9. What is the equation in standard form of the line which passes through (-2, 6) and has a slope of -1? (5 points) O x + y = -4 O x + y = 4 O x - y = -4 O x - y = 4​

The value of the infinite series as n tends to 0 is: 0

Infinite series is defined as the sum of infinitely many numbers related in a given way and listed in a given order. Infinite series are important in mathematics and in such disciplines as physics, chemistry, biology, and engineering.

From the infinite series, we want to find the value of the series as n tends to 0.

We are given the series as:

x/2ˣ

At x = 0, we have:

0/2⁰ = 0/1 = 0

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To find the particular solution, we need additional information such as the initial condition \(y(x_0) = y_0\), where \(x_0\) and \(y_0\) are known values.

To find the particular solution to a differential equation, we need to know the specific form of the differential equation. Without this information, it is not possible to determine the particular solution.

A differential equation is an equation that relates a function and its derivatives. The form of the differential equation determines the method used to solve it and find the particular solution.

For example, a simple linear first-order ordinary differential equation has the form:

\(\frac{dy}{dx} = f(x)\).

To find the particular solution, we need additional information such as the initial condition \(y(x_0) = y_0\), where \(x_0\) and \(y_0\) are known values.

The method of solution depends on the specific type of differential equation, which can include linear equations, separable equations, exact equations, etc. Each type of equation requires different techniques to find the particular solution.If you provide the specific form of the equation you want to solve or any additional information or context, I can guide you through the process of finding the particular solution. Otherwise, without the differential equation, it is not possible to determine the particular solution.

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The height of a cylinder having surface area of 78π and radius of 3 inches is 10 inches.

What is surface area?

The area is the area occupied by a two-dimensional flat surface. It has a square unit of measurement. The surface area of a three-dimensional object is the space taken up by its outer surface. Square units are used to measure it as well.

The surface area of a cylinder is = 78π in²

The radius of a cylinder is = 3 in

The total surface area of a cylinder is equal to the sum of the areas of all its faces. The total surface area with radius ‘r’, and height ‘h’ is equal to the sum of the curved area and circular areas of the cylinder.

The formula is given as -

2πr(h + r)

Substitute the values into the equation -

TSA = 2πr(h + r)

78π = 2π(3)(h + 3)

78π = 6π(h + 3)

78π = 6πh + 18π

6πh = 78π - 18π

6πh = 60π

h = 60π/6π

h = 10 in

Therefore, the height is obtained as 10 inches.

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The surface area of a cylinder with a radius of 3 inches is 78π square inches. What is the height of the cylinder in inches? (Do not enter units)

Answer:

Your answer should be 35 :)

Step-by-step explanation:

Hope this helps!

Answer:

B, D and E

Step-by-step explanation:

Using the rules of exponents/ radicals

\(a^{-m}\) = \(\frac{1}{a^{m} }\)

\(a^{\frac{1}{2} }\) = \(\sqrt{a}\)

Given

\(49^{-\frac{1}{2} }\) = \(\frac{1}{49^{\frac{1}{2} } }\)  → E

= \(\frac{1}{\sqrt{49} }\)  → B

= \(\frac{1}{7}\) → D

Answer:

45

Step-by-step explanation:

Based on the given conditions, formulate: \(5.5\div\text{tan}7^o\)

Calculate the approximate value: \(\frac{5.5}{0.122785}\)

Calculate: \(44.793745\)

Find the closest integer: 45

Answer: 45

a) The probability that no defective component will be chosen when selecting 5 components at random is approximately 0.7738, or 77.38%.

b) The probability that exactly 2 out of the 5 components will be defective is approximately 0.0874, or 8.74%.

a) To calculate the probability that no defective component will be chosen when selecting 5 components at random, we need to determine the probability of selecting a non-defective component for each selection.

Since 5% of the components are faulty, the probability of selecting a non-defective component in each selection is 1 - 0.05 = 0.95.

The probability of selecting no defective components can be calculated using the multiplication rule for independent events. We multiply the probabilities of each selection being non-defective:

Probability of selecting no defective components = (0.95)⁵

Probability of selecting no defective components = 0.7738

b) To calculate the probability that exactly 2 out of the 5 components will be defective, we need to consider the different combinations of selecting 2 defective components out of 5.

The probability of selecting exactly 2 defective components can be calculated using the binomial probability formula:

Probability = (Number of ways to choose 2 defective components) * (Probability of selecting a defective component)^(Number of defective components) * (Probability of selecting a non-defective component)^(Number of non-defective components)

Probability = (5 choose 2) * (0.05)² * (0.95)³

Probability = (5! / (2! * (5-2)!)) * (0.05)² * (0.95)³

Probability = 0.0874

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Answer:

No solutions

Step-by-step explanation:

6z + 1 = 2(3z - 1)
6z + 1 = 6z - 2 (using pemdas you use the distributive property)

Next you want to combine like terms.
To get both z's on the same side you have to subtract it from one side. However, what you do to one side you must do to the other. Once you subtract 6z from both sides you are left with only numbers. Since you do not have a variable to solve for now this equation has no solutions.

Hope this helps!

The equation 6z + 1 = 2(3z - 1) has no solutions.

Solutions are the values of an equation where the values are substituted in the variables of the equation and make the equality in the equation true.

We have,

6z + 1 = 2(3z - 1)

Solve for z.

6z + 1 = 2 (3z - 1)

6z + 1 = 6z - 2

1 = -2

This means,

No solutions.

Thus,

There are no solutions.

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Answer:

Step-by-step explanation:

95%+15%=110% so, 110%-100% is 10% and this means that 10% of both, costs 1.20. now, 10 times 1.20 is 12 dollars and we know that the whole purchace costs 12 dollars. 15 percent of 12 dollars is 1.8 dollars or, one dollar and 80 cents

Answer: Deena is correct

Step-by-step explanation:

Deena is correct because the number doesn't terminate nor does it repeat. If it does not repeat or terminate it means it is irrational.

Answer:

Step-by-step explanation:

To find the length of the arc of the circular helix from the point (3, 0, 0) to the point (3, 0, 2), we need to integrate the magnitude of the derivative of the vector equation with respect to the parameter t over the desired interval.

The vector equation of the circular helix is given by r(t) = 3cos(t)i + 3sin(t)j + tk.

To find the derivative of r(t), we differentiate each component with respect to t:

r'(t) = (-3sin(t))i + (3cos(t))j + k

The magnitude of the derivative is given by ||r'(t)|| = sqrt((-3sin(t))^2 + (3cos(t))^2 + 1^2) = sqrt(9sin^2(t) + 9cos^2(t) + 1) = sqrt(9(sin^2(t) + cos^2(t)) + 1) = sqrt(9 + 1) = sqrt(10).

Integrating this magnitude from t = 0 to t = 2 (the desired interval), we have:

Length of the arc = ∫[0 to 2] ||r'(t)|| dt = ∫[0 to 2] sqrt(10) dt = sqrt(10) ∫[0 to 2] dt = sqrt(10) [t] [0 to 2] = sqrt(10)(2 - 0) = 2sqrt(10).

Therefore, the length of the arc of the circular helix from the point (3, 0, 0) to the point (3, 0, 2) is 2sqrt(10) units.

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Integrating this expression will yield the volume of the solid of revolution. Evaluating the integral requires performing the integration step by step, and the final result will give the volume of the solid.

To find the volume of the solid generated by revolving the region bounded by the graphs of the equations y = 25 - x^2, y = 0, and x = 4 about the y-axis, we can use the method of cylindrical shells.

The volume of the solid can be calculated using the integral:

V = ∫(a to b) 2πx * h(x) dx

where a and b are the x-values where the curves intersect, 2πx represents the circumference of a cylindrical shell at each x-value, and h(x) represents the height of the cylindrical shell.

In this case, the region is bounded by the y-axis (x = 0), the parabola y = 25 - x^2, and the vertical line x = 4. To determine the limits of integration, we need to find the x-values where these curves intersect.

Setting y = 0 in the equation y = 25 - x^2 gives:

0 = 25 - x^2

x^2 = 25

x = ±5

Since we are revolving the region about the y-axis, we only need to consider the positive x-values. Thus, the limits of integration for x are 0 to 5.

The height of each cylindrical shell can be represented as h(x) = (25 - x^2) - 0 = 25 - x^2.

Now, we can calculate the volume:

V = ∫(0 to 5) 2πx * (25 - x^2) dx

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Answer:

P(17.4 < X < 22.6) = P((X-20)/2.6 < (22.6-20)/2.6) = P(Z < 1.38)

From a standard normal table, we find that P(Z < 1.38) = 0.9128

Step-by-step explanation:

Give me Brainliest if that helped! :)

Answer:

a) The mass is released at t = 0 when h is minimum. Half a cycle later h reaches its maximum and another half a cycle it reaches its minimum again. Hence over one cycle, h varies with t as follows:

b) According to the graph obtained in part a), h(t) could be modeled by a cosine function shifted (translated) vertically up and horizontally to the right. Hence

Step-by-step explanation:

The space between the 1/3 and 1/6 is 3.83.

Division is a mathematical operation that involves dividing one number (the dividend) by another number (the divisor) to determine the quotient. Division can be used to solve problems involving fractions, decimals, and percentages. It is also used to simplify complex equations and to break down large numbers into smaller, more manageable parts. Division is one of the four basic operations of arithmetic, along with addition, subtraction, and multiplication.

To calculate this, first add 3/4 and 1/3 to get 1.08, then add 1/6 to get 1.14, then subtract 1/2 to get the final answer of 3.83.

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given the equation:

The coefficient of x has 2 decimals, to clear the decimal point, the number should be multiplied by 100

so, the answer will be:

To clear the decimals multiply each term by 100

Answer and Step-by-step explanation: The triangles are plotted and shown in the attachment.

SAS Similarity Theorem is by definition: if two sides in one triangle are proportional to two sides of another triangle and the angles formed by those sides in each triangle is congruent, the triangles are similar.

For the triangles on the grid, we know that ΔJKL and ΔJMN have a congruent angle in J as shown in the image. To prove they are similar, we find the slope of sides KL and MN:

Slope of KL:

slope = \(\frac{y_{K} - y_{L} }{x_{K} - x_{L} }\)

slope = \(\frac{3-1}{2-4}\)

slope = -1

Slope of MN:

slope = \(\frac{y_{N} - y_{M} }{x_{N} - x_{M} }\)

slope = \(\frac{1-5}{7-3}\)

slope = -1

Since the slopes of KL and MN are the same and the angle is congruent, we can conclude that ΔJKL~ΔJMN.

Answer:

\(x = - 1\)

\(y = 3\)

Step-by-step explanation:

\(y - 4x = 7(eqn \: 1)\)

\(2y + 4x = 2(eqn \: 2)\)

\(solving \: by \: eliminating \: one \: variable\)

\((y - 4x = 7)\)

\( + (2y + 4x = 2)\)

\(3y = 9\)

\(y = 3\)

\(y - 4x = 7\)

\(3 - 4x = 7\)

\( - 4x = 7 - 3\)

\( \frac{ - 4x}{ - 4} = \frac{4}{ - 4} \)

\(x = - 1\)

The solution to this system of linear equations will be (–1, 3). Then the correct option is D.

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

The equations are given below.

 y − 4x = 7   ...1

2y + 4x = 2  ...2

Add both equations, then we have

3y = 9

 y = 3

Put y = 3 in equation 1, then we have

3 − 4x = 7

     4x = –4

       x = –1

The solution to this system of linear equations will be (–1, 3).

Then the correct option is D.

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Answer:is C

Step-by-step explanation:

Hope this helps :D

and feel free to click that thanks button

Answer:

B. \(\sqrt{29}\)

Step-by-step explanation:

\((4,7 )=(x_1,y_1)\\(2,2)=(x_2,y_2)\\\\d =\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}\\\\d = \sqrt{\left(2-4\right)^2+\left(2-7\right)^2}\\\\d = \sqrt{(-2)^2 +(-5)^2}\\ \\d = \sqrt{4+25} \\\\d = \sqrt{29}\)

Answer:

all you have to do it go to 44 and 52 so ur answer is b and d

Step-by-step explanation:

Answer:

9

It's right! Hope this helps!!

Answer:

C 9

Step-by-step explanation:

Answer:

  A = C²/(4π)

Step-by-step explanation:

You want a formula for the area of a circle, given its circumference.

Relevant relations for a circle are ...

  A = πr² . . . . . . . . A = area, r = radius

  C = 2πr . . . . . . . . C = circumference

Solving the circumference equation for r, we find ...

  r = C/(2π)

Substituting that into the area equation, we have ...

  A = π(C/(2π))²

  A = C²/(4π)

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The function that models the area A of a circle in terms of its circumference C is A = C²/(4π).

The formula for the circumference of a circle is C = 2πr or C = πd, where r is the radius and d is the diameter. To find a function that models the area A of a circle in terms of its circumference C, we can rearrange the formula for the circumference to solve for the radius: r = C/(2π). Substituting this value of r into the formula for the area, we get A = π(C/(2π))² = C²/(4π).

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To obtain the desired 60% alcohol solution, you will need to add approximately 133.33 mL of the 85% alcohol mixture.

Let's denote the volume of the 85% alcohol mixture needed as V mL.

To determine the amount of the 85% alcohol mixture needed to obtain the desired 60% alcohol solution, we can set up the following equation based on the alcohol content:

0.15 * 175 + 0.85 * V = 0.60 * (175 + V)

In this equation, the left side represents the total amount of alcohol in the initial mixture and the added 85% mixture, while the right side represents the total amount of alcohol in the desired 60% solution.

Simplifying the equation, we have:

26.25 + 0.85V = 105 + 0.60V

Rearranging the equation:

0.25V = 105 - 26.25

0.25V = 78.75

V = 78.75 / 0.25

V = 315 mL

Therefore, you will need 315 mL of the 85% alcohol mixture to obtain the desired 60% alcohol solution. However, since you only have 175 mL of the 15% alcohol mixture on hand, you cannot add the full 315 mL. Thus, the maximum amount you can add is limited to the remaining volume of the 60% solution:

V = 175 mL (maximum)

So, you will need 133.33 mL (rounded to 133.33 mL) of the 85% alcohol mixture.

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Answer:

B/ it represents a perfectly linear positive correlation between x and y

Step-by-step explanation:

correlation

of -1.0 indicates a perfect negative correlation, and a correlation of 1.0 indicates a perfect positive correlation.

The correlation coefficient for the data represents a perfectly linear positive correlation between x and y.

It means the variable should be shifted together by having the similar percentage and the direction.

Here it shows the direct relationship between two variables it can be anything like the demand for the product, and the price of the product.

hence, The correlation coefficient for the data represents a perfectly linear positive correlation between x and y.

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The largest number of flights required to travel from any destination to any other destination in MathWorld can be determined by finding the diameter of the graph representing the flight connections.

In a graph representation, each destination is a node, and the flights between destinations are the edges connecting the nodes. To find the largest number of flights needed, we need to find the longest path between any two nodes, which is known as the diameter of the graph.

To determine the diameter, we can use a matrix representation of the graph, where each entry (i, j) in the matrix represents the number of flights required to travel from destination i to destination j. By finding the maximum value in the matrix, we can determine the largest number of flights needed to reach any destination from any other destination in MathWorld.

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The number 3.23×10^6, expressed in standard decimal notation, is 3,230,000. In scientific notation, a number is expressed as the product of a coefficient and a power of 10.

In this case, the coefficient is 3.23, and the power of 10 is 6. To convert this number into standard decimal notation, we need to multiply the coefficient by the corresponding power of 10. The power of 10, in this case, is 10^6, which means 10 raised to the power of 6. This is equivalent to 1 followed by six zeros: 1,000,000. To obtain the standard decimal notation, we multiply the coefficient, 3.23, by 1,000,000.

Calculating the multiplication, we have:

3.23 × 1,000,000 = 3,230,000.

Hence, the number 3.23×10^6, expressed in standard decimal notation, is 3,230,000. This means that the number is equal to 3.23 million.

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Some important concept before solving answer :-

\( \\ \)

When ever there is three dimensional figure remember, where one figure is related to other then there's always relation with volume.

So it may get pretty difficult to understand therefore I am dividing into small parts for better understanding.

\( \\ \)

\( \pmb{ \bf \dag\cal{Part \ One:}}\)

As we know there will be relation of volume, so let's find volume of the cone first.

\( \\ \)

Given :-

⭑Height = 10 cm

⭑radius = 3cm

\( \\ \)

To find :

⭑volume of cone

\( \\ \)

Let represent :-

⭑Height as : h

⭑radius as : r

⭑volume of cone as : v

\( \\ \\ \)

Formula to find volume of cone :-

\( \\\)

\( \bigstar\boxed{ \rm v = \pi {r}^{2} \times \frac{h}{3} }\)

\( \\ \)

So let's find v!

\( \\ \)

\( \dashrightarrow\sf v = \pi {r}^{2} \times \dfrac{h}{3} \)

\( \\ \\ \)

\( \dashrightarrow\sf v = \dfrac{22}{7} \times {3}^{2} \times \dfrac{10}{3} \)

\( \\ \\ \)

\( \dashrightarrow\sf v = \dfrac{22}{7} \times {3} \times 3\times \dfrac{10}{3} \)

\( \\ \\ \)

\( \dashrightarrow\sf v = \dfrac{22}{7} \times {\cancel3} \times 3\times \dfrac{10}{\cancel3} \)

\( \\ \\ \)

\( \dashrightarrow\sf v = \dfrac{22}{7}\times 3\times \dfrac{10}{1} \)

\( \\ \)

\( \dashrightarrow\sf v = \dfrac{22}{7}\times 3\times10\)

\( \\ \\ \)

\( \dashrightarrow\sf v = \dfrac{22\times 3\times10}{7}\)

\( \\ \\ \)

\( \dashrightarrow\sf v = \dfrac{22\times 30}{7}\)

\( \\ \\ \)

\( \dashrightarrow\sf v = \dfrac{660}{7}\)

\( \\ \\ \)

\( \dashrightarrow\bf v =94.3 {cm}^{3} \)

\( \\ \\ \)

\( \pmb{ \bf \dag\cal{Part \: \: Two:}}\)

So remember that cone filled with water is equal to volume of cone.

volume of water filled in cone = volume of water in cuboid.

So you probably thinking that above sentence is wrong , cause they haven't told volumes of cuboid and cone are equal, but we have to find depth of water filled not depth of cuboid.

\( \\ \\ \)

Given :-

⭑Volume of cuboid = 94.3 cm³

⭑Length of cuboid = 5cm

⭑Width of cuboid = 3cm

\( \\ \)

To find :-

⭑Depth of water in cuboid

\( \\ \)

Let represent:-

⭑Volume of cuboid as : V'

⭑Length of cuboid as : L

⭑Width of cuboid as : W

⭑Depth of water in cuboid as : D

\( \\ \\ \)

Formula to find volume of cuboid :-

\( \\ \\ \)

\( \bigstar\boxed{ \rm V'= W \times L \times D }\)

By using this formula we can find depth of cuboid.

\( \\ \\ \)

\( : \implies \sf V'= W \times L \times D \)

\( \\ \\ \)

\( : \implies \sf 94.3= D \times 3 \times 5\)

\( \\ \\ \)

\( : \implies \sf \dfrac{943}{10\times 3 \times 5} = D \)

\( \\ \\ \)

\( : \implies \sf \dfrac{943}{10 \times 15} = D \)

\( \\ \\ \)

\( : \implies \sf \dfrac{943}{150} = D \)

\( \\ \\ \)

\( : \implies \sf D = \dfrac{943}{150} \)

\( \\ \\ \)

\( : \implies \bf D = 6.3cm\)

\( \\ \\ \)

Required Answer:-

Depth = 6.3 cm

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Step-by-step explanation:

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You did it please don't delete

Answer: In algebra, a quadratic equation (from the Latin quadratus for " square ") is any equation having the form where x represents an unknown, and a, b, and c represent known numbers, with a ≠ 0. If a = 0, then the equation is linear, not quadratic, as there is no term.

Step-by-step explanation:

Answer:

 B                                                  

Step-by-step explanation:

Hey there !!!

the question is incomplete the full question is Which of the following statements is TRUE/CORRECT about Quadratic Equations? A quadratic equation is _____

with options

A) an expression with a single variable and degree 2

B) an equation with a single variable and degree 2

c) an equation with only degree to 2

D) an equation with single variable only

and the correct answer is B

because Quadratic Equation states that An equation with one variable and degree 2 is a Quadratic Equation. Only option b satisfies the two basic conditions of a quadratic equation i.e. one/single  variable and degree 2. Hence b is the correct answer.

Hope it helped