Complete the following proof.

Given: Two concentric circles with a tangent to a smaller circle at R



Prove: AR = RB

The volume of the gas approximately directly proportional to its number of moles of gas when both temperature and pressure are constant.

V∝ n at constant P and T

V = constant × (n)

Vn = constant

This can be mathematically stated as follows: As before, we can anticipate what will change to the volume of the a sample of gas as we adjust the number of moles using Avogadro's law.

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Answer:108

ummm multiply all numbers.

The correct conclusion is:

"The doctor can be 95% confident that the mean height of male students at the college is between 63.5 inches and 74.4 inches."

Given,

At a huge institution, a doctor is determining the typical height of the male students.

Inches are used to measure the heights of a sample of 40 male baseball team players.

The doctor computes the 95% confidence interval using this information (63.5, 74.4).

The following conclusions is valid:

"The doctor can be 95% confident that the mean height of male students at the college is between 63.5 inches and 74.4 inches."

We can guarantee that the target variable will be within the confidence interval for a given confidence level since we know the confidence interval reflects an interval.

The true mean of heights for male students at the college where the doctor measured heights is represented by the provided case's confidence level of 95% and confidence interval of (63.5, 74.4).

The doctor is therefore 95% certain that the range of the mean height of male students at the college is valid (63.5, 74.4).

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The correct sampling method described in the question is a stratified random sample among the simple random sample,  stratified random sample, cluster random sample and  Voluntary random sample

The sampling method described in the question is a stratified random sample.

In a stratified random sample, the population is divided into subgroups or strata based on certain characteristics or criteria. Then, a random sample is selected from each stratum. The key idea behind this method is to ensure that each subgroup is represented in the sample proportionally to its size or importance in the population. This helps to provide a more accurate representation of the entire population.

In the given sampling method, the population is divided into subgroups, and a fixed number of units is taken from each group. This aligns with the process of a stratified random sample. The sample selection is random within each subgroup, but the number of units taken from each group is fixed.

Other sampling methods mentioned in the question are:

Simple random sample: In a simple random sample, each unit in the population has an equal chance of being selected. This method does not involve dividing the population into subgroups.

Cluster random sample: In a cluster random sample, the population is divided into clusters or groups, and a random selection of clusters is included in the sample. Within the selected clusters, all units are included in the sample.

Voluntary random sample: In a voluntary random sample, individuals self-select to participate in the sample. This method can introduce bias as those who choose to participate may have different characteristics than those who do not.

Therefore, the correct sampling method described in the question is a stratified random sample.

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Answer:

3.74 x 10^5

Step-by-step explanation:

First expand the term in scientific notation into normal notation.

3.3 x 10^5   -   Here the ^5 tells us to move the decimal five places to the right, so we go from

3.30000 to

330000.00

So 3.3 x 10^5 = 330,000

Now add that to 44,000 and you get 374,000.

Return this number to scientific notation.  Move the decimal back to its spot before the 3.  We go from

374,000.00 to

3.74000

Once again the decimal has moved five places, so that is the number in the exponent of the our scientific notation, and therefore our answer is

3.74 x 10^5

Answer:

b and c

Step-by-step explanation:

x+30<60 -->x < 60 -30 = 30 --> x < 30

Answer:

B and C

Step-by-step explanation:

We can solve for x in the inequality just like you do when solving algebra equations of an = sign.

x + 30 < 60

x + 30 - 30 < 60 -30

x < 30

"<" means the number on the left is smaller than the number on the right. Both numbers must not be equal to each other.

Since x is smaller than 30, and is not 30,

the only option that is correct is B, 1 and C, 29.

Answer:

lhs = (5+2√3)/(7+4√3)

= [(5+2√3)(7-4√3)]/[(7-4√3)(7+4√3)]

=[35-20√3+14√3-24]/[7²-(4√3)²]

=[11-6√3]/[49-48]

=11-6√3

therefore

11-6√3 = a+b√3

compare both sides

a= 11, b= -6

Step-by-step explanation:

Hope this answer helps you :)

Have a great day

Mark brainliest

Answer:

a = 11, b = 6

Step-by-step explanation:

Given

\(\frac{5+2\sqrt{3} }{7+4\sqrt{3} }\)

Rationalise the denominator by multiplying numerator/ denominator by the conjugate of the denominator.

The conjugate of 7 + 4\(\sqrt{3}\) is 7 - 4\(\sqrt{3}\)

= \(\frac{(5+2\sqrt{3})(7-4\sqrt{3}) }{(7+4\sqrt{3})(7-4\sqrt{3} }\) ← expand numerator/ denominator using FOIL

= \(\frac{35-20\sqrt{3}+14\sqrt{3}-24 }{49-28\sqrt{3}+28\sqrt{3}-48 }\)

= \(\frac{11-6\sqrt{3} }{1}\)

= 11 - 6\(\sqrt{3}\)

with a = 11 and b = 6

Answer:

7225000000 people

Step-by-step explanation:

85000*  85000

=7225000000  pessoas

Answer:

26.82 (2 d.p.)

Step-by-step explanation:

tan(17)*m=8.2

8.2/tan(17) = m

= 26.82

Answer:

Its 0

Step-by-step explanation:ur not smart if u dont know that

The final Table will look like this:x1x2s1s2s3RHS 1 0 0 7/6 -11/6 29/6 0 1/2 0 -1/6 2/3 29/6 0 0 -1/2 1/6 5/3

Linear Programming (LP) is a method of optimising an objective function subject to a set of constraints using linear equations.

In this problem, we are required to maximise z=3x1+5x2 subject to three constraints.

We will use the Simplex Method to solve this problem.

Here are the steps to solve this problem using the Simplex Method :

Step 1: Convert the inequalities into equalities by adding slack variables. The standard form of the problem will look like this:

max z = 3x1 + 5x2subject tox1 + 0x2 + s1 = 42x1 + 0x2 + s2 = 123x1 + 2x2 + s3 = 18 where s1, s2, and s3 are the slack variables.

Step 2: Write the initial tableau and compute the relative profits of each variable. The relative profit is the ratio of the objective function coefficient to the coefficient of the variable in the row of the pivot column. The pivot column is the one with the most negative relative profit.x1x2s1s2s3RHS 1 0 1 0 0 42 0 0 1 0 12 3 5 0 0 0 0

Step 3: Select the pivot element. The pivot element is the smallest positive number in the RHS column. In this case, it is 12. The pivot row is the one with the smallest non-negative ratio of the RHS to the coefficient of the pivot element. In this case, it is row 3, since 18/2 is smaller than 42/1 or 12/0. The pivot element is 2. We divide row 3 by 2 to make the pivot element 1.3x1 + 2x2 + s3 = 18/2 = 9/2x1 x2 s1 s2 s3 RHS 1 0 1/2 0 -1/4 9/4 0 0 1/2 1 0 21/2 0 0 -3/2 0 1 -1/2 0 15/2

Step 4: Perform row operations to make the other elements in the pivot column zero. We subtract 2 times row 1 from row 3 to make the s1 element zero.3x1 + 2x2 + s3 = 9/2-2x1 + 0x2 - s1 = -2x2 = 3/2 - (1/2)s3x1 x2 s1 s2 s3 RHS 1 0 1/2 0 -1/4 9/4 -2 0 -1/2 1 1/2 3 0 0 3/2 1 0 1/2 0 -3/2

Step 5: Repeat steps 3 and 4 until there are no more negative elements in the RHS column or the objective function cannot be further maximized. In this case, the solution is z=29 at (x1, x2) = (3, 3/2).

The final table will look like this:x1x2s1s2s3RHS 1 0 0 7/6 -11/6 29/6 0 1/2 0 -1/6 2/3 29/6 0 0 -1/2 1/6 5/3

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Take into consideration the solid that results from rotating the area enclosed by the provided curves about the x-axis. y = 2/7 x^2, y = 9/7 - x^2 . the volume of the solid is approximately 1.412 cubic units.

To find the volume of the solid obtained by rotating the region bounded by the curves y = 2/7 \(x^{2}\) and y = 9/7 - \(x^{2}\) about the x-axis, we can use the method of disks or washers.

First, we need to find the limits of integration. The curves intersect when:

2/7\(x^{2}\) = 9/7 - \(x^{2}\)

Multiplying both sides by 7, we get:

2\(x^{2}\) = 9 - 7\(x^{2}\)

9\(x^{2}\) = 9

\(x^{2}\) = 1

x = ±1

Therefore, the limits of integration are x = -1 and x = 1.

Next, we need to express the curves in terms of y. Solving for x in each equation, we get:

x = ±√(7/2 y)

x = ±√(9/7 - y)

Using the method of disks, we can find the volume of the solid by integrating the areas of circular disks with radius y from y = 0 to y = 9/7.

The radius of each disk is given by the difference between the upper and lower curves evaluated at y:

r = √(9/7 - y) - √(7/2 y)

The area of each disk is given by:

A = π\(r^{2}\)

Substituting for r, we get:

A = π [√(9/7 - y) - √(7/2 y)]

Expanding and simplifying, we get:

A = π [9/7 - y + 7/2 y - 2√(9/7 y)]

A = π [9/7 + 3/2 y - 2√(9/7 y)]

Integrating with respect to y, we get:

V = ∫[0, 9/7] π [9/7 + 3/2 y - 2√(9/7 y)] dy

V = π [(9/7) y + (3/4) - (4/9) \(9/7^{3/2}\) \(y^{3/2}\)] [0, 9/7]

V = π [81/28 - (64/81)  \(9/7^{3/2}\)]

V ≈ 1.412

Therefore, the volume of the solid is approximately 1.412 cubic units.

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Answer:

8.5

Step-by-step explanation:

:)

The equation that requires the multiplication property of equality to be solved is:

\(\boxed{\sf \dfrac{a}{6}=420}\)

Multiplication property of equality states that if both the sides of an equation are multiplied by the same number, the expressions on the both sides of the equation remain equal to each other.

The multiplication property states that:

Out of the given options, \({\sf \dfrac{a}{6}=420}\) requires the multiplication property of equality to be solved.

That is:

\(\text{If} \ {\sf \dfrac{a}{6}=420}\)

\({\sf \dfrac{a}{6}\times6=420\times6\)

\(\sf a=2520\)

Hence, the equation that requires the multiplication property of equality to be solved is:

\({\sf \dfrac{a}{6}=420}\)

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The price of the book at the furniture store is $150

Given the parameters:

The price of book in the furniture store would be :

Hence, we have :

125 + (0.2 * 125)

125 + 25

= 150

Therefore, the price at the furniture store is $150

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If only two out of the five people show up for the meeting, it is possible in 10 different ways.

If five people plan to meet after school and there will be one group of five people if they all show up, but only two people show up, we need to determine the number of ways this can happen.

To find the number of ways two people can show up out of the five, we can use combinations. In a combination, the order of selection does not matter.

The number of ways to choose two people out of five can be calculated using the formula for combinations, denoted as "nCr", where n is the total number of people and r is the number of people we want to choose.

In this case, we want to choose 2 people out of 5, so the calculation would be:

5C2 = (5!)/(2!(5-2)!) = (5!)/(2!3!) = (5 \(\times\) 4)/(2 \(\times\) 1) = 10

Therefore, there are 10 possible ways for two people to show up out of the five if all of them plan to meet after school.

These 10 possibilities could be different combinations of any two individuals out of the five.

To determine the specific combinations, you can list all the pairs or use a combination formula calculator.

It's important to note that the order in which the two people show up does not matter, as long as they are two out of the five originally planning to meet.

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Answer:

x = 18

Step-by-step explanation:

According to the property of the angle, 2x = 36, so x = 36/2 = 18.

The model which properly represent the information in given axioms is Cross geometry (+).

In the given question we have following information,

by using the above axioms we draw a geometry of Cross sign Geometry as seen above .

We can draw a line which contains three points and these points are only from given five points another line also follow this . this geometry follows all given axioms . The two lines intersect each other at a point . The point of intersection is one of point from five points . both of lines are linear and consists three points .

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Answer:

Reflection over the X axis.

Answer:

Maya collected data about the number of ice cubes and milliliters of juice in several glasses of juice and organized the data into this table.

Ice Cubes 4 2 3 5 5 3 1

Juice (milliliters) 177 234 202 140 155 210 265

She used a graphing tool to display the data in a scatter plot, with x representing the number of ice cubes and y representing the milliliters of juice. Then she used the graphing tool to find the equation of the line of best fit:

y = -29.202x + 293.5.

Based on the line of best fit, approximately how many milliliters of juice will be in a glass with 7 ice

Step-by-step explanation:

Based on the line of best fit, approximately how many milliliters of juice will be in a glass with 7 ice.

Maya collected data about the number of ice cubes and milliliters of juice in several glasses of juice and organized the data into this table.

Ice Cubes             4        2      3        5       5      3        1

Juice (milliliters)  177    234   202   140   155   210   265

She used a graphing tool to display the data in a scatter plot, with x representing the number of ice cubes and y representing the milliliters of juice. Then she used the graphing tool to find the equation of the line of best fit:

y = -29.202x + 293.5.

A line of best fit refers to a line through a scatter plot of data points that best expresses the relationship between those points. Statisticians typically use the least-squares method to arrive at the geometric equation for the line, either through manual calculations or regression analysis software.

Based on the line of best fit, approximately how many milliliters of juice will be in a glass with 7 ice.

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Using the mean absolute deviation concept, it is found that:

1. One set of possible locations is given as follows: (40, 40, 40, 60, 60, 60).

2.  Another set of possible locations is given as follows: (39, 40, 41, 59, 60, 61).

Hence, for a mean of 50 and a mean absolute deviation of 10, with 6 pennies, we want data-sets with these following characteristics:

Hence:

1. One set of possible locations is given as follows: (40, 40, 40, 60, 60, 60).

2.  Another set of possible locations is given as follows: (39, 40, 41, 59, 60, 61).

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Answer:

Option D

AC , CB , AB

Step-by-step explanation:

The shortest side is opposite to the small angle

58 < 59 < 63

AC < CB <AB

C. The two quantities are equal.  We can see that both Quantity A and Quantity B have the same value of 1. Hence, the two quantities are equal.

Since we know that the length of each side of triangle T is 6 times the length of each side of triangle X, we can set up the following equations:
Length of side of T = 6 * Length of side of X
To compare the ratios of the sides, we can use the following formula:
Ratio of one side to another = Length of one side / Length of another side
For Quantity A, we can choose any two sides of triangle T and find their ratio. Let's choose the two adjacent sides:

To further explain the concept, let's consider the properties of equilateral triangles.
An equilateral triangle is a special type of triangle where all three sides are equal in length. Hence, if we know the length of one side, we automatically know the length of all three sides.
Now, coming back to the given question, we are told that the length of each side of triangle T is 6 times the length of each side of triangle X. This means that if the length of one side of triangle X is 'a', then the length of one side of triangle T is 6 times 'a', which is '6a'.
Hence, we can write:
Length of side of T = 6a
Length of side of X = a
Now, let's compare the ratios of the sides.
For Quantity A, we need to find the ratio of one side of triangle T to another side of T. Let's choose the two adjacent sides:
Ratio of adjacent sides of T = Length of side of T / Length of adjacent side of T
Since all three sides of an equilateral triangle are equal, the adjacent side of T is also 6a. Hence, we get:
Ratio of adjacent sides of T = (6a) / (6a) = 1
For Quantity B, we need to find the ratio of one side of triangle X to another side of X. Let's again choose the two adjacent sides:
Ratio of adjacent sides of X = Length of side of X / Length of adjacent side of X
Since all three sides of an equilateral triangle are equal, the adjacent side of X is also 'a'.

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For the given frustum of a regular square pyramid with base lengths of 5 and 9, and a slant height of 6, the volume is approximately 299.503 cubic units and the surface area is 151 square units.

We may apply the following formulas to determine the volume and surface area of the frustum of a regular square pyramid:

Volume of a square pyramid's frustum:

V = (1/3)h (A1 + A2 + (A1 * A2)).

where V is the volume, h is the frustum's height, A1 is the top base's area, and A2 is the bottom base's area.

Surface area of a square pyramid's frustum is given by

S = A1 + A2 + (A1 * A2), where S stands for surface area, A1 for top base area, and A2 for bottom base area.

Given:

- The longer base's length is 9.

- The smaller base's length is 5.

Slant height is six.

We can use the Pythagorean theorem to determine the height:

(h^2) = (6^2) - ((9 - 5)^2) = 36 - 16 = 20 h = √20 = 2√5

Calculating the volume:

V = (1/3)h (A1 + A2 + √(A1 * A2))

V = (1/3)(5.99)(25 + 81 + √(25 * 81))

V = (1/3)(5.99)(25 + 81 + √(2025))

V = (1/3)(5.99)(25 + 81 + 45)

V = (1/3)(5.99)(151)

V ≈ 299.503 cubic units

Therefore, the volume of the frustum is approximately 299.503 cubic units.

Calculating the surface area:

S = A1 + A2 + √(A1 * A2)

S = 25 + 81 + √(25 * 81)

S = 25 + 81 + √(2025)

S = 25 + 81 + 45

S = 151 square units

Therefore, the surface area of the frustum is 151 square units.

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Answer:

Step-by-step explanation:

1/2b+8b+(-b) = 7 and 1/2 b

(-9)+(-7) +14 = -2

so the answer is: 7 1/2b -2

Answer:

x = - 8

Step-by-step explanation:

Based On A Math Calculator Online

The product measure on R² of Lebesgue measures and the set D = (0,∞) x (0,∞), we need to compute the integral of (1+y)(1+22y) with respect to the measure du(x, y) over D.

The value of this integral is then used to prove that the functions Ï(x) and g(x) are bounded and continuous, and that their integral over X satisfies [f(x)g(x)dX(x) = [f(x)g(x)dX(x).

Computing the Integral: To compute the integral of (1+y)(1+22y) with respect to the measure du(x, y) over D, we need to integrate with respect to both x and y over the given range (0,∞). The exact integration process and result would depend on the specific form of the function and the limits of integration.

Proving Boundedness and Continuity: To prove that Ï(x) and g(x) are bounded and continuous, we need to show that they satisfy the conditions of boundedness and continuity. This can involve demonstrating that the functions are well-defined, continuous, and have finite values within their respective domains.

Establishing the Integral Equality: To prove that [f(x)g(x)dX(x) = [f(x)g(x)dX(x), we need to show that the integral of Ï(x) and g(x) over X, with respect to the Lebesgue measure, yields the same result. This can be demonstrated using techniques from measure theory and Lebesgue integration, such as approximating functions by simple functions and applying the appropriate integration theorems.

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Answer:

i think 7

Step-by-step explanation:

you cant go diagonal and count it as one unit. however doing stairs up to the second point gets you 7 units