haing the Product of Integers
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Find the product of the integers:

2(-4) =

The 2013 survey conducted by the Statistics Times one week before the election asked voters which candidate for the state's governor they would vote for. The survey found that 32% of the respondents said they would vote for the Democratic candidate.

On election day, the actual voting results showed that 38% of the voters voted for the Democratic candidate.

To summarize:

1. In the pre-election survey, 32% of the respondents said they would vote for the Democratic candidate.
2. On election day, 38% of the voters actually voted for the Democratic candidate.

It's important to note that the survey results are not always perfectly accurate in predicting the actual election outcome. This difference between the survey results and the actual voting results can occur due to various factors such as changes in voters' opinions, last-minute decisions, or sampling error in the survey itself.

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The polygon which on rotated gives the given cylinder is a rectangle with dimensions 10 inches × 9 inches.

Given a cylinder with the diameter of the base 18 inches and the height of the cylinder 10 inches.

This cylinder is formed by rotating some polygon around YZ.

The polygon must be a rectangle which has the height or the length equal to the height of the cylinder.

So length = 10 inches

The width of the rectangle will be half of the diameter.

Width = 18/2 = 9 inches

Hence the rotated polygon is a rectangle with length 10 inches and width 9 inches.

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Answer:

8/25

Step-by-step explanation:

4/32 = 8 so the numerator is 8 and 4/100 = 25 so the denominator is 25

8/25 cannot be simplified further so it is in simplest form.

(32/100 can be simplified to 8/25, giving us the final answer.)

Answer:

\(\frac{8}{25}\)

Step-by-step explanation:

32% = \(\frac{32}{100}\) ( divide numerator/denominator by common factor of 4 )

32% = \(\frac{8}{25}\) ← in simplest form

Answer:

y=1

You can put equations in a graphing calculator if you aren't sure.

we find that the numerical approximation using Euler's method gives y(2) ≈ 1.865, while the analytical solution gives y(2) = 2.5.

Using the formula y(n+1) = y(n) + Δx * f(x(n), y(n)), where f(x, y) = x² √y, we can calculate the values of y at each step. Here's the step-by-step calculation:

Step 1: For x = 0, y = 1 (initial condition).

Step 2: For x = 0.2, y = 1 + 0.2 * (0.2)² * √1 = 1.008.

Step 3: For x = 0.4, y = 1.008 + 0.2 * (0.4)² * √1.008 = 1.024.

Step 4: For x = 0.6, y = 1.024 + 0.2 * (0.6)² * √1.024 = 1.052.

Step 5: For x = 0.8, y = 1.052 + 0.2 * (0.8)² * √1.052 = 1.094.

Step 6: For x = 1.0, y = 1.094 + 0.2 * (1.0)² * √1.094 = 1.155.

Step 7: For x = 1.2, y = 1.155 + 0.2 * (1.2)² * √1.155 = 1.238.

Step 8: For x = 1.4, y = 1.238 + 0.2 * (1.4)² * √1.238 = 1.346.

Step 9: For x = 1.6, y = 1.346 + 0.2 * (1.6)² * √1.346 = 1.483.

Step 10: For x = 1.8, y = 1.483 + 0.2 * (1.8)² * √1.483 = 1.654.

Step 11: For x = 2.0, y = 1.654 + 0.2 * (2.0)² * √1.654 = 1.865.

Therefore, using Euler's method with a step size of Δx = 0.2, we approximate y(2) to be 1.865.

To obtain the analytical solution to the ODE, we can separate variables and integrate both sides:

∫(1/√y) dy = ∫x² dx

Integrating both sides gives:

2√y = (1/3)x³ + C

Solving for y:

y = (1/4)(x³ + C)²

Using the initial condition y(0) = 1, we can substitute x = 0 and y = 1 to find the value of C:

1 = (1/4)(0³ + C)²

1 = (1/4)C²

4 = C²

C = ±2

Since C can be either 2 or -2, the general solution to the ODE is:

y = (1/4)(x³ + 2)² or y = (1/4)(x³ - 2)²

Now, let's evaluate y(2) using the analytical solution:

y(2) = (1/4)(2³ + 2)² = (1/4)(8 + 2)² = (1/4)(10)² = 2.5

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Answer:

Step-by-step explanation:

For a given sample proportion of 0.5, the sample size that will produce the widest confidence interval is the largest option given, which in this case is 80.

The sample size that will produce the widest 95% confidence interval, given a sample proportion of 0.5, is option b, 80. This is because the width of the confidence interval is directly proportional to the sample size, meaning that as the sample size increases, the confidence interval becomes narrower.

Additionally, the width of the confidence interval is inversely proportional to the square root of the sample size. Therefore, for a given sample proportion of 0.5, the sample size that will produce the widest confidence interval is the largest option given, which in this case is 80.

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Answer:

$126.5

Step-by-step explanation:

Find how much 15% is in 55, then add it to 55 and multiply by 2!

The vertex is at (-2, -9).

From the equation:

y = x² + 4x - 5

Transpose the c-value to the left side of the equation:

y + 5 = x² + 4x

Complete the square of the expression on the right side of the equation to get a perfect square trinomial:

y + 5 = x² + 4x + 4 - 4

by adding and subtracting 4 to the right side of the equation to maintain its balance.

Add the numbers on the left and factor the trinomial on the right:

y + 9 = (x + 2)²

Transpose the number across to the right side to get the equation into the vertex form, y = a(z-h)² + k:

y = (x + 2)² - 9

Make sure the addition and subtraction signs are correct to give the proper vertex form.

Here, the vertex is at (-2, -9).

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Given:-

To find:-

Answer:-

1) Firstly we are told to transpose the c value to LHS .

With respect to standard form of a quadratic equation, \( ax^2+bx + c \) ,the value of c here will be -5 . So on transposing c to LHS , we have;

\(\implies y + 5 = x^2 + 4x\\\)

w) Next we are told to complete the square on the RHS of the equation. For that add and subtract 4 .

\(\implies y + 5 = x^2 + 4x + 4 - 4 \\\)

\(\implies y + 5 =\{ (x)^2 + 2.2.x + 2^2 \}- 4\\\)

The terms inside the curly brackets are in the form of \( a^2+2ab + b^2\) , which is the whole square of \( (a + b )\) . That is \( ( a + b)^2\) . So , we can rewrite it as ,

\(\implies y + 5 = (x +2)^2 - 4 \\\)

\(\implies y + 5 + 4 = (x+2)^2 \\\)

3) Next we have to add the number on the left and factor the trinomial on right as ,

\(\implies y + 9 = (x+2)^2 \\\)

4) Now we are told to transpose the number on the LHS to RHS and get the equation into vertex form which is \( y = a(z-h)^2+ k \) .

\(\implies\underline{\underline{ y = (x+2)^2 - 9}} \\\)

This is our required answer in vertex form. Also on comparing to the standard equation of vertex form, we have;

\(\implies vertex = ( -2,-9) \\\)

and we are done!

Answer:

x= 11

Step-by-step explanation:

The amount that Frank will pay for the couch is 1.08d.

An equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.

It is vital to note that an equation is a mathematical statement which is made up of two expressions that are connected by an equal sign.

In this case, since the couch costs d dollars, and sales tax is 8%., the amount to be paid will be:

= Cost of couch + Tax

= d + (8% × d)

= d + 0.08d

= 1.08d

The amount is 1.08d.

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Answer: 140 dollars

Step-by-step explanation:

0.3x=42   x=140

Answer:

33/400

Step-by-step explanation:

0.0825=825/10000

=165/2000

=33/400

Answer:

B

Step-by-step explanation:

The value of the expression 564 divided by 5 is 112 R4.

An expression simply means the illustration of the information given using variables.

In this case, it should be noted that the question is about the division of 564 divided by 5.

This will be:

= 564 ÷ 5

= 112 4/5

This can be illustrated as 112 R 4.

Note that the options weren't given in the question but the question was explained to further enhance your understanding.

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Answer:

  3/2

Step-by-step explanation:

Finding the slope of a line on a graph is easier if you can identify places where the line crosses grid intersections. We see two of those to be ...

  (4, 1) and (6, 4)

The second of these points is 4-1 = 3 grid squares higher than the first point. It is also 6 -4 = 2 grid squares to the right. The slope is the ratio of these values:

  slope = "rise"/"run" = 3/2

The slope of the graphed line is 3/2.

Answer: 6 weeks

Step-by-step explanation: 42 days in weeks would be 6 weeks

0.53333333333 is your answer, this is a decimal just put the decimal into a fraction

Rounding to the nearest cent, the expected profit for one round of the coin game is approximately -$0.38.

To calculate the expected profit for one round of the coin game, we need to consider the probabilities of winning and losing, as well as the corresponding amounts won or lost.

There are 2 possibilities for winning: either getting all three heads or all three tails. Each of these outcomes has a probability of (1/2) * (1/2) * (1/2) = 1/8.

The amount won in each winning case is $15. Therefore, the expected profit from winning is:

(1/8) * $15 = $1.875

The probability of losing is 1 - probability of winning. In this case, it is 1 - (1/8 + 1/8) = 6/8 = 3/4.

The amount lost in each losing case is $3. Therefore, the expected loss from losing is:

(3/4) * (-$3) = -$2.25

Finally, we can calculate the expected profit by subtracting the expected loss from the expected profit from winning:

$1.875 - $2.25 = -$0.375

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Answer:

12*cos(k)*(t^2/2) - 12*i*sin(k)*(t^2/2) + C. This is the simplified expression using Euler's formula.

Step-by-step explanation:

To evaluate the integral ∫e^(-k) [6(t-6) + 6(t + 6)] dt using Euler's formula, we need to simplify the expression first.

Expanding the expression inside the integral, we have:

∫e^(-k) [6t - 36 + 6t + 36] dt

= ∫e^(-k) [12t] dt

Now, we can apply Euler's formula, which states that e^(ix) = cos(x) + i*sin(x), where i is the imaginary unit.

Using Euler's formula, we can rewrite e^(-k) as cos(-k) + i*sin(-k), which simplifies to cos(k) - i*sin(k).

Substituting this into our integral, we have:

∫[12t * (cos(k) - i*sin(k))] dt

Expanding further, we get:

∫[12t*cos(k) - 12t*i*sin(k)] dt

Now, we can integrate term by term:

= 12*cos(k)∫t dt - 12*i*sin(k)∫t dt

Evaluating the integrals, we have:

= 12*cos(k)*(t^2/2) - 12*i*sin(k)*(t^2/2) + C

Therefore, the evaluated integral is:

12*cos(k)*(t^2/2) - 12*i*sin(k)*(t^2/2) + C

This is the simplified expression using Euler's formula.

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Step-by-step explanation:

You must specify the length or the breadth either in values, variables or ratio. ..

There are infinite answers for this question., so I guess you have missed printing some information in it.. so rewrite the question please

Raven can travel 5.71 miles or less under her limit.

Inequality is defined as the relation which makes a non-equal comparison between two given functions. If the equation or inequality contains variable terms, then there might be some values of those variables for which that equation or inequality might be true. Such values are called solution to that equation or inequality.

Let x b the number of miles Raven travels, we can write an expression relating the amount he spends. So there:

3.00 + 0.50= 3.50

Consider that total cost per mile be less than equal to the amount the Raven can spend:

3.50x ≤ 20

We can determine x;

x ≤ 5.71

Therefore, Raven can travel 5.71 or less under her limit.

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To rotate a coordinate system onto another coordinate system using matrices, you can follow these steps:

1. Determine the angle of rotation: First, determine the angle by which you want to rotate the coordinate system. This angle will be used to create a rotation matrix.

2. Create a rotation matrix: The rotation matrix is a 2x2 or 3x3 matrix that represents the transformation of points in the original coordinate system to points in the rotated coordinate system. The elements of the rotation matrix can be determined based on the angle of rotation.

For a 2D rotation, the rotation matrix is:

 \(\[ \begin{matrix} cos\theta & -sin\theta \\ sin\theta & cos\theta \end{matrix} \]\)

For a 3D rotation around the x-axis, y-axis, and z-axis, the rotation matrices are:

\(Rx = \left[\begin{array}{ccc}1&0&0\\0&cos\theta&-sin\theta\\0&sin\theta&cos\theta\end{array}\right]\)

\(Ry = \left[\begin{array}{ccc}cos\theta&0&sin\theta\\0&1&0\\-sin\theta&0&cos\theta\end{array}\right]\)

\(Rz = \left[\begin{array}{ccc}cos\theta&-sin\theta&0\\sin\theta&cos\theta&0\\0&0&1\end{array}\right]\)

Note that θ represents the angle of rotation.

3. Apply the rotation matrix: To rotate a point or a set of points, multiply the coordinates of each point by the rotation matrix. This will yield the coordinates of the points in the rotated coordinate system.

For example, if you have a 2D point P(x, y), and you want to rotate it by angle θ, the rotated point P' can be obtained by multiplying the column vector [x, y] by the rotation matrix:

  [ x' ]  =  [ cosθ  -sinθ ]   [ x ]

  [ y' ] =   [ sinθ   cosθ  ] * [ y ]

Similarly, for 3D rotations, you would multiply the column vector [x, y, z] by the appropriate rotation matrix.

Rotating a coordinate system onto another coordinate system using matrices involves the use of rotation matrices. These matrices define how points in the original coordinate system are transformed to points in the rotated coordinate system.

The rotation matrices are constructed based on the desired angle of rotation. The elements of the matrix are determined using trigonometric functions such as cosine and sine. The size of the rotation matrix depends on the dimensionality of the coordinate system (2D or 3D).

To apply the rotation, the coordinates of each point in the original coordinate system are multiplied by the rotation matrix. This matrix multiplication yields the coordinates of the points in the rotated coordinate system.

By performing this transformation, you can effectively rotate the entire coordinate system, including all points and vectors within it, onto the desired orientation defined by the angle of rotation.

Matrix transformations provide a mathematical and systematic approach to rotating coordinate systems, allowing for precise control over the rotation angle and consistent results across different coordinate systems. They are widely used in computer graphics, robotics, and various scientific and engineering fields.

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θ°, we need to use the inverse tangent function (also known as arctan or tan⁻¹) to solve for θ. Using a scientific calculator or mathematical software, we can find the inverse tangent of 0.63056645.

θ° = tan⁻¹(0.63056645)

Using a calculator, the approximate value of θ° is 31.446° (rounded to three decimal places).

Therefore, θ° ≈ 31.446°.

The tangent function (tan) relates the ratio of the opposite side to the adjacent side of a right triangle. To find the value of θ that satisfies tan θ = 0.63056645, we need to find the angle whose tangent is approximately equal to 0.63056645.

The inverse tangent function (tan⁻¹) or arctan allows us to find the angle when we know the tangent ratio. In this case, we use the inverse tangent function to find the angle θ whose tangent is approximately 0.63056645.

By evaluating tan⁻¹(0.63056645) using a calculator, we find that θ° is approximately 31.446°. This value lies within the given interval [0°, 90°].

Therefore, θ° ≈ 31.446°.

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Therefore, the volume of the paper cone to the nearest tenth is 418.7 inches cubed.

The volume of the paper cone that Gretchen made to hold a gift for a friend is given by;V= (1/3)πr²hWhere;r = radius of the paper coneh = height of the paper coneπ = 3.14

Given that;Height of the paper cone (h) = 16 inches Radius of the paper cone (r) = 5 inchesWe are to find the volume (V) of the paper cone to the nearest tenth of an inch.

To obtain the volume of the paper cone, we can substitute the values of r and h in the formula above to obtain;

\(V= (1/3)\pir^2hV\)= \((\frac{1}{3} ) \times 3.14\times5^2 \times16V = (\frac{1}{3} ) \times 3.14\times25\times16V = (\frac{1}{3}) \times 1256V=418.7\)

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Answer:

1 meter :))) yeah points pls

Answer:

0.75 ounce

Step-by-step explanation:

64 candles= 16 ounce

3 candies= x ounce

(cross multiplication)

x= (3×16)÷64= 0.75 ounce

hope it helps

Answer:

the answer is d=20.5 hope this helped

Answer:

d= 20.5

Step-by-step explanation:

d/4+7/8=6

(we know that to add fractions, we have to have both denomiators the same number. We aslo know that that means 8. Using that information, we know that to top number must be 48. 48/8 = 6. We can substract)

48-7= 41

(we then need to divide by 2 as we would have had to already multiplyed 4 by 2.)

41/2 = 20.5

Answer:

T(r) = (16 ties/racks)r

Step-by-step explanation:

Total number of ties = (16 ties/rack)(number of racks), or

T(r) = (16 ties/racks)r