Potential Energy is ____ energy

The required volume of the sphere is given as 33.49 cubic centimeters.

Volume is defined as the mass of the object per unit density while for geometry it is calculated as profile area multiplied by the length at which that profile is extruded.

Here,
Radius of sphere = 2 cm
The volume of the sphere = 4/3πr³
                                 = 4/3 × 3.14 × 2³
                                 = 33.49 cm³

Thus, the required volume of the sphere is given as 33.49 cubic centimeters.

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Work Shown:

r = 6 = radius

V = volume of a sphere of radius r

V = (4/3)*pi*r^3

V = (4/3)*pi*6^3

V = 904.77868423386

V = 904.8

I used my calculator's stored version of pi (instead of something like pi = 3.14)

The units "cubic meters" can be abbreviated to m^3 or \(m^3\)

The volume of the given sphere is 904.8 cubic meters. Thus, option B is the answer.

         The volume of a sphere can be calculated using the formula:

V = \(4/3 * \pi * r^3\),

Where V is the volume and r is the radius of the sphere.

\(\pi\) = 3.14

The radius of the sphere (r) = 6m

Plugging in the given radius of 6m into the formula, we get:

V = (4/3) * \(\pi\) * (6^3)

V = 1.333 * \(\pi\) * 216

V = 1.333 * 3.14 * 216

V = 4.1866 * 216

V = 904.8 cubic meters

Therefore, when the radius of the sphere is 6m, the volume of the sphere is 904.8  cubic meters.

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Answer: A and D

Step-by-step explanation:

This is the REAL correct answer.

Answer: B. The environment of the zoo may cause the lions to behave

differently than they would in a natural habitat.  

                                         and

D. The presence of the researchers may affect the lions' behavior.

Step-by-step explanation:  Studying lion behavior in zoos has limitations. The artificial environment of a zoo can affect how lions behave compared to their behavior in the wild.  Additionally, the presence of researchers may influence the lions' behavior, making it difficult to observe and understand their natural interactions.

B. The environment of the zoo may cause the lions to behave differently than they would in a natural habitat.

In a zoo, lions are confined to a limited space and are provided with a controlled environment.  This artificial setting may not accurately reflect their natural habitat and can influence their behavior.  For example, the availability of food, different social dynamics, and reduced hunting opportunities in a zoo can lead to altered behaviors that may not be representative of how lions behave in the wild.

D. The presence of the researchers may affect the lions' behavior.

When researchers observe animals in a zoo, their presence can influence the behavior of the lions.  The presence of unfamiliar humans can cause the animals to become more cautious, stressed, or exhibit abnormal behavior.  This could potentially alter the social interactions and dynamics observed by the researchers, making it challenging to accurately understand and interpret natural lion behavior.

Answer:

D

Step-by-step explanation:

None of them show the Unit Rate

Answer:

B because unit rate is for a single unit.

Answer: 45 (cm)

Step-by-step explanation:

Since the discs have the same thickness, we will think about the areas.

Let say x the new radius:

\(\pi*5^2+\pi*20^2+\pi*40^2=\pi*x^2\\\Longrightarrow\ 5^2+20^2+40^2=x^2\\\\\Longrightarrow\ 2025=x^2\\\\\Longrightarrow\ x=\sqrt{2025} =45\)

Answer:

n / -5 = 2

n = - 10

the monthly payment of $ 668.75 will be paid for the loan for the car.

Total payment for the car = $ 27,635

Money for down payment = $ 5000

Interest for 3 year loan = 6.36 %

Amount on which this interest will be applied = $ 27,635 - $ 5000

Amount = $ 22,635

Interest = 6.36 % of $ 22,635

Interest = 6.36 / 100 × $ 22,635

Interest = 1440 (approx.)

Total amount of loan = $ 22,635 + $ 1440

= $ 24075

Number of months = 3 × 12 = 36 months

So, monthly payment = $ 24075 / 36
= $ 668.75

Therefore, we get that, the monthly payment of $ 668.75 will be paid for the loan for the car.

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Answer:

1716

Step-by-step explanation:

These ribbons be awarded to 3 of 13 pigs in 1716

We have given that,

13 pigs are entered in the best pig competition at the country fair the judges will award very special pigs with blue, red, and white ribbons

We have to determine how many different ways can these ribbons be awarded to 3 of 13 pigs.

A permutation of a set is, loosely speaking, an arrangement of its members into a sequence or linear order, or if the set is already ordered, a rearrangement of its elements.

So the judges are going to pick 3 pigs from the 13 to give a ribbon. Since the ribbons are different, the order does matter.

So this is a permutation. This can be set up like this:

Therefore we get,

13*12*11=1716

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Answer:

24:66

Step-by-step explanation:

Answer:16

Step-by-step explanation:

Answer:

What is the equation of the graphed line written in standard form?" has four options: 2x + 3y = -6, 2x + 3y = 6, y=-2/3x-2, and y= 2/3x-2. The standard form of a linear equation is Ax + By = C, where A, B, and C are constants. In this case, the first two options, 2x + 3y = -6 and 2x + 3y = 6 are already in standard form. The last two options, y=-2/3x-2 and y= 2/3x-2 are not in standard form. However, without additional information such as a graph or coordinates of points on the line, it is not possible to determine which of these options is the correct equation for the graphed line.

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a) the dimension of its column space is also 2. b) the rank of A is 2. c) the nullity of matrix A is 1. d) the dimension of the solution space of the homogeneous system \(A_x = 0\) is also 1.

(a) The dimension of the row space of a matrix is equal to the dimension of its column space. So, if the dimension of the row space of matrix A is 2, then the dimension of its column space is also 2.

(b) The rank of a matrix is defined as the maximum number of linearly independent rows or columns in the matrix. Since the dimension of the row space of matrix A is 2, the rank of A is also 2.

(c) The nullity of a matrix is defined as the dimension of the null space, which is the set of all solutions to the homogeneous equation Ax = 0. In this case, the matrix A is a 3 x 3 matrix, so the nullity can be calculated using the formula:

nullity = number of columns - rank

nullity = 3 - 2 = 1

Therefore, the nullity of matrix A is 1.

(d) The dimension of the solution space of the homogeneous system Ax = 0 is equal to the nullity of the matrix A. In this case, we have already determined that the nullity of matrix A is 1. Therefore, the dimension of the solution space of the homogeneous system \(A_x = 0\) is also 1.

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Answer:

Triangle, Pentagon, Hexagon, Decagon

Step-by-step explanation:

Triangle = 3 sides

Pentagon = 5 sides

Hexagon = 6 sides

Decagon = 10 sides

sorry for the late response

C

The mistake the arrangers made is in the second inequality. They considered the number of caps to be bought should be at least 5 times greater than the number of blouses, not the other way around. The correct inequality should be C

The correct answer is D) The first inequality should be s + h ≤ 1800.

The organizers made an error in the first inequality. The given inequality 10s + 8h ≤ 1800 represents the total cost of buying shirts (10s) and hats (8h) should be less than or equal to $1800. However, this does not take into account the fact that the organizers want to buy at least 5 times as many shirts as hats, as indicated by the second inequality h ≥ 5s.

The correct way to represent this constraint is by using the equation s + h ≤ 1800, which ensures that the total number of shirts and hats purchased does not exceed $1800 in cost. This is because the organizers want to make sure that the total cost of shirts and hats combined does not exceed the budget of $1800.

Answer: The given vector can be expressed as a linear combination of u, v, and w as (14, 9, 14) = u - v + 3w.

Question: Express the following as a linear combination of u =(3, 1,6), v = (1.-1.4) and w=(8,3,8). (14, 9, 14) = ____ u- _____ v+ _____

Current Progress: To express the given vector as a linear combination of u, v, and w, we need to find scalars a, b, and c such that (14, 9, 14) = a*u + b*v + c*w.

Step 1: Write the equation in component form:
(14, 9, 14) = (3a + b + 8c, a - b + 3c, 6a + 4b + 8c)

Step 2: Equate the corresponding components and solve for a, b, and c:
3a + b + 8c = 14
a - b + 3c = 9
6a + 4b + 8c = 14

Step 3: Solve the system of equations using any method (substitution, elimination, etc.). One possible solution is a = 1, b = -1, and c = 3.

Step 4: Plug the values of a, b, and c back into the linear combination equation:
(14, 9, 14) = 1*u + (-1)*v + 3*w

Step 5: Simplify the equation:
(14, 9, 14) = u - v + 3w

Answer: The given vector can be expressed as a linear combination of u, v, and w as (14, 9, 14) = u - v + 3w.

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Answer:

5y + 15x = 25, 9x - y = -4

Step-by-step explanation:

The standard form is Ax + By = C. We can make this simple by first creating the slope intercept equations of both questions:

1.  y = (-3/5)x + 5

2. y = 9x + 4

For the first one, we must first get rid of the denominator by multiplying everything by 5, so we get 5y = -15x + 25, and then you can add 3x to both sides to arrive at your first standard eqn, 5y + 15x = 25.

For the second, all you need to do is swap the y and the 4, subtracting both y and 4 from each side, arriving at 9x - y = -4

Answer:

the pattern is going by 3s and u would multiply 3 by each number

Answer:

Step-by-step explanation:

In first quadrent,   reference angle is equal to 332

in secodn quadrent, 332-180

angle - 180 so 332-180

fouth Quadrent, 360-332  

                                                     Answer is equal to 28

Answer:

Quadrant 1: 152°

Quadrant 2: 28°

Quadrant 3 (Given): 332°

Quadrant 4: 208°

Step-by-step explanation:

A 332° angle in standard position has its terminal side in quadrant 3 since 332° is between 180° and 360°.

332° - 180° = 152°

The reference angle for 332° is 152°

Quadrant 1: 152°

Quadrant 2: 180° - 152° = 28°

Quadrant 3 (Given): 332°

Quadrant 4: 360° - 152° = 208°

The length of the diameter, in meters, of the circular area that gets watered by the sprinkler for this condition is given by: Option B: 8 m

If a circle O has radius of r units length and that it has got its center positioned at (h, k) point of the coordinate plane, then, its equation is given as:

\((x-h)^2 + (y-k)^2 = r^2\)

For this case, the equation of the circle that models tha circular area considered is:

\((x-9)^2 + (y+11)^2=16\)

Writing this in standard form and comparing it with the standard equation, we get:

\((x-9)^2 + (y+11)^2=16\\(x-9)^2 + (y - (-11) )^2 = 4^2\) (didn't took (-4)² = 16 since radius cannot be negative).

Thus, we get center's coordinate as (9,-11) and radius of 4

The diameter of that circular area = twice of radius of the circle which models it = 2 × 4 = 8 meters.

Thus, the length of the diameter, in meters, of the circular area that gets watered by the sprinkler for this condition is given by: Option B: 8 m

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Answer:

x = - 6

Step-by-step explanation:

Remark

When parallel lines are cut by a transversal (as these lines are) then there are only 2 values for the angles can be made.  In this case, the angles formed are alternate interior angles.

Alternate interior angles are equal.

Solution

x + 86   = 80               Subtract 86 from both sides.

x + 86-86 = 80 -86

x = - 6

Nathan worked less than Abigail per hour.

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

Given:

Abigail earned $203 in 7 hours.

So, Abigail earned in 1 hour

= 203/7

= $29

and, Nathan Earn $210 in 10 hour.

So, Nathan earned in 1 hour

= 210/10

= $21

Hence, Nathan worked less than Abigail per hour.

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The number of collisions per square inch of the larger container is \(1.342 × 10¹⁰ * T.\)

Given that there are 2850 molecules of the gas that collide with a square-inch area of the container at any given instant, we need to find out how many collisions will occur per square inch of this larger container when the volume is increased to 24.8 L at constant temperature.

We can use the ideal gas law formula\(PV = nRT\), where P is the pressure of the gas, V is the volume of the gas, n is the number of moles of gas, R is the universal gas constant, and T is the temperature of the gas. We assume that the gas is an ideal gas, which follows the ideal gas law at all conditions.

When the volume of the gas is increased to 24.8 L, the new pressure P2 can be found using the equation P1V1 = P2V2, where P1 is the initial pressure, V1 is the initial volume, P2 is the final pressure, and V2 is the final volume. Since the temperature is constant, P1 = P2.

The number of molecules or moles of gas is proportional to the volume of the gas. Therefore, the number of moles of gas (n) remains constant at constant temperature. The number of molecules of gas N can be calculated using N = n * NA, where NA is Avogadro's number and is equal to \(6.022 × 10²³\) molecules/mole.

The number of collisions per unit area is proportional to the pressure of the gas. We can calculate it using the equation P = N/V * kB * T, where kB is the Boltzmann constant.

The number of collisions per unit area in the new container can be calculated as \(P2 = N/V2 * kB * T.\)

Thus, the number of collisions per square inch of the larger container is given by

\(P2 * (24.8/6.20)² = \\(2850 * NA / 6.20) / (24.8/6.20) * kB * T =\\ 4 × P2 = 4 × (2850 * NA / 6.20) / (24.8/6.20) * kB * T = \\4 * 8.345 * 10¹⁰ * T / 24.8 = 1.342 × 10¹⁰ * T.\)

Answer: The number of collisions per square inch of the larger container is \(1.342 × 10¹⁰ * T.\)

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In the larger container, there will be approximately 713 collisions per square inch.

To determine the number of collisions per square inch in the larger container, we can use the concept of the ideal gas law and the ratio of the volumes.

First, let's calculate the initial number of collisions per square inch in the smaller container. We know that 2850 molecules collide with a square-inch area at any given instant.

To find the number of collisions per square inch in the larger container, we need to consider the ratio of the volumes. The initial volume is 6.20 L, and the final volume is 24.8 L.

The ratio of the volumes is:

24.8 L / 6.20 L = 4

Since the volume increased by a factor of 4, the number of collisions per square inch will decrease by the same factor.

Therefore, the number of collisions per square inch in the larger container will be:

2850 molecules / 4 = 712.5 collisions

However, it's important to note that the number of collisions cannot be expressed as a fraction. We need to round the result to the nearest whole number.

So, in the larger container, there will be approximately 713 collisions per square inch.

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Answer:

0.14

Step-by-step explanation:

If winning holds a probability of 0.5 and a draw holds a probability of 0.3, then that means that losing has a probability of 0.2 (1 - 0.5 - 0.7 = 0.2). Therefore, to find the probability of Vishi losing exactly one of the two games we need to multiply the probability of him losing one game by the probability of him winning or tying the second game like so...

0.2 * (0.5 + 0.3) = x

0.2 * 0.7 = x

0.14 = x

Finally, we can see that the probability of Vishi losing exactly one of the two games is 0.14

\(x^4 +2x^3 -11x^2-12x+36\\ \\=x^4-2x^3+4x^3-8x^2-3x^2 +6x-18x+36\\\\=x^3(x-2) +4x^2(x-2) -3x(x-2) -18(x-2)\\\\=(x-2)(x^3 +4x^2 -3x -18)\\\\=(x-2)(x^3+3x^2+x^2+3x-6x-18)\\\\=(x-2)\textbf{[}x^2(x+3)+x(x+3)-6(x+3)\textbf{]}\\\\=(x-2)(x+3)(x^2 +x -6)\\\\=(x-2)(x+3)(x^2 +3x -2x-6)\\\\=(x-2)(x+3)\textbf{[}x(x+3) -2(x+3)\textbf{]}\\\\=(x-2)(x-2)(x+3)(x+3)\\\\=(x-2)^2(x+3)^2\)

Answer:

15/16

Step-by-step explanation:

Answer:

15/16

Step-by-step explanation:

The value of the sample proportion of people from Vermont who exercised for at least 30 minutes a day, 3 days a week is 0.653.

We have,
Vermont had 65.3% of respondents who said yes to exercising for at least 30 minutes a day, 3 days a week.

To find the sample proportion, you can convert the percentage to a decimal by dividing the percentage by 100.

Step 1:

Convert the percentage to a decimal.
65.3 / 100 = 0.653

Thus,
The value of the sample proportion of people from Vermont who exercised for at least 30 minutes a day, 3 days a week is 0.653.

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Answer:

102 / 105 = 0.971428571

Step-by-step explanation:

i used a calculator c:

The expressions which are equivalent to 35 + 30s - 45t are:

5(7+6s−9t)

(−35−30s+45t)×(−1)

The correct answer options are options B and C

An expression is any mathematical statement which consists of numbers, variables and an arithmetic operation between them. 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.

here, we have,

We have to determine equivalent expression:

35 + 30s - 45t

Check all options

A. 7⋅(5+30s−45t)

= 35 + 210s - 315t

False

B. 5(7+6s−9t)

= 35 + 30s - 45t

True

C. (−35−30s+45t)×(−1)

= 35 + 30s - 45t

True

D. 10×(3.5+3s−4.5)

= 35 + 30s - 45

False

E. ( 35/2 - 15s + 45/2t) ⋅ (-2)

= (17.5 - 15s + 22.5t) (-2)

= -35 + 30s - 45t

False

Therefore, the equivalent expression is an expression which has an equal value to each other.

Complete question:

Which expressions are equivalent to 35 + 30s - 45t?

A. 7⋅(5+30s−45t)

B. 5(7+6s−9t)

C. (−35−30s+45t)×(−1)

D. 10×(3.5+3s−4.5)

E. ( 35/2 - 15s + 45/2t) ⋅ (-2)

choose 2 answers

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The characteristic equation is -λ(λ-4)(λ+3) = 0, and the corresponding eigenvalues and eigenvectors are:

λ1 = 0, v1 = [1, 3]

λ2 = 4, v2 = [5, -4, 3]

λ3 = -3, v3 = [1, 1, 0]

What is an identity matrix?

An identity matrix is a square matrix with ones (1) along the main diagonal (from the upper left to the lower right) and zeros (0) everywhere else. It is denoted by I, and its size is indicated by a subscript. For example, I2 represents a 2x2 identity matrix:

To find the characteristic equation and eigenvalues of the given matrix, we need to compute the determinant of the matrix A - λI, where λ is the eigenvalue and I is the identity matrix.

A = 0 -3 5

-4 4 -10

0 0 4

A - λI = -λ -3 5

-4 4-λ -10

0 0 4-λ

The determinant of A - λI is given by:

det(A - λI) = (-λ) [(4-λ)(-3) - (-10)(-4)] - (-4)[(-4)(-3) - (-10)(-λ)] + (0)[(-4)(5) - (4-λ)(-3)]

= -λ(λ-4)(λ+3)

Therefore, the characteristic equation is:

-λ(λ-4)(λ+3) = 0

The eigenvalues are the roots of this equation, which are:

λ = 0, 4, -3

To find the eigenvectors corresponding to each eigenvalue, we solve the system of linear equations (A - λI)x = 0.

For λ = 0, we have:

(A - λI)x = -3 5

-4 4

0 0

which leads to the equation -3x + 5y = 0 and -4x + 4y = 0. Solving this system of equations, we get:

x = y/3

So, the eigenvector corresponding to λ = 0 is:

v1 = [1, 3]

For λ = 4, we have:

(A - λI)x = -4 -3 5

-4 0 -10

0 0 0

which leads to the equation -4x - 3y + 5z = 0 and -4x - 10z = 0. Solving this system of equations, we get:

x = (5/3)z

y = (-4/3)z

So, the eigenvector corresponding to λ = 4 is:

v2 = [5, -4, 3]

For λ = -3, we have:

(A - λI)x = 3 -3 5

-4 7 -10

0 0 7

which leads to the equation 3x - 3y + 5z = 0, -4x + 7y - 10z = 0 and 7z = 0. Solving this system of equations, we get:

x = y

z = 0

So, the eigenvector corresponding to λ = -3 is:

v3 = [1, 1, 0]

Therefore, the characteristic equation is -λ(λ-4)(λ+3) = 0, and the corresponding eigenvalues and eigenvectors are:

λ1 = 0, v1 = [1, 3]

λ2 = 4, v2 = [5, -4, 3]

λ3 = -3, v3 = [1, 1, 0]

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Answer: \(\displaystyle 2x^4 + 9x^3-8x^2+9x -13\)

Step-by-step explanation:

     Given:

\(\displaystyle (2x^4 + 9x^3 -8)-(8x^2-9x+5)\)

     Subtract the second term:

\(\displaystyle (2x^4 + 9x^3 -8)-8x^2+9x-5\)

     Reorder by the power's degree:

\(\displaystyle 2x^4 + 9x^3-8x^2+9x -8-5\)

     Combine like terms:

\(\displaystyle 2x^4 + 9x^3-8x^2+9x -13\)