Find the area of the the regular polygon.

V = π [(3(\(\sqrt{18/2}\))³/1) - (2(\(\sqrt{18/2}\))⁵/15)] - π [0]

Simplifying this expression will give us the final volume of the solid.

, we need to evaluate the triple integral:

V = ∫₀²π ∫₀ᵣ ∫(18 - 2r²) r dz dr dθ

Integrating with respect to z first, we have:

V = ∫₀²π ∫₀ᵣ (18 - 2r²) r dr dθ

Integrating the volume with respect to r, we get:

V = ∫₀²π [(9r² - 2/3r⁴)]ᵣ₀ dθ

Simplifying the expression inside the brackets and evaluating the integral, we have:

V = ∫₀²π (9r² - 2/3r⁴) dθ

V = π [(9/3)r³ - (2/15)r⁵]ᵣ₀

V = π [(3r³/1) - (2r⁵/15)]ᵣ₀

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Answer:

414.69

Step-by-step explanation:

2*pi*r

The measures of the angles are ∠1 = 127°, ∠2 = 53°, ∠3 = 127°, ∠4 = 37°, ∠5 = 53°, ∠6 = 90°, ∠7 = 37°, ∠8 = 143°, ∠9 = 37° and ∠10 = 143°

From the question, we have the following parameters that can be used in our computation:

The transversal lines and the other lines

So, we have

∠1 = 180 - 53

Evaluate

∠1 = 127°

Also, we have

∠5 = 53°

By vertical angles, we have

∠2 = 53°

∠3 = 127°

Next, we have

∠4 = 127 - 90°

∠4 = 37°

Solving further, we have

∠6 = 90°

By corresponding angles, we have

∠7 = 37°

∠9 = 180 - 90 - 53°

∠9 = 37°

∠10 = 90 + 53°

∠10 = 143°

∠8 = 143°

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Answer:

It would be 7/4 and 3. This is because the slope is positive and those are the only 2 positive answers. Hope this helps

The slope of the line is -2 or -8.5.

Options A and B are the correct answer.

The equation of a line is given by:

y = mx + c

where m is the slope of the line and c is the y-intercept.

Example:

The slope of the line y = 2x + 3 is 2.

The slope of a line that passes through (1, 2) and (2, 3) is 1.

We have,

From the graph,

We can have two coordinates:

(x, 0) and (0, y)

Now,

Slope.

= (y - 0)/(0 - x)

= y/-x

= - y/x

Now,

The slope is a negative value.

This means,

-2 and -8/5 can be the slope.

Thus,

The slope of the line is -2 or -8.5.

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Answer:

The choice C) 34°

Step-by-step explanation:

\(75 + (x + 42) + (x + 79) = 180 \\ 2x + 196 = 180 \\ 2x = 180 - 196 \\ 2x = - 16 \\ \\ x = \frac{ - 16}{2} \\ \\ x = - 8 \\ \\ x + 42 = > - 8 + 42 = 34\)

The probability that all three Escher prints will be placed consecutively is 3/5 or 0.6

The probability that all three pieces by Escher will be placed consecutively when hanging the 10 pieces of art in a random order is the probability that the 3 Escher prints will be in a row among the other 7 pieces.

There are 10!/(3! × 7!) = 120 ways to order the 10 pieces of art, and 3! = 6 ways to order the 3 Escher prints among themselves.

So the total number of ways to order the art such that the Escher prints are consecutive is 120 × 6 = 720.

Now to find the probability that all three Escher prints will be placed consecutively, we divide the number of ways that this can happen (720) by the total number of ways the art can be arranged (120) to get 720/120 = 6/10 = 3/5.

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For an associative algebraic structure, the inverse of every invertible element: d. is unique

Amongst the following, the characteristic features of a group are: c. All of these closure, associativity, identity and inverse

For an associative algebraic structure, the inverse of every invertible element is unique. This statement is true because the uniqueness of the inverse of every invertible element is a property that belongs to associative algebraic structures.

An inverse of an element is that element, when combined with another element, results in the identity element. When talking about algebraic structures, invertible elements are those elements that have an inverse. Associative algebraic structures, thus, are algebraic structures that obey the associative property. The inverse of every invertible element in such structures is unique.

Features of a group:

A group is a set of elements, together with an operation (binary operation), that meets four fundamental properties (axioms).These axioms are: Closure, Associativity, Identity and Inverse.

Closure is when the product of two elements within a group produces another element in that group.

Associativity is the property where the way in which the group's elements are paired is unimportant.

Identity is the existence of an element within the group that behaves similarly to the number 1.

Finally, Inverse refers to the existence of a counterpart to each element that produces the identity element when combined with that element. Therefore, the characteristic features of a group are identity and inverse.

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Answer:

b ,................................

a) The Taylor Polynomial of degree 2 of the polynomial 3x² + 4x - 2 at x = 2 is 13 + 10(x - 2) + 3(x - 2)².

b) The Taylor Polynomial of degree 3 of the polynomial 4+x³+x²+x+1 at x=1 is 5 + 6(x - 1) + 12(x - 1)² + 6(x - 1)³.

To find the Taylor Polynomial of a function centered at a particular point, we use the formula given by the Taylor Series. The formula for the Taylor Series is f(a) + f'(a)(x-a) + f''(a)(x-a)²/2! + ... + fⁿ(a)(x-a)ⁿ/n!.

Using this formula, we can calculate the Taylor Polynomials for both the given polynomials centered at the given points. For part (a), we find the derivatives of the function and evaluate them at x = 2, then substitute them in the Taylor Series formula. Similarly, for part (b), we find the derivatives of the function and evaluate them at x = 1, then substitute them in the Taylor Series formula.

In summary, the Taylor Polynomial of degree 2 of the polynomial 3x² + 4x - 2 at x = 2 is 13 + 10(x - 2) + 3(x - 2)², and the Taylor Polynomial of degree 3 of the polynomial 4+x³+x²+x+1 at x=1 is 5 + 6(x - 1) + 12(x - 1)² + 6(x - 1)³.

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Answer:

(a²b)³(b²c²)=a⁶b⁵c²

Answer:

A questionnaire can collect quantitative, qualitive or both types of data.

Step-by-step explanation:

Answer:

Categorical data

Step-by-step explanation:

Data that relates to certain categories e.g males, females or any types of car

The t value will be the result that is  58.851995039

The t-statistic for the observed correlation coefficient of 0.951 can be calculated to determine if it is statistically significant. Using the T.INV() spreadsheet function and the appropriate degrees of freedom.

We can test the null hypothesis of no correlation at the 5% significance level. Additionally, the T.DIST() function can be used to calculate the p-value of the t-statistic.

To calculate the t-statistic, we need to know the sample size (n) and the observed correlation coefficient (r). In this case, we have 37 monthly observations and a correlation coefficient of 0.951. The t-statistic can be calculated using the formula t = r x sqrt((n - 2) / (1 - r^2)). Plugging in the values, we find t = 0.951 x sqrt((37 - 2) / (1 - 0.951^2)).

By comparing this t-statistic to the critical value at the desired significance level (5% in this case), we can determine if the null hypothesis of no correlation can be rejected. Additionally, the p-value can be calculated using the T.DIST() function to determine the probability of obtaining a t-statistic as extreme as the observed value. If the p-value is less than the chosen significance level, the null hypothesis can be rejected.

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Answer:

15.52 ft

Step-by-step explanation:

the length of the rope can be determined using Pythagoras theorem

The Pythagoras theorem : a² + b² = c²

where a = length

b = base

c =  hypotenuse

√15² + 4²

= √225 + 16

=√ 241

= 15.52 ft

Answer:

the answer is b the square root of 160

Step-by-step explanation:

i did it on the assignment

Answer:

i think it might be the letter D

The volume of solid B is about 5.497 cubic meters (rounded to the nearest thousandth).

The volume of solid A is given by V(A) = 112π.

The volume of a cylinder is given by V = πr²h, where r is the radius of the base and h is the height. Since the solids are similar, the corresponding dimensions of the two cylinders are related by a scale factor of k.

Let r(A) and h(A) be the radius and height of cylinder A, respectively. Then, the radius and height of cylinder B are given by:

r(B) = k·r(A) = (1/4)·r(A)

h(B) = k·h(A) = (1/4)·h(A)

The volume of cylinder B is then:

V(B) = π[r(B)]²·h(B)

= π[(1/4)·r(A)]²·[(1/4)·h(A)]

= (1/64)πr(A)²h(A)

= (1/64)V(A)

= (1/64)(112π)

= 7π/4

≈ 5.497

Therefore, the volume of solid B is about 5.497 cubic meters (rounded to the nearest thousandth).

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Answer:

ummmm??

Step-by-step explanation:

Answer:

y=-30

Step-by-step explanation:

3y+24=2y-6

The corresponding probabilities for these outcomes are 0.25, 0.35, and 0.15, respectively.

What is the probability?

Probability is the study of the chances of occurrence of a result, which are obtained by the ratio between favorable cases and possible cases.

To fill in the blanks, we need to use the given information to complete the probability distribution table.

We can see that there were 3 dogs (out of the 60) that did not use any toys, and the probability of a dog not using any toys is 0.05 or 5%. There were 12 dogs (out of the 60) that used 1 toy, and the probability of a dog using 1 toy is 0.2 or 20%. Similarly, there were 15 dogs that used 2 toys, 21 dogs that used 3 toys, and 9 dogs that used all 4 toys. The corresponding probabilities for these outcomes are 0.25, 0.35, and 0.15, respectively.

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Answer:

The original Slope is y=-1/3x-2

The perpendicular slope would be y=3x+b

Step-by-step explanation:

Original Slope:

You already have the y-interecpet, (0,-2), and you know two points (0,-2) and (-6,0), so you can find the slope with (y1-y2)/(x1-x2) so in this case, it would be (0-(-2))/(-6-0)= -1/3 and you can find y=1/3x-2.

Perpendicular Slope:

The slope of any perpendicular line would be the reciprocal of the original. So the reciprocal of -1/3 is 3. The b can be any real number because no matter the y-intercept the slope would still be perpendicular

The sampling technique that depends on the judgment of the researcher, who hand-picks the cases to be included in the sample, is known as purposive sampling or judgmental sampling.

Now let's explore the explanation behind this answer. Purposive sampling is a non-probability sampling technique where the researcher selects specific individuals or cases for inclusion in the sample based on their judgment and expertise. Unlike random sampling, where each member of the population has an equal chance of being selected, purposive sampling involves a deliberate and subjective selection process.

Researchers typically employ purposive sampling when they seek to include participants who possess specific characteristics or qualities relevant to their research objectives. By hand-picking cases that are deemed to be most representative or informative, the researcher aims to maximize the relevance and richness of the data collected.

This sampling technique provides flexibility and control over the sample composition, allowing the researcher to target specific individuals or cases that are believed to provide valuable insights or unique perspectives. However, it is important to acknowledge that purposive sampling may introduce potential biases and limit the generalizability of the findings since the sample may not be representative of the entire population of interest.

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Answer:

x=76°

Step-by-step explanation:

BD║XY  76°=x

The required value of x is 76°, and line BD is parallel to line XY.

Parallel lines in a plane are two or more lines that are equidistant from each other at all points. This implies that no matter how far apart they are, they will never meet or cross.

As per the given diagram, we can see that line BD is parallel to line XY.

As per we know that corresponding angles are generated in matching corners or corresponding corners with the transversal when two parallel lines and the transversal are intersected.

Thus, ∠x = 76°

Therefore, the correct answer is B.

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Answer:

1

Step-by-step explanation:

Anything (besides 0) to the 0 power is 1.

Answer:

D because 0.75 in fraction form is 3/4 and 3/4 is greater then 2/3 which is the graphs rate of change.

Step-by-step explanation:

A common everyday counting unit that is used to mean 12 of an object is a Dozen

Dozen is derived from the Old French word "douzaine" which means twelve each. In most situations, a dozen is used to refer to a group of twelve items. The term dozen is also used in informal situations to refer to a very large number of objects. For example, one might say "I have dozens of friends!" to mean that they have a lot of friends.

Dozen is a useful term when counting items. It allows for large numbers to be easily broken down into manageable groups. For example, if you have 120 pencils, you could easily count them by saying that you have 10 dozen pencils. It can also be useful when talking about fractions. For example, instead of saying "one and a half of an item," one could say "one and a half dozen of an item."

Dozen is a common everyday counting unit that is used to mean 12 of an object. It is a useful term when counting items and when talking about fractions, and can be used in both formal and informal settings.

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From the provided equations, the equation which has no solution is 3 4 x less-than-or-equal-to 2 +4x. Option 2 is correct.

Inequality equation is the equation in which the two expressions are compared with greater than, less than or other inequality signs.

From the given equations, the equation which has no solution has to be found out. When the value, does not equate for the expression, then the expression has no solution.

The first equation given in the problem is,

\(6 (x +2) > x-3\)

Solve it further,

\(6 x +12 > x-3\\6x-x > -3-12\\5x > -15\\x > -3\)

The second equation given in the problem is,

\(3+ 4x \leq 2 (1 +2x)\)

Solve it further,

\(3+ 4x \leq 2 +4x\\4x- 4x \leq 2-3\\0\leq-1\)

The value of 0 is greater than the number -1. Thus, this inequality has no solution.

The option 3 and 4 has a solution. Hence, from the provided equations, the equation which has no solution is 3 4 x less-than-or-equal-to 2 +4x. Option 2 is correct.

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Answer:

\(y=-\frac{1}{2} x+\frac{7}{2}\)

Step-by-step explanation:

Hi there!

What we need to know:

1) Determine the slope (m)

\(y=2r-7\)

From the given equation, we can identify clearly that 2 is in the place of m, making it the slope. The negative reciprocal of 2 is -1/2, so therefore, the slope of a perpendicular line would be -1/2. Plug this into \(y=mx+b\):

\(y=-\frac{1}{2} x+b\)

2) Determine the y-intercept (b)

\(y=-\frac{1}{2} x+b\)

Plug in the given point (-5,6) and solve for b

\(6=-\frac{1}{2} (-5)+b\\6=\frac{5}{2}+b\)

Subtract 5/2 from both sides to isolate b

\(6-\frac{5}{2}=\frac{5}{2}+b-\frac{5}{2}\\\frac{7}{2} =b\)

Therefore, the y-intercept of the line is \(\frac{7}{2}\). Plug this back into \(y=-\frac{1}{2} x+b\):

\(y=-\frac{1}{2} x+\frac{7}{2}\)

I hope this helps!

a) Since the triangles are congruent, and ΔABC is congruent to ΔDEF, segments AB and DE have the same value. Therefore, you can use algebra to solve for x when using the knowledge that (12 - 4x) is equal to (15 - 3x).

To solve:

12 - 4x = 15 - 3x

12 = 15 + x

-3 = x

Therefore, x is equal to -3.

b) To find the value of AB, plug in the value of x found in part a).

12 - 4x

12 - 4(-3)

12 - (-12)

12 + 12 = 24

Thus, segment AB is equal to 24.

c) As shown in part b), plug in the value of x found in part a) to find the value of segment DE.

15 - 3x

15 - 3(-3)

15 - (-9)

15 + 9 = 24

Thus, segment DE is also equal to 24.

We can confirm the knowledge of the equal side lengths because the triangle are congruent. This means that all the side lengths in the triangle are the same, which is confirmed when algebraically plugging in the value of x to solve for the values of the segments AB and DE.

I hope this helps!