If 6 times the 6th term of an A.P., is equal to 9 times the 9th term, find its 15th term

Without the histograms, there's no specific region as an answer. However, you can follow these steps to determine the region with the least standard deviation in level of interest based on the provided data.

To determine the region with the least standard deviation in level of interest, we need to analyze the histograms for each region. Standard deviation is a measure of how spread out the data is. The region with the least standard deviation will have data points that are more closely clustered around the mean (average) level of interest.


1. Examine the histograms for each region.
2. Look for the region where the data points are more tightly grouped around the mean level of interest. This indicates less variability and a smaller standard deviation.
3. Identify the region with the least standard deviation in level of interest.

To determine the region with the least standard deviation in the level of interest, examine the histograms for each region and identify the one where data points are tightly clustered around the mean level. Calculate the standard deviation for each region and select the region with the smallest value, indicating a more concentrated and less variable distribution of the level of interest.

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Answer:

The line \(y=-6\) never intersects with the circle \(x^{2} +y^{2} =6\)

Step-by-step explanation:

The equation of a circle with center \((h,k)\) and radius of \(r\) units is given by:

\((x-h)^{2} +(y-k)^{2} =r^{2}\)

So, for the circle:

\(x^{2} +y^{2} =6\)

\(h=0\\k=0\\r=\sqrt{6}\approx 2.54\)

Which is a circle centered at the origin and radius of 2.45.

The line \(y=-6\) is a horizontal line with a constant value of -6. Hence, the line never intersect the circle.

I attached you the graphs.

When we subtract a velocity vector from another velocity vector, the result is B. another velocity.

When we subtract a velocity vector from another velocity vector, we are essentially finding the difference between the two velocities. This difference is also a velocity vector, but in a different direction and with a different magnitude. Therefore, the answer is another velocity, option B.

It is important to note that acceleration is a change in velocity, not the result of subtracting one velocity from another. Scalar refers to a quantity with only magnitude, whereas velocity is a vector quantity with both magnitude and direction. Displacement refers to the change in position of an object and is not directly related to subtracting velocity vectors.

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Answer:

To solve this problem, we can use a combination formula. We need to distribute 12 identical blackboards among 4 schools, so the total number of possible divisions is:

C(12+4-1, 4-1) = C(15, 3) = 455

However, we need to consider the condition that school a receives at least 2 boards and school b receives at least one board. We can use a complementary counting approach to solve this.

First, let's find the total number of divisions where school a receives less than 2 boards and school b receives less than 1 board. If school a receives 0 or 1 board, that leaves 11 or 10 boards to be divided among the remaining schools. Similarly, if school b receives 0 boards, that leaves 12 boards to be divided among the remaining schools. Using the combination formula, we can find the number of possible divisions:

C(11+3-1, 3-1) * C(12+3-1, 3-1) = C(13, 2) * C(14, 2) = 8190

Now, we can subtract this number from the total number of possible divisions to find the number of divisions that satisfy the conditions:

455 - 8190 = -7735

Wait, that's a negative number! What does it mean? It means that there are no possible divisions that satisfy the conditions. In other words, it's impossible to distribute 12 blackboards among 4 schools such that school a receives at least 2 boards and school b receives at least one board.

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To find the slope of the tarp, we can use the concept of rise over run, which is the ratio of the vertical change (the rise) to the horizontal change (the run). In this case, the rise is the distance from the corner of the tarp to the top of the pole, and the run is the distance from the corner of the tarp to the bottom of the pole.

We can use the Pythagorean theorem to find the length of the hypotenuse of the right-angled triangle formed by the corner of the tarp, the bottom of the pole and the top of the pole.

The length of the hypotenuse is the distance from the corner of the tarp to the top of the pole and the length of the adjacent side is the distance from the corner of the tarp to the bottom of the pole.

We know that:

adjacent side = 10 ft

Hypotenuse = h

Applying the Pythagorean theorem:

h^2 = 10^2 + 6^2

h = √(10^2 + 6^2)

h = √(100 + 36) = √136 = 11.66 ft

Now we can calculate the slope:

slope = rise/run = (h-10) / 6

slope = (11.66-10) / 6 = 1.66/6 = 0.277

So the slope of the tarp from the corner to the top of the pole is 0.277 or approximately 0.28.

The Relationship between the points D(6, 9) and A(8, 12) can be described as a dilation with a factor of 1.5. Point A is located 1.5 times farther from the origin compared to point D, in both the horizontal and vertical directions. Additionally, A is an enlargement of D.

The relationship between the points D(6, 9) and A(8, 12) can be described in terms of dilations. In mathematics, a dilation is a transformation that changes the size of an object while keeping its shape intact. It involves scaling the object by a certain factor, either enlarging or reducing it.

To understand the relationship between D and A, we can calculate the dilation factor. The dilation factor, denoted by 'k', is the ratio of the corresponding side lengths or distances between the pre-image (original object) and the image (transformed object).

The dilation factor between D(6, 9) and A(8, 12):

First, we need to find the change in x-coordinates and y-coordinates:

Δx = 8 - 6 = 2

Δy = 12 - 9 = 3

Next, we calculate the dilation factor:

k = Δy / Δx = 3 / 2 = 1.5

The dilation factor of 1.5 indicates that the image point A is 1.5 times as far from the origin (point D) compared to the pre-image. This means that A is located at a greater distance from the origin than D, both horizontally and vertically.

Moreover, since the dilation factor is positive, the dilation is an enlargement. This means that A is enlarged with respect to D. The ratio of the corresponding side lengths will also be 1.5.

the relationship between the points D(6, 9) and A(8, 12) can be described as a dilation with a factor of 1.5. Point A is located 1.5 times farther from the origin compared to point D, in both the horizontal and vertical directions. Additionally, A is an enlargement of D.

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Answer:

0.772

Step-by-step explanation:

Original equation:

\(18 * 2^{5t}=261\)

Divide both sides by 18

\(2^{5t} = 14.5\)

Rewrite in logarithmic form (\(b^x=c \implies log_bc=x\))

\(log_214.5 = 5t\)

Divide both sides by 5

\(\frac{log_214.5}{5}=t\)

Rewrite the equation so that base is 10 using change of base formula: \(log_ba = \frac{log_na}{log_nb}\)

\(\frac{(\frac{log14.5}{log2})}{5}=y\)

Keep, change, flip

\(\frac{log14.5}{log2}*\frac{1}{5} = \frac{log14.5}{5 * log2}\)

Use a calculator to approximate log14.5 and log2

\(\frac{1.161368}{5 * 0.301029996} = t\)

Multiply in denominator

\(\frac{1.161368}{1.505149978} = t\)

Divide two values

\(t\approx 0.771596\)

Round to nearest thousandth

\(t\approx 0.772\)

Answer:

It would be -4 + 11 = 7. :D

Step-by-step explanation:

Answer:

9

Step-by-step explanation:

since they're similair then similair sides will be proportional

CB is similair to EF

\(\frac{6}{8}\)= \(\frac{3}{4}\)

same thing if you try with the hypotenuse AB similair to DE

\(\frac{13.5}{18}\)= \(\frac{3}{4}\)

So, if you multiply  r (DF) by 3/4  you will get the similair side AC

rx 3/4=12

r= 12÷ 3/4

r=16

The value of a in the equation in the simplest form will be 17 / 6.

We are given an equation:

x³ / x^(1/6) = x^(a)

We need to evaluate the left hand side to find the value of a in the equation in simplest form.

We know that:

x^ (a) / x^ (b) = x^ ( a - b)

Using this, we get that:

x^ (3 - 1/6) = x^ (a)

x^ (17/6) = x^ (a)

By comparing the bases, we get the value of a as:

a = 17 / 6.

Therefore, the value of a in the equation in the simplest form will be 17 / 6.

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Check the picture below.

The terminal side of the angle fall in the quadrant 1.

Angles are the figure formed by the intersection of two lines or rays by sharing a common point. This point is called the vertex of the angle.

Angles are usually measured in degrees or radians.

Given angle is -302°.

This means that the angle is measured in clockwise direction.

Sum of a full anticlockwise direction = 360°.

Sum of a full clockwise direction = -360°.

The angle will be starting from quadrant 4.

After -90 degrees, it moves to quadrant 3.

After -180 degrees, it moves to quadrant 2.

After -270 degrees, it moves to quadrant 1.

Given that the angle is -302°.

So in between -270 degrees and -360 degrees lies the terminal side of angle -302°.

Hence the terminal side lies in quadrant 1.

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Average rate of change of the function F (x ) = 9/ -2 (x)-7. Average rate is -3, 9

The average rate at which one quantity changes in relation to another's change is referred to as the average rate of change function. A method that determines the amount of change in one item divided by the corresponding amount of change in another is known as an average rate of change function.

Divide the change in y-values by the change in x-values to determine the average rate of change. In order to determine changes in measurable parameters like average speed or average velocity, finding the average rate of change is extremely helpful.

f (x ) = -2

f (x) = 9/ -2 (-2)-7

      = 9 / 4 - 7

      =9 / -3

      = -3

f (x ) = -4

f (x) = 9/ -2 (4)-7

      = 9 / 8 - 7

      =9 / 1

      = 9

Average rate is -3, 9

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To find the equation that represents the new area, N, of the rectangular cage after increasing both dimensions of the floor by 3 feet, we first need to find the original area, A, of the cage.

Let's assume that the width of the floor is w feet, then the length of the floor is 3 feet greater, which means it is (w+3) feet long. Therefore, the original area, A, of the cage can be calculated by multiplying the width by the length:

A = w(w+3)

A = w^2 + 3w

Now, when we increase both dimensions of the floor by 3 feet, the new width becomes (w+3) + 3 = w+6, and the new length becomes (w+3) + 3 = w+6. Therefore, the new area, N, of the cage can be calculated by multiplying the new width by the new length:

N = (w+6)(w+6)

N = w^2 + 12w + 36

Therefore, the equation that represents the new area, N, of the cage is N = w^2 + 12w + 36.

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Answer:

x-2y=10

Step-by-step explanation:

It's parralel. If this helped, please mark me as brainliest.

Answer:

3

Step-by-step explanation:

Answer:16500

Step-by-step explanation:

That is, for every 100 people, there are 26 people aged between 11 and 20. So 63500 will have 16500 people aged 20.

Answer:

y= 2/3 x + 4

y- intercept= (0,4)

and slope of the line is 2/3

Answer:

B.

Step-by-step explanation:

y = mx + b

The y-intercept is the point (0, 4), so you get b = 4

You now have

y = mx + 4

Now start at the y-intercept, (0, 4). Go up 2 units and right 3 units to a point on the line; rise = 2; run = 2.

slope = m = rise/run = 2/3

Now you have

y = 2/3 x + 4

Answer: B.

Answer: your answer should be HI i hope it helps

Step-by-step explanation:

I think it's y=x² +6 because this is a quadratic equation

The equation used to determine the number of days, x, required for the substance to decay to 63 grams is: x ≈ 83.60

To determine the number of days, x, required for a radioactive substance to decay to 63 grams, we can use the exponential decay formula. The equation that represents the decay of a radioactive substance over time is:

N(t) = N₀ * (1/2)^(t/h)

Where:

N(t) is the remaining mass of the substance at time t

N₀ is the initial mass of the substance

t is the time elapsed

h is the half-life of the substance

In this case, we have an initial mass of 475 grams, and we want to find the number of days required for the substance to decay to 63 grams. We can set up the equation as follows:

63 = 475 * (1/2)^(x/20)

To solve for x, we can isolate the exponential term on one side of the equation:

(1/2)^(x/20) = 63/475

Next, we can take the logarithm (base 1/2) of both sides to eliminate the exponential term:

log(base 1/2) [(1/2)^(x/20)] = log(base 1/2) (63/475)

By applying the logarithmic property log(base b) (b^x) = x, the equation simplifies to:

x/20 = log(base 1/2) (63/475)

Finally, we can solve for x by multiplying both sides of the equation by 20:

x = 20 * log(base 1/2) (63/475)

Using a calculator to evaluate log(base 1/2) (63/475) ≈ 4.1802, we find:

x ≈ 20 * 4.1802

x ≈ 83.60

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The value of the function given by term h(x) = \(\frac{x^2-3x+2}{-x^2-4x+4}\) , the n the value of the function h'(-5) is -239.

Let h(x) = \(\frac{x^2-3x+2}{-x^2-4x+4}\)

so to find the value of h'(5),

h(x) = \(\frac{x^2-3x+2}{-x^2-4x+4}\)

by using the formula,

\(\frac{d}{dx} \frac{f(x)}{g(x)} = \frac{g(x)d/dxf(x) - f(x) d/dxg(x)}{g(x)^2}\)

h'(x) = \(\frac{(-x^2-4x+4)(2x-3)-(x^2-3x+2)(-2x-4)}{(-x^2-4x+4)^2} \\\\\frac{(-(-5)^2-4(-5)+4)(2(-5)-3)-((-5)^2-3(-5)+2)(-2(-5)-4)}{(-(-5)^2-4(-5)+4)^2} \\\\\= \frac{13-252}{1\\} \\\\= -239\)

A function is a relationship between a set of inputs and a set of allowable outputs that has the condition that each input is associated to precisely one output. Let A and B be any two non-empty sets; mapping from A to B is only a function if every element in set A has one end and only one image in set B.

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Answer:

c. 55.4%

Step-by-step explanation:

We calculate what percentage this year's bill of $862.40 is compared to last year's bill of $1935.67.

862.4/1935.67 × 100% = 44.55304%

Since this year's bill is 44.6% of last year's bill, the percent saved is

100% - 44.6% = 55.4%

Answer: c. 55.4%

The length of the rectangle is 7 cm and the width is 5 cm.

The whole distance covered by the rectangle's borders or its sides is known as its perimeter. As we know the rectangle will have 4 sides then the perimeter of the rectangle will be equal to the total of its four sides. And the unit will be in meters, centimeters, inches, feet, etc.        

The formula for the Perimeter of the rectangle is given by

Here we have

The length of a rectangle is 2cm greater than the width of the rectangle

And perimeter of the rectangle = 24 cm

Let x be the width of the rectangle

From the given data,

Length of the rectangle = (x + 2) cm  

As we know Perimeter of rectangle = 2(Length+width)

=> Perimeter of rectangle = 2(x+2 + x) = 2(2x +2)

From the given data,

Perimeter of rectangle =  24cm

=> 2(2x +2) = 24 cm

=> (2x +2) = 12     [ Divided by 2 into both sides ]

=>  2x = 12 - 2

=>  2x = 10

=>   x = 5         [ divided by 2 into both sides ]  

Length of rectangle, (x+2) = 5 + 2 = 7 cm

Therefore,

The length of the rectangle is 7 cm and the width is 5 cm.

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On factorizing the polynomial 3m²-9 we get 3(m²-3).

The factor of polynomial is defined as the process of expressing the polynomial as a product of two or more polynomials.

For Example : the factors of x²-16 are (x+4)(x-4).

In the given question we need to factor

3m²-9

here 9 can be written as 3*3

rewriting the above equation we get

3m²-3*3

As both the terms contain 3 we can take 3 common from both the terms ;

taking 3 common from each term we get ,

=3(m²-3)

Therefore , On factorizing 3m²-9 we get 3(m²-3) .

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Answer:

0.1

Step-by-step explanation:

hwhhehhejejeejjrjr

Answer:

167.55 ur welcom

The value of f(0.025) is approximately ±2.086 for an f-curve with df = (20, 5).

The t-distribution is a way of describing a set of observations where most observations fall close to the mean, and the rest of the observations make up the tails on either side. It is a type of normal distribution used for smaller sample sizes, where the variance in the data is unknown.

To find f(0.025) for an f-curve with df = (20, 5), we need to use a t-distribution table.

First, we need to determine the critical value for a two-tailed test with a significance level of 0.05 and 20 degrees of freedom (df).

Looking at the t-distribution table, we find that the critical value is approximately ±2.086.

Next, we can use the formula for the t-distribution to calculate f(0.025):
f(0.025) = t(0.025, 20) = ±2.086

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To find the volume of the solid generated by revolving the region bounded by the graphs of the equations, either the disk method or the shell method can be used.

When finding the volume of a solid generated by revolving a region around a line, we have two methods at our disposal: the disk method and the shell method.

1. Disk Method:

The disk method involves dividing the region into infinitesimally thin disks perpendicular to the axis of rotation. The volume of each disk can be calculated using the formula for the volume of a cylinder (V = πr^2h), where r represents the radius of the disk and h represents its height. By summing up the volumes of all the disks, we obtain the total volume of the solid.

2. Shell Method:

The shell method, on the other hand, involves dividing the region into infinitesimally thin cylindrical shells parallel to the axis of rotation. Each shell has a thickness of Δx, where x is the variable that defines the boundaries of the region. The volume of each shell is calculated by multiplying the height of the shell (given by the difference in the y-values of the two bounding curves) by the circumference of the shell (given by 2πx). By summing up the volumes of all the shells, we obtain the total volume of the solid.

Both methods yield the same result for the volume of the solid. The choice between the two methods depends on the shape of the region and the convenience of integrating with respect to either x or y.

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