if the circumference of a circle is four and the radius is two what is the diameter and area

The sum of the first 6 terms of the given sequence is -1350.

What is sum?

In mathematics, the term "sum" refers to the result of adding two or more numbers or quantities together. The sum of two numbers a and b is denoted by a + b. Similarly, the sum of three numbers a, b, and c is denoted by a + b + c.

The given sequence is a finite geometric sequence with a common ratio of -3. To find the sum of the first 6 terms of this sequence, we can use the formula for the sum of a finite geometric series:

[tex]S_n = a(1 - r^n) / (1 - r)[/tex]

where S_n is the sum of the first n terms of the sequence, a is the first term of the sequence, r is the common ratio, and n is the number of terms in the sequence.

Substituting the given values, we get:

[tex]S_6 = 18(1 - (-3)^6) / (1 - (-3))\\\\S_6 = 18(1 - 729) / 4\\\\S_6 = -1350[/tex]

Therefore, the sum of the first 6 terms of the given sequence is -1350.

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Answer:

Step-by-step explanation:

-1,092

Angles complementary to ∠BEA are ∠BED and ∠ABE.

Angles supplementary to ∠BFC are ∠AFB and ∠EFC.

Angle supplementary to ∠CAE is ∠FCD.

Complementary angles are defined as two angles whose sum is 90 degrees.

Complementary angles sum up to 90 degrees.

Supplementary angles are those angles that sum up to 180 degrees.

Therefore, the sum of the angles is 180 degrees.

Let's find the angles that are supplementary or complementary to the highlighted angles.

Therefore,

Angles complementary to ∠BEA are ∠BED and ∠ABE.

Angles supplementary to ∠BFC are ∠AFB and ∠EFC.

Angle supplementary to ∠CAE is ∠FCD.

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The number of hours it will take to complete the resurfacing project is:

51 hours

We are told that the department of  transportation is resurfacing 12. 75 miles of roadways in Collin County.

Now, we are also given that:

Number of miles completed each hour = 1/4 mile in section = 0.25 mile per hour

Thus, the number of hours it will take to complete the resurfacing project is:

That would be 12.75 divided by 0.25 hours

= 12.75/0.25

= 51 hours

Thus, we conclude that is the total time it will take to complete the project

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Answer: y - 2 = 2(x - -3)

The slope is 2 is you find the intercept.

Step-by-step explanation:

:)

Answer:

a maybe

Step-by-step explanation:

a. The Hamiltonian is given by:

H = T + V = (p² / 2I) + 0 = p² / 2I

b. Since the commutator is zero, we can conclude that the Hamiltonian and L commute.

c. The energy eigenfunctions are given by:

ψ[tex]_{n}[/tex](θ, φ) = √((2n + 1) / (4π)) × [tex]e^{(inφ)[/tex] × P[tex]_{n}[/tex](cosθ)

When time is not explicitly included in the function, it is used to characterize a dynamic system (such as the motion of a particle) in terms of momentum components and coordinates of space and time, and it is equal to the total energy of the system.

(a) The Hamiltonian is given by:

H = T + V = (p² / 2I) + 0 = p² / 2I

where T is the kinetic energy and V is the potential energy. Since the rotator is constrained to rotate in the x-y plane, there is no potential energy.

b. To show that the Hamiltonian and L commute, we need to calculate their commutator:

[H, L] = HL - LH

where L is the angular momentum operator given by L = r x p, where r is the position vector and p is the momentum operator.

HL = (p² / 2I) × (r × p) - (r × p) × (p² / 2I)

  = (1/2I) × (p² × r × p - r × p × p²)

  = (1/2I) × [p², r x p]

LH = (r x p) × (p² / 2I) - (p² / 2I) × (r x p)

  = (1/2I) × (r × p × p² - p² × r x p)

  = -(1/2I) × [p², r x p]

Therefore, [H, L] = [p², r x p] / 2I - [p², r x p] / 2I = 0.

Since the commutator is zero, we can conclude that the Hamiltonian and L commute.

c. The allowed energies of the rigid rotator are given by:

E[tex]_{n}[/tex]= (n² × h²) / (8I)

where n is a positive integer and h is Planck's constant. The energy levels are quantized and spaced equally apart, with the energy increasing as n increases.

The energy eigenfunctions are given by:

ψ[tex]_{n}[/tex](θ, φ) = √((2n + 1) / (4π)) * [tex]e^{(inφ)[/tex] * P[tex]_{n}[/tex](cosθ)

where θ is the polar angle and φ is the azimuthal angle, and P_n(x) is the n-th order Legendre polynomial. The eigenfunctions are normalized and orthogonal, with each energy level having a unique set of eigenfunctions.

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Answer:  

Distant with current is 30, distance against current is 24.

Rate with current is 6, rate against current is 4.

Time with current is 8 hours, time against current is 14

Step-by-step explanation:  

2nd question answer: 24 - 6x = 8.

The one less likely to be picked is the one with less & (Vice Versa).

To find the probability: (#of paper clips/total amount of items)

4,396 flowers are needed to surrond the circular garden.

We know that the circumference of a circle of radius R is:

C = 2*3.14*R

Here the radius is 175ft, then the circumference is:

C = 2*3.14*175ft = 1,099ft

And we know that:

1ft = 12in

Then the circumference in inches is:

1,009*12 in = 13,188 in

If each flower is separated by 3 inches, the number needed is:

13,188 in/3in = 4,396 flowers.

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Answer:

The definition of LCD is Least Common Denominator.

Step-by-step explanation:

Question 2:

LCD of 7/8 and 3/4 is 8

Question 3 :

7/8 - 3/4

7/8 - 6/8

1/8

Hope this helps :) !!

Answer:

Step-by-step explanation: First of all, the full form of LCD is "Lowest Common Denominator"

LCD is the least common denominator that can be used for all types of fractions.

For example, if we have the fractions 1/2 and 2/3, we can write:

1/2 as 2/4,3/6 or 4/8

           and

2/3 as 4/6,6/9 or 8/12

Hence, the least common denominator of 1/2 and 2/3 is 6, since it is present in the denominators of all the fractions.

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Answer:

 92.5°

Step-by-step explanation:

You want the angle where chords cross, given that they intercept arcs of 55° and 130°.

The angle x° is the average of the measures of the intercepted arcs:

  x° = (55° +130°)/2

  x° = 92.5°

The measure of ∠CFE is 40°

To solve for triangle ∠CEF, we know that

Parallel to DE is BC

Arc length BD = 58°

Arc length DE = 142°

We can then draw a diameter across the center of the circle and give it a name as the first step. The diameter in this situation is line ZT.

The arcs BD and DE are split in half by the line ZT.

Which is:

Arc SC = 1/(1/2(arc BC) = 1/(58)

Arc SC = 29°

142 = 1/2(arc DE) + arc TE

Arc TE = 71°

Sum of the angles of a semicircle is 180 degrees: Arc SC + Arc CE + Arc TE

29° + Arc CE + 71° = 180°

Arc CE + 100° = 180°

Arc CE = 180-100

Arc CE = 80°

Angle inscribed equals half of angle intercepted

CFE = 1/2 of Arc CE

<CFE = 1/2(80)

< CFE = 40°

The above answer is based on the full question below;

In circle A shown, BC || DE , mBC=58° and mDE=142°. Determine the measure of ZCFE . Show how you arrived at your answer

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So the measure of angle HLK is 45 degrees.

In geometry, an arc is a part of a curve that is typically a segment of a circle. It is defined by any two points on the curve, which are called its endpoints, and by all the points that lie along the curve between those two endpoints. An arc can be measured by its degree measure, which is the measure of the central angle that intercepts the arc, or by its length, which is the distance between its endpoints along the curve. In the context of a circle, an arc is also called a circular arc.

Here,

Since the measure of minor arc HK is 90°, we know that angle HJK is also 90°, since it is an inscribed angle that intercepts the same arc.

By the inscribed angle theorem, the measure of angle HLK is half the measure of arc HK. Therefore,

measure of angle HLK = 1/2 * measure of arc HK

= 1/2 * 90°

= 45°

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The measure of angle ∠B in triangle ABC will be 35.89°.

Given that:

Sides, AC = 23 miles and AB = 22 miles

Angle, ∠A = 110°

The sine law in the triangle ΔABC is given as,

AB / sin C = BC / sin A = AC / sin B

23 / sin C = BC / sin 110° = 23 / sin B

The value of BC is calculated as,

BC² = AB² + AC² - 2 AB·AC cos A

BC² = 22² + 23² - 2 x 22 x 23 x cos 110°

BC² = 1359.124

BC = 36.87 miles

The value of angle B is calculated as,

36.87 / sin 110° = 23 / sin B

sin B = 0.586

∠B = 35.89°

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The side length of the juice box is given as follows:

5 cm³.

The volume of a cube of side length a is given by the cube of the side length, as follows:

V(a) = a³.

The total volume of the box in this problem is given as follows:

55 + 40 + 30 = 125 cm³.

Hence the side length of the juice box is given as follows:

a³ = 125

a³ = 5³

a = 5 cm.

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On solving the provided query we have Another characteristic of parallelograms is that one of the diagonals, BC, bisects the other side, AD, as stated in statement (4).

A mathematical equation is a formula that connects two claims and uses the equals symbol (=) to denote equivalence. An equation in algebra is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign places a space between the variables 3x + 5 and 14. The relationship between the two sentences that are written on each side of a letter may be understood using a mathematical formula. The symbol and the single variable are frequently the same. as in, 2x - 4 equals 2, for instance.

The facts (3) ABCD and AB are insufficient to demonstrate that ABCD is a parallelogram.

The diagonals are bisected by each other, which is a characteristic of parallelograms, according to statement (1).

According to statement (2), opposing sides of a parallelogram are congruent and parallel, which is another characteristic of parallelograms.

Another characteristic of parallelograms is that one of the diagonals, BC, bisects the other side, AD, as stated in statement (4).

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Answer: Symbol max-min and answer 10-4

Step-by-step explanation:

The initial exercise time is 30 minutes, so the y-intercept of the line is 30. The athlete increases their exercise time by 3 minutes each day, which means the slope of the line is 3. The correct answer is option: A.

We use the point-slope form of a line, which is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope. Using the first day's exercise time as our point, we get (1, 30) as our (x1, y1) values. Substituting these values into the point-slope form and simplifying, we get y - 30 = 3(x - 1), that  is option A. Hence option A is correct.

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Tangent ratios can be greater than or equal to 1 because acute angle is between 45 degrees and 90 degrees.

If the opposite side is longer than the adjacent side, then the tangent ratio will be greater than 1.

Similarly, if the opposite side is equal in length to the adjacent side, then the tangent ratio will be equal to 1.

In general, the tangent ratio can be greater than or equal to 1 when the opposite side is longer or equal in length to the adjacent side. This occurs when the acute angle is between 45 degrees and 90 degrees.

It is important to note that when the acute angle is less than 45 degrees, the tangent ratio will always be less than 1. Conversely, when the acute angle is greater than 90 degrees, the tangent ratio will be negative and less than 1.

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Answer:

Step-by-step explanation:

A cuz if we do 7-9=1 and he has one pound of each

Hence, the  equivalent expression  of 8(m + 4) is 8 m + 32.

In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

Two  expressions are equivalent  if they can be simplified to the same  third expression or if one of the expressions can be written like the other. In  addition, you can also determine if two expressions are equivalent when values are substituted in for  the variable and both arrive at the same answer.

we  know  that,  the  distributive  property of multiplication over addition,

that  is  a(b + c) = ab + ac.

So, apply  this  property in  8(m + 4),

than we get:

8(m + 4) = 8 m + 8(4)

8(m + 4) = 8 m + 32

Therefore,  the  equivalent  expression  for 8(m + 4) is 8 m + 32.

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We can expand 12.907.054 as 1 × 10,000,000,000 + 2 × 1,000,000,000 + 9 × 100,000,000 + 0 × 10,000,000 + 7 × 1,000,000 + 0 × 100,000 + 5 × 10 + 4 × 1.

To expand a decimal number by showing each digit by value, we need to break it down into its place values. For example, in the number 12.907.054, the first digit to the left of the decimal point is in the billions place, the second digit is in the hundred millions place, and so on.

So, we can expand 12.907.054 as follows:

1 × 10,000,000,000 + 2 × 1,000,000,000 + 9 × 100,000,000 + 0 × 10,000,000 + 7 × 1,000,000 + 0 × 100,000 + 5 × 10 + 4 × 1

This means that 12.907.054 can be written as the sum of its place values. The first digit to the left of the decimal point is worth 10 billion, the second digit is worth 1 billion, and so on until we reach the ones place.

Expanding a decimal number by showing each digit by value is a way to better understand the place values of each digit and to break down the number into smaller parts for easier analysis.

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Answer:

An equivalent equation would be 2x = 4.

Step-by-step explanation:

Expanding the brackets and simplifying, we get:

8x + 4 - 3x + 6 = 20

Combining like terms, we get:

5x + 10 = 20

Subtracting 10 from both sides, we get:

5x = 10

Dividing both sides by 5, we get:

x = 2

So an equivalent equation would be 2x = 4.

Answer:

The equivalent equation to 4(2x+1)-3(x-2)=20 is 5x+11=20

Step-by-step explanation:

Answer: Im gonna guess and say its c

Step-by-step explanation:

The estimated standard error and measures of effect size such as r2 and Cohen's d larger variance increases the standard error but decreases measures of effect size. B.

Larger variance increases the standard error but decreases measures of effect size.

The standard error is a measure of how much the sample mean is likely to vary from the true population mean.

It is calculated as the standard deviation of the sample divided by the square root of the sample size.

If the sample variance is large, the standard deviation of the sample will also be large, resulting in a larger standard error.

Measures of effect size, such as r2 and Cohen's d, indicate the strength of the relationship between variables or the size of the difference between groups, respectively.

Larger sample variances indicate greater variability in the data, which can make it more difficult to detect significant effects.

This can result in smaller effect sizes, as the magnitude of the effect is reduced relative to the variability in the data.

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The length of the radius of the cylinder with a volume of 490π cubic inches and a height of 10 inches is 7 inches.

The formula for the volume of a cylinder is V = πr²h,in which r= radius , h= cylinder height. Now we can rearrange formula by equating for r which gives the following formula:

V = πr²h

r² = V/(πh)

r = √(V/(πh))

By putting the values in the formula we can get:

r = √(490π/(π*10))

r = √49

r = 7

Therefore, the length of the radius is 7 inches.

Cylinder's volume can be viewed as the area that it takes up. It is computed by dividing the cylinder's height by the base's area, which is a circle. In this instance, we are informed that the height is 10 inches and the capacity is 490 cubic inches.

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The statement that is true about having a salaried job is "The employee is paid the same amount each week regardless of the number of hours worked." So, correct option is B.

Salaried jobs typically offer a set salary for a specified period, such as weekly, bi-weekly, or monthly, regardless of the number of hours worked. This is in contrast to hourly jobs where an employee is paid based on the number of hours worked.

Salaried employees often have a contract that specifies their salary and may include additional benefits, such as health insurance, paid vacation days, or retirement plans.

The amount of the salary is often negotiated during the hiring process and may be based on factors such as the employee's experience, education, and qualifications.

While salaried employees are expected to work a certain number of hours per week, the salary remains the same regardless of whether the employee works more or less than the expected hours.

So, correct option is B.

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Answer:

(-13.82, ∞)

Step-by-step explanation:

To solve this inequality, we need to isolate the variable X on one side of the equation. First, we can subtract 3.8 from both sides of the inequality, which gives us:

X > -10.02 - 3.8

Simplifying this expression, we get:

X > -13.82

Therefore, the solution set for this inequality is all the values of X that are greater than -13.82. In interval notation, we can write the solution set as (-13.82, ∞).

Answer:

Step-by-step explanation:

This graph represents the line of best fit for some dataset.

It is reduced to a linear function in this instance with a constant slope, where x represents the independent variable and y, the dependent variable. This shows us quiz score is supposedly directly proportional to the time spent on homework per week in hours.

To find the amount of time someone should expect to study to get a 96% on their quiz you need to resolve the linear function modeled by y=mx+b which is in slope-intercept form. where m is the slope and b is the y-intercept. the y-intercept can be found when x = 0  which is shown in the graph to be 63, to solve for slope you can use the equation [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex] which is rise/ run. then plug in any 2 points I will use (1,69) and (2,75) [tex]\frac{75-69 }{2-1 }[/tex] or 6 which means m = 6, therefore, our equation is y = 6x + 63 and because we know that y must be 96 for this question, we can solve for x using inverse operations. 96 = 6x + 63 subtract 63 from both sides and 6x = 33 then divide by 6 and 33/6 = 5.5 so a person should expect to study 5.5 hours to get a quiz score of 96%