What is the geometric mean of 6 and 16?

The student would use the following step for the proof

Show that the solutions to \(7x - 8y = 6\) and \(8x - 5y = 11\) is the same as the solution of the original system

The system of equations is given as:

\(x + 3y = 5\)

\(7x - 8y = 6\)

Add both equations

\(x + 7x + 3y- 8y = 5 + 6\)

\(8x - 5y = 11\)

So, the new system of equations would be:

\(7x - 8y = 6\)

\(8x - 5y = 11\)

To prove that both equations would have the same solution, the student has to solve for x and y in both systems

Read more about systems of equations at:

https://brainly.com/question/14323743

Answer: Rotation

Step-by-step explanation:

If the representative fraction scale is 1:48000, then the verbal scale from inches to feet is  1 inch represents 0.00025 feet.

We have to find the verbal (written) scale from inches to feet that represents a map with a representative-fraction (RF) scale of 1:48,000,

We use the formula:

⇒ Verbal scale = RF × Inches per foot,

We know that the RF scale is 1:48,000, which means that one unit on the map represents 48,000 units in the real world.

There are 12 inches in a foot,

So, we can convert the verbal scale to inches-per-foot by dividing by 12:

⇒ Inches per foot = (Verbal scale)/(12),

⇒ Inches per foot = (1/48000) × (12/1) = 0.00025

Therefore, the verbal scale from inches to feet is : 1 inch represents 0.00025 feet.

Learn more about Scale here

https://brainly.com/question/30530331

#SPJ4

The statement equation is  3+ \(14\div 2\) = e and value of e is 10.

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

Here the given statement is , 14 eggs divides into 2 then,

=> \(14\div 2\)

3 more than 14 eggs divided into 2 then,

=> 3+ \(14\div 2\)

This is equal to e, then

=> 3+ \(14\div 2\) = e

Now simplifying them ,

=> 3+ 7= e

=> e = 10.
Hence the statement expression is  3+ \(14\div 2\) = e and e=10.

To learn more about equation refer the below link

https://brainly.com/question/29336774

#SPJ1

1) The gravimetric moisture content of the soil at field capacity is approx 27.62%.

2) The dry bulk density of the sample is approximately 1.193 g/cm^3.

3) The porosity of the sample, as a percentage of the total volume, is approximately 54.96%.

1) The gravimetric moisture content of the soil at field capacity can be calculated using the following formula:

Gravimetric Moisture Content = ((Wet Weight - Dry Weight) / Dry Weight) * 100

Given:

Wet Weight = 274.1 g

Dry Weight = 214.7 g

Using the formula, we can substitute the values:

Gravimetric Moisture Content = ((274.1 - 214.7) / 214.7) * 100

Gravimetric Moisture Content = (59.4 / 214.7) * 100

Gravimetric Moisture Content ≈ 27.62%

The gravimetric moisture content of the soil at field capacity is approximately 27.62%.

The gravimetric moisture content represents the amount of water present in a given mass of soil. By subtracting the dry weight of the soil from the wet weight and dividing by the dry weight, we can determine the proportion of water in the sample. Multiplying by 100 gives the moisture content as a percentage.

1a. The dry bulk density of the sample can be calculated using the following formula:

Dry Bulk Density = Dry Weight / Sample Volume

Given:

Dry Weight = 214.7 g

Sample Volume = 180 cm^3

Substituting the values into the formula:

Dry Bulk Density = 214.7 g / 180 cm^3

Dry Bulk Density ≈ 1.193 g/cm^3

The dry bulk density of the sample is approximately 1.193 g/cm^3.

Dry bulk density refers to the mass of dry soil per unit volume. To calculate it, we divide the dry weight of the soil by the sample volume.

1b. The porosity of the sample can be calculated using the following formula:

Porosity = (1 - (Dry Bulk Density / Particle Density)) * 100

The particle density for soil is usually around 2.65 g/cm^3.

Given:

Dry Bulk Density = 1.193 g/cm^3

Particle Density = 2.65 g/cm^3

Substituting the values into the formula:

Porosity = (1 - (1.193 / 2.65)) * 100

Porosity ≈ 54.96%

The porosity of the sample, as a percentage of the total volume, is approximately 54.96%.

Porosity represents the void space within a soil sample. It is calculated by subtracting the ratio of the dry bulk density to the particle density from 1 and multiplying by 100 to get the percentage. In this case, the particle density of 2.65 g/cm^3 is a typical value for soil.

To know more about gravimetric moisture content, visit;

https://brainly.com/question/33657666
#SPJ11

Answer:

hmmmm

Step-by-step explanation:

The area of the supplied trapezium is 20 \(cm^{2}\).

                   The four sides of a trapezium, a geometric shape, consist of a single pair of parallel sides, commonly referred to as the "bases". An additional set of sides, which may or may not be parallel, are referred to as the "legs" of a trapezium. The term "area" refers to the entire space a trapezium takes up on a two-dimensional plane.

                 The area of a trapezium is determined by \(\frac{1}{2} (a+b)h\).  where h is the distance between the two parallel side lengths, a and b. By counting the shaded squares in this graph, one can determine the length of parallel sides.

Here, an is 3 cm and b is 7 cm. The trapezium is 4 cm tall.

Applying the calculation above,

Area= = \(\frac{1}{2} (3+7) 4\)

\(=\frac{1}{2}(10)4\)

\(=\frac{40}{2}\)

=20 \(cm^{2}\)

Learn more about trapezium here,

https://brainly.com/question/30042904

Answer:

x+133 =131

x. =131-133

x. =(-2)

Answer:o,kl,,k,

Step-by-step explanation:,,,k,

Answer:

The answer would be 51x^5 y^3 z^6

Step-by-step explanation:

Its basically purely multiplying the expressions for example i got 51X because I multiplied -17 by -3 making it an even 51 :)).

Hope this helps:)) Please mark Brainliest :)

Answer:

The population of the world is 200 times of the population of Canada.

Step-by-step explanation:

Given that,

Canada's population = \(3.5\times 10^7\)

The population of world =  \(7.0\times 10^9\)

We need to find how many times larger is the population of the world compared to Canada's population. It can be solved as follows :

\(\dfrac{W}{C}=\dfrac{7.0\times 10^9}{3.5\times 10^7}\\\\\dfrac{W}{C}=200\\\\W=200C\)

So, the population of the world is 200 times of the population of Canada.

Therefore, there are 480 different ways to arrange individuals in a row so that no two engineers sit together.

An alternative name for a combo is a choice. A combination is a choice made from a predetermined group of options. I won't organize anything here. They will be my choice. The number of distinct r selections or combinations from a set of n objects is indicated by the symbol \(^nC_{r}\).

There are eight participants in the focus group, including three software engineers, two nurses, one doctor, and two technicians.

So the 3 software engineers =3! ways, 2 nurses =2! ways,

doctor =1! way , 2 technicians =2! ways.

We must determine how many different configurations are possible so that no two pieces of software may coexist.

In order to prevent two software engineers from being seated next to each other, we first arrange five persons in a row with a space between them.

\(We get that in 6 places they can sit in ^6C_{3} ways\\ xi.e ^6C_3 = 20 (by formula of combination)\\ Therefore total ways are,6 X 2 X 1 X2 X 20 = 480.\)

Therefore, there are 480 different ways to arrange individuals in a row so that no two engineers sit together.

To know more about combination visit:

https://brainly.com/question/20211959

#SPJ4

Here, x = 6 is a vertical asymptote of f, so the function approaches infinity as x approaches 6 from both sides.

Let's start by integrating f'(x) to get f(x). We have:

f'(x) = 16(x+2)(6-x)³ - 32(x+6)

Integrating both sides with respect to x:

f(x) = ∫[16(x+2)(6-x)³ - 32(x+6)] dx

Simplifying the integral, we get:

f(x) = -2(x+2)²(6-x)⁴ + 16(x+6) + C

where C is the constant of integration.

Next, we can find the critical points of f(x) by setting f'(x) = 0:

f'(x) = 16(x+2)(6-x)³ - 32(x+6) = 0

Solving for x, we get x = -2 and x = 6 as critical points.

Now, we can use the second derivative f''(x) to determine the concavity of the function. We have:

f''(x) = (6x-x)⁴ = x⁴

Since the second derivative is always positive for x > 0, the function is concave up on the interval (6, ∞).

Similarly, since the second derivative is always negative for x < 0, the function is concave down on the interval (-∞, -2).

At x = -2 and x = 6, the function has an inflection point.

Finally, we know that x = 6 is a vertical asymptote of f, so the function approaches infinity as x approaches 6 from both sides.

Learn more about the function visit:

https://brainly.com/question/11624077

#SPJ4

Answer:

there is your answer hope that helps

The closed formula of h(t) and f(t) for

h(0)=f(0)=100b => h(t) = 100(2t+1), f(t) = 100(2t-1) ,

h(0)=200, f(0)=100 => h(t) = 200(2t+1), f(t) = 100(2t-1)

h(0)=600, f(0)=500 =>h(t) = 300 + 200(2t+\((-1)^{t}\)), f(t) = 200 - 100\((-1)^{t}\)

The recursive equations for the given two interacting population of hares and foxes are

h(t+1)=4h(t)-2f(t)

f(h+1)=h(t)+f(t)

for the given initial population in parts from a to c we need to create a close formula for h(t) and f(t)

h(t) = 100(2t+1)

f(t) = 100(2t-1)

h(t) = 200(2t+1)

f(t) = 100(2t-1)

h(t) = 300 + 200(2t+\((-1)^{t}\))

f(t) = 200 - 100\((-1)^{t}\)

The closed formula of h(t) and f(t) for

h(0)=f(0)=100b => h(t) = 100(2t+1), f(t) = 100(2t-1) ,

h(0)=200, f(0)=100 => h(t) = 200(2t+1), f(t) = 100(2t-1)

h(0)=600, f(0)=500 =>h(t) = 300 + 200(2t+\((-1)^{t}\)), f(t) = 200 - 100\((-1)^{t}\)

To learn more about recursive equations,

https://brainly.com/question/29224065

#SPJ4

Answer: It does not appear to show a function because the numbers are not multiples of each other

Step-by-step explanation: Hope this helps :-)

When a user searches for a street name and the search engine returns a single business located on that street, it indicates that the business is highly relevant to the search query. The relevance of this result can be explained by the following points:

Proximity: When a user searches for a street name, they are likely interested in finding businesses that are located on that street or nearby. If the search engine returns a single business located on that street, it suggests that the business is in close proximity to the user's location and can be easily accessed.

Context: The street name provides context to the search query and helps the search engine understand the user's intent. For example, if a user searches for "Main Street," the search engine may assume that the user is looking for businesses that are located on Main Street. If the search engine returns a single business on Main Street, it suggests that the business is highly relevant to the user's search query.

Accuracy: When the search engine returns a single business on a particular street, it indicates that the search engine is able to accurately match the user's search query with the relevant business. This can be attributed to the search engine's ability to understand the context of the search query and provide highly accurate results.

In conclusion, when a search engine returns a single business on a street name search query, it indicates that the business is highly relevant to the user's search query, is in close proximity to the user's location, and the search engine is able to accurately match the user's search query with the relevant business.

Learn more about business here brainly.com/question/15826604

#SPJ4

If a rock needs to weigh 2,000 lb in order not to be shifted by waves, the volume of this basalt rock is equal to 0.625 in³.

In Science, the density of a chemical substance such as lead can be calculated by using this formula:

Density = M/V

Where:

Making volume the subject of formula, we have the following:

Volume = Mass/Density

Volume = 2,000/3,200

Volume = 0.625 in³.

Read more on density here: brainly.com/question/14035509

#SPJ1

The absolute value of the difference between the point estimate and the population parameter it estimates is sampling error.

The number's absolute value, which ignores orientation, indicates how far it is from zero on the number line. A number can never be negative in absolute terms.

Concepts which are used in the given problems:

The incorrect options can be found below:

Because the precision is the estimate that is near from the various samples, the absolute magnitude of the difference between the point estimate and the population parameter would not be a precision. Additionally, it is not a standard error since a standard error is an error that is far beyond the range of the sample mean. However, it is not a confidence error since a confidence error is a measure of how far the findings would deviate from the population under consideration.

By using the  concept of precision, standard error and error of confidence, the incorrect choices are discovered.

The correct choice may be found below:

Sampling error is the measurement of the distance or difference between the population parameter and the sample's point estimate. The sampling mistake is an inaccuracy that results from drawing conclusions about the sample rather than the population being studied.

The idea of sampling error is used to calculate the absolute value of the distinction between both the point estimate and the population parameter is predicts.

Thus, the absolute value of the difference between the point estimate and the population parameter it estimates is sampling error.

To know more about absolute value refer to:

https://brainly.com/question/12928519

#SPJ4

Answer:

10m

Step-by-step explanation:

Perimeter means adding up all of the sides of a shape.

One property of a square is that all lengths of a square are the same.

We also know squares have 4 sides.

Lets set up an expression to solve the length for each side with variable S representing the length of a side:

4 * S = 40

Divide each side by 4:

S = 10

Therefore, each side of the square has a length 10m

Answer:

-5

Step-by-step explanation:

Subtracting a negative is just like adding a positive. A way to think about this is that the negative cancel each other out are you left with a positive number.

You can rewrite this as -87 + 82.

Then, you solve and get -5.

Answer:

-5

Step-by-step explanation:

When you are subtracting a negative number, it is the same as adding a positive. We can re-write the expression as:

-87 + 82

When adding a negative and positive number, the one with the larger absolute value controls what sign the sum has. In this case the sum would be negative because 87 > 82. Also, we would subtract these absolute values: 87-82 = 5. This has to be negative, meaning the answer is -5.

The given statement "In performing a lower-tailed z-test for one mean, the value of the test statistic was z=0.51, which would yield a p-value of 0.695." is true because we perform null hypothesis.

In a lower-tailed z-test for one mean, we test a null hypothesis that the population mean (μ) is greater than or equal to a certain value, against an alternative hypothesis that the population mean is less than that value.

To perform the test, we calculate the z-test statistic using the sample mean, sample standard deviation, sample size, and the hypothesized population mean. If the calculated z-test statistic falls in the rejection region (below the critical value), we reject the null hypothesis and conclude that the population mean is less than the hypothesized value.

In this case, the calculated z-test statistic is 0.51, which falls in the non-rejection region (above the critical value) for a lower-tailed test with a significance level of 0.05. Therefore, the p-value is greater than 0.05, and we do not reject the null hypothesis. The statement that the p-value is 0.695 is consistent with this conclusion.

To know more about z-test here

https://brainly.com/question/14790912

#SPJ4

Answer:

11.  A)   207 \(yards^2\)

12.  B)  480 \(cm^2\)

Step-by-step explanation:

Answer:

X

\( \frac{y2 - y1}{x2 - x1} - \frac{y - y1}{x - x1} \)

Step-by-step explanation:

in every point given put one as (x1, y1) and the other is (x2, y2)

simplify the formula and you'll get you linear equation

The power delivered by the student's biceps is 51.45 watts (W).

To calculate the power delivered by the student's biceps while doing a pull-up, we use the formula:

Power = Work/Time

Since the physics student lifts her 42 kg body to a distance of 0.25 m, the work done is given by:

Work = Force x Distance

The force exerted by the student is equal to her weight, which is given by:

F = mg

where m = 42 kg (mass of the student) and

g = 9.8 m/s² (acceleration due to gravity)

Therefore,

F = 42 kg x 9.8 m/s²

= 411.6 N (weight of the student)

Hence, the work done by the student is:

Work = Force x Distance

= 411.6 N x 0.25 m

= 102.9 J (joules)

The time taken by the student to complete the pull-up is given as 2 seconds.

Therefore:Time = 2 s

Now we can substitute the values into the formula for power:

Power = Work/Time

= 102.9 J/2 s

= 51.45 W

Know more about the work done

https://brainly.com/question/30257290

#SPJ11

There are indeed 48 triangles that can be chosen from the rectangular array shown .

To find the 48 triangles, you should use the Combination formula which will show you the number of ways to pick 3 points when given 8 points.

C ( n, k ) = n! / ( k ! x ( n - k ) ! )

C ( 8 , 3 ) = 8 ! / (3 ! x ( 8 - 3 ) ! )

C ( 8, 3 ) = 336 / 6

C ( 8, 3) = 56

Now, there are technically 56 ways to pick the points but some of these ways are collinear and these cannot form triangles. Each row will have 4 such points so the number of ways to pick triangles is:

= 56 - ( 4 x 2 )

= 48 triangles

Find out more on triangles at https://brainly.com/question/30391270

#SPJ1

CosA is negative for the largest angle in an obtuse triangle. Using the law of cosines, a²>b²+c², a>b, and a>c are derived.

Step 1: As the obtuse triangle has the largest angle A (more than 90 degrees), the cosine function's value is negative.

Step 2: By applying the Law of Cosines in the triangle, a²>b²+c², which is derived from a²=b²+c²-2bccosA, and hence a>b and a>c can be derived.

Step 3: From the previously derived inequality a²>b²+c², we can conclude that a>b and a>c as a²-b²>c². The value of a² is greater than both b² and c² when a>b and a>c.

Therefore, the largest angle of an obtuse triangle is opposite the longest side.

Step 4: In triangle ABC, A=103°, a=25, and c=30.

a² = b² + c² - 2bccos(A),

a² = b² + 900 - 900 cos(103),

a² = b² + 900 + 900 cos(77),

a² > b² + 900, so a > b.

Similarly, a² > c² + 900, so a > c.

Therefore, triangle ABC satisfies a>b and a>c.

To know more about the obtuse triangle visit:

https://brainly.com/question/3250447

#SPJ11