The length of each side is quadrupled. How many times larger is the new area when compared to the original?

2 times

8 times

4 times

16 times

If the hexagon is changed to an octagon, the area of the shaded portion will be; smaller

We are given;

Diameter of circle = 5 ft

Thus;

radius; r = 5/2 = 2.5 ft

Now, the long diagonal of the hexagon is given as 5ft and we know that if the side of the hexagon is a, then;

a = d/2

where d is the length of the long diagonal

Formula for area of hexagon is;

A = (3/2) * √3 * a²

Thus;

A =  (3/2) * √3 * 2.5²

A = 16.24 ft²

Area of circle is gotten from the formula;

A = πr²

A = π * 2.5²

A = 19.635 ft²

Thus;

Area of shaded portion = 19.635 ft² - 16.24 ft² = 3.395 ft²

If the hexagon is changed to an octagon, the formula for length of diagonal is;

L = a√(4 + 2√2)

where a is side length

Thus;

5 = a√(4 + 2√2)

a = 5/√(4 + 2√2)

Area of octagon is from the formula;

Area = 2a²(1 + √2)

Area = 2(5/√(4 + 2√2))²(1 + √2)

Area = 2(25/(4 + 2√2))(1 + √2)

Area = 17.678 ft²

Area of shaded portion = 19.635 ft² - 17.678 ft² = 1.957ft²

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Answer:

i think its 3

Step-by-step explanation:

Follow the formula and do the steps

Yes , rotating is  a congruence transformation.

What is a congruence transformation?

A transformation that changes the position of the figure while not dynamical its size or form is termed a congruity transformation.

Main body:

A congruity transformation is that the movement or locating of a form specified it produces a form that is congruent to the initial.

Translations, reflections, and rotations are the three types of congruence transformations. That is, the pre-image and the image are always congruent.

Hence ,rotating is  a congruence transformation.

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The rate at which body cover distance is given by speed.

The formual for the speed is,

For the given question, distance is d=34 miles and time is t=4/5 hours.

Substitute the value in the formula to obtain the speed of Camden.

So the speed at which camden cover distance is 85/2 miles per hour.

Answer:

y = 4x + 2

Step-by-step explanation:

This is the formula:  \(y - y_{1} = m(x - x_{1})\)

y - 2 = 4(x - 0) (distribute the 4)

y - 2 = 4x (add 2 on both sides)

y = 4x + 2

That's all she wrote!

Hope this helps ya!!

Answer:

sorry dont know the answer im new to this website

Step-by-step explanation:

Answer:

1.x=11

2.x=+5=+2.2362

3.x=+3.750=+1.93649

Using the same guideline, for a four-credit class, you would ideally spend:

4 credits * 2-3 hours/credit = 8-12 hours per week.

it is suggested that students allocate around 2-3 hours of study time per credit hour per week for a college-level course. However, the actual study time required may vary based on individual learning styles, prior knowledge, and the specific requirements set by professors or institutions.

Let's apply this general guideline to your scenario:

One three-credit class that is less demanding:

Assuming 2-3 hours of study per credit hour, for a three-credit class, you would ideally spend:

3 credits * 2-3 hours/credit = 6-9 hours per week.

Two three-credit classes that are typically demanding:

Similarly, for each of the two three-credit classes, you would spend:

3 credits * 2-3 hours/credit = 6-9 hours per week.

Since you have two such classes, the total time would be:

2 * (6-9) hours = 12-18 hours per week.

One four-credit class that is very challenging:

Using the same guideline, for a four-credit class, you would ideally spend:

4 credits * 2-3 hours/credit = 8-12 hours per week.

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Answer:

you mean y = mx + b?

Step-by-step explanation:

if so you find the two cordinates x, y and put them with the slope as in m. and you just solve it and find b

There are 8 observations with x1 values greater than 30, when the data is sorted in ascending order the first observation has x1 value of 10, x2 value of 1 and x3 value of 1.

After sorting the data in ascending order,

Value of x1 - 10

Value of x2 - 1

Value of x3 - 1

c. Sort the data by xi and x2 both in descending order. What are the x1, x2, and x3 values of the first observation after the data are sorted? Value of X1 - 35

Value of x2 - 10

Value of x3 - 5

d. How many missing values are there in x1, x2, and x3?

The number of missing values in X1 - 0

The number of missing values in X2 - 0

The number of missing values in X3 - 0

a. How many observations have x1 values greater than 30? Number of observations - 8

b. Sort the data by x1, x2, and then x3 all in ascending order. What are the x1, x2, and x3 values of the first observation after the data are sorted? Value of x1 - 10

Value of x2 - 1

Value of X3 - 1

c. Sort the data by xi and x2 both in descending order. What are the x1, x2, and x3 values of the first observation after the data are sorted? Value of X1 - 35

Value of x2 - 10

Value of x3 - 5

d. How many missing values are there in x1, x2, and x3? The number of missing values in X1 - 0

The number of missing values in X2 - 0

The number of missing values in X3 - 0

There are 8 observations with x1 values greater than 30, when the data is sorted in ascending order the first observation has x1 value of 10, x2 value of 1 and x3 value of 1. When the data is sorted in descending order, the first observation has x1 value of 35, x2 value of 10 and x3 value of 5. There are no missing values in x1, x2, and x3.

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Answer:

y=10x+15

Step-by-step explanation:

The slope intercept form is represent by this equation

\(y = mx + b\)

Where m is the slope, and b is the y intercept( when x is zero).

Looking at the graph, we already found the y intercept.

When x=0, y is at 15 so our y intercept is 15 so our equation updated look like

\(y = mx + 15\)

Now let find the slope

Slope is

\( \frac{change \: of \: y}{change \: of \: x} \)

Let use two arbitrary points to find the slope

Let use (3,45) and 6,75).

\( \frac{75 - 45}{6 - 3} = \frac{30}{3} = 10\)

So our slope is 10 so our equation look like

\(y = 10x + 15\)

Answer:

-13

Step-by-step explanation:

−2+3(1−4)−2

=−2+(3)(−3)−2

=−2+−9−2

=−11−2

=−13

Step-by-step explanation:

Is this ok

If its correct, please don't forget to like and mark me

Answer:

  99.6 cm²

Step-by-step explanation:

You want to know the area of a sector that has radius 6 cm, and subtends an arc of 317°.

The formula for the area of a sector is ...

  A = 1/2r²θ . . . . . . where θ is the central angle in radians

  A = 1/2(6 cm)²(317·π/180) ≈ 99.6 cm²

The area of the sector is about 99.6 square centimeters.

Answer:

5/9

Step-by-step explanation:

we add all of the values and divide by the total number in this case 9, all of them add to make 5 so we do 5÷9 to get 5/9

Answer:

x = 4.5, 4/7

Step-by-step explanation:

To find the roots of a factored equation you need to set the y value at 0, that way you can solve for x. Once you solve for x you get two quantities, which can be graphed. These two quantities are where the x intercepts are.

By evaluating the above integral over this region, we can find the probability of ppy ě xq. This expression is useful for calculating conditional probabilities in multivariate distributions.

To find ppy ě xq, we can use the following expression:
∫∫ f(x,y) dy dx over the region where y ≥ p, y ≤ q, and x ≤ xq
This expression represents the integral of the joint density function f(x,y) over the desired region, where y is between p and q, and x is less than or equal to xq. The result of this integration will give us the probability that a random variable (x,y) falls within this region.
To visualize this, we can draw the region of the joint density function f(x,y) on a two-dimensional plane. The horizontal axis represents x, and the vertical axis represents y. Then, we can shade in the area where y is between p and q, and x is less than or equal to xq. This shaded region represents the desired area that we want to find the probability of.

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For an exam next week, Julietta spends 2 hours studying each night for 7 nights, while Mark crams his sessions into 2 blocks of 7 hours, hence based on spacing effect, it can be predicted that Julietta’s memory would be stronger than Mark.

Spacing effect refers to an observation that repetitions that is spaced in time (spaced learning) can produce stronger long-term memories than repetitions massed closer together in time (massed learning). According to research, spaced learning has demonstrated consistently to offer benefit memory as opposed to massed learning. Spaced learning can lead to enhanced long-term memory and recollection of information learn becomes more easier than in massed learning.

In this case, Julietta opted for spaced learning, spend two hour each night studying for seven nights (the repetition of subject topic spaced over a period of week).  Mark opted for massed learning, cram his session in two blocks of seven hours straight (repetition of subject topic contracted over a short period of two blocks). Hence, Julietta will be enabled to remember the material more easily than Mark

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Answer:

a) 199

f(-6)= 5(-6)^2 - 3 (-6) + 1 =199

b) 37

f(3)= 5(3)^2 - 3 (3) + 1 =37

Answer:

To simplify the expression (-3+1)+(-4-i), we can perform the addition operation within the parentheses first:

(-3+1)+(-4-i) = -2 + (-4-i)

Next, we can simplify the addition of -2 and -4 by adding their numerical values:

-2 + (-4-i) = -6 - i

Therefore, (-3+1)+(-4-i) simplifies to -6-i.

Step-by-step explanation:

The length of the segment in the complex plane is 5.

The length of a segment in the complex plane can be found using the distance formula. To find the length of the segment with endpoints at 4+2i and 7-2i, we can use the formula:

Distance formula = sqrt((x2 - x1)^2 + (y2 - y1)^2)

In this case, the coordinates of the first endpoint are x1 = 4 and y1 = 2i, while the coordinates of the second endpoint are x2 = 7 and y2 = -2i.

Plugging these values into the formula, we have:

Distance = sqrt((7 - 4)^2 + (-2 - 2)^2)
         = sqrt(3^2 + (-4)^2)
         = sqrt(9 + 16)
         = sqrt(25)
         = 5

Therefore, the length of the segment in the complex plane is 5.

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Number of roots in the RHP of the complex plane: 31.2. Number of roots in the RHP of the complex plane: 0

The Routh-Hurwitz stability criterion is a technique for deciding the stability of linear time-invariant systems.

The Routh-Hurwitz criteria are a collection of necessary and sufficient conditions for the stability of a polynomial whose coefficients are real numbers.

It can be used to calculate the location of the roots of a polynomial's characteristic equation. Below are the solutions to the given polynomial equations:

Solution 1: Using Routh-Hurwitz criterion for s⁵ + 3s⁴ + 9s³ + 8s² + 65 + 4= 0:

Routh table is given below: s⁵ = 1 3 4 0 0

s⁴ = 3 8 65 0

s³ = 2.36 16.6 0

s² = 8.9 65 0

s¹ = 68 0

s⁰ = 4

There are three poles in the right half plane (RHP) of the complex plane for the given equation.

Hence, the system is unstable.

Solution 2: Using Routh-Hurwitz criterion for s⁵ + 6s³ + 5s² + 8s + 20=0:

Routh table is given below: 

s⁵ = 1 5

s⁴ = 6 8

s³ = 2 20

s² = 4 -20

s¹ = -10

s⁰ = 20

There are no poles in the RHP of the complex plane for the given equation.

Therefore, the system is stable.

Hence, the answer is:1.1

Note: When the roots of the characteristic equation are located on the imaginary axis, the Routh-Hurwitz criteria fail.

A little change in the equation coefficients leads to no information on stability.

Hence, we cannot conclude the stability of the system.

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The translation that represents T–4, 6(x, y) is (b) a trapezoid on a coordinate plane that is translated 4 units to the left and 6 units up

The translation rule is given as:

T–4, 6(x, y)

This can be rewritten as

T(x- 4, y + 6)

The above represents a translation 4 units left and 6 units up

Hence, the translation that represents T–4, 6(x, y) is (b) a trapezoid on a coordinate plane that is translated 4 units to the left and 6 units up

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Based on the calculations, the true statements are:

A. The angular velocity is 10π rad/sec.

E. The angular velocity is 600π rad/min.

Mathematically, angular velocity can be calculated by using this formula:

ω = θ/t

Where:

Note: 1/2 revolution = 0.5 × 2π = π radians.

Substituting the given parameters into the formula, we have;

ω = θ/t

ω = π/0.1

ω = 10π rad/s.

Next, we would convert the time in seconds to minutes:

ω = 10π × 60

ω = 600π rad/min.

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Complete Question:

A golfer’s arm rotates 1/2 of a revolution in 1/10 of a second. If the angular displacement is measured in radians, which statements are true? Check all that apply.

A. The angular velocity is 10π rad/sec.

B. The angular velocity is 10π rad/min.

C. The angular velocity is 60π rad/min.

D. The angular velocity is 600π rad/sec.

E. The angular velocity is 600π rad/min.

Answer:

A,

Step-by-step explanation:

Edge202

(a)The amount of water in the tank is increasing.

(b)Evaluate  \(\int\limits^{18}_0(W(t) - R(t)) dt\) to get the number of gallons of water in the tank at t = 18.

(c)Solve part (b) to get the absolute minimum from the critical points.

(d)The equation can be set up as   \(\int\limits^k_{18}-R(t) dt = 1200\) and solve this equation to find the value of k.

What is the absolute value of a number?

The absolute value of a number is its distance from zero on the number line. It represents the magnitude or size of a real number without considering its sign.

To solve the given problems, we need to integrate the given rates of water flow to determine the amount of water in the tank at various times. Let's go through each part step by step:

a)To determine if the amount of water in the tank is increasing at time t = 15, we need to compare the rate of water being pumped in with the rate of water being removed.

At t = 15, the rate of water being pumped in is given by \(W(t) = 95Vt sin^2(\frac{t}{6})\) gallons per hour. The rate of water being removed is \(R(t) = 275 sin^2(\frac{1}{3})\) gallons per hour.

Evaluate both rates at t = 15 and compare them. If the rate of water being pumped in is greater than the rate of water being removed, then the amount of water in the tank is increasing. Otherwise, it is decreasing.

b) To find the number of gallons of water in the tank at time t = 18, we need to integrate the net rate of water flow from t = 0 to t = 18. The net rate of water flow is given by the difference between the rate of water being pumped in and the rate of water being removed. So the integral to find the total amount of water in the tank at t = 18 is:

\(\int\limits^{18}_0(W(t) - R(t)) dt\)

Evaluate this integral to get the number of gallons of water in the tank at t = 18.

c)To find the time t when the amount of water in the tank is at an absolute minimum, we need to find the minimum of the function that represents the total amount of water in the tank. The total amount of water in the tank is obtained by integrating the net rate of water flow over the interval [0, 18] as mentioned in part b. Find the critical points and determine the absolute minimum from those points.

d. For t > 18, no water is pumped into the tank, but water continues to be removed at the rate R(t) until the tank becomes empty. To find the value of k, we need to set up an equation involving an integral expression that represents the remaining water in the tank after time t = 18. This equation will represent the condition for the tank to become empty.

The equation can be set up as:

\(\int\limits^k_{18}-R(t) dt = 1200\)

Here, k represents the time at which the tank becomes empty, and the integral represents the cumulative removal of water from t = 18 to t = k. Solve this equation to find the value of k.

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Answer:

y = 2/3x

Step-by-step explanation:

Use (rise)/(run) formula

Rise: 2

Run: 3

Answer:

y = \(\frac{2}{3}\) x

Step-by-step explanation:

the equation of a line passing through the origin is

y = mx ( m is the slope )

calculate m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (- 3, - 2) and (x₂, y₂ ) = (3, 2) ← 2 points on the line

m = \(\frac{2-(-2)}{3-(-3)}\) = \(\frac{2+2}{3+3}\) = \(\frac{4}{6}\) = \(\frac{2}{3}\)

y = \(\frac{2}{3}\) x ← equation of line

Answer:

m∠6 = 90°

Step-by-step explanation:

∠1 and ∠2 are a linear pair.  This means they are supplementary, or their measures sum to 180°.  To find m∠2, we subtract m∠1 from 180:

180-140 = 40°

The measure of ∠2 is 40°.

The sum of the measures of the angles in a triangle is 180°.  We have ∠2 and ∠3; to find the measure of ∠6, we subtract these two from 180:

180-(40+50) = 180-90 = 90°

A and B

I hoped it helped you

In the consolidated financial statements, the intercompany sales between Perez, Inc. and Senior, Inc. need to be eliminated to avoid double counting of the profits.

When Perez, Inc. sells goods to Senior, Inc., the intercompany sales should be eliminated in the consolidated financial statements. This means that the revenue and cost of goods sold related to these transactions should be removed from both companies' individual income statements.

Since Perez, Inc. sold goods with a 40% gross profit to Senior, Inc., the gross profit on these intercompany sales needs to be eliminated. This adjustment ensures that the consolidated financial statements reflect only the external sales and expenses of the group as a whole.

Furthermore, as Perez, Inc. owns 80% of Senior, Inc., the consolidated income statement should also reflect the portion of Senior, Inc.'s income that belongs to the non-controlling interest (20% ownership not held by Perez, Inc.). This adjustment ensures that the consolidated financial statements accurately reflect the economic interest of both the parent company (Perez, Inc.) and the non-controlling interest (the remaining 20% ownership in Senior, Inc.).

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erez, Inc., owns 80% of Senior, Inc. During the year just ended, Perez sold goods with a 40% gross profit to Senior. Senior sold all of these goods during the year. In its consolidated financial statements for the year, how should the summation of Perez and Senior income statement items be adjusted?

On solving the provided question, we can say that in the provided rectangle the fence is 14 m wide.

A rectangle in Euclidean plane geometry is a quadrilateral with four right angles. You might also describe it as follows: a quadrilateral that is equiangular, which indicates that all of its angles are equal. The parallelogram might also have a straight angle. Squares are rectangles with four equally sized sides. A quadrilateral of the shape of a rectangle has four 90-degree vertices and equal parallel sides. As a result, it is sometimes referred to as an equirectangular rectangle. Because its opposite sides are equal and parallel, a rectangle is also known as a parallelogram.

provided

let length will be = 3w

width = w

perimeter of rectangle = 2(l+b) = 2(3w+w) = 8w

8w = 120

w = 14

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