The sum of the first three terms of an A.P. is 18. If the sum of first two terms is subtracted from the third term then it would be 0. Find the three terms of the series.​

Log x+y = logbx − logbyGiven log630 ≈ 1.898 and log62 ≈ 0.387, log615 ≈ 2.086.

Given log 630 ≈ 1.898 and log 62 ≈ 0.387,

We have log 630 = log (6 * 62 * 10) = log 6 + log 62 + log 10 = 1 + 0.387 + 1 = 2.387

And log 615 = log (6 * 62 * 5) = log 6 + log 62 + log 5 = 1 + 0.387 + 0.699 = 2.086

So, log 615 ≈ 2.086

In the example given, log 630 ≈ 1.898 and log 62 ≈ 0.387. These logarithmic values are used to simplify other logarithmic expressions and, the logarithm of 615 was found to be approximately 2.086.

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Answer:

k=12

Step-by-step explanation:

From X=3 , Y=2

k = 12

Step-by-step explanation:

Given,

\({ \tt{x = 3}}\)

\({ \tt{y = 2}}\)

The given Eqⁿ is,

\({ \purple{ \tt{2x + 3y = k}}}\)

Substitute the value of x and y in the given Eqⁿ then,

\({ \purple{ \tt{2}}(}{ \red{ \tt{3}}}) + { \purple{ \tt{3}}(} \red{ \tt{2}}) = { \purple{ \tt{k}}}\)

\({ \purple{ \tt{6 + 6 = k}}}\)

\({ \boxed{ \red{ \sf{k = 12}}}}\)

Answer:

Step-by-step explanation:

x-intercept if when y is 0, so, on the x-axis. as we can see the x-intercept is -40

y-intercept if when x is 0, so, on the y-axis. as we can see the y-intercept is 15

Answer:

x-intercept: \((-40,0)\)

y-intercept: \((0,15)\)

Step-by-step explanation:

The x-intercept is the point where the line meets the x-axis, and the y-intercept is the point on the line which meets the y-axis.

The line intersects the y-axis at \(15\), so the y-intercept is \((0, 15)\).

The line intersects the x-axis at \(-40\), so the x-intercept is \((-40, 0)\).

Hope this helps :)

Step-by-step explanation:

Magnitude = sqrt ( (-12)^2 + (-4)^2 ) = sqrt 160 = 12.649

Angle = arctan(-4/-12) = 198 degrees

The Magnitude: 12.649 and Direction: 18° (option c).

To find the magnitude and direction of the vector v = (-12, -4), we can use the following formulas:

Magnitude (or magnitude) of v = |v| = √(vₓ² + \(v_y\)²)

Direction (or angle) of v = θ = arctan(\(v_y\) / vₓ)

where vₓ is the x-component of the vector and \(v_y\) is the y-component of the vector.

Let's calculate:

Magnitude of v = √((-12)² + (-4)²) = √(144 + 16) = √160 ≈ 12.649 (rounded to the thousandths place)

Direction of v = arctan((-4) / (-12)) = arctan(1/3) ≈ 18.435°

Since we need to round the direction to the nearest degree, the direction is approximately 18°.

So, the correct answer is:

Magnitude: 12.649 (rounded to the thousandths place)

Direction: 18° (rounded to the nearest degree)

The correct option is: 12.649; 18°

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The area between z = -0.74 and z = 0.74 under the standard normal curve is approximately 0.5408.

To find the area between z = -0.74 and z = 0.74 under the standard normal curve, we need to calculate the cumulative probabilities for each value and then find the difference between the two probabilities.

We can use a standard normal table to find the cumulative probabilities. The table provides values for the cumulative probability up to a certain z-score.

Looking at page 1 of the standard normal table, we search for the closest value to z = -0.74. We find that the closest value is -0.7 in the leftmost column, and the closest value in the row is 0.04. The corresponding value in the table represents the area to the left of z = -0.74.

Using the same process, we find that the closest value to z = 0.74 is 0.7, and the corresponding value in the table represents the area to the left of z = 0.74.

To find the area between z = -0.74 and z = 0.74, we subtract the cumulative probability of z = -0.74 from the cumulative probability of z = 0.74:

P(-0.74 < z < 0.74) = P(z < 0.74) - P(z < -0.74)

Using the standard normal table, we find that the cumulative probability for z = 0.74 is 0.7704, and the cumulative probability for z = -0.74 is 0.2296.

Substituting these values into the formula, we get:

P(-0.74 < z < 0.74) = 0.7704 - 0.2296 = 0.5408

It is important to note that this answer is rounded to four decimal places, as requested in the question. However, in practice, it is advisable to keep more decimal places for accuracy in statistical calculations.

In summary, using the standard normal table, we found that the area between z = -0.74 and z = 0.74 under the standard normal curve is approximately 0.5408.

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Answer:

Step-by-step explanation:

  \(9xy\cdot(\frac{2}{3}x)^3=3^2xy\cdot\dfrac{2^3x^3}{3^3}\\\\=\dfrac{8}{3^{3-2}}x^4y=\boxed{\dfrac{8}{3}}x^4y\)

__

The applicable rules of exponents are ...

  (ab)^c = (a^c)(b^c)

  (a^b)/(a^c) = 1/(a^(c-b))

Answer:

x=-7

Step-by-step explanation:

you bring the 5 to the right and them divide them and divide by 2 both sides which equales to 7

Inequalities help us to compare two unequal expressions. For the given inequality to be satisfied the value of x should be greater than -7. The graph of the inequality can be made as shown below.

Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed. It is mostly denoted by the symbol <, >, ≤, and ≥.

The given inequality 2x+5>-9 can be solved as shown below.

2x + 5 > -9

Subtract 5 from both the sides of the inequality.

2x + 5 - 5 > -9 - 5

2x > -14

Divide both the sides of the inequality by 2,

2x/2 > -14/2

x > -7

Hence, for the given inequality to be satisfied the value of x should be greater than -7.

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Answer:

shook

Step-by-step explanation:

The x-coordinate of each point where the graphs of y = f(x) and y = g(x) intersect corresponds to a solution of the equation. To check the solutions, first substitute x = 0 and then substitute x = 2 into the equation and verify the statement is true when x equals each of those values.

Answer:

its b

Step-by-step explanation:

got it right on edge

The volume of the metal in the cylinderical pipe given the dimensions of the larger and smaller cylinders is 271.30 mm³.

A cylinder is a three-dimensional object. It is a prism with a circular base.

Volume of a cylinder = nr^2h

Where:

The volume of the metal in the cylinderical pipe = 3.14 x 10 x [(8.4/2)² - 6/2)²] = 271.30 mm³

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Answer:

C

Step-by-step explanation:

A rational number is a number that can be expressed as the quotient or fraction p/q of two integers, a numerator p and a non-zero denominator q.

C is the correct answer since it can be expressed as a fraction which equals to 7/9.

Hope it helps:)

Answer:

A

Step-by-step explanation:

Pi is an irrational number so it can't be B.

√(5) is an irrational number so it can't be D.

It could be either A or C... Hm, go with A. Let me know if it works.

The cylinder which would have the greater volume is that in which the two shorter sides together, you get a short, fat cylinder.

It follows from the task content that the cylinder is made from the same paper dimensions.

On this note, it follows that when the shorter sides are joined, the longer side represents the height of the cylinder formed.

Consequently, the shorter cylinder has the greater volume.

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Answer:

30.48cm

Step-by-step explanation:

It is a basic to know

Answer:

596/1000 and 59.6%

Step-by-step explanation:

because when we make 596/1000 is 0.596

Calculating the values will give the distance between the two points in meters.

(a) To determine the Cartesian coordinates of the given points, we can use the following formulas:

x = r * cos(theta)

y = r * sin(theta)

For the point (2.70 m, 40.0°):

x = 2.70 * cos(40.0°)

y = 2.70 * sin(40.0°)

For the point (3.90 m, 110.0°):

x = 3.90 * cos(110.0°)

y = 3.90 * sin(110.0°)

Evaluating these equations will provide the Cartesian coordinates of the given points.

(b) To determine the distance between the two points, we can use the distance formula:

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

Substituting the Cartesian coordinates of the two points into the distance formula will yield the distance between them.

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The 30-foot distance between single-family residences in the Desert Vista subdivision is called a "setback" in development terms.

This setback ensures that the neighborhood maintains adequate spacing between homes for privacy, safety, and aesthetics.

The distance between single-family residences in the new Desert Vista subdivision in Mesa is known as the "setback" in subdivision development terms.

Setbacks are regulations that define the minimum distance a building, such as a single-family residence, must be located from property lines or other structures.

These regulations ensure adequate spacing between buildings for various reasons, including privacy, safety, and aesthetics.
1. The student question mentions that the distance between single-family residences in the new Desert Vista subdivision in Mesa is 30 feet.
2. In subdivision development terms, such a distance is referred to as a "setback."
3. Setbacks are important for maintaining privacy, safety, and aesthetics in a neighborhood.
4. These regulations ensure that there is enough space between buildings, preventing overcrowding and allowing for proper ventilation, sunlight, and access to emergency services.
5. Setbacks vary depending on the type of structure and local zoning laws, which determine the minimum distance required between buildings.

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To duplicate angle ABC, draw a line segment, position the compass on point A, and then draw an arc that intersects the line segment. Next, position the compass on point B, and then draw a second arc that intersects the first arc at a point on the line segment. Finally, position the compass on the point where the two arcs intersect, but without changing the width, and draw a third arc that intersects the line segment.

When two straight lines or rays intersect at a single endpoint, an angle is created. The vertex of an angle is the location where two points come together. The Latin word "angulus," which means "corner," is where the term "angle" originates.

Common instruments used to measure angles are:

1. Protractor

2.Compass

3.Digital Angle finder

4.Angle finder

5.Clinometer

6. Inclinometer

You can take the following actions to copy angle ABC:

Create a line segment that will serve as the foundation for the new angle you're going to create.

Draw an arc that crosses the line segment you produced in step 1 by positioning the compass on point A.

Draw a second arc that crosses the previous arc at a point on the line segment by setting the compass on point B.

Place the compass on the intersection of the two arcs without adjusting the compass's width, then create another arc that crosses the line segment.

Point D is where the second arc crosses the line segment. To finish the new angle, join points D and C.

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The equivalent expression of 8(x+3)−14(20x−56)​ is - 272x + 808.

Two algebraic expressions are equivalent, when the two expressions have the same value when we plug in the same value(s) for the variable(s).

In other words, two algebraic expressions are said to be equivalent if their values obtained by substituting the values of the variables are same.

Therefore, the equivalent expression of 8(x+3)−14(20x−56)​ can be found as follows;

8(x+3) − 14(20x−56)​

open the parenthesis

8x + 24 -  280x + 784

combine the like terms

8x + 24 -  280x + 784

8x -  280x + 24 + 784

Therefore, the equivalent expression is as follows:

- 272x + 808

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Answer:

the equation for the function m(t) point-stope form will be:

Hence, option D is correct.

The graph is attached below.

Step-by-step explanation:

Given

Point (10, 25)

Slope m = 2.5

To determine

Write the equation for the function m(t) point-stope form.

We know that the point-slope form of the line equation is

\(y-y_1=m\left(x-x_1\right)\)

where

In our case:

so

substituting the values m = 2.5 and the point (10, 25) in the equation

\(y-y_1=m\left(x-x_1\right)\)

\(y - 25 = 2.5 (x - 10)\)

Therefore, the equation for the function m(t) point-stope form will be:

Hence, option D is correct.

The graph is attached below.

Answer:

Step-by-step explanation:

true

In this case, the experimental probability is D. 0.860

First, note that Experimental probability, also known as Empirical probability, is founded on real experiments and adequate documentation of events.

In the table we can see that he rolled the cube 1000 times, and he recorded that 140 of those times he rolled a 5.

Then, the probability of rolling a 5 will be equal to:

P1 = 140/1000 = 0.14

Now, the probabilty of NOT rolling a 5, is equal to the rest of the probabilities, this is:

P2 = 1 - 0.14 = 0.86

then the correct option is D

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Full Question:

Although part of your question is missing, you might be referring to this full question:

Jimmy rolls a number cube multiple times and records the data in the table above. At the end of the experiment, he counts that he had rolled 140 fives. Find the experimental probability of not rolling a five, based in Jimmy’s experiment. Round the answer to the nearest thousandth.

A. 0.140

B. 0.167

C. 0.667

D. 0.860

Enchanted Rock State Natural Area is located at latitude 30.506130 and longitude -98.820064. The geographic coordinates of Enchanted Rock State Natural Area in Fredericksburg, United States, are 30° 30' 22.068" N and 98° 49' 12.2304" W. Enchanted Rock State Natural Area falls under the Mysterious Sites category.

The standard datum used by default for GPS devices used for commercial and recreational purposes is WGS84. GPS users are advised to always verify the datum of the maps they are utilising.

WGS 84, also known as the datum, is now in use by US forces.

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Answer:

3a+9

Step-by-step explanation:

Answer:

3a+9

Step-by-step explanation:

5-2=3 then 3a=9 it pretty simple

Answer:

12.5\(\sqrt{3}\)

Step-by-step explanation:

30-60-90 triangles always have the height be    sqrt3 the base.

Therefore, the volume of the solid bounded by the coordinate planes and the plane 6x + 4y + z = 24 is 96 cubic units.

To find the volume of the solid bounded by the coordinate planes (xy-plane, xz-plane, and yz-plane) and the plane 6x + 4y + z = 24, we need to determine the region in space enclosed by these boundaries.

First, let's consider the plane equation 6x + 4y + z = 24. To find the x-intercept, we set y = 0 and z = 0:

6x + 4(0) + 0 = 24

6x = 24

x = 4

So, the plane intersects the x-axis at (4, 0, 0).

Similarly, to find the y-intercept, we set x = 0 and z = 0:

6(0) + 4y + 0 = 24

4y = 24

y = 6

So, the plane intersects the y-axis at (0, 6, 0).

To find the z-intercept, we set x = 0 and y = 0:

6(0) + 4(0) + z = 24

z = 24

So, the plane intersects the z-axis at (0, 0, 24).

We can visualize that the solid bounded by the coordinate planes and the plane 6x + 4y + z = 24 is a tetrahedron with vertices at (4, 0, 0), (0, 6, 0), (0, 0, 24), and the origin (0, 0, 0).

To find the volume of this tetrahedron, we can use the formula:

Volume = (1/3) * base area * height

The base of the tetrahedron is a right triangle with sides of length 4 and 6. The area of this triangle is (1/2) * base * height = (1/2) * 4 * 6 = 12.

The height of the tetrahedron is the z-coordinate of the vertex (0, 0, 24), which is 24.

Plugging these values into the volume formula:

Volume = (1/3) * 12 * 24

= 96 cubic units

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The two numbers are 3 and 11 respectively

From the information given, we have that

The first number is x

The second number is y

Also,

2x - y = -5

x + y = 14

Make 'x' the subject from equation 2

x = 14 - y

Make 'x' the subject

2(14-y) - y = -5

28 - 2y - y= -5

collect like terms

-3y = -33

y = 11

Substitute the values

x = 3

Hence, the values are 3 and 11

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The lowest score you can earn and still be qualified for an interview is approximately 67.2.

To find the lowest score you can earn and still be qualified for an interview, we need to determine the score that corresponds to the top 10% of scores.

From the problem statement, we know that the scores are normally distributed with a mean of 80 and a standard deviation of 10. We can use the cumulative distribution function (CDF) of the normal distribution to find the score that corresponds to the top 10%.

Using a table or calculator for the standard normal distribution, we can find the z-score that corresponds to the top 10%:

P(Z > z) = 0.1

Z = invNorm(0.1) ≈ -1.28

Here, P(Z > z) is the probability that a random variable from a standard normal distribution is greater than z, and invNorm(0.1) represents the inverse of the CDF of the standard normal distribution evaluated at 0.1, which gives us the z-score corresponding to the top 10%.

Now, we can use the formula for standardizing a normal distribution to find the score that corresponds to this z-score:

z = (x - μ)/σ

where x is the score we want to find, μ is the mean of the distribution (80), and σ is the standard deviation of the distribution (10).

Substituting the values, we have:

-1.28 = (x - 80)/10

Solving for x, we get:

x = (-1.28 * 10) + 80 ≈ 67.2

Therefore, the lowest score you can earn and still be qualified for an interview is approximately 67.2.

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Answer:

True, 52-2 equals 50, 50 is greater than 6.

Step-by-step explanation:

The statement 'When you try to find the most appropriate input probability distribution in a simulation model, you first have to choose the most appropriate family, and then you have to select the most appropriate member of that family' is generally true because in simulation modeling, input probability distributions are used to represent uncertain or random factors in the system being modeled.

These distributions are often classified into different families, such as normal, exponential, uniform, and so on, based on their properties and mathematical characteristics.

When selecting an appropriate distribution for a simulation model, it is important to first identify the family of distributions that best represents the underlying random process being modeled.

For example, if the data is symmetric and bell-shaped, then the normal distribution might be a suitable family to consider. However, if the data is non-negative and skewed, then the exponential or gamma distribution might be more appropriate.

Once the appropriate family of distributions is selected, the next step is to identify the most appropriate member or parameter values of that family that best fit the data being modeled.

This often involves using statistical methods to estimate the parameters of the distribution based on historical data or expert knowledge.

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Answer:

27 oranges

Step-by-step explanation:

Number of oranges are : 27

The relation between two numbers which shows how much bigger one quantity is than other.

According to question ,

apples/ oranges = 2 / 6                           equation 1

now, substituting the number of apples in equation 1 , we get

9/oranges = 2/6

oranges = 9 * 6 / 2 = 27

number of oranges are 27

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The explicit function for the sequence is: \(f(n) = 3(4)^(n-1)\)

An arithmetic progression (AP) is a progression in which the difference between two consecutive terms is constant.we have to know the first term (a), the number of terms(n), and the common difference (d) between consecutive terms

To find the explicit function for the given sequence, we need to determine the values of a and b in the equation f(n) = \(a(b)^(n-1\)), given that f(1) = 3.

We can find the value of a by substituting n=1 into the equation:

f(1) =\(a(b)^(1-1)\)= a

3 = a

So, we will substitute 3 for a in the equation f(n) = \(a(b)^(n-1).\)

To find the value of b, we can use the fact that the ratio between consecutive terms in the sequence is constant. We can calculate this ratio by dividing any term by its preceding term.

The ratio between the second and first terms is:

12/3 = 4

The ratio between the third and second terms is:

48/12 = 4

The ratio between the fourth and third terms is:

192/48 = 4

The ratio between the fifth and fourth terms is:

768/192 = 4

Since the ratio is constant and equal to 4, we can write:

b = 4

Therefore, the explicit function for the sequence is:

f(n) = \(3(4)^(n-1)\)

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