividing a number, a conversion factor can be used to change one set of units to another. The right conversion factor to an equal value must be used when a conversion is required. The correct conversion factor, for instance, is 12 inches to 1 foot when converting between inches and feet.

The height of the mt. Everest is : 29035 feet.

The unit conversion is given as :

5280 feet = 1 mile

1 feet = 1/5280 mile

So, 29035 feet =29035 × 1/5280 miles

29035 feet = 29035/5280 miles

29035 feet = 5.499 miles

So, the height of the mt. Everest in miles is 5.499 miles.

The complete question is:

In the Himalaya mountains along the border of Tibet and Nepal, mount Everest reaches a record height of 29,035 feet. how high is mt. Everest in miles? use the conversion equivalency of 1 mile = 5280 feet.

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Answer:  The height of the Mount Everest in miles is 5.499 miles

Step-by-step explanation:

1 miles = 5,280 feet

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The solutions for all the equations would be

1. p = 30

2. h = 99

3. t = 31.4

4. r = 57

5. t = 5

6. w = 8

7. y = 9

8. p = 7

9. a = 13

10. w = 12

11. h = 24

12. g = 128

13. a = 21

14. y = 39

15. d = 16

16. w = 25

What is an equation?

An equation is a statement that asserts the equality of two expressions. The expressions on either side of the equation are separated by an equals sign (=), and they must have the same value for the equation to be true.

1) 30p = 900

  p = 900/30

  p = 30

2) h/9 = 11

   h = 9 * 11

   h = 99

3) t + 32.4 = 62

   t = 62 - 32.4

   t = 31.4

4) r - 17 = 40

   r = 40 + 17

  r = 57

5)  5t = 25

      t = 25/5

      t = 5

6) 8w = 64

    w = 64/8

   w = 8

7)  9y = 81

     y = 81/9

     y = 9  

8) p + 5 = 12

   p = 12 - 5

   p = 7

9)  a + 2 = 15

    a = 15 - 2

    a = 13

10)  w + 8 = 20

      w = 20 -8

      w = 12

11)  h/6 = 4

    h = 6 * 4

    h = 24

12) g/8 = 16

    g = 16 * 8

    g = 128

13) a/7 = 3

    a = 3 * 7

    a = 21

14) y - 11 = 28

    y = 28 + 11

    y = 39

15) d - 4 = 12

    d = 12 + 4

    d = 16

16) w - 10 = 15

    w = 15 + 10

    w = 25

Hence, solutions for all the equations would be

1. p = 30

2. h = 99

3. t = 31.4

4. r = 57

5. t = 5

6. w = 8

7. y = 9

8. p = 7

9. a = 13

10. w = 12

11. h = 24

12. g = 128

13. a = 21

14. y = 39

15. d = 16

16. w = 25

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