A regular hexagon is rotated about its center. Which degree measure will carry the regular hexagon onto itself?

A. 45
B. 90
C. 120
D. 135

If the radius of Jasmine's swimming pool is 4.2 meter, then it's circumference is 26.4 meters.

The "Circumference" of a circle is known as the distance around the boundary of a circle.

The circumference of a circle is given by the formula : 2 × π × radius,

where π (pi) is a mathematical constant approximately equal to 3.14,

We are given that Jasmine's swimming pool has a radius of 4.2 meters.
So, we can calculate the circumference of the pool as :

⇒ Circumference = 2 × 3.14 × 4.2 meters,

⇒ Circumference ≈ 26.4 meters,

Therefore, the circumference of Jasmine's swimming pool is 26.4 meters.

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1. When we simplify sec² x + tan² xsec² x, the result obtained is sec⁴x

2. When we simplify (sec² x - 1) / sin² x, the result obtained is sec² x

3. When we simplify (1/sec² x) + (1/csc² x), the result obtained is 1

4. When we simplify (sec x / sin x) - (sin x / cos x), the result obtained is cot x

5. When we simplify (1 + sin x)(1 - sin x), the result obtained is cos² x

6.  When we simplify cos x + sin xtan x, the result obtained is sec x

We can simplify the trig identities as follow:

1. Simplification of sec² x + tan² xsec² x

sec² x + tan² xsec² x = sec² x(1 + tan² x)

Recall

sec² x = 1 + tan² x

Thus,

sec² x(1 + tan² x) = sec² x × sec² x

sec² x(1 + tan² x) = sec⁴x

Therefore, the simplified is written as

sec² x + tan² xsec² x = sec⁴x

2. Simplification of (sec² x - 1) / sin² x

(sec² x - 1) / sin² x

Recall,

sec² x - 1 = tan² x

Thus,

(sec² x - 1) / sin² x = tan² x / sin² x

Recall

tan² x = sin² x / cos² x

Thus,

tan² x / sin² x = (sin² x / cos² x) / sin² x

tan² x / sin² x = 1/ cos² x

Recall

1/ cos² x = sec² x

Therefore, the simplified expression is written as:

(sec² x - 1) / sin² x = sec² x

3. Simplification of (1/sec² x) + (1/csc² x)

(1/sec² x) + (1/csc² x)

Recall

sec² x = 1/cos² x

Thus,

cos² x = 1/sec² x

Also,

csc² x = 1/sin² x

Thus,

sin² x = 1/csc² x

Therefore, we have

(1/sec² x) + (1/csc² x) = cos² x + sin² x

Recall

cos² x + sin² x = 1

Thus, the simplified expression of (1/sec² x) + (1/csc² x) is:

(1/sec² x) + (1/csc² x)  = 1

4. Simplification of (sec x / sin x) - (sin x / cos x)

(sec x / sin x) - (sin x / cos x) = (sec xcos x - sinx sinx) / sinx cos x

Recall

sec x = 1/cos x

sinx sinx = sin² x

Thus,

(sec x / sin x) - (sin x / cos x) = [(cos x/cos x) - sin² x] / sinx cos x

(sec x / sin x) - (sin x / cos x) = [1 - sin² x] / sinx cos x

Recall

1  - sin² x = cos² x

Thus, we have

[1 - sin² x] / sinx cos x = [cos² x] / sinx cos x

[1 - sin² x] / sinx cos x = cos x / sin x

Recall

cos x / sin x = cot x

Thus, the simplified expression of (sec x / sin x) - (sin x / cos x) is:

(sec x / sin x) - (sin x / cos x) = cot x

5. Simplification of (1 + sin x)(1 - sin x)

(1 + sin x)(1 - sin x)

Clear bracket

1 - sin x + sin x - sin² x

1 - sin² x

Recall

1 - sin² x = cos² x

Thus, we have

(1 + sin x)(1 - sin x) = cos² x

6. Simplification of cos x + sin xtan x

cos x + sin xtan x

Recall

tan x = sin x / cos x

cos x + sin xtan x = cos x + sin x (sin x / cos x)

cos x + sin xtan x = cos x + (sin² x / cos x)

cos x + sin xtan x = (cos² x + sin² x) / cos x

Recall

cos² x + sin² x = 1

cos x + sin xtan x = 1 / cos x

1/cos x = sec x

Thus,

cos x + sin xtan x = sec x

The simplified expression of cos x + sin xtan x is sec x

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By differentiating the function, we obtain 1/2x^-1/2.

The term derivative is obtained from calculus. The derivative of a number can be obtained by differentiation. In this case now, we want to find the derivative of the function f(x)=√x and it has to be by differentiation.

Given that;

y = ax^n

dy/dx = n.ax^n-1

Thus to differentiate the function we have;

f(x)= x^1/2

dy/dx =1/2 . x^1/2 - 1

dy/dx =1/2x^-1/2

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The length of the third side is 14.4 units.

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

We find the third side of a triangle by using Pythagoras theorem.

In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides

8²+12²=x²

64+144=x²

208=x²

Take square root on both sides

x=14.4

Hence, the length of the third side is 14.4 units.

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The loss on selling 50 shares of stock would be 87.50.

To calculate the loss on selling 50 shares of stock originally bought at

\(13\frac{3}{4}\) and sold at 12, we need to determine the difference between the purchase price and the selling price, and then multiply it by the number of shares sold.

First, let's convert the purchase price from a mixed fraction to a decimal. \(13\frac{3}{4}\) can be expressed as 13.75.

Next, we calculate the difference between the purchase price and the selling price:

\(13.75 - 12 = 1.75.\)

Finally, we multiply the difference by the number of shares sold:

\(1.75 \times50 = 87.50.\)

Therefore, the loss on selling 50 shares of stock would be 87.50.

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Answer:

x = 3

Step-by-step explanation:

Let's solve your equation step-by-step.

7x−3=18

Step 1: Add 3 to both sides.

7x−3+3=18+3

7x=21

Step 2: Divide both sides by 7.

7x/7 = 21/7

x=3

1598 cm square is the area of the container.

According to the statement

we have given that the container is rectangular prism

And Length of rectangular prism is 34cm

Width of rectangular prism is 17 cm

Height of rectangular prism is 20 cm

we use the below written formula to find the surface area

Surface area formula A=(wl+hl+hw)

To find the surface area of the container.

Substitute the values of Length, width and height in the formula then

A=(wl+hl+hw)

A=((17)(34)+(20)(34)+(20)(17))

After solving the values

A=(578+680+340)

A= 1598

So, 1598 cm square is the area of the container.

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As a result, the experimental probability of landing on heads is 48%, probability which means that we should expect heads approximately 48 times out of 100 coin flips.

Probability is a measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, with 0 indicating an unlikely event and 1 indicating an unavoidable event. Because there are two equally likely outcomes, switching a fair coin and coin flips has a probability of 0.5 or 50%. (Either heads or tails). Probability theory, a branch of mathematics, is concerned with the investigation of random events rather than their properties. It is used in a variety of fields, including statistics, finance, science, and engineering.

The following formula can be used to calculate the relative frequency or experimental probability of landing on heads:

Number of Heads / Total Number of Flips = Experimental Probability of Heads

The number of heads in this case is 48, and the total number of flips is 100. Therefore,

Heads Experimental Probability = 48 / 100 = 0.48

We can multiply this by 100 to get a percentage:

Heads Experimental Probability = 0.48 * 100 = 48%

As a result, the experimental probability of landing on heads is 48%, which means that we should expect heads approximately 48 times out of 100 coin flips.

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A Budget is best defined as a financial plan that estimates how much money you will need to spend to cover your expenses. That is option D.

Budget can be defined as the financial document that is used to show the estimation of intending expenses, and how much would be required to meet such expenditures.

The importance of budget include the following:

Therefore budget is used by companies and business organizations to estimate how much money they will need to spend to cover their expenses.

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The Distance the handler will move from the starting point to the return point will be approximately 439.8204 feet.

The distance the handler will move from the starting point to the return point when creating an arc of a circle with a radius of 70 feet, we need to find the length of the arc.

The formula to calculate the length of an arc is given by:

Length of arc = (θ/360) * 2πr

Where:

θ is the central angle of the arc (in degrees)

r is the radius of the circle

In this case, since the handler is creating a full circle, the central angle is 360 degrees.

Length of arc = (360/360) * 2π * 70

Length of arc = (1) * 2π * 70

Length of arc = 2π * 70

Length of arc = 140π

To find the approximate value in feet, we can use the approximation π ≈ 3.14159.

Length of arc ≈ 140 * 3.14159

Length of arc ≈ 439.8204 feet

Therefore, based on the given theory and using a circle with a radius of 70 feet, the distance the handler will move from the starting point to the return point will be approximately 439.8204 feet.

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A) The probability that a piece of toast lands butter side down when dropped from a 2.5-foot high table is 0.81 means that out of all possible outcomes of dropping a piece of toast from that height, 81% of the time it will land with the butter side facing down.

B) No, it does not mean that exactly 81 out of 100 pieces of toast will land butter side down. The probability of a single piece of toast landing butter-side down is 0.81, so when 100 pieces of toast are dropped, we can expect around 81 of them to land butter-side down on average, but the actual number may vary due to randomness.

C) Maria may or may not be surprised, depending on her expectations and the level of significance she sets for her test. To carry out a simulation, we can use a random number generator to simulate dropping 10 pieces of toast with a probability of 0.81 of landing butter side down. We can repeat this simulation multiple times, say 1000 times, and count the number of times the simulation yields 4 or fewer pieces of toast landing butter side down. If this rarely happens (e.g., less than 5% of the time), we can say that Maria should be surprised.

D) The dot plot displaying the results of 50 simulated trials of dropping 10 pieces of toast can provide some information about the variability of the outcomes. If most of the dots are clustered around 8 or 9 (which would correspond to 80% or 90% of the pieces of toast landing butter side down), then Maria's result of only 4 out of 10 pieces landing butter side down would be considered unusual, and she should be surprised. However, if the dots are spread over a wide range, it would suggest that getting 4 out of 10 is not that uncommon, and Maria should not be surprised.

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Answer:

Neck

Step-by-step explanation:

Which one is closest to your head?

T-T

Both men are committing fallacies in their reasoning. The occurrence of a hurricane on that land cannot be predicted with certainty, and making decisions based on fallacious reasoning can lead to poor outcomes.

A fallacy refers to the statement in an argument that makes an error in logic. Fallacies are very dangerous because they lead to incorrect thinking about certain topics and may lead to an incorrect conclusion about that topic most of the time.

The fallacy in Poindexter's uncle's reasoning is known as the fallacy of induction. This fallacy occurs when someone assumes that because a certain event has happened in the past, it is likely to happen again in the future. While it is true that the land has been hit by hurricanes 160 times in the past, it doesn't necessarily mean that it will happen again in the near future.

On the other hand, Poindexter's nephew is committing the fallacy of the Gambler's Fallacy. This fallacy occurs when someone assumes that because something hasn't happened in a while, it is more likely to happen soon. In this case, the nephew assumes that a hurricane must be due soon simply because it hasn't happened in the past 13 years. However, the occurrence of a hurricane is not influenced by the time that has passed since the last one. Each hurricane is a unique event that is not influenced by previous occurrences.

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Answer:

4x + 1

Step-by-step explanation:

g(f(x)) = (4x + 3) - 2

         = 4x + 1

Answer:

4x² + 24x + 36

Step-by-step explanation:

(2x + 6)² = (2x + 6)(2x + 6) = 4x² + 12x + 12x + 36 = 4x² + 24x + 36

Answer:

392 ft^2

Step-by-step explanation:

area = length * width

a = lw

392 = 14 * 28

Don't forget the unit is ft^2 since we are finding the area of a 2-dimensional shape in feet!

Answer:

Step-by-step explanation:

the area of a rectangle is L*W

A=14*28=392 ft^2

Therefore the answer is 27 or more months to depreciate to less than £1200 at a rate of 5% per month.

Depreciation is a phrase that covers two different elements of the same idea: first, the real decline in an asset's fair value, such as the annual decline in the worth of industrial equipment.

Your balance sheet may be broken down into two categories, assets and liabilities, in its most basic form. A company's assets are any possessions that have the potential to provide future financial gain. Your debts to other people are called liabilities. In other words, assets increase your wealth while obligations decrease it.

The value of the motorbike will decrease by 5/100 = 0.05 (or 5%) each month. So, to find out how many months it will take for the value of the motorbike to decrease from £2550 to less than £1200, you need to solve the following equation:

£2550 - (0.05 * x) < £1200

where x is the number of months.

You can re-arrange the equation to solve for x:

x > (2550 - 1200) / 0.05

x > (1350) / 0.05

x > 27

So it will take the motorbike 27 or more months to depreciate to less than £1200 at a rate of 5% per month.

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Answer:

If it is a fair die then it should have 6 faces, each one having a number 1-6. The probability of landing on a single number is 1/6. Because the die is fair there should be an equal probability of landing on a number 1-6 giving you a probability of 1/6. However, if the number of times rolled is changed, then the answer would be multiplied or added (depending on the question).

Answer:

35 cm

Step-by-step explanation:

Answer:

0.35 meters^2 or 35 cm^2

Step-by-step explanation:

we break up the shape and the problem into two parts.

we will begin by finding the area of the triangle first (or you could find the square's area first) and we know the area formula for a triangle is

Area (triangle) = (1/2) base x height

height = 0.04 meters or 4cm

base = 0.05 meters or 5 cm

therefore the area is:

(1/2) (5cm)(4cm) = 10 cm^2

now we find the area of the square which is very easy. it is simply base times the height (b x h)

Area (square) = 5cm x 5cm = 25cm^2

finally, we add the total area

Area (total) = Area (square) + Area (triangle) = 10 cm^2 + 25 cm^2

= 35 cm^2

(n-1) where n= 3

Answer is 2

(n - 1)!

n = 3

( 3 - 1)!

2!

= 1 × 2

= 2

n = 2

(2 - 1)!

1!

= 1

n = 5

(5 - 1)!

4!

= 1 × 2 × 3 × 4

= 24

n = 6

(6 - 1)!

5!

= 1 × 2 × 3 × 4 × 5

= 120

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There are 14 Geometry problems in Vardan's homework assignment.

The number of geometry problems in Vardan's homework assignment, we need to calculate 58 1/3 percent of the total number of problems.

First, let's convert 58 1/3 percent to a decimal by dividing it by 100:

58 1/3 percent = 58.33/100 = 0.5833

Next, we multiply the decimal by the total number of problems:

Number of geometry problems = 0.5833 * 24

To calculate this, we can multiply 0.5833 by 24:

Number of geometry problems = 0.5833 * 24 = 14

Therefore, there are 14 geometry problems in Vardan's homework assignment.

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The solution is, the simplification of the equation is :

4x^2 - 4 = (2x -2 ) (2x+2)

Here, we have,

given that,

the expression is:

4x^2 - 4

now, we have to simplify this.

we know that ,

The a^2 - b^2 formula is also known as "the difference of squares formula". The a square minus b square is used to find the difference between the two squares without actually calculating the squares.

It is one of the algebraic identities.

It is used to factorize the binomials of squares.

The a^2 - b^2 formula is given as:

a^2 - b^2 = (a - b) (a + b).

so, we have,

4x^2 - 4

= (2x)^2 - 2^2

= (2x -2 ) (2x+2)

Hence, The solution is, the simplification of the equation is :

4x^2 - 4 = (2x -2 ) (2x+2)

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The magnitude of vector is 8.24 and angle is 75.9638.

What is vector?

A vector could be a amount that not solely describes the magnitude however additionally describes the movement of an object or the position of an object with reference to another purpose or object.

Main body:

we know that the magnitude of vector is found out by,

| u | = \(\sqrt{i^{2}+j^{2} }\)

so here , u = 2i + 8j

|u| = \(\sqrt{2^{2} +8^{2} }\)

|u| = \(\sqrt{68}\)

|u| = 8.24

now to find the direction , angle

tan∅ = j/k

tan∅ = 8/2

∅ = tan⁻¹ (4)

∅ = 75.9638°

Hence , direction angle of the following vector is ∅ = 75.9638°

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1-9/16 :) good luck my friend

The measure in radians of angle POQ is given as follows:

π/4 radians.

The measure of angle POQ is obtained applying the proportions in the context of the problem.

Angle POR is one fourth of the unit circle, which is of 360º, hence it's measure is given as follows:

POR = 0.25 x 360

POR = 90º.

Angle POQ is halfway between 0 radians and angle POR, hence it's measure is given as follows:

POQ = (0 + 90)/2 = 45º.

180º is equivalent to π radians, and 180/45 = 4, hence the measure in radians of angle POQ is given as follows:

π/4 radians.

The diagram is given by the image presented at the end of the answer.

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Answer: Hello!

Step-by-step explanation: After measuring the two triangles I can conclude they are congruent!

Finn, tenth grader straight A student.

Have a great day.

Answer:

5m

Step-by-step explanation:

regla de 3:

1m = 3ft

15 pies ÷ 3 = 5m

The area of the square with a side length of 3.1 meters is 9.61 square meters.

To find the area of a square, we need to multiply the length of one side by itself. In this case, the square has a side length of 3.1 m.

Area of a square = side length × side length

Substituting the given side length into the formula:

Area = 3.1 m × 3.1 m

To perform the calculation:

Area = 9.61 m²

It's worth noting that when calculating the area, we are working with squared units. In this case, the side length is in meters, so the area is expressed in square meters (m²). The area represents the amount of space enclosed within the square.

Remember, to find the area of any square, you simply need to multiply the length of one side by itself.

The area of the square with a side length of 3.1 meters is 9.61 square meters.

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