a vector function representing the curve intersection between the cylinder and the plane is given by

The volume V of the solid is obtained by rotating the region bounded by the given curves about the specified line. y = 27x^3, y = 0, x = 1; about x = 2 is 81π/5

Shell method:

The shell method is an integration for calculating the volume of a solid of revolution when integrating along an axis perpendicular to the axis of revolution. This is in contrast to disc integration which integrates along the axis parallel to the axis of revolution.

V=2π∫01(2-x). 27x³dx

  = 2π.27([tex]x^{4}[/tex]/2 - [tex]x^{5}[/tex]/5)01

  =54π(1/2-1/5)

  = 81π/5

Therefore The volume V of the solid is obtained by rotating the region bounded by the given curves about the specified line. y = 27x^3, y = 0, x = 1; about x = 2 is 81π/5

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The statement that is true according to the Central Limit Theorem is B. the original PD must also be normal.

According to the central limit theorem, if you take sufficiently large samples from a population, the means of the samples will be normally distributed even if the population is not normally distributed. The central limit theorem (CLT) states that as sample size increases, the distribution of sample means approaches a normal distribution, regardless of the distribution of the population.

The central limit theorem says that the sampling distribution of the mean will always be normally distributed, as long as the sample size is large enough.

In conclusion, the correct option is B.

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Answer:

sqrt2

Step-by-step explanation:

csc (x)= 1/sin(x)

sin(x)= (sqrt22)/(sqrt22*sqrt2)= 1/sqrt2

1/(1/sqrt2)=sqrt2/1=sqrt2

Answer:

With 99% confidence we can say that the mean of the population is between 43.1 and 46.1

Step-by-step explanation:

Answer:

12.244 cm long

Step-by-step explanation:

The area of a rectangle is equal to its height times its width, so if the piece of cardboard has an area of 66 square centimeters and is 5 centimeters longer than it is tall, we can write the following equation to represent the dimensions of the piece of cardboard:

height * (height + 5) = 66

To solve this equation, we can first divide both sides of the equation by the height of the piece of cardboard to get:

height + 5 = 66 / height

We can then subtract 5 from both sides of the equation to get:

height = 66 / height - 5

We can then multiply both sides of the equation by the height to get:

height^2 = 66 - 5 * height

We can then use the quadratic formula to solve for the height of the piece of cardboard:

height = (-5 +/- sqrt(5^2 - 4 * 1 * -66)) / (2 * 1)

The value of the square root in the quadratic formula must be positive, so we take the positive value for the height:

height = (-5 + sqrt(5^2 + 4 * 1 * 66)) / (2 * 1)

This simplifies to:

height = (5 + sqrt(61)) / 2

The height of the piece of cardboard is approximately 7.244 centimeters. Since the piece of cardboard is 5 centimeters longer than it is tall, it must be 5 + 7.244 = 12.244 centimeters long.

Therefore, the piece of cardboard is approximately 12.244 centimeters long.

Null Hypothesis: There is no association between handedness and career for Accountants. And Alternative Hypothesis: There is an association between handedness and career for Accountants.

Profession 1: Lawyer

Null Hypothesis: There is no association between handedness and career for Lawyers.

Alternative Hypothesis: There is an association between handedness and career for Lawyers.

Profession 2: Pilot

Null Hypothesis: There is no association between handedness and career for Pilots.

Alternative Hypothesis: There is an association between handedness and career for Pilots.

Profession 3: Accountant

Null Hypothesis: There is no association between handedness and career for Accountants.

Alternative Hypothesis: There is an association between handedness and career for Accountants.

Profession 4: Nurse

Null Hypothesis: There is no association between handedness and career for Nurses.

Alternative Hypothesis: There is an association between handedness and career for Nurses.

Profession 5: Teacher

Null Hypothesis: There is no association between handedness and career for Teachers.

Alternative Hypothesis: There is an association between handedness and career for Teachers.

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The value of the minimum sample size required to estimate the population proportion is 438.

Your results will vary from the actual population value by how many percentage points, as indicated by the margin of error. A 95% confidence interval with a 4% margin of error, for instance, indicates that your statistic will, 95% of the time, be within 4% of the true population figure.

Given:

The margin of error, ME = 0.04,

The value of p = 0.12,

The confidence level =  99%,

Calculate the minimum sample size as shown below,

ME = z √[p(1 - p) / n]

Calculate the value of z from the table attached below considering the confidence level, z = 2.576,

0.04 = 2.576 √[0.12(1 - 0.12) / n]

Squaring both sides,

0.0016 = 6.636 × 0.12 × 0.88 / n

n = 0.7 / 0.0016

n = 437.9 or 438

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On a scatter diagram, you can see outliers if there is a regression line. The point or points that are furthest distant from the regression line are considered outliers in a scatter diagram.

In a scatter plot, dots are used to show the values of two separate numerical variables. To see how different variables relate to one another, utilize scatter plots. The link between an independent and dependent variable is shown as a straight line in a linear regression.

If a linear model is adequate, the residuals scatterplot should display random scatter and the histogram should appear about normal. The linear model is inappropriate if we see a curved connection in the residual plot. The residuals are displayed against the explanatory variable in a different form of residual plot.

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The probability distribution for the statistic is ; for m = 0 , P(0) =  0.216  , for m = 5 ,P(5) = 0.296 and for m = 10 , P(10) = 0.488  .

In the question ,

it is given that ,

the box has 10 sealed envelopes , that contains number from 1,2,...,10 .

the first six envelopes has no money .

next two envelopes has $5

and the last two contains $10 bill .

if x₁, x₂, and x₃ denote the amounts in the selected envelopes,

the statistic of interest is m = maximum of X₁ , X₂ and X₃ .

we need to find probability distribution for the statistic m,

So , P(m = 0) = P( all three envelope contains no money) = (6/10)³ = 0.216

and P(m = 5) = P( all from 8 envelope which contains at most $5) - P(all three envelope with 0 money)

= (8/10)³ - 0.216

= 0.296

and P(m = 10) = 1 - (8/10)³ = 0.488

Therefore , the required probability is P(0) = 0.216 ,   P(5) =  0.296 and P(10) = 0.488  .

The given question is incomplete , the complete question is

A box contains ten sealed envelopes numbered 1, . . . , 10. the first six contain no money, the next two each contains $5, and there is a $10 bill in each of the last two. a sample of size 3 is selected with replacement (so we have a random sample), and you get the largest amount in any of the envelopes selected. if x₁, x₂, and x₃ denote the amounts in the selected envelopes, the statistic of interest is M = the maximum of X₁ ; X₂ , and X₃ .  Obtain the probability distribution of this statistic ?

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The sampling distribution of statistics is the allocation of all matters of the statistic when all viable examples of the exact size n are taken from the exact people.

What is sampling distribution mean?

The group of averages drawn from all feasible random samples of a certain size (n) drawn from a particular population is referred to as the distribution of sample means.

A statistical probability distribution that results from selecting random samples from a specific population is referred to as a sampling distribution.

It depicts the distribution of frequencies on how dispersed various outcomes will be for a particular population and is also referred to as a finite-sample distribution.

To determine the sample distribution, you must know the population's standard deviation.

Divide the total number of observations in the sample by the sum of all the observations.

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We need to use the concept of Relative Abundance. Relative Abundance of A,B and C are 14.28,57.14 and 28.57% respectively.

The percentage of an organism of a specific sort in relation to the overall number of organisms in the area is known as relative abundance. Relative species abundances frequently follow particular patterns, some of the most well-known and extensively researched patterns in macroecology. Over a large variety of biological ecosystems, relative species abundances exhibit relatively similar patterns. Most species are rare (represented by a single individual in a community sample), while only a small number of species are prolific, according to a histogram of the number of species represented by 1, 2, 3,..., n individuals.

(M1)(x) + (M2)(1-x) = M(E) is the formula for Relative Abundance.

A weighs 12g, B weighs 16g and C weighs 24g.

A customer buys 1 apple A, 3 apples B and 1 apple

So assume A,B and C as different isotopes of apples.

Relative Abundance of A=12/84 ×100⇒14.28%

Relative Abundance of B=48/84 ×100⇒57.14%

Relative Abundance of C=24/84 ×100⇒28.57%

We need to use the concept of Relative Abundance. Relative Abundance of A,B and C are 14.28,57.14 and 28.57% respectively.

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The equation of line b that passes through the point (-3,2) is  y=-1/4x+5/4

to get the equation of a line given a point and its slope.

Recognize the slope.

Decide on the point.

In the point-slope form, y y 1 = m (x x 1), substitute the values. y − y 1 = m (x − x 1) .

Slope-intercept form should be used to write the equation.

There are three major forms of linear equations: point-slope form, standard form, and slope-intercept form.

In the above question we see that,

The line b passes through the point (-3,2)

the equation of line should satisfy this point

In the given option the only line that satisfy the point is

option C

y=-1/4x+5/4

hence option C ,y=-1/4x+5/4 is the answer

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Answer:

Step-by-step explanation:

10 months=10/12=5/6 years.

Amount=Principal+ Interest

A=P+I

A=P+P×r×t

A=P(1+rt)

18500=P(1+4%×5/6)

18500=P(1+20/600)

18500=P(1+1/30)

18500=P(31/30)

P=18500×30/31≈17903.2258≈17903.23

The inner loop iterates 'n' times, outer loop iterates 'm' times and total loop iterates (m×n) times.

Given program,

for j = 1 to m

   k = 1 to n

statement in the body of innerloop. None contain branching statements that lead outside the loop.

next j

next k

Here, in the inner loop k iterates from 1 to n that is n times and j iterates from 1 to m that is m times.

Finally, the whole loop iterates m×n times because for every value of j from 1 to m, k value increases from 1 to n.

So, the inner loop iterates 'n' times, outer loop iterates 'm' times and total loop iterates (m×n) times.

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As per the concept of exponential decay, the initial mass of the sample is 5,254.87 kg

What is meant by Exponential decay:

In math, the term exponential decay is a very common process especially when we are talking about radioactive materials.

The standard  formula for this type of behavior which is written below:

A = Pe^-rt

where

A refers the amount left after time t

P refers the initial amount at t=0

r refers the rate

Here we have given that the mass of a radioactive substance follows a continuous exponential decay model, with a decay rate parameter of per day. a sample of this radioactive substance was taken six days ago.

And we need to find if the sample has a mass of today, then the initial mass of the sample.

Now, we have to substituting the values,

Then we get the equation as,

=> A = (9575 kg)(e^-0.12*5)

When we simplify this one, then we get,

=> A = 5,254.87 kg

Therefore, the initial mass of the sample is 5,254.87 kg

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Lk+1 is the k+1th regular language, for example. The presented hypothesis states that f(n) = f(k+1) is regular since f(k) and Lk+1 are both regular.

The induction hypothesis's function The assumption made at the beginning of the induction phase is known as the induction hypothesis, and it is the situation where n = k for the proposition we are trying to prove ("P(k)"). If you don't bring this hypothesis into play at any point throughout the proof of the induction phase, something is amiss.

Given:

It is normal for two regular languages to be combined.

Give the function f(n) the name "union of n regular languages."

Question Is the language f(n) regular?

The union of a single regular language is regular

if n = 1. Base Case

The provided hypothesis tells us that f(2) is regular

if n = 2.

Assume that f(n) is regular for every n = k.

This is the inductive hypothesis.

Let n equal k+1 in the inductive step. The inductive premise tells us that f(k) is a regular language.

Consequently, f(n) = f(k+1) = Lk+1 U f(k) (k)

Lk+1 is the k+1th regular language,

for example. The presented hypothesis states that f(n) = f(k+1) is regular since f(k) and Lk+1 are both regular.

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it is 6.1

Step-by-step explanation:

Dependent variable: A dependent variable is a variable that changes or is impacted by other factors. independent variable: An independent variable is a variable that does not change or are impacted by other factors.

Regression is a method for figuring out the relationship between two or more variables. In other words, it is determined by how the predictor variable changes and how the dependent variable changes. Additionally, when more than one independent variable is included in a regression analysis, the change in the dependent is examined while maintaining the same values for the other independent variables.

The best fit for the data is linear regression if the data set is bivariate. The data with two variables are best represented by the straight line known as the least squares regression line.

When the explanatory variable has a value of zero, the response variable's projected value is shown by the regression line's y-intercept (though be wary of extrapolation in interpreting the intercept or other values outside the original data range).

The best fit for the data is linear regression if the data set is bivariate. The data with two variables are best represented by the straight line known as the least squares regression line. The line's equation is provided by,

y = a+bx

where,

a—Intercept

b—Regression coefficient

y—Predicted value of the dependent variable

x —Independent or predictor variable

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1000 times were added to the n=30 sample. Even with n=30, the sample variance distribution is still very biased.

Probability refers to possibility.

A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.

The degree to which something is likely to happen is basically what probability means.

You will understand the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution.

Knowing the total number of outcomes is necessary before we can calculate the likelihood that a specific event will occur.

According to our question-

The sample variance's variance (SD) is still very large. The range is from 20 to 30%.

Because we are utilizing estimated population variance rather than the genuine population variance, which has some degree of uncertainty, the e t distribution has a longer tail when degrees of freedom are limited. Given that the estimated population variance is nearer to the actual population variance when sample size = 30, the t distribution will be closer to the z distribution.

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The standard equation of a circle is [tex](x-1)^{2} + (y+5)^{2}= (\sqrt{3})^{2}[/tex]. The equation of the circle in general form is (x-1)² + (x-1)² = 3.

Standard form of circle equation is (x – a)² + (y – b)² = r²

General form of Equation of a Circle.

x² + y² + 2gx + 2fy + c = 0, for all values of g, f and c.

The equation of a circle is

(x-h)²+ (y-k)² = r²

So, it's given that radius,

r = √3

h=1 and k=-5

So, by substituting all values to the standard equation of a circle is :

[tex](x-1)^{2} + (y+5)^{2}= (\sqrt{3})^{2}[/tex]

The equation of the circle in the general form is written as :

(x-1)² + (x-1)² = 3

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given a triangle with side of  lengths of 5 and 8 then c^2 =89 inequality describes all possible lengths of the third side

In the right triangle of sides a, b, and c

a^2 + b^2 = c^2

Since a = 5 and c = 8

Substitute them in the given rule

we get

25+64= c^2

89= c^2

Take a square root for both sides

c= sqrt 89

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Answer:

Step-by-step explanation:

If the diameter increases by 10%,

new diameter = d+⅒ = 1.1d

also new radius = 0.55r

Height also increasesby 10%,

New height = h+⅒h = 1.1h

hence diameter of larger can =

π*(0.55)²*1.1= 1.0453

hence percentage change in volume

is 4.53% which can be rounded off to

Answer:

Step-by-step explanation:

To find the y-intercept of the equation y - 6 = -2(x + 5), we can set x equal to 0, since the y-intercept is the point where the graph of the equation crosses the y-axis.

Substituting 0 for x, we get:

y - 6 = -2(0 + 5)

y - 6 = -2(5)

y - 6 = -10

y = -4

Therefore, the y-intercept of the equation y - 6 = -2(x + 5) is (0, -4). This means that the graph of the equation crosses the y-axis at the point (0, -4).

The graph of the inequality y > 4x - 3  , 3y - x ≤ 9 . is shown below.

In the question ,
the inequalities are given ,

we have to graph given inequalities ,

the inequalities are y > 4x - 3

3y - x ≤ 9 .

in the first inequality , y > 4x - 3

we put x = 0 , y is = -3 .

we put y = 0 , x is = 3/4 .

So ,the points for the line will be  (0,-3) and (3/4,0) .

since the inequality does not have equal to  sign , the line will be a dotted line .

in the second inequality ,3y - x ≤ 9 .

we put x = 0 ,  y is = 3 .

we put y = 0 ,  x is = -9 .

the points for the line will be (0,3) and (-9,0).

Since the inequality has equal to sign . Thus, line will be solid line .

Therefore , the for the given inequality is shown below.

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Answer: In Shay's wind farm their can be 4 arrays

Search up the meaning of a Array if you are confused

Step-by-step explanation:

24 has 4 pairs of factors.

Answer:

26

Step-by-step explanation:

To find the value of the expression 2|x-4|-3y³ when x=3 and y=-2, we need to substitute the values of x and y into the expression and then simplify. The absolute value part of the expression, |x-4|, is the distance between the number x and 4 on the number line. When x=3, this distance is |3-4|=1. So the expression becomes 2*1-3(-2)³ = 2-3(-8) = 2+24 = 26. Therefore, when x=3 and y=-2, the value of the expression 2|x-4|-3y³ is 26.

The Shannon's %Net market contribution = 40%

What is NMC (Net market contribution)?

Net market contribution (NMC) is equal to total sales revenue less total costs (except market costs) minus market costs.

Cost overall (not including market expenses):

150000 packaged (in cans and bottles).

Kegs =80000

WIP Loss/Reduction = 42000

Labor Contracts = 9000

Total Direct Labor: 240000

18000 inbound pounds

180000 in compensation

Total= 719000

Consumer advertising costs 26850 on the market.

Marketing for trade = 31761

Promotional Sales = 18000

Total=76611 Net market contribution=1320271-719000-76611=$ 524660 %NMC=524660/1320271=0.3974=39.74%=40%

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To figure this out, you set up the fraction

    [tex]\dfrac{\text{number that meet the criteria}}{\text{total possible number}}[/tex]

In this case, it's [tex]\dfrac{7 \text{ A's}}{20 \text{ total students}}[/tex].

You then divide 7/20 = 0.35 and convert that decimal into a percent: 35%

Answer:

see explanation

Step-by-step explanation:

given Δ ABD is isosceles with AB = AD then base angles are congruent, so

∠ ADB = ∠ ABD = 72°

then

∠ BAD = 180° - (72 + 72)° = 180° - 144° = 36° ( sum of angles in a triangle )

given Δ ABC is isosceles , then

∠ BCD = ∠ BAD = 36°

the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

∠ ADB is an exterior angle of Δ BCD , then

∠ BCD + ∠ DBC = ∠ ADB

36° + ∠ DBC = 72° ( subtract 36° from both sides )

∠ DBC = 36°

So ∠ BCD = ∠ DBC = 36°

Thus the base angles of Δ BCD are congruent , then

Δ BCD is isosceles with BD = CD

Answer:

12

Step-by-step explanation: