The price of a television was reduced $250 to $200. By the percentage was the price of the television reduced?
A. 20%
B. 25%
C. 80%
D. 50%

please help I'm not good at math!!

Answer:

B)

Step-by-step explanation:

Answer:

I think b

Step-by-step explanation:

Given:

The ratio of the amount of money Kate has to that of Nora is 3 : 5.

After Nora gives $150 to Kate, the ratio of the amount of money Kate has to that of Nora becomes 7 : 9.

To find:

The sum of money Kate had initially.

Solution:

Let the initial amount of money Kate and Nora have are 3x and 5x respectively.

After Nora gives $150 to Kate, the ratio of the amount of money Kate has to that of Nora becomes 7 : 9.

The amount of Kate = 3x+150

The amount of Nora = 5x-150

Now,

\(\dfrac{3x+150}{5x-150}=\dfrac{7}{9}\)

\(9(3x+150)=7(5x-150)\)

\(27x+1350=35x-1050\)

\(1350+1050=35x-27x\)

\(2400=8x\)

Divide both sides by 8.

\(300=x\)

Putting x=300 in 3x, to get the amount of money Kate has initially.

\(3(300)=900\)

Therefore, the Kate initially had $900.

Answer: 5(7) over x

Step-by-step explanation:

We get that statements 2 and 3 are correct statements.

We have given that the

6>-2

We have to find the correct statement from the given statement,

Less than or equal to relation is one of the inequalities used to represent the relation between two non-equal numbers or other mathematical expressions.

1) 6/2<2/-2

3<-1

This is not possible therefore first statement is not correct

2) 6/-2<-2/-2

-6<1

This is the correct statement.

3)

6/2<-2/2

3<-1

This is the correct condition.

Therefore this is a correct statement.

Therefore we get that statements 2 and 3 are a correct statements.

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Answer:

A D F

Step-by-step explanation:

dont waste your time :)

Answer:

x=2

Step-by-step explanation:

Remove parentheses

collect like terms

move constants to the right

calculate

divide both sides

Considering the triangle midsegment theorem, the length WT is given as follows:

WT = 15.

The triangle midsegment theorem states that the midsegment of the triangle divides the two sides of the triangle into proportional parts.

The proportional relationship for the lengths is given as follows:

10/6 = 25/WT

5/3 = 25/WT.

Applying cross multiplication, the length WT is given as follows:

5WT = 75

WT = 15.

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Answer:

220

Step-by-step explanation:

The new circumference of the circle will be 220 feet if the circumference of a circular lawn is 110 feet.

It is described as a set of points, where each point is at the same distance from a fixed point (called the center of a circle)

We have:

The circumference of a circular lawn is 110 feet.

2πr = 110

r = 55/π

Double the radius:

R = 2r= 110/π

New circumference = 2πR = 2π(110/π) = 220 feet

Thus, the new circumference of the circle will be 220 feet if the circumference of a circular lawn is 110 feet.

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Answer:

3, 6, 9 (the multiples of three within 11)

3 out of 11 numbers are multiples of 3

so you have a 3 out of 11 probability to grab a multiple of three

3/11 is your answer

Step-by-step explanation:

Probability of picking a ball of multiple of 3 is equals to (3/11).

" Probability is a mathematical expression which represents the ratio of number of favourable outcomes to the total number of outcomes."

Formula used

Probability = \(\frac{Number of favourable outcomes}{Total number of outcomes}\)

According to the question,

'B' represents the ball

Possible outcomes = { B₁, B₂, B₃, ...., B₁₀, B₁₁}

favourable outcomes multiple of 3 = { B₃, B₆, B₉}

Total number of outcomes= 11

Number of favourable outcomes = 3

Substitute the value in the formula we get,

Probability of picking ball multiple of 3 = ( 3 / 11)

Hence, probability of picking a ball of multiple of 3 is equals to (3/11).

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Isolate the variable x and bring it on one side

then solve the equation

Hope this helps

The equation will be 12a – 360 = 216. Then the value of the variable a will be 48.

The solution of the equation means the value of the unknown or variable.

When you multiply a number by 12 and subtract the product from 360, the difference is 216.

Let the number be a.

Then we have the equation

12a – 360 = 216

By solving the equation, we have

12a = 216 + 360

12a = 576

   a = 576/12

   a = 48

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1. 4 -3y =1

2. 3 × 5 or 6

Step-by-step explanation:

I just guessed

Answer:

Answer is: 0.0052441

Answer:

0.0052441

hope it helps.

Answer:

\(P(sister) = \frac{8}{30} \\ \)

Step-by-step explanation:

\(P(sister) = \frac{8}{30} \\ P(brother) = \frac{13}{30} \\ P(SnB) = \frac{3}{30} \\ \)

The equation Ax = b does not have a solution for all possible b. The set of all b for which Ax = b does have a solution is the set of all b such that 6b3 - 3b2 + 2b1 = 0.

The equation Ax = b is equivalent to the system of equations:
x1 - 4x2 - 3x3 = b1
-4x1 + 4x2 + 0x3 = b2
2x1 + 0x2 + 6x3 = b3

we add the first two equations, we get:
-3x3 = b1 + b2

This means that 6b3 - 3b2 + 2b1 = 0. So, the set of all b for which Ax = b has a solution is the set of all b such that 6b3 - 3b2 + 2b1 = 0.
Step-by-step solution:
1.We can write the equation Ax = b as a system of equations:
x1 - 4x2 - 3x3 = b1
-4x1 + 4x2 + 0x3 = b2
2x1 + 0x2 + 6x3 = b3

2.Add the first two equations:

-3x3 = b1 + b2

3.This means that 6b3 - 3b2 + 2b1 = 0.

4.Therefore, the set of all b for which Ax = b has a solution is the set of all b such that 6b3 - 3b2 + 2b1 = 0.

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The set of all b for which Ax = b does have a solution can be described as: b = b1*[1, -4, -3] + b2*[-4, 4, 0] = [b1 - 4b2, -4b1 + 4b2, -3b1].

To show that the equation Ax = b does not have a solution for all possible b, we can row reduce the matrix A to determine if it has a pivot position in every row. If there is a row without a pivot position, it means that the corresponding equation in the system is inconsistent, and thus the system does not have a solution for all possible b.

Let's row reduce the matrix A:

1 -4 -3

-4  4  0

2   4  6

Performing row operations:

R2 + 4R1 -> R2

R3 - 2R1 -> R3

1 -4 -3

0   0  12

0   12 12

Now, we can see that the second row consists of all zeros, which means there is no pivot position in that row. Therefore, the system Ax = b does not have a solution for all possible b.

To describe the set of all b for which Ax = b does have a solution, we need to consider the column space of matrix A. The column space is the span of the columns of A, and any vector b that can be written as a linear combination of the columns of A will have a solution.

The columns of A are:

[1, -4, 2]

[-4, 4, 4]

[-3, 0, 6]

We can see that the third column is a multiple of the second column, so the column space of A is actually spanned by the first two columns. Therefore, any vector b that can be expressed as a linear combination of the first two columns will have a solution to Ax = b.

Thus, the set of all b for which Ax = b does have a solution can be described as:

b = b1*[1, -4, -3] + b2*[-4, 4, 0] = [b1 - 4b2, -4b1 + 4b2, -3b1]

Here, b1 and b2 are scalar coefficients that can vary, and bz is set to 1 as indicated in the question.

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Let A = 1-4 -3 -4 4 0 2 4 6 and b = b2 . Show that the equation Ax=b does not have a solution for all possible b, and describe the set of all b for which Ax=b does have a solution. How can it be shown that the equation Ax = b does not have a solution for all possible b? Describe the set of all b for which Ax=b does have a solution. 0= (Type an expression using b1,b2, and bz as the variables and 1 as the coefficient of bz.)

Answer:

Step-by-step explanation:

A bitmap is a digital image format that is made up of a grid of square colored dots called pixels.

Each pixel in the bitmap contains information about its color and position, which allows the computer to display the image on a screen or print it on paper. Bitmaps are commonly used for photographs, illustrations, and other complex images that require a high degree of detail and color accuracy.

However, because bitmaps store information for each individual pixel, they can be memory-intensive and may result in large file sizes. Additionally, resizing a bitmap can lead to a loss of quality, as the computer must either interpolate or discard pixels to adjust the image size.

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Answer:

5563.85 But round the nearest whole number is 5564

Step-by-step explanation:

Formule is P=Ie^(r)(t)

If, In 2010 the Network Club membership was 2,500. With an annual growth rate of approximately 8%, compounded continuously,  then 5563.85 is the population in 2022.

percentage, a relative value indicating hundredth parts of any quantity.

Given,

In 2010 the Network Club membership was 2,500.

Annual growth rate of approximately 8%

8% is converted to decimal value by dividing 8 with 100

8/100=0.08

\(P=Ie^{rt}\)

p is the final population

I is the initial population

\(p=Ie^{0.08(10)}\)

\(p=2500e^{0.8}\)

p=5563.85

Hence, 5563.85 is the population in 2020.

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Answer:

D

Step-by-step explanation:

Just took the quiz

The confidence interval that  would produce the widest interval when estimating the mean of a population should be 83%.

It refers to the range of values where the sample should be watched also in this the value should be determined that correctly represent the population.

Also, the more the confidence interval the more should be the widest interval.

Therefore, the last option is correct.

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The expected value of the die roll is 2.47.  Finding the value of kProbability is the measure of the likelihood of an event taking place. The sum of the probability of all events occurring must equal one, otherwise, the set of events would be incomplete, which is not possible.

Therefore, we have 0.28 + k + 0.15 + 0.3 = 1 where k is the probability of getting 2 on the die.Solving for k:k = 1 - 0.28 - 0.15 - 0.3k = 0.27Therefore, the value of k is 0.27. b. Calculating the expected valueThe expected value of the die roll is the sum of each score multiplied by its probability of occurrence. This is also called the mean of the probability distribution, given by: E(X) = ΣxP(x)where X is the random variable and P(x) is the probability of X being equal to x.Using the given table of probabilities:E(X) = 1(0.28) + 2(0.27) + 3(0.15) + 4(0.3)E(X) = 0.28 + 0.54 + 0.45 + 1.2E(X) = 2.47Therefore, the expected value of the die roll is 2.47.

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Answer:

(10,-2) x=10 y=-2

Step-by-step explanation: I used substitution

In the Rayleigh-Ritz method, we use the eigenfunctions v₁,..., Un as the test functions and apply the method to estimate the smallest eigenvalue λ₁ of the Hermitian matrix A.

The Rayleigh-Ritz method is a numerical technique used to approximate solutions to differential equations, particularly in the field of structural analysis and mechanics. It is also known as the variational method or the method of weighted residuals.

Let v₁,..., Un be the first n eigenfunctions of the eigenvalue problem -Au = Au in D u=0 on ᎯᎠ.

To prove that if you use these v₁,..., Un as the n test functions to the Rayleigh-Ritz Approximation, you will have the Rayleigh-Ritz method:

In the Rayleigh-Ritz method, you attempt to estimate the smallest eigenvalue λ₁ of a Hermitian matrix A by projecting A onto an appropriately chosen finite-dimensional subspace and then minimizing the Rayleigh quotient over that subspace.

The Rayleigh quotient of a matrix is given by (Ax, x) / (x, x) where A is a Hermitian matrix, x is a nonzero vector, and (·, ·) denotes the inner product.

Using the above terminology, let V be the linear subspace of L²(D) generated by v₁,..., Un, and let P be the orthogonal projection onto V.

Using the Rayleigh quotient with the test functions v₁,..., Un, we obtain the Rayleigh-Ritz method.

The method yields an estimate of the eigenvalue λ₁ as follows:λ₁ ≤ (Aφ, φ) / (φ, φ),where φ = ∑ cᵢvᵢ, with the sum over i from 1 to n and cᵢ being arbitrary scalars.

In the Rayleigh-Ritz method, we use the eigenfunctions v₁,..., Un as the test functions and apply the method to estimate the smallest eigenvalue λ₁ of the Hermitian matrix A.

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Given: A arrangement of the letter 'PATTERNS' is given.

Required: To determine the number of paths that spell the word 'PATTERNS' if all paths must start at the top and move diagonally through the

letters.

Explanation: The Pascal Triangle can be used to determine the number of ways the word 'PATTERNS' can be spelled.

The Pascal Triangle is shown below

One exciting thing about Pascal's Triangle is if we move diagonally from top to bottom, each number denotes the number of ways to get to the position from the top.

Hence to spell the word 'PATTERNS', we would need to get to the 8th row.

Hence we need to add all the entries of the 8th row to get the total number of ways to spell the word.

Final Answer: The total number of paths that spells the word 'PATTERNS' is 128.

Answer:

I think its B.

Step-by-step explanation:

sorry if i am wrong.

Answer:

a(n) = -8n -9

a(28)  = -233

Step-by-step explanation:

a(n) = a(1) + (n - 1)d

n is the nth term, a(1) is the first term, d is the common difference.

*d = -25 - (-17) = -8

a(n) = -17 + (n - 1)(-8)

      = -17 + (-8n + 8)

      = -17 - 8n + 8

      = -8n - 9

For the 28th term

a(28) = -8(28) - 9

        = -224 - 9

        = -233

In part (a), we are asked to sketch the graph of the function f based on the inequality given. In part (b), we need to use the definition of a derivative to determine if the function is differentiable

(a) To sketch the graph of the function f based on the inequality -r² + 2x ≤ 1, we can rewrite the inequality as 2x ≥ r² - 1. This equation represents the region above the curve of the function f. The graph will depend on the range of x and r values specified.

(b) To determine if the function is differentiable at r = L, we need to check if the derivative of the function exists at that point. Using the definition of a derivative, we calculate the limit as Δr approaches 0 of (f(L + Δr) - f(L))/Δr. If the limit exists, the function is differentiable at r = L.

(c) To determine if the function is continuous at r = 1, we need to check if the function is defined and the limit as r approaches 1 exists and is equal to the value of the function at r = 1. If the function is defined at r = 1 and the limit exists, and the two are equal, then the function is continuous at r = 1.

In conclusion, in part (a), we sketch the graph of the function f based on the given inequality. In part (b), we use the definition of a derivative to determine differentiability at r = L. In part (c), we determine continuity at r = 1 by checking the function's definition and the limit as r approaches 1.

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Answer:

0.028x-6-0.48x-2+0.552x

(0.028-0.48+0.552)x-6-2

0.1x-8

The simplified expression, when evaluated for x=36, is -4.4, when following expression and evaluate for x=36 b= 0.02(1.4x - 300)-0.2(2.4x+10)+0.552x

To simplify the expression and evaluate it for x=36, let's break it down step by step:

0.02(1.4x - 300) - 0.2(2.4x + 10) + 0.552x

First, let's simplify the terms within each set of parentheses:

0.02 * (1.4 * 36 - 300) - 0.2 * (2.4 * 36 + 10) + 0.552 * 36

Next, perform the multiplications and additions/subtractions within each set of parentheses:

0.02 * (50.4 - 300) - 0.2 * (86.4 + 10) + 0.552 * 36

0.02 * (-249.6) - 0.2 * (96.4) + 19.872

Now, evaluate the remaining multiplications:

-4.992 - 19.28 + 19.872

Finally, perform the additions and subtractions:

-4.992 - 19.28 + 19.872 = -4.4

Therefore, the simplified expression, when evaluated for x=36, is -4.4.

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Answer:

t≤ 9

Step-by-step explanation:

3.5+4t≤ 39.5

subtract 3.5 from each side

4t≤ 36

divide each side by 4

t≤ 9

Answer:

t ≤ 9

Step-by-step explanation:

3.5 + 4t ≤ 39.5

3.5 + 4t - 3.5 ≤ 39.5 - 3.5

4t ≤ 36

4t ÷ 4 ≤ 36 ÷ 4

t ≤ 9

Answer:

c.

Step-by-step explanation:

(x-3)(x²-4x-7)=x(x²-4x-7)-3(x²-4x-7)=x³-4x²-7x-3x²+12x+21=

=x³+(-4x²-3x²)+(-7x+12x)+21=x³-7x²+5x+24

Main Answer:The volume of the solid is 32\(\pi\) cubic units.

Supporting Question and Answer:

How can we use cylindrical coordinates to find the volume of the solid defined by the given equations?

By expressing the equations of the solid in cylindrical coordinates, determining the limits of integration for each variable, and setting up the appropriate triple integral, we can calculate the volume of the solid.

Body of the Solution:To find the volume of the solid defined by the given conditions, we can use cylindrical coordinates. In cylindrical coordinates, we have:

x = r cos(θ)

y = r sin(θ)

z = z

The solid is inside the sphere x^2 + y^2 + z^2 = 16 and outside the cone

z = √(x^2 + y^2).

Converting the equations of the solid into cylindrical coordinates, we have: r^2 + z^2 = 16 (equation of the sphere) z = r (equation of the cone)

To find the limits of integration, we need to determine the range of values for r, θ, and z.

Since the solid is inside the sphere, we have r^2 + z^2 ≤ 16, which implies r ≤ √(16 - z^2).

The cone z = r intersects the sphere at z = 0 and z = √16 = 4. Thus, the limits for z are 0 ≤ z ≤ 4.

For the angular coordinate θ, we can take the full range of 0 ≤ θ ≤ 2\(\pi\).

Now, we can set up the triple integral to calculate the volume of the solid:

V = ∭ dV

Where dV is the volume element in cylindrical coordinates, given by dV = r dz dr dθ.

Integrating over the limits of r, θ, and z, the volume becomes:

V = ∫[0 to 2\(\pi\)] ∫[0 to 4] ∫[0 to √(16 - z^2)] r dz dr dθ

Evaluating the integral, we find:

V = ∫[0 to 2\(\pi\)] ∫[0 to 4] [(1/2)(16 - z^2)] dr dθ

V = ∫[0 to 2\(\pi\)] [(1/2)(16z - (1/3)z^3)]|[0 to 4] dθ

V = ∫[0 to 2\(\pi\)] [(1/2)(64 - (64/3))] dθ

V = ∫[0 to 2\(\pi\)] [(96/6)] dθ

V = (96/6) ∫[0 to 2\(\pi\)] dθ

V = (96/6) [θ]|[0 to 2\(\pi\)]

V = (96/6) [2\(\pi\) - 0]

V = (96/6) (2\(\pi\))

V = 32\(\pi\)

Final Answer:Therefore, the volume of the solid is 32\(\pi\)cubic units.  

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The volume of the solid is 32 cubic units.

By expressing the equations of the solid in cylindrical coordinates, determining the limits of integration for each variable, and setting up the appropriate triple integral, we can calculate the volume of the solid.

To find the volume of the solid defined by the given conditions, we can use cylindrical coordinates. In cylindrical coordinates, we have:

x = r cos(θ)

y = r sin(θ)

z = z

The solid is inside the sphere x^2 + y^2 + z^2 = 16 and outside the cone

z = √(x^2 + y^2).

Converting the equations of the solid into cylindrical coordinates, we have: r^2 + z^2 = 16 (equation of the sphere) z = r (equation of the cone)

To find the limits of integration, we need to determine the range of values for r, θ, and z.

Since the solid is inside the sphere, we have r^2 + z^2 ≤ 16, which implies r ≤ √(16 - z^2).

The cone z = r intersects the sphere at z = 0 and z = √16 = 4. Thus, the limits for z are 0 ≤ z ≤ 4.

For the angular coordinate θ, we can take the full range of 0 ≤ θ ≤ 2.

Now, we can set up the triple integral to calculate the volume of the solid:

V = ∭ dV

Where dV is the volume element in cylindrical coordinates, given by dV = r dz dr dθ.

Integrating over the limits of r, θ, and z, the volume becomes:

V = ∫[0 to 2] ∫[0 to 4] ∫[0 to √(16 - z^2)] r dz dr dθ

Evaluating the integral, we find:

V = ∫[0 to 2] ∫[0 to 4] [(1/2)(16 - z^2)] dr dθ

V = ∫[0 to 2] [(1/2)(16z - (1/3)z^3)]|[0 to 4] dθ

V = ∫[0 to 2] [(1/2)(64 - (64/3))] dθ

V = ∫[0 to 2] [(96/6)] dθ

V = (96/6) ∫[0 to 2] dθ

V = (96/6) [θ]|[0 to 2]

V = (96/6) [2 - 0]

V = (96/6) (2)

V = 32

Therefore, the volume of the solid is 32cubic units.  

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The equation relating x, y, and z is:

z = 0.5 * x * y.

In the given problem, the relationship between x, y, and z can be expressed by the equation z = k * x * y, where k represents the constant of proportionality. By substituting the values of x = 4 and y = 5, when z is equal to 10, we can determine the value of the constant of proportionality, k, and further define the relationship between the variables.

To find the constant of proportionality, we substitute the known values of x = 4, y = 5, and z = 10 into the equation z = k * x * y. This gives us the equation 10 = k * 4 * 5. By simplifying the equation, we have 10 = 20k. To isolate k, we divide both sides of the equation by 20, resulting in k = 0.5. Therefore, the equation relating x, y, and z is z = 0.5 * x * y, meaning that z is directly proportional to the product of x and y with a constant of proportionality equal to 0.5.

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