FIND THE SUM OF ALL NATURAL NUMBERS FROM 1 TO 100 (ARITHMETIC PROGRESSION)

Since the diameter of this circle is 76 inches, a measurement which the circumference of this circle has include the following: C. 238.64 inches.

Mathematically, the circumference of a circle can be calculated by using this mathematical expression:

C = 2πr or C = πD

Where:

Substituting the given parameters into the circumference of a circle formula, we have;

Circumference of circle, C = πD

Circumference of circle, C = 3.14 × 76

Circumference of circle, C = 238.64 inches.

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Complete Question:

The diameter of a circle is 76 inches. Which measurement does the circumference of this circle have?

A. 123.45 inches.

B. 438.65 inches.

C. 238.64 inches.

D. 338.64 inches.

If Jupiter is about 5.2 Astronomical Units (AU) from the Sun and Neptune is about 30.1 AU from the Sun, Neptune is about 5.79 times far from the Sun as Jupiter.

Therefore the answer is 5.79.

To find how many times as far from the Sun Neptune is as Jupiter, we need to divide the distance from the Sun to Neptune by the distance from the Sun to Jupiter.

Neptune is about 30.1 AU from the Sun and Jupiter is about 5.2 AU from the Sun, so:

= Distance from the Sun to Neptune / Distance from the Sun to Jupiter

= 30.1 / 5.2

= 5.79

So, Neptune is about 5.78 times as far from the Sun as Jupiter.

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On solving the provided question, we can say that - the valuye os the complementary angle is 83.0000000004.

When two angles add up to 90 degrees, they are said to be complimentary. When two angles add up to 180 degrees, they are said to be subservient. . When the sum of two angles equals 90 degrees, they are called complementary angles. For example, 30 and 60 degrees are supplementary angles. A supplementary angle is two angles that add up to 180 degrees, and a supplementary angle is two angles that add up to 90 degrees. of 30 and 60 degrees are supplementary. A supplementary angle is two angles combined to make a 180 degree angle, while a supplemental angle is two angles combined to make a 90 degree angle. Two angles are referred to as complimentary if their total is 90 degrees. Alternatively said, a right angle is created by the complementary angles (90 degrees).

here we have

(12x + 7) = 90

12x = 83

x= 6.9166666667

12x = 83.0000000004

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A statement that correctly compares the measures of center in the two sets of data is: Both the mean and median are greater for Plot A than for Plot B.

The correct answer is an option (A)

Consider plot A.

The data value represented on the dot plot:

3, 4, 4, 5, 5, 6, 6, 7, 7, 10

Using the formula of mean, the mean of Plot A would be:

mean = (3 + 4 + 4 + 5 + 5 + 6 + 6 + 7 + 7 + 10) / 10

mean = 57/10

mean = 5.7

The middle value of the data is: 5, 6

So, the median is:

Median = (5 + 6)/2

            = 11/2

            = 5.5

Consider plot B.

The data value represented on the dot plot:

3, 4, 4, 5, 5, 5, 6, 6, 6, 7

mean = (3 + 4 + 4 + 5 + 5 + 5 + 6 + 6 + 6 + 7)/10

mean = 51/10

mean = 5.1

The middle value of the data is: 5, 6

So, the median is:

Median = (5 + 5)/2

            = 5

Hence, both the mean and median are greater for Plot A than for Plot B.

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The complete question is:

Which statement correctly compares the measures of center in the two sets of data? Both the mean and median are greater for Plot A than for Plot B. Both the mean and median are greater for Plot B than for Plot A. Plot A has a greater median than Plot B, but Plot B has a greater mean. Plot B has a greater median than Plot A, but Plot A has a greater mean.

Answer:

polygon has 12 sides

Step-by-step explanation:

the sum of the exterior angles of a polygon is 360°

the sum of the interior angles of a polygon is

sum = 180° (n - 2 ) ← n is the number of sides

given the sum of the interior angles is 5 times sum of exterior angles, then

sum = 5 × 360° = 1800° then

180° (n - 2) = 1800 ( divide both sides by 180 )

n - 2 = 10 ( add 2 to both sides )

n = 12

Thus the polygon has 12 sides

Answer: 1st, 4th, and 5th choices

If we chosen the one year subscription we have to pay  7.49 per each month.

What is Linear Equation ?

Linear Equation can be defined as the equation in which the highest degree of the variable is one.

Given,

The cost of an online newspaper is 7.99

And if we bought the one year subscription the cost is 89.88

Let the the cost of the each month if we bought the one year subscription be x .

for one year the cost is 89.88

for one month could be

that is, x = 89.88/12

x = 7.49

Hence , If we chosen the one year subscription we have to pay  7.49 per each month.

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If you want to have $70,000 in 15 years, you need start saving money now in a savings account that earns 6.0% annually compounded weekly.

When you earn interest on your interest earnings as well as the money you have saved, this is known as compound interest.Compounding is effective for both promised and unguaranteed products. All or part of your money could be lost.

Use the compound interest formula and enter the figures you are familiar with. Then find a solution for the unknown number.

A = P(1 +r/n)^(nt)

where A represents the balance of the account, P represents the amount invested, r represents the yearly rate, n represents the number of times per year interest is compounded, and t is the number of years.

Filling in the given values, we have ...

70000 = P( 1 + 0.06/52)^(52*15) = P(2.4583)

P = 70000/2.4583 = 28474.96

You would need to deposit 28474.96 in order to have 70000 in 15 years.

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The area of the figure given is 49 square feet's.

       ∫dA = ∫∫F(x, y) dx dy

       A =  ∫∫F(x, y) dx dy

Given is a figure as shown in the image attached.

We can write the area of the figure as -

A = A{T} + A{R}

A = (4 x 10) + (1/2 x 6 x 3)

A = 40 + 9

A = 49 square feet's

Therefore, the area of the figure given is 49 square feet's.

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Answer:

7) perpendicular

8) perpendicular

Step-by-step explanation:

If the equations are in the form:

y = mx + b

(they all are in this form in these questions)

the m, the number in front of the x, is the slope.

If the slopes are the "negative reciprocals" (opposite signs and flipped over from each other) of each other, then the lines are perpendicular.

You can also do a quick check by, if the m values are multiplied together you should get -1.

1/3 • - 3 = -1

1 • -1 = -1

1/3 and -3 have opposite signs and are reciprocals (flipped over)

1 and -1 are opposite signs. It isn't very obvious maybe that they are reciprocals, but they are. Like 1/1 flipped over is 1/1.

As per the graph, there is no restrictions for the domain but the range has a minimum value at y = - 4.

The domain is any real number:

The range is any real number not less than - 4:

The projected population of Haleyville in 2020 is 4139.

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

Population in 2010 = 4403

The decline in population per year = 0.06%

Now,

The population in 2020.

There are 10 years between 2010 and 2020.

The function used to find the population after x years.

= 4403 x [tex]0.994^x[/tex]

Now,

x = 10

= 4403 x [tex]0.994^{10}[/tex]

= 4403 x 0.94

= 4139

Thus,

The population in 2020 is 4139.

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In order to maintain soil fertility and productivity, soil must be protected from erosion and other forms of deterioration. Water use and watershed management are typically included.

Eliminating the existing vegetation is the first step in making a garden bed. Weeds can be manually pulled. Just be certain to remove the roots to prevent regrowth. You might want to rent a gas-powered sod cutter to get rid of the grass if you're starting with a lawn.

Better soil conservation techniques that affect both erosion and fertility include crop rotation, cover crops, conservation tillage, and installed windbreaks.

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15 + 25 = 40

10% of 40 = 4

Therefore, Caleb gave $4 to the church!

Hope this helps :D

The coefficient is -1

(x - 3) is a factor of the polynomial f(x) = x³ - 3x² + 4x - 12 since f(3) = 0.

To solve the problem, recall the factor theorem.

Factor Theorem states that if we have a polynomial f(x) and if (x - a) is a factor of f(x), then f(a) = 0

The given function is:

f(x) = x³ - 3x² + 4x - 12

To see whether x - 3 is a factor of f(x) = x³ - 3x² + 4x - 12, we need to find f(3).

Substitute x = 3 into f(x):

f(3) =3³ - 3(3)² + 4(3) - 12

f(3) = 27 - 27 + 12 - 12

f(3) = 0

Since f(3) = 0, then x -3 is a factor of  x³ - 3x² + 4x - 12

Your question is incomplete, but most probably your question was:

Is x - 3 a factor of the polynomial  x³ - 3x² + 4x - 12?

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Answer:

24.90 pound

1 dollar equivalent to 0.8301 pound

so 30 dollar will be 30 multiply by 0.8301

which equals 24.903 pounds

Answer:

£15158.00

Step-by-step explanation:

The profit on the sale of 1 computer is the difference between the selling price and the buying price.

Profit on 1 computer:

£2081.00 - £915.00 = £1166.00

The profit on 13 computers is 13 times the profit on 1 computer.

13 × £1166.00 = £15158.00

Answer: £15158.00

Answer: To estimate the tip, you can first round the bill to the nearest ten dollars. In this case, $706.03 rounded to the nearest ten dollars is $710.

Next, you can calculate the tip by multiplying the rounded bill amount by the tip percentage, 15% in this case.

15% of $710 is 15/100 * 710 = 106.50

So the amount of the tip is approximately 106.50

It's worth mentioning that this method of approximation is not always precise, but it can be a quick and easy way to calculate an estimate when you don't need a very precise answer.

Step-by-step explanation:

a) To write an equation in slope-intercept form to represent the growth of the Magnolia trees over time, we can use the formula y = mx + b, where x represents the number of years, y represents the height of the tree in feet, m represents the slope (or rate of growth) of the tree, and b represents the y-intercept (or the height of the tree at x = 0).

In this case, the slope (m) of the tree is 3/4 feet per year and the y-intercept (b) is 3 feet, as the trees are initially 3 feet tall when they are purchased. Plugging these values into the formula gives us:

y = (3/4)x + 3

This equation represents the growth of the Magnolia trees over time.

b) The y-intercept of an equation in slope-intercept form represents the value of y when x is equal to 0. In this case, the y-intercept of the equation y = (3/4)x + 3 is 3 feet. This means that when x is equal to 0 (when no years have passed), the height of the tree is 3 feet.

c) To determine the height of the tree in 3 years, we can substitute 3 for x in the equation y = (3/4)x + 3 and solve for y. This gives us:

y = (3/4)(3) + 3

= 9/4 + 3

= 21/4

= 5.25 feet

Therefore, the height of the tree in 3 years is approximately 5.25 feet.

The ratio of the volume of the cone to the cylinder is 1:3.

A cone has a circular base and the base is made of a radius and diameter.

A cylinder is a three-dimensional solid shape that makes of two parallel bases linked by a curved surface.

                   V1=  πr²h

Here,

'r' is the radius of the cylinder

'h' is the height of the cylinder

π is a constant whose value is 22/7.

The ratio of the volume of the cone to the cylinder is

=  (1/3)πr²h :  πr²h

= 1 : 3

So, the ratio is - 1:3.

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The Iroquois perform rituals in "The World on Turtle's Back" to honour the twins, demonstrating their belief that they must carry out specific rituals in order to preserve the Earth.

A ritual is a set sequence of actions involving gestures, words, actions, or objects. The customs of a group, including a religious group, may dictate rituals. Formalism, traditionalism, invariance, rule-governance, sacral symbolism, and performance are characteristics of rituals but not what defines them.

All known human societies have rituals. In addition to the rites of passage, atonement, and purification, oaths of allegiance, dedication ceremonies, coronations, presidential inaugurations, marriages, funerals, and other ceremonies, they also include the worship rites and sacraments of organised religions and cults. Even routine behaviours like shaking hands and saying "hello" can be categorised as rituals.

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The number 59 in the equation represents the following:

"A student's expected quiz score if they spent no time on their homework"

What is an equation?

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

y=59+6x

When x=0, y=59+6*0 = 59+0 = 59

This means,  y=59 is the  student's expected quiz score if they spent no time on their homework.

The number 59 in the equation represents the following:

"A student's expected quiz score if they spent no time on their homework"

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The 4 quadrants are called as Quadrant I, Quadrant II, Quadrant III and Quadrant IV.

The term quadrant in math is also known as the coordinate grid, cartesian coordinate system, or Cartesian plane, are basically constructed by taking a vertical axis, or the y-axis and setting it against a horizontal axis, or the x-axis and it creates a grid with four quadrants.

According to the cartesian system, here the coordinate plane is divided into four equal parts by the intersection of the x-axis and the y-axis such as the vertical number line.

Here the four quadrants are written as,

Quadrant I that is placed upon the upper right quadrant is the first quadrant, denoted as Quadrant I and the value on the x-axis and the y-axis both have positive numbers.

Next one is Quadrant II which is placed on the upper left quadrant is the second quadrant, denoted as Quadrant II and the value of the x-axis has negative numbers and the y-axis has positive numbers.

Third one is Quadrant III placed on the bottom left quadrant is the third quadrant, denoted as Quadrant III and the value of both the x-axis and the y-axis have negative numbers.

Final one is Quadrant IV which is placed on the bottom right quadrant is the fourth quadrant, denoted as Quadrant IV and here the value of the x-axis has positive numbers and the y-axis has negative numbers.

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The maximum possible value for the greatest common divisor (GCD) of 11n + 3 and 2n + 1 as n ranges over the positive integers is 1.

The GCD of two integers is the largest integer that divides both integers without leaving a remainder. We can use the Euclidean algorithm to find the GCD of two numbers.

The Euclidean algorithm states that for two integers a and b, we can find the GCD of a and b by repeatedly applying the following steps:

Divide a by b to get a quotient q and a remainder r

Replace a with b and b with r

Repeat the process until r is 0

If we apply this algorithm to 11n + 3 and 2n + 1, we get the following:

GCD(11n+3, 2n+1)

As 11n + 3 = 3(2n + 1) + 5n

= GCD(2n+1, 5n )

As 2n + 1 = (2/5)(5n) + 1

= GCD(5n, 1)

= GCD(1, 0)

= 1

So as n ranges over the positive integers, the maximum possible value for the GCD of 11n + 3 and 2n + 1 is 1.

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Answer:

C,A, and F

Step-by-step explanation:

the ones that basically give him a chance is the very first one on the left side and the 3rd one down on the left side and the 2nd column the 2nd one hope this helps

The coordinate of the reflection is (-y, -x)

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

Point = (x, y)

Reflection:  Across the line y=−x

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

So, we have

Image = (-y, -x)

Hence, the image is (-y, -x)

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Answer:

2 pie over r

Step-by-step explanation:

Step-by-step explanation:

the circumference is given by:

[tex]2\pi(radius)[/tex]

in this case x is the radius hence the circumference would be:

[tex]2\pi(x)[/tex]

hope this helps :)