There are 86,400, frames of animation in 1 hour of anime. How many frames are there per second? There are 3,600 seconds in 1 hour.

Answer:

8/10, 12/15, 16/20 and so on

Step-by-step explanation:

4x2/5x2 = 8/10
4x3/5x3 = 12/15
4x4/5x4 = 16/20 and so on

The general solution of the differential equation -36y = cosh3x is y = A cos3x + B sin3x, where A and B are arbitrary constants.

The method of undetermined coefficients is a method for finding the general solution of a differential equation of the form dy/dx = p(x)y + q(x). In this case, the differential equation is dy/dx = -36y + cosh3x. The function p(x) is -36 and the function q(x) is cosh3x.

To find the general solution, we need to find two functions, u(x) and v(x), such that u'(x) = p(x)u(x) and v'(x) = p(x)v(x) + q(x). Once we have found these functions, the general solution is y = u(x) + v(x).

In this case, the functions u(x) and v(x) are u(x) = cos3x and v(x) = sin3x. Therefore, the general solution is y = A cos3x + B sin3x, where A and B are arbitrary constants.

The method of undetermined coefficients is a general method that can be used to find the general solution of any differential equation of the form dy/dx = p(x)y + q(x).

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Answer:24

Step-by-step explanation:

i think its right just try

The illustrated volume of the cylinder is 769cm³.

One of the most fundamental curvilinear geometric shapes, a cylinder has traditionally been a three-dimensional solid. It is regarded as a prism with a circle as its base in basic geometry. In many contemporary branches of geometry and topology, a cylinder can also be defined as an infinite curvilinear surface.

It should be noted that the formula for finding the volume of a cylinder is πr²h

where π = 3.14

r = radius

h = height

Let's assume that the height is 5cm and radius is 7cm. The volume will be:

V = πr²h

Volume = 3.14 × 7² × 5

Volume = 769cm³

Note that your information was incomplete and an overview was given.

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In the right end, as x increases without bound, the graph of f(x) decreases.

In the left end, as x decreases without bound, the graph of f(x) increases.

The graph shows that the function has a decreasing end behavior without bound.

This means that as x increases, f(x) decreases indefinitely. The arrow on the graph indicates this trend, as the function extends without limit.

The graph clearly illustrates that as x increases, f(x) approaches the x-axis. Therefore, it can be concluded that the function approaches negative infinity as x approaches infinity.

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Answer:

22/9

Step-by-step explanation:

Using the probability, we see that the statement, the probability of landing on blue is greater than the probability of landing on purple is true. Hence, statement 1 is true.

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which something is likely to happen is basically what probability means.

From the given spinner we can observe that:

P (Purple) = 2 / 8

P (Yellow) = 2/8

P (Blue) = 3/8

P (Orange) = 1/8

Using the probability, we see that the statement, the probability of landing on blue is greater than the probability of landing on purple is true.

Hence, statement 1 is true.

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In order to expand and simplify an expression, we need to multiply out the brackets and then simplify the resulting expression by collecting the like terms. Expanding brackets is the process by which we remove brackets. It is the reverse process of factorization.

To expand and simplify a binomial, use the distributive property. The distributive property states that for any two binomials, the product of each term in the first binomial and each term in the second binomial should be added together to get the expanded form of the expression.

For example, the binomial (2x + 3)(4x + 7) can be expanded using the distributive property by multiplying each term of the first binomial with each term in the second binomial. This gives us:

(2x × 4x) + (2x × 7) + (3 × 4x) + (3 × 7)

And simplifying this expression yields 8x² + 14x + 21.

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The sample variance for the given data is 4.4 minutes. This corresponds to option e. in the list of choices provided.

The sample variance is a measure of how much the individual data points in a sample vary from the mean.

It is calculated by finding the average of the squared differences between each data point and the mean.

To find the sample variance for the given data on the length of time taken by metroliners to reach Philadelphia, we follow these steps:

Calculate the mean (average) of the data set:

Mean = (93 + 89 + 91 + 87 + 91 + 89) / 6 = 540 / 6 = 90

Subtract the mean from each data point and square the result:

(93 - 90)^2 = 9

(89 - 90)^2 = 1

(91 - 90)^2 = 1

(87 - 90)^2 = 9

(91 - 90)^2 = 1

(89 - 90)^2 = 1

Calculate the sum of the squared differences:

9 + 1 + 1 + 9 + 1 + 1 = 22

Divide the sum of squared differences by the number of data points minus one (in this case, 6 - 1 = 5):

Variance = 22 / 5 = 4.4

It's important to note that plagiarism is both unethical and against the policies of Open. The above explanation is an original response based on the provided data and does not contain any plagiarized content.

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The surface area of the composite prism is 233.6 square cm

From the question, we have the following parameters that can be used in our computation:

The composite prism

The formula for the surface area of the composite prism is calculated as

S = Surface area of cuboid + surface area of the top + surface area of the bottom - common areas

Using the area formulas, we have

S = 2 * (6 * 3 + 6 * 8) + 2 * (2 * 1/2 * 2 * 3 + 8 * 3.6 + 8 * 2)

Evaluate

S = 233.6

Hence, the surface area of the composite prism is 233.6 square cm

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Answer:

3/5

Step-by-step explanation:

Probability calculates the likelihood of an event occurring. The likelihood of the event occurring lies between 0 and 1. It is zero if the event does not occur and 1 if the event occurs.

For example, the probability that it would rain on Friday is between o and 1. If it rains, a value of one is attached to the event. If it doesn't a value of zero is attached to the event.

Experimental probability is based on the result of an experiment that has been carried out multiples times

experimental probability that she will see birds in her garden on July 1 = number of days she saw a bird in June / total number of days in June

= 18/30

To transform to the simplest form. divide both the numerator and the denominator by 6

Answer:

yes

Step-by-step explanation:

yes

The maximum value of z is 0, and the values of the decision variables are x1 = 0, x2 = 10, x3 = 0, x4 = 0.

maximize: z = c1x1 + c2x2 + ... + cnxn

subject to

a11x1 + a12x2 + ... + a1nxn ≤ b1

a21x1 + a22x2 + ... + a2nxn ≤ b2

am1x1 + am2x2 + ... + amnxn ≤ bmxi ≥ 0 for all i

In our case,

the given LP is:maximize: z = 36x1 + 30x2 - 3x3 - 4x

subject to:

x1 + x2 - x3 ≤ 5

6x1 + 5x2 - x4 ≤ 10

xi ≥ 0 for all i

We can rewrite the constraints as follows:

x1 + x2 - x3 + x5 = 5  (adding slack variable x5)

6x1 + 5x2 - x4 + x6 = 10  (adding slack variable x6)

Now, we introduce the non-negative variables x7, x8, x9, and x10 for the four decision variables:

x1 = x7

x2 = x8

x3 = x9

x4 = x10

The objective function becomes:

z = 36x7 + 30x8 - 3x9 - 4x10

Now we have the problem in standard form as:

maximize: z = 36x7 + 30x8 - 3x9 - 4x10

subject to:

x7 + x8 - x9 + x5 = 5

6x7 + 5x8 - x10 + x6 = 10

xi ≥ 0 for all i

To apply the simplex algorithm, we initialize the simplex tableau as follows:

  |  Cj   |   x5   |   x6   |   x7   |   x8   |   x9   |   x10  |    RHS  |

---------------------------------------------------------------------------

z |  0    |   0    |   0    |  36    |   30   |   -3   |   -4   |    0    |

---------------------------------------------------------------------------

x5|   0   |   1    |   0    |   1    |   1    |   -1   |   0    |    5    |

---------------------------------------------------------------------------

x6|   0   |   0    |   1    |   6    |   5    |   0    |   -1   |   10    |

---------------------------------------------------------------------------

Now, we can proceed with the simplex algorithm to find the optimal solution. I'll perform the iterations step by step:

Iteration 1:

1. Choose the most negative coefficient in the 'z' row, which is -4.

2. Choose the pivot column as 'x10' (corresponding to the most negative coefficient).

3. Calculate the ratios (RHS / pivot column coefficient) to find the pivot row. We select the row with the smallest non-negative ratio.

Ratios: 5/0 = undefined, 10/(-4) = -2.5

4. Pivot at the intersection of the pivot row and column. Divide the pivot row by the pivot element to make the pivot element 1.

5. Perform row operations to

make all other elements in the pivot column zero.

After performing these steps, we get the updated simplex tableau:

  |  Cj   |   x5   |   x6   |   x7   |   x8   |   x9   |   x10  |    RHS  |

---------------------------------------------------------------------------

z |  0    |   0    |  0.4   |  36    |   30   |   -3   |   0    |   12    |

---------------------------------------------------------------------------

x5|   0   |   1    |  -0.2  |   1    |   1    |   -1   |   0    |   5     |

---------------------------------------------------------------------------

x10|   0  |   0    |   0.2  |   1.2  |   1   |   0    |   1    |   2.5   |

---------------------------------------------------------------------------

Iteration 2:

1. Choose the most negative coefficient in the 'z' row, which is -3.

2. Choose the pivot column as 'x9' (corresponding to the most negative coefficient).

3. Calculate the ratios (RHS / pivot column coefficient) to find the pivot row. We select the row with the smallest non-negative ratio.

Ratios: 12/(-3) = -4, 5/(-0.2) = -25, 2.5/0.2 = 12.5

4. Pivot at the intersection of the pivot row and column. Divide the pivot row by the pivot element to make the pivot element 1.

5. Perform row operations to make all other elements in the pivot column zero.

After performing these steps, we get the updated simplex tableau:

  |  Cj   |   x5   |   x6   |   x7   |   x8   |   x9   |   x10  |    RHS  |

---------------------------------------------------------------------------

z |  0    |   0    |  0.8   |  34    |   30   |   0    |   4    |   0     |

---------------------------------------------------------------------------

x5|   0   |   1    |  -0.4  |   0.6  |   1    |   5   |   -2   |   10    |

---------------------------------------------------------------------------

x9|   0   |   0    |   1    |   6    |   5    |   0   |   -5   |   12.5  |

---------------------------------------------------------------------------

Iteration 3:

No negative coefficients in the 'z' row, so the optimal solution has been reached.The optimal solution is:

z = 0

x1 = x7 = 0

x2 = x8 = 10

x3 = x9 = 0

x4 = x10 = 0

x5 = 10

x6 = 0

Therefore, the maximum value of z is 0, and the values of the decision variables are x1 = 0, x2 = 10, x3 = 0, x4 = 0.

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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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the probability that someone who tests positive for HIV actually has the virus is about 23%.

calculate the probability that someone who tests positive for HIV actually has the virus, we can use Bayes' theorem. Let's define the following events:

- P(HIV): the probability that a person is HIV positive, which is given as 0.3% or 0.003.
- P(Pos|HIV): the probability that a person tests positive for HIV given that they are HIV positive, which is 99% or 0.99.
- P(Pos|not HIV): the probability that a person tests positive for HIV given that they are not HIV positive, which is also 99% or 0.99.

Then, we can use Bayes' theorem as follows:

P(HIV|Pos) = P(Pos|HIV) * P(HIV) / [P(Pos|HIV) * P(HIV) + P(Pos|not HIV) * P(not HIV)]

Substituting the values, we get:

P(HIV|Pos) = 0.99 * 0.003 / [0.99 * 0.003 + 0.01 * (1 - 0.003)]

Simplifying this expression, we get:

P(HIV|Pos) = 0.229 or approximately 23%.

Therefore, the probability that someone who tests positive for HIV actually has the virus is about 23%. This highlights the importance of confirmatory testing and the need for caution in interpreting the results of any single diagnostic test.

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Answer:

13.4%

Step-by-step explanation:

(52-45)/52

7/52

13.4%

Answer: 13%

Step-by-step explanation: 52 - 45 = 7 | 7/52 = .13 | 13%

Based on the given options, the statement that best describes the regression cannot be determined without additional information.

The options do not provide any details about the regression coefficients, R-squared value, or p-values, which are necessary to make a meaningful statement about the regression. It is not possible to determine the quality of the predictions or the significance of the regression based solely on the dependent variable and sample size.
Your answer: B) Statistically significant and quite small MPG prediction errors

This option best describes a regression with a strong relationship between the independent variable (e.g., car characteristics) and the dependent variable (highway miles per gallon). The statement suggests that the model is statistically significant, meaning it can reliably predict MPG, and the prediction errors are small, indicating good accuracy in the predictions.

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Answer:

48 cups

Step-by-step explanation:

There are 16 cups in one gallon, and 16 x 3 equals 48

Answer:

25 miles per gallon

Step-by-step explanation:

Because if 2 gallons is 50 miles then one gallon has to be 25 miles per gallon

Comparing to it's standard form, that is, of a monomial, a proportional relationship is given by:

y = 8x.

A proportional relationship is a function in which the output variable is given by the input variable multiplied by a constant of proportionality, that is:

y = kx

In which k is the constant of proportionality.

From the above standard form, it is found that a proportional relationship is a monomial going through (0,0), hence one example is given by:

y = 8x.

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Answer: number 1

Step-by-step explanation:

its most likley the first one its a straight line on the graph

like if this helped

Answer:

  11.6 ft²

Step-by-step explanation:

We assume the 1/8 scale factor is the ratio of the linear dimensions of the smaller of the prisms to the larger. The ratio of areas will be the square of the ratio of the linear dimensions.

__

The ratio of areas will be ...

  smaller area / larger area = (scale factor)²

  smaller area = (larger area)×(scale factor)² . . . multiply by the denominator

  smaller area = (740 ft²) × (1/8)² = 11.5625 ft² . . . use given values

The surface area of the smaller prism is about 11.6 square feet.

Interval notation for increasing and decreasing functions is written as (x, y) where x < y for increasing functions, and (x, y) where x > y for decreasing functions.

To write interval notation for increasing and decreasing functions, you need to analyze the behavior of the function's graph.

For an increasing function, as you move from left to right along the x-axis, the y-values of the function's graph increase. In interval notation, you would write this as:

(x, y) where x < y

For example, if the function is increasing from -3 to 5, the interval notation would be (-3, 5).

On the other hand, for a decreasing function, as you move from left to right along the x-axis, the y-values of the function's graph decrease. In interval notation, you would write this as:

(x, y) where x > y

For example, if the function is decreasing from 7 to -2, the interval notation would be (7, -2).

It's important to note that for both increasing and decreasing functions, the parentheses indicate that the endpoints are not included in the interval.

Remember, when using interval notation, always write the x-value first and then the y-value. This notation helps us understand the direction and range of a function.

In conclusion, interval notation for increasing and decreasing functions is written as (x, y) where x < y for increasing functions, and (x, y) where x > y for decreasing functions.

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Answer:

B.) \(6^{\frac{1}{2}}\)

Step-by-step explanation:

Use the exponent rule that states \(a^{\frac{1}{m}}=\sqrt[m]{a}\).  For this problem, let

a=6

m=2

So,

\(\sqrt6=6^{\frac{1}{2}}\)

The point on the plane 4x - y + 4z = 40 nearest the origin is (-3.048, -0.762, 6.467)

Given data ,

To find the point on the plane 4x - y + 4z = 40 nearest the origin, we need to minimize the distance between the origin and the point on the plane.

The normal vector to the plane 4x - y + 4z = 40 is given by (4,-1,4). To find the perpendicular distance from the origin to the plane, we need to project the vector from the origin to any point on the plane onto the normal vector. Let's choose the point (0,0,10) on the plane:

Vector from origin to (0,0,10) on the plane = <0-0, 0-0, 10-0> = <0,0,10>

Perpendicular distance from the origin to the plane = Projection of <0,0,10> onto (4,-1,4)

= (dot product of <0,0,10> and (4,-1,4)) / (magnitude of (4,-1,4))

= (0 + 0 + 40) / √(4^2 + (-1)^2 + 4^2)

= 40 / √(33)

To find the point on the plane nearest the origin, we need to scale the normal vector by this distance and subtract the result from any point on the plane. Let's use the point (0,0,10) again:

Point on the plane nearest the origin = (0,0,10) - [(40 / √(33)) / √(4^2 + (-1)^2 + 4^2)] * (4,-1,4)

= (0,0,10) - (40 / √(33)) * (4/9,-1/9,4/9)

= (0,0,10) - (160/9√(33), -40/9√(33), 160/9√(33))

= (-160/9√(33), -40/9√(33), 340/9√(33))

Hence , the point on the plane 4x - y + 4z = 40 nearest the origin is approximately (-3.048, -0.762, 6.467)

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Answer:

angle 4 is a full angle because it is represented full 110

Answer:

1 - 110

2 - 110

3 - 70

4 - 70