Evaluate 7-5{p}+3q7−5p+3q7, minus, 5, p, plus, 3, q when p=1p=1p, equals, 1 and q=7q=7q, equals, 7.

The angle whose tangent is 456/321 is 54.85°

The tangent of an angle in trigonometry is the ratio of the lengths of the adjacent side to the opposing side. In order for the value of the cosine function to not be 0, it is the ratio of the sine and cosine functions of an acute angle.

The Tangent Formula is given as:

Tan A = Opposite Side/Adjacent side

In terms of sine and cosine, tangent may be represented as:

Tan A = Sin A / Cos A

We know that the sine of an angle is equal to the length of the opposite side divided by the length of the hypotenuse side whereas the cosine of the angle is the ratio of the length of the adjacent side to the ratio of the hypotenuse side.

That is, Sin A = Opposite Side/ Hypotenuse Side

Cos A = Adjacent Side/ Hypotenuse Side

Therefore, tan A = Opposite Side/ Adjacent Side

\(tan^{-1} (1.42056)\) =54.85°

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Answer:

750 gallons per hour

Step-by-step explanation:

divide 18000 by 24 and you get 750

Answer:

x = 7, x = 5

Step-by-step explanation:

\(\frac{3x+3}{8}\) = 2x - 11 ( multiply both sides by 8 to clear the fraction )

3x + 3 = 16x - 88 ( subtract 3x from both sides )

3 = 13x - 88 ( add 88 to both sides )

91 = 13x ( divide both sides by 13 )

7 = x

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

\(\frac{4x-6}{7}\) = 2 ( multiply both sides by 7 )

4x - 6 = 14 ( add 6 to both sides )

4x = 20 ( divide both sides by 4 )

x = 5

3x + 3 / 8 = 2x - 11

Multiply both sides by 8

8 × ( 3x + 3 / 8 ) = 8 × ( 2x - 11 )

3x + 3 = 16x - 88

Add both sides 88

3x + 3 + 88 = 16x - 88 + 88

3x + 91 = 16x

Subtract both sides 3x

3x - 3x + 91 = 16x - 3x

91 = 13x

Divide both sides by 13

91 ÷ 13 = 13x ÷ 13

7 = x

x = 7

_________________________________

4x - 6 / 7 = 2

Multiply both sides by 7

( 4x - 6 / 7 ) × 7 = 2 × 7

4x - 6 = 14

Add both sides 6

4x - 6 + 6 = 14 + 6

4x = 20

Divide both sides by 4

4x ÷ 4 = 20 ÷ 4

x = 5

Answer:

84

Step-by-step explanation:

substitute n = 5 into the expression

16n + 4

= 16(5) + 4

= 80 + 4

= 84

Answer:

The expression will have the value of 84

Step-by-step explanation:

\(16n + 4\)

given expression

Thus, plug n=5

\(16(5) + 4 \\ 80 + 4 = 84\)

Finally, we get the value 84

The speed of the charge when it is at a great distance from the origin is 0 m/s.

To find the speed of the charge when it is at a great distance from the origin, we can apply the principle of conservation of mechanical energy.

The initial mechanical energy of the charge at the origin is given by the sum of its potential energy and kinetic energy:

E_initial = U_initial + K_initial

The potential energy at the origin is zero since there are no other charges present. Therefore, we only need to consider the kinetic energy:

E_initial = K_initial

The final mechanical energy of the charge when it is at a great distance from the origin is given by:

E_final = U_final + K_final

Since the charge is at a great distance, we can assume that the potential energy is zero. Therefore:

E_final = K_final

According to the conservation of mechanical energy, the initial mechanical energy should be equal to the final mechanical energy:

E_initial = E_final

K_initial = K_final

Now let's calculate the initial kinetic energy:

K_initial = (1/2) * m * v_initial^2

Since the charge is released from rest, its initial velocity is zero:

K_initial = (1/2) * m * 0^2

K_initial = 0

This means that the initial kinetic energy is zero.

Now let's calculate the final kinetic energy:

K_final = (1/2) * m * v_final^2

Since the charge is at a great distance from the origin, it is assumed to have a negligible potential energy. Therefore:

E_final = K_final = (1/2) * m * v_final^2

Setting the initial kinetic energy equal to the final kinetic energy, we have:

K_initial = K_final

0 = (1/2) * m * v_final^2

Since the initial kinetic energy is zero, we can solve for the final velocity:

v_final^2 = 0

Taking the square root of both sides, we find:

v_final = 0

Therefore, the speed of the charge when it is at a great distance from the origin is 0 m/s.

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Answer:

Explanation:

The diameter of the virus is given below:

The microscope is set so that the object appears 5 x 10² times larger than its actual size.

Therefore, the diameter of the virus when viewed under the mīcroscope is:

We then simplify our result by collecting like terms.

The length of interval AB is approximately 6.4 units.

In mathematics, the length of an interval is a measure of the size or extent of the interval on the real number line. The length of an interval is defined as the absolute value of the difference between the endpoints of the interval.

For example, if we have an interval [a, b] on the real number line, where a and b are real numbers, then the length of the interval is given by:

length of interval [a, b] = |b - a|

In other words, the length of an interval is the distance between its endpoints. This is a useful concept in a variety of mathematical contexts, such as calculus, geometry and analysis.

if point A is located at (-4, 0) and point B is located at (0, 5), use the distance formula to find the length of the interval AB. The distance formula is:

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

where (x1, y1) and (x2, y2) are the coordinates of points A and B, respectively.

Substituting the values

\(Distance AB = \sqr((0 - (-4))^2 + (5 - 0)^2)\)

\(Distance AB = \sqrt(16 + 25)\)

\(Distance AB = \sqrt(41)\)

distance AB ≈ 6.4 (rounded to 1 decimal place)

Therefore, the length of interval AB is approximately 6.4 units.

      |

   6  |   B

      |

      |

   5  |      

      |

      |

   4  |      

      |

      |

   3  |      

      |

      |

   2  |      

      |

      |

   1  |      

      |

      |

   0  |---|---|---|---|---|---|---|---|

      -4   -3  -2  -1   0   1   2   3   4

            |

            |

            | A

The horizontal line represents the x-axis, with tick marks at each integer value. The vertical line represents the y-axis, also with tick marks at each integer value. Point A is located at (-4, 0) on the x-axis, and point B is located at (0, 5) on the y-axis. The line segment connecting the two points represents interval AB, and its length is approximately 6.4 units.

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"Statistics: The Art and Science of Learning from Data" (4th edition) is a valuable resource for understanding and applying statistical principles, providing insights into data analysis and decision-making processes.

Statistics is the art and science of learning from data. It involves collecting, organizing, analyzing, interpreting, and presenting data to gain insights and make informed decisions. In the 4th edition of the book "Statistics: The Art and Science of Learning from Data," you can expect to find a comprehensive exploration of these topics.

This edition may cover important concepts such as descriptive statistics, which involve summarizing and displaying data using measures like mean, median, and standard deviation. It may also delve into inferential statistics, which involve making inferences and drawing conclusions about a population based on a sample.

Additionally, the book may discuss various statistical techniques such as hypothesis testing, regression analysis, and analysis of variance (ANOVA). It may also provide real-world examples and case studies to illustrate the application of statistical methods.

When using information from the book, it is important to properly cite and reference it to avoid plagiarism. Be sure to consult the specific edition and follow the guidelines provided by your instructor or institution.

In summary, "Statistics: The Art and Science of Learning from Data" (4th edition) is a valuable resource for understanding and applying statistical principles, providing insights into data analysis and decision-making processes.

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To code a categorical variable with 8 levels, you would need 8 indicator variables, also known as dummy variables, each representing one level of the categorical variable.

To code a categorical variable with 8 levels (A, B, C, D, E, F, G, H), you can use a technique called one-hot encoding. One-hot encoding involves creating binary indicator variables for each level of the categorical variable.

In this case, since there are 8 levels, you would need 8 indicator variables to code the categorical variable. Each indicator variable represents one level of the variable and takes a value of 1 if the observation belongs to that level, and 0 otherwise.

For example, if we have a categorical variable "Category" with levels A, B, C, D, E, F, G, H, the indicator variables would be:

Indicator variable for A: 1 if the observation belongs to category A, 0 otherwise.

Indicator variable for B: 1 if the observation belongs to category B, 0 otherwise.

Indicator variable for C: 1 if the observation belongs to category C, 0 otherwise.

Indicator variable for D: 1 if the observation belongs to category D, 0 otherwise.

Indicator variable for E: 1 if the observation belongs to category E, 0 otherwise.

Indicator variable for F: 1 if the observation belongs to category F, 0 otherwise.

Indicator variable for G: 1 if the observation belongs to category G, 0 otherwise.

Indicator variable for H: 1 if the observation belongs to category H, 0 otherwise.

By using one-hot encoding with 8 indicator variables, you can represent each level of the categorical variable uniquely and independently.

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Answer:1386cm2

Step-by-step explanation:

Answer: (6, 5)

Step-by-step explanation: (2+4,-3-2) = (6, -5)

After reflection on x - axis, the y value changes the sign from negative to positive (to the opposite) : (6,5)

Answer:

Y=1/3(x-1)*2-4

Step-by-step explanation:

jus look at the answer bra

The value of the lesser integer is -7.

From the information, the sum of an integer and 5 times the next consecutive odd integer is -32.

Let the small integer be x

Let the big integer be x + 2.

This will be illustrated thus:

x + 5(x + 2) = -32

Open parentheses

x + 5x + 10 = -32

Collect like terms

6x = -32 - 10

6x = -42

Divide

x = - 42 / 6

x = -7

The small integer is -7.

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When developing the Object Relational Model in the models.py file for a Django project, data types for each attribute must be specified is true statement.

The statement "When developing the Object Relational Model in the models.py file for a Django project, data types for each attribute must be specified" is true.

In Django, the models.py file defines the Object Relational Model (ORM) that maps the database tables to Python classes. Each attribute in the model represents a column in the corresponding database table. In order to define the attribute, you must specify the data type for the corresponding column.

Django supports several built-in data types for attributes, such as CharField, IntegerField, DateField, BooleanField, etc. You can also define custom data types by creating your own model fields.

By specifying the data type for each attribute, Django can ensure that the values entered into the database are of the correct type and can perform appropriate data validation. This is essential for maintaining data integrity and avoiding data-related errors.

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9514 1404 393

Answer:

  20 ounces

Step-by-step explanation:

We can multiply the given ratio by 5 to see the answer:

  4 oz : 10 gal = 5·4 oz : 5·10 gal = 20 oz : 50 gal

20 ounces of fertilizer are required.

Answer:c

Step-by-step explanation:

Answer:

2 is the answer because you add then tske away

The lengths of the two pieces of a wire will be 19,19.

A square is a closed, two-dimensional object with four equal sides and four vertices. On either side, it has parallel sides.

The square of a square's side determines its area.

Given data -

Length of a wire = 38 m

As the wire is divided into two pieces,

Let the length of two pieces of wire be x and y m respectively.

As per given data, x + y = 38

Therefore, y = 38 - x    

As each piece is bent into a square, area of squares will be

\((x/4)^{2}\)  and  \((y/4)^{2}\)

Therefore, the sum of areas of two squares will be A = \((x/4)^{2}\) +      \((y/4)^{2}\)

A = \(x^{2}\)/16 + \(y^{2}\)/16

A = \(x^{2}\)/16 + \((38-x)^{2}\)/16

By differentiating, we will get

A' = \(\frac{2x}{16}\) - \(\frac{2(38-x)}{16}\)

In order to minimize the the sum of the areas of the two squares, we will take A' = 0

0 = x - (38 - x)

2x = 38

x = 19

Therefore y = 19

The length of two pieces of a wire should be 19 m each.

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Answer:

4

Step-by-step explanation:

The Fourier series expansion of f(x) on [-π, π] is:

πx ≈ (2/π) Σ[n odd] [(1-(-1)^n)/(n^2)] sin(nx)

To find the Fourier sine series expansion of f(x) = πx on the interval [0, π], we need to first extend the function to be odd and periodic with period 2π. We can do this by defining:

f(x) = πx, for 0 ≤ x ≤ π

f(x) = -π(x-2π), for π ≤ x ≤ 2π

Since f(x) is odd, its Fourier series will only have sine terms. Thus, we need to find the coefficients bn:

bn = (2/π) ∫[0,π] f(x) sin(nx) dx

= (2/π) ∫[0,π] πx sin(nx) dx

= (2/π^2) [(-1)^n - 1] n

Therefore, the Fourier sine series expansion of f(x) on [0, π] is:

πx ≈ (4/π) Σ[n odd] [(1-(-1)^n)/(n^2)] sin(nx)

To find the Fourier series expansion of f(x) = πx on the interval [-π, π], we need to extend the function to be periodic with period 2π. We can do this by defining:

f(x) = πx, for -π ≤ x < π

f(x) = f(x + 2π), for all x

Since f(x) is an odd function, the Fourier series will only have sine terms. Thus, we need to find the coefficients bn:

bn = (1/π) ∫[-π,π] f(x) sin(nx) dx

= (1/π) ∫[-π,π] πx sin(nx) dx

= (2/π^2) [(-1)^n - 1] n

Therefore, the Fourier series expansion of f(x) on [-π, π] is:

πx ≈ (2/π) Σ[n odd] [(1-(-1)^n)/(n^2)] sin(nx)

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Answer:

Step-by-step explanation:

The volume of a cube.

The formula is V = s^3 where is the the "whole side length" of the cube. The cube requires three dimensions be multiplied together to find its volume.

That's why the formula is written as V = s^3. It means that V = s * s * s which is three sides multiplied together. They also need to be at right angles to each other.

Answer:

$12 per shirt

Step-by-step explanation:

$300/25=$12

Answer:

11.96 per shirt

Step-by-step explanation:

299/25 = 11.96 you do this instead of 300/25 because it says less than 300

The dimensions of the cylindrical can that will minimize the cost of the metal to manufacture it is 0.04 m and 0.027 m for height and radius respectively.

The given information of the question is that we have to create a cylindrical can that holds 1.4 litres of oil and we have to find the dimensions that will minimize the cost of the metal to manufacture the can.

We will solve the given problem through Lagrange Multipliers method.

Steps for solving the given problem are as follows:

Step 1: Let us assume that the cylindrical can has radius r and height h.

Therefore, we have to find the dimensions of r and h to minimize the cost of the metal.

Step 2: The total surface area (SA) of the cylindrical can is given as: SA = 2πr² + 2πrh

This equation represents the cost of the metal to manufacture the cylindrical can.

Step 3: The volume of the cylindrical can is given as: V = πr²h = 1.4 litres.

Now, let us convert 1.4 litres into cubic metres.

1 litre = 10⁻³ cubic metres 1.4 litres = 1.4 × 10⁻³ cubic metres

V = 1.4 × 10⁻³ = πr²h

Therefore, h = (1.4 × 10⁻³)/(πr²)

Step 4: Now, we have to use the Lagrange Multipliers method to find the dimensions that will minimize the cost of the metal.

Let us assume that C is the cost of the metal.

C = k(2πr² + 2πrh)

This is the objective function.

Now, let us assume that f is the constraint function.

f = πr²h - 1.4 × 10⁻³

This is the constraint function.

Step 5 : The next step is to find the partial derivatives of both the objective function and the constraint function with respect to r, h and λ (Lagrange Multiplier).

∂C/∂r = 4πrk + 2πh∂C/∂h

= 2πr(k + λ) + 2πr²∂C/∂λ

= f∂f/∂r

= 2πrh∂f/∂h

= πr²∂f/∂λ

= 0

Step 6: Now, we have to solve these equations and find the values of r and h that minimize the cost of the metal.

4πrk + 2πh = 2πr(k + λ) + 2πr²......(1)πr²h = 1.4 × 10⁻³......(2)

2πrh = λπr²......(3)

Substitute (3) in (1) and simplify it.

4πrk + 2πh = 2πr(k + λ) + 2πr²2πr(k + λ) + λπr² = 2πr² + 2πhλr² = 2h/k

Substitute λr² = 2h/k in (2) and simplify it.

π(2h/k) = 1.4 × 10⁻³h

= (1.4 × 10⁻³)(k/2π)π(2/k)(1.4 × 10⁻³)(k/2π)

= 1.4 × 10⁻³r²

= 1.4 × 10⁻³/(2πh/k)

= 0.00001003h

= 0.04 m and r

= 0.027 m.

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Ok so firstly, you need to remember that when a radius is touching a tangent, the angle is always equal to 90°. So x + 57° = 90°. That means your angle is 33°. You have drawn a right angle which is correct so the left triangle's angle is 90° - 33° = 57°. Now because both sides of the triangle is radius, that means c and 57° are equal. That means c = 57°.

Answer:

c = 57 degrees.

Step-by-step explanation:

This is the Alternate Segment theorem:

The angle between a chord of a circle and a tangent to the circle = the angle subtended by the chord in the alternate segment.

So c = 57 degrees.

Answer:

(3x - 9)/(x² - 5x + 12)

Step-by-step explanation:

Answer attached, please refer it.

Hope it helps :)

Answer:

You can get approximate values by drawing a graph,

Step-by-step explanation:

The formula to find the tangent line to a curve at a given point is y = f'(x) (x - x₀) + f(x₀).

The derivative of the function, f'(x) is calculated at the given point, x₀. Then, the equation of the tangent line is found by substituting the x₀ and f'(x) values into the formula.

To find the tangent line to a curve at a given point, the formula for the slope of the tangent line must be used. The slope of a tangent line is equal to the derivative of the function at that point. The resulting equation is a line with a slope equal to the derivative of the function at the given point, and a y-intercept equal to the value of the function at the given point. For example, if you want to find the tangent line to the function f(x) = 4x² + 3 at the point (2, 19), the derivative of the function at that point is f'(x) = 8x = 8(2) = 16. Then, the equation of the tangent line is y = 16(x - 2) + 19.

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